JP7015684B2 - Phase modulation layer design method - Google Patents

Description

The present invention relates to a method for designing a phase modulation layer.

Patent Document 1 describes a technique relating to a semiconductor light emitting device. This semiconductor light emitting device includes an active layer, a pair of clad layers sandwiching the active layer, and a phase modulation layer optically coupled to the active layer. The phase modulation layer includes a basic layer and a plurality of different refractive index regions having different refractive indexes from the basic layer. When an XYZ Cartesian coordinate system with the thickness direction of the phase modulation layer as the Z-axis direction is set and a virtual square grid with a grid spacing a is set in the XY plane, each different refractive index region is the position of the center of gravity. Is arranged so as to deviate from the grid point position in the virtual square grid by a distance r. The distance r satisfies 0 <r ≦ 0.3a.

International Publication No. 2016/148507

A light emitting device that outputs an arbitrary light image by controlling the phase spectrum and the intensity spectrum of light emitted from a plurality of light emitting points arranged in a two-dimensional manner has been studied. As one of the structures of such a light emitting device, there is a structure including a phase modulation layer provided on the substrate. When the phase modulation layer has a basic layer and a plurality of different refractive index regions having different refractive indexes from the basic layer, and a virtual square lattice is set in a plane perpendicular to the thickness direction of the phase modulation layer. In addition, the position of the center of gravity of each different refractive index region deviates from the position of the grid point of the virtual square grid according to the optical image. Such a light emitting device is called an S-iPM (Static-integrable Phase Modulating) laser, and outputs an optical image having an arbitrary shape in a direction inclined with respect to a direction perpendicular to the main surface of the substrate.

From such a light emitting device, primary light and -1st order light modulated in the direction opposite to the primary light are output. The primary light forms the desired output light image in the first direction, which is tilted with respect to the direction perpendicular to the main surface of the substrate. The -1st order light forms an optical image that is rotationally symmetric with the output optical image in the second direction that intersects the main surface of the substrate and is symmetric with respect to the first direction with respect to the axis extending in the direction perpendicular to the main surface. do. However, depending on the application, one of the primary light and the -1st primary light may not be required. In such a case, it is desirable to dimm the unnecessary light of the primary light and the -1st order light with respect to the necessary light.

The present invention has been made in view of such problems, and is a phase modulation layer design method capable of dimming one of the primary light and the -1st order light with respect to the other light. The purpose is to provide.

In order to solve the above-mentioned problems, the phase modulation layer design method according to the present invention has a basic layer and a plurality of different Cartesian regions having different amplitudes from the basic layer, and is provided on a substrate with a light emitting unit. A method of designing a phase modulation layer for a light emitting device that comprises an optically coupled phase modulation layer and outputs an optical image in a direction perpendicular to the main surface of the substrate, a direction inclined with respect to the direction, or both. Therefore, a virtual square grid is set in the plane perpendicular to the thickness direction of the phase modulation layer , the X axis is parallel to one side of the square grid, and the Y axis is parallel to the other side of the square grid. When an XY Cartesian coordinate system whose origin coincides with the center point of the phase modulation layer is set , the first region where the X-axis coordinates are positive, the second region where the X-axis coordinates are negative, and the Y-axis When defining the third region where the coordinates are positive and the fourth region where the Y-axis coordinates are negative, the first traveling wave traveling in the positive direction of the X-axis and the second traveling wave traveling in the negative direction of the X-axis. , The first step of preparing a plurality of complex amplitude distributions corresponding to the optical image for each of the third traveling wave traveling in the positive direction of the Y axis and the fourth traveling wave traveling in the negative direction of the Y axis, and each traveling wave. The second step of modifying the complex amplitude distribution, the third step of superimposing the modified complex amplitude distribution for each progressive wave to obtain the comprehensive complex amplitude distribution, and extracting the phase distribution from the comprehensive complex amplitude distribution. , A fourth step of determining the position of the center of gravity of each Cartesian region based on the phase distribution. In the second step, the positive / negative of the phase term of the complex amplitude distribution regarding the first progressive wave is inverted and the positive / negative of the phase term of the complex amplitude distribution regarding the third progressive wave is inverted , or the second traveling wave. Invert the positive and negative of the phase term of the complex amplitude distribution with respect to the fourth progressive wave and invert the positive and negative of the phase term of the complex amplitude distribution with respect to the fourth progressive wave . In the fourth step, the center of gravity of each different refractive index region passes through the grid points of a virtual square lattice and is tilted with respect to the X axis (counterclockwise angle with 0 ° when parallel to the X axis) θ. Is arranged on a straight line where 0 ° <θ <90 ° or 180 ° <θ <270 °, and the distance between the center of gravity of each different refractive index region and the corresponding grid point is determined based on the phase distribution. ..
Further, another phase modulation layer design method according to the present invention has a basic layer and a plurality of different Cartesian regions having different amplitudes from the basic layer, and is provided on a substrate and optically coupled to a light emitting portion. It is a method of designing a phase modulation layer of a light emitting device having a phase modulation layer and outputting an optical image in a direction perpendicular to the main surface of the substrate, a direction inclined with respect to the direction, or both. A virtual square grid is set in a plane perpendicular to the thickness of the layer, the X axis is parallel to one side of the square grid, the Y axis is parallel to the other side of the square grid, and the origin is the phase modulation layer. When an XY Cartesian coordinate system that matches the center point of is set, the first region where the X-axis coordinates are positive, the second region where the X-axis coordinates are negative, and the region where the Y-axis coordinates are positive. When defining a third region and a fourth region in which the Y-axis coordinates are negative, the first traveling wave traveling in the positive direction of the X-axis, the second traveling wave traveling in the negative direction of the X-axis, and the positive direction of the Y-axis The first step of preparing a plurality of complex amplitude distributions corresponding to the optical image for each of the traveling third traveling wave and the fourth traveling wave traveling in the negative direction of the Y axis, and modifying the complex amplitude distribution for each traveling wave. The second step, the third step of superimposing the modified complex amplitude distribution for each traveling wave to obtain the comprehensive complex amplitude distribution, and the third step of extracting the phase distribution from the comprehensive complex amplitude distribution, based on the phase distribution. Includes a fourth step of determining the position of the center of gravity of each Cartesian region. In the second step, the positive / negative of the phase term of the complex amplitude distribution of the first progressive wave is inverted and the positive / negative of the phase term of the complex amplitude distribution of the fourth progressive wave is inverted, or the complex amplitude distribution of the second progressive wave is inverted. Invert the positive and negative of the phase term of the third traveling wave and invert the positive and negative of the phase term of the complex amplitude distribution with respect to the third progressive wave. In the fourth step, the center of gravity of each different refractive index region passes through the grid points of a virtual square lattice, and the angle of inclination with respect to the X axis (counterclockwise angle with 0 ° when parallel to the X axis) θ is 90. It is arranged on a straight line where ° <θ <180 ° or 270 ° <θ <360 °, and the distance between the center of gravity of each different refractive index region and the corresponding lattice point is determined based on the phase distribution.

According to the findings of the present inventor, beam patterns in opposite directions can be obtained from traveling waves traveling in opposite directions. For example, when the beam pattern of the primary light is mainly obtained from the first traveling wave, the beam pattern of the -1st order light is mainly obtained from the second traveling wave. Similarly, when the beam pattern of the primary light is mainly obtained from the third traveling wave, the beam pattern of the first-order light is mainly obtained from the fourth traveling wave. In view of these facts, in the above design method, in the second step, the positive and negative of the phase term of the complex amplitude distribution for one of the first traveling wave and the second traveling wave is reversed, and the third traveling wave and the fourth traveling wave are reversed. Inverts the positive and negative of the phase term of the complex amplitude distribution for one of the progressive waves. If the beam pattern of the -1st order light is mainly obtained before the sign of the phase term is inverted, the beam pattern of the primary light is mainly obtained after the sign of the phase term is inverted. On the contrary, when the beam pattern of the primary light is mainly obtained before the sign of the phase term is inverted, the beam pattern of the -1st order light is mainly obtained after the sign of the phase term is inverted. Therefore, according to the above design method, a beam pattern of primary light (or -1st order light) can be mainly obtained from all traveling waves, and one of primary light and -1st order light can be obtained. , Can be dimmed with respect to the other light.

In the above phase modulation layer design method, the complex amplitude distribution for each traveling wave may be weighted in the second step. As a result, when the complex amplitude distribution for each progressive wave is superimposed to obtain the comprehensive complex amplitude distribution, the contribution of the complex amplitude distribution of each traveling wave to the comprehensive complex amplitude distribution is used as the intensity ratio of each traveling wave. It can be arbitrarily adjusted according to the situation, and the desired optical image can be expressed more accurately. If the intensities of the 1st and 2nd progressive waves and the intensities of the 3rd and 4th progressive waves are different from each other, they are added to each complex amplitude distribution of the 1st and 2nd progressive waves. The weight to be applied and the weight added to each complex amplitude distribution for the third traveling wave and the fourth traveling wave may be different from each other. Further, the ratio of the intensity of the first traveling wave and the second traveling wave to the intensity of the third traveling wave and the fourth traveling wave changes depending on the inclination angle θ of the straight line with respect to the X axis . Therefore, the ratio of the weight added to each complex amplitude distribution for the first traveling wave and the second traveling wave and the weight added to each complex amplitude distribution for the third traveling wave and the fourth traveling wave is set to the straight line and the X-axis . It may be determined based on the angle θ formed by.

In the above phase modulation layer design method, the inclination angle of the straight line with respect to the square lattice may be constant. This makes it possible to easily design the arrangement of the center of gravity in the different refractive index region. Further, in this case, the inclination angle may be an angle other than 0 °, 90 °, 180 ° and 270 °. Further, the tilt angle may be 45 °, 135 °, 225 ° or 315 °. As a result, four fundamental waves traveling along the square grid (when the X-axis and Y-axis along the square grid are set, the light traveling in the positive direction of the X-axis, the light traveling in the negative direction of the X-axis, and the positive direction of the Y-axis). The traveling light and the light traveling in the negative direction of the Y-axis) can contribute evenly to the optical image. When the inclination angle is 0 °, 90 °, 180 °, or 270 °, the straight line corresponds to the X-axis or Y-axis of the square grid, but at this time, for example, when the inclination angle is 0 ° or 180 °. When the straight line is along the X-axis, two of the four fundamental waves facing each other in the Y-axis direction do not undergo phase modulation and therefore do not contribute to the signal light. Further, when the inclination angle is 90 ° or 270 ° and the straight line is along the Y axis, the two traveling waves facing each other in the X-axis direction do not contribute to the signal light. Therefore, when the inclination angle is 0 °, 90 °, 180 °, or 270 °, the signal light cannot be obtained with high efficiency.

In the above phase modulation layer design method, the light emitting portion may be an active layer provided on the substrate. As a result, the light emitting unit and the phase modulation layer can be easily optically coupled.

According to the phase modulation layer design method of the present invention, one of the primary light and the -1st order light can be dimmed with respect to the other light.

It is a perspective view which shows the structure of the semiconductor light emitting element as the light emitting device which concerns on one Embodiment of this invention. It is sectional drawing which shows the laminated structure of the semiconductor light emitting element. It is a figure which shows the laminated structure of the semiconductor light emitting element when the phase modulation layer is provided between the lower clad layer and the active layer. It is a top view of the phase modulation layer. It is a figure which shows the positional relationship of the different refractive index region in a phase modulation layer. It is a top view which shows the example which applied the refractive index substantially periodic structure only in the specific region of a phase modulation layer. It is a figure for demonstrating the relationship between the light image obtained by forming an image of the output beam pattern of a semiconductor light emitting element, and the distance distribution in a phase modulation layer. It is a figure for demonstrating the coordinate transformation from the spherical coordinate to the coordinate in the XYZ Cartesian coordinate system. It is a figure explaining (a), (b) the phase angle distribution obtained from the Fourier transform result of an optical image, and the point to keep in mind when deciding the arrangement of the different refractive index regions. (A) An example of a beam pattern (light image) output from a semiconductor light emitting device is shown. (B) It is a graph which shows the light intensity distribution in the cross section which intersects with the light emitting surface of a semiconductor light emitting element and includes the axis perpendicular to the light emitting surface. (A) It is a figure which shows the phase distribution corresponding to the beam pattern shown in FIG. 10 (a). (B) It is a partially enlarged view of FIG. 11 (a). It is a top view which conceptually shows the phase modulation layer of a square lattice type S-iPM laser. It is a figure which conceptually shows the example of the beam pattern of the traveling wave in each direction. In this example, the inclination angle of the straight line D with respect to the X-axis and the Y-axis is 45 °. It is a graph which shows the intensity distribution of the traveling wave in the plane of a phase modulation layer. It is a graph which shows the intensity distribution of the traveling wave in the plane of a phase modulation layer. It is a graph which shows the intensity distribution of the traveling wave in the plane of a phase modulation layer. It is a graph which shows the intensity distribution of the traveling wave in the plane of a phase modulation layer. It is a flowchart which shows the design method of the phase modulation layer by one Embodiment. (A) It is a figure which shows the conventional method of rotating a different refractive index region around a grid point. (B) It is a figure which shows the traveling wave. (A) It is a figure which shows the method which the different refractive index region moves on the axis which passes through a lattice point and is inclined with respect to a square lattice. (B) It is a figure which shows the traveling wave. It is a top view which shows the example of the shape in the XY plane of a different refractive index region. It is a top view which shows the example of the shape in the XY plane of a different refractive index region. It is a top view of the phase modulation layer which concerns on the 2nd modification. It is a figure which shows the positional relationship of the different refractive index region in the phase modulation layer of the 2nd modification. It is a top view which shows another example of the shape of the different refractive index region in an XY plane. It is a top view which shows another example of the shape of the different refractive index region in an XY plane. It is a figure which shows the structure of the light emitting device by the 3rd modification. It is a figure which shows the cross-sectional structure of the semiconductor light emitting element which concerns on 2nd Embodiment. It is a figure which shows the laminated structure of the semiconductor light emitting element when the phase modulation layer is provided between the lower clad layer and the active layer. It is a top view which looked at the semiconductor light emitting element from the surface side. It is a table which shows the layer structure when the laser element is made of a GaAs compound semiconductor (emission wavelength 940 nm band). It is the refractive index distribution and mode distribution of the laser element which has the layer structure shown in FIG. It is a table which shows the layer structure when the laser element is made of an InP compound semiconductor (emission wavelength 1300 nm band). It is the refractive index distribution and mode distribution of the laser element which has the layer structure shown in FIG. 33. It is a table which shows the layer structure when the laser element is made of a nitride compound semiconductor (emission wavelength 405 nm band). It is the refractive index distribution and mode distribution of the laser element which has the layer structure shown in FIG. 35. It is sectional drawing and the refractive index distribution for demonstrating the case which approximates the waveguide structure by the 6-layer slab type waveguide. It is sectional drawing and the refractive index distribution for demonstrating the case which approximates the waveguide structure by the slab type waveguide of 5 layers. It is sectional drawing and refractive index distribution which show the 3 layer slab structure about the optical waveguide layer in the 6-layer slab type waveguide. It is sectional drawing and refractive index distribution which show the 3 layer slab structure about the contact layer in the 6-layer slab type waveguide. It is sectional drawing and refractive index distribution which show the three-layer slab structure about the optical waveguide layer in the five-layer slab type waveguide. It is sectional drawing and refractive index distribution which show the 3 layer slab structure about the contact layer in the 5 layer slab type waveguide. It is sectional drawing which shows the three-layer slab structure which consists of the lower clad layer, the optical waveguide layer, and the upper clad layer, and the refractive index distribution thereof. It is a table which shows the example of the 5-layer slab structure when the laser element is made of a GaAs compound semiconductor. The table shows the refractive indexes n ₁ , n ₂ , and n ₃ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer used in the calculation, and the table showing the calculation results of the lower limit value and the upper limit value. 6 is a graph showing the relationship between the standardized waveguide width V ₁ of the optical waveguide layer represented by the equations (1) and (2) and the normalized propagation coefficient b. It is a table showing the refractive index n ₄ , n ₅ , and n ₆ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer used in the calculation, and a table showing the calculation result of the upper limit value. 6 is a graph showing the relationship between the normalized waveguide width V ₂ of the contact layer represented by the equations (5) and (6) and the normalized propagation coefficient b. FIG. 44 is a refractive index distribution and a mode distribution of a laser device having a layer structure shown in FIG. It is a table which shows the example of the 6-layer slab structure when the laser element is made of an InP compound semiconductor. The table shows the refractive indexes n ₁ , n ₂ , and n ₃ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer used in the calculation, and the table showing the calculation results of the lower limit value and the upper limit value. 6 is a graph showing the relationship between the standardized waveguide width V ₁ of the optical waveguide layer represented by the equations (1) and (2) and the normalized propagation coefficient b. It is a table showing the refractive index n ₄ , n ₅ , and n ₆ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer used in the calculation, and a table showing the calculation result of the upper limit value. 6 is a graph showing the relationship between the normalized waveguide width V ₂ of the contact layer represented by the equations (5) and (6) and the normalized propagation coefficient b. It is the refractive index distribution and mode distribution of the laser element which has the layer structure shown in FIG. It is a table which shows the example of the 6-layer slab structure when the laser element is made of a nitride compound semiconductor. The table shows the refractive indexes n ₁ , n ₂ , and n ₃ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer used in the calculation, and the table showing the calculation results of the lower limit value and the upper limit value. 6 is a graph showing the relationship between the standardized waveguide width V ₁ of the optical waveguide layer represented by the equations (1) and (2) and the normalized propagation coefficient b. It is a table showing the refractive index n ₄ , n ₅ , and n ₆ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer used in the calculation, and a table showing the calculation result of the upper limit value. 6 is a graph showing the relationship between the normalized waveguide width V ₂ of the contact layer represented by the equations (5) and (6) and the normalized propagation coefficient b. FIG. 56 is a refractive index distribution and a mode distribution of a laser device having a layer structure shown in FIG.

Hereinafter, embodiments of the phase modulation layer design method according to the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are designated by the same reference numerals, and duplicate description will be omitted.

FIG. 1 is a perspective view showing a configuration of a semiconductor light emitting device 1A as a light emitting device according to an embodiment of the present invention. An XYZ Cartesian coordinate system is defined in which the axis extending in the thickness direction of the semiconductor light emitting device 1A through the center of the semiconductor light emitting device 1A is the Z axis. The semiconductor light emitting element 1A is an S-iPM laser that forms a standing wave in the XY in-plane direction and outputs a phase-controlled plane wave in the Z-axis direction. As will be described later, the semiconductor substrate 10 is a main surface 10a. It outputs a two-dimensional arbitrary-shaped optical image including a direction perpendicular to (that is, a Z-axis direction) and / or a direction inclined with respect to the direction.

FIG. 2 is a diagram schematically showing a laminated structure of the semiconductor light emitting device 1A. As shown in FIGS. 1 and 2, the semiconductor light emitting device 1A has an active layer 12 as a light emitting portion provided on the main surface 10a of the semiconductor substrate 10 and an active layer 12 provided on the main surface 10a. It includes a pair of clad layers 11 and 13 to be sandwiched, and a contact layer 14 provided on the clad layer 13. These semiconductor substrates 10 and each layer 11 to 14 are composed of compound semiconductors such as GaAs-based semiconductors, InP-based semiconductors, and nitride-based semiconductors. The energy bandgap of the clad layer 11 and the energy bandgap of the clad layer 13 are larger than the energy bandgap of the active layer 12. The thickness direction of the semiconductor substrate 10 and each layer 11 to 14 coincides with the Z-axis direction.

The semiconductor light emitting device 1A further includes a phase modulation layer 15 optically coupled to the active layer 12. In this embodiment, the phase modulation layer 15 is provided between the active layer 12 and the clad layer 13. If necessary, an optical guide layer may be provided between the active layer 12 and the clad layer 13 and at least one of the active layer 12 and the clad layer 11. When the optical guide layer is provided between the active layer 12 and the clad layer 13, the phase modulation layer 15 is provided between the clad layer 13 and the optical guide layer. The thickness direction of the phase modulation layer 15 coincides with the Z-axis direction. The optical guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

As shown in FIG. 3, the phase modulation layer 15 may be provided between the clad layer 11 and the active layer 12. When the optical guide layer is provided between the active layer 12 and the clad layer 11, the phase modulation layer 15 is provided between the clad layer 11 and the optical guide layer.

The phase modulation layer 15 is composed of a basic layer 15a made of a first refractive index medium and a second refractive index medium having a refractive index different from that of the first refractive index medium, and a plurality of different refractive index regions existing in the basic layer 15a. It is configured to include 15b. The plurality of different refractive index regions 15b include a substantially periodic structure. When the effective refractive index of the phase modulation layer 15 is n, the wavelength λ ₀ (= a × n, a is the lattice spacing) selected by the phase modulation layer 15 is included in the emission wavelength range of the active layer 12. .. The phase modulation layer 15 can select the wavelength λ ₀ of the emission wavelengths of the active layer 12 and output it to the outside. The laser light incident on the phase modulation layer 15 forms a predetermined mode according to the arrangement of the different refractive index regions 15b in the phase modulation layer 15, and is external from the semiconductor light emitting element 1A as a laser beam having a desired pattern. Is emitted to.

The semiconductor light emitting device 1A further includes an electrode 16 provided on the contact layer 14 and an electrode 17 provided on the back surface 10b of the semiconductor substrate 10. The electrode 16 is in ohmic contact with the contact layer 14, and the electrode 17 is in ohmic contact with the semiconductor substrate 10. Further, the electrode 17 has an opening 17a. The electrode 16 is provided in the central region of the contact layer 14. The portion of the contact layer 14 other than the electrode 16 is covered with the protective film 18. The contact layer 14 that is not in contact with the electrode 16 may be removed. The portion of the back surface 10b of the semiconductor substrate 10 other than the electrode 17 (including the inside of the opening 17a) is covered with the antireflection film 19. The antireflection film 19 in the region other than the opening 17a may be removed.

When a driving current is supplied between the electrode 16 and the electrode 17, recombination of electrons and holes occurs in the active layer 12, and the active layer 12 emits light. The electrons and holes that contribute to this light emission, as well as the generated light, are efficiently confined between the clad layer 11 and the clad layer 13.

The light emitted from the active layer 12 enters the inside of the phase modulation layer 15 and forms a predetermined mode according to the lattice structure inside the phase modulation layer 15. The laser beam emitted from the phase modulation layer 15 is directly output from the back surface 10b through the opening 17a to the outside of the semiconductor light emitting device 1A, or is reflected by the electrode 16 and then passes through the back surface 10b through the opening 17a. Is output to the outside of the semiconductor light emitting device 1A. At this time, the 0th-order light included in the laser light is emitted in the direction perpendicular to the main surface 10a. On the other hand, the signal light (primary light and -1st order light) included in the laser light is emitted in a two-dimensional arbitrary direction including a direction perpendicular to the main surface 10a and a direction inclined with respect to the main surface 10a. It is the signal light that forms the desired light image.

In one example, the semiconductor substrate 10 is a GaAs substrate, and the clad layer 11, the active layer 12, the clad layer 13, the contact layer 14, and the phase modulation layer 15 are compounds composed of Group III elements and Group V elements, respectively. It is a semiconductor layer. In one embodiment, the clad layer 11 is an AlGaAs layer, the active layer 12 has a multiple quantum well structure (barrier layer: AlGaAs / well layer: InGaAs), and the basic layer 15a of the phase modulation layer 15 is GaAs. The different refractive index region 15b is a hole, the clad layer 13 is an AlGaAs layer, and the contact layer 14 is a GaAs layer.

In AlGaAs, the energy band gap and the refractive index can be easily changed by changing the composition ratio of Al. In Al _x Ga _1-x As, when the composition ratio x of Al having a relatively small atomic radius is decreased (increased), the energy band gap positively correlated with this becomes smaller (larger), and the atomic radius becomes smaller (larger) in GaAs. When InGaAs is made by mixing a large amount of In, the energy band gap becomes small. That is, the Al composition ratio of the clad layers 11 and 13 is larger than the Al composition ratio of the barrier layer (AlGaAs) of the active layer 12. The Al composition ratio of the clad layers 11 and 13 is set to, for example, 0.2 to 1.0, and is 0.4 in one embodiment. The Al composition ratio of the barrier layer of the active layer 12 is set to, for example, 0 to 0.3, and is 0.15 in one example.

Note that noise light having a mesh-like dark portion may be superimposed on the beam pattern corresponding to the light image emitted from the semiconductor light emitting device 1A. According to the research of the inventor, the noise light having the mesh-like dark portion is caused by the higher-order mode in the stacking direction inside the semiconductor light emitting device 1A. Here, the basic mode in the stacking direction is a mode having an intensity distribution including the active layer 12 and having one peak over the region sandwiched between the clad layer 11 and the clad layer 13, and is a higher-order mode. Is a mode having an intensity distribution in which two or more peaks are present. The peak of the intensity distribution in the basic mode is formed in the vicinity of the active layer 12, while the peak of the intensity distribution in the higher order mode is also formed in the clad layer 11, the clad layer 13, the contact layer 14, and the like. Further, there are a waveguide mode and a leakage mode as modes in the stacking direction, but since the leakage mode does not exist stably, only the waveguide mode is focused here. Further, the waveguide mode includes a TE mode in which the electric field vector exists in the in-plane direction of the layer and a TM mode in which the electric field vector exists in the vertical direction of the layer surface. Here, only the TE mode is focused on. When the refractive index of the clad layer 13 between the active layer 12 and the contact layer is larger than the refractive index of the clad layer 11 between the active layer 12 and the semiconductor substrate, such a higher-order mode occurs remarkably. .. Usually, the refractive indexes of the active layer 12 and the contact layer 14 are much larger than the refractive indexes of the clad layers 11 and 13. Therefore, when the refractive index of the clad layer 13 is larger than the refractive index of the clad layer 11, light is also confined in the clad layer 13 and a waveguide mode is formed. This results in a higher order mode.

In the semiconductor light emitting device 1A of the present embodiment, the refractive index of the clad layer 13 is equal to or lower than the refractive index of the clad layer 11. As a result, the generation of the higher-order mode as described above can be suppressed, and the noise light having a mesh-like dark portion superimposed on the beam pattern can be reduced.

ここで、ＴＥモードは層厚方向の伝搬モード、ｎ₁は活性層１２を含む光導波路層の屈折率、ｎ₂は光導波路層に隣接する層のうち屈折率の高い層の屈折率、Ｎ_１はモード次数、ｎ_ｃｌａｄはクラッド層１１の屈折率、ｎ_３は光導波路層に隣接する層のうち屈折率の低い層の屈折率、ｎ_ｅｆｆは３層スラブ導波路構造におけるＴＥモードの等価屈折率である。 Further, the three-layer slab waveguide structure composed of the optical waveguide layer and the two layers adjacent to the optical waveguide layer preferably satisfies the following conditions. Specifically, the optical waveguide layer in the three-layer slab waveguide structure is composed of the active layer 12 when the refractive index of the phase modulation layer 15 is smaller than the refractive index of the clad layer 11. On the other hand, the optical waveguide layer is composed of the phase modulation layer 15 and the active layer 12 when the refractive index of the phase modulation layer 15 is equal to or higher than the refractive index of the clad layer 11. In any case, the optical waveguide layer does not include the clad layers 11 and 13. In such a three-layer slab waveguide structure, the normalized waveguide width V1 in TE mode is defined by the following equations ( ₁ ) and (2), and the asymmetric parameter a'and the normalized propagation coefficient b are defined as follows. When the real numbers satisfy the equations (3) and (4), the normalized waveguide width V ₁ and the normalized propagation coefficient b are set so that only one solution of the normalized waveguide width V ₁ exists. Is set.

Here, TE mode is a propagation mode in the layer thickness direction, n ₁ is the refractive index of the optical waveguide layer including the active layer 12, n ₂ is the refractive index of the layer adjacent to the optical waveguide layer and has a high refractive index, N. ₁ is the mode order, n _clad is the refractive index of the clad layer 11, n ₃ is the refractive index of the layer adjacent to the optical waveguide layer and has a low refractive index, and n _eff is the equivalent of TE mode in the three-layer slab waveguide structure. Refractive index.

According to the research by the inventors, it was found that the high-order mode also occurs in the optical waveguide layer (high refractive index layer) including the active layer 12. Then, they have found that the higher-order mode can be suppressed by appropriately controlling the thickness and the refractive index of the optical waveguide layer. That is, when the value of the normalized waveguide width V ₁ of the optical waveguide layer satisfies the above condition, the generation of the higher-order mode is further suppressed, and the noise light having a mesh-like dark portion superimposed on the beam pattern is obtained. Further reduction is possible.

Further, another three-layer slab waveguide structure composed of a contact layer and two layers adjacent to the contact layer preferably satisfies the following conditions. Specifically, in such another three-layer slab waveguide structure, the standardized waveguide width V2 of the contact layer 14 is defined by the following equations (5) and (6), and the asymmetric parameter _a'and standardization are performed. When the propagation coefficient b is a real number satisfying the following equations (7) and (8), the normalized waveguide width V ₂ and the normalized waveguide width V ₂ are standardized so as to be within the range where there is no solution. The propagation coefficient b is set.

ここで、ｎ₄はコンタクト層１４の屈折率、ｎ_５はコンタクト層１４に隣接する層のうち屈折率の高い層の屈折率、ｎ_６はコンタクト層１４に隣接する層のうち屈折率の低い層の屈折率、Ｎ_２はモード次数、ｎ_ｅｆｆは上記別の３層スラブ導波路構造におけるＴＥモードの等価屈折率である。

Here, n ₄ is the refractive index of the contact layer 14, n ₅ is the refractive index of the layer adjacent to the contact layer 14 having a high refractive index, and n ₆ is the refractive index of the layer adjacent to the contact layer 14 having a low refractive index. The refractive index of the layer, N ₂ is the mode order, and n _eff is the equivalent refractive index of the TE mode in the above-mentioned another three-layer slab waveguide structure.

By appropriately controlling the thickness of the contact layer 14 in this way, the generation of the waveguide mode caused by the contact layer 14 can be suppressed, and the generation of the higher-order mode generated in the laser element can be further suppressed.

In another example, the semiconductor substrate 10 is an InP substrate, and the clad layer 11, the active layer 12, the phase modulation layer 15, the clad layer 13, and the contact layer 14 are made of, for example, an InP-based compound semiconductor. In one embodiment, the clad layer 11 is an InP layer, the active layer 12 has a multiple quantum well structure (barrier layer: GaInAsP / well layer: GaInAsP), and the basic layer 15a of the phase modulation layer 15 is GaInAsP. The different refractive index region 15b is a hole, the clad layer 13 is an InP layer, and the contact layer 14 is a GaInAsP layer.

In yet another example, the semiconductor substrate 10 is a GaN substrate, and the clad layer 11, the active layer 12, the phase modulation layer 15, the clad layer 13, and the contact layer 14 are made of, for example, a nitride compound semiconductor. In one embodiment, the clad layer 11 is an AlGaN layer, the active layer 12 has a multiple quantum well structure (barrier layer: InGaN / well layer: InGaN), and the basic layer 15a of the phase modulation layer 15 is GaN. The different refractive index region 15b is a hole, the clad layer 13 is an AlGaN layer, and the contact layer 14 is a GaN layer.

The clad layer 11 is provided with the same conductive type as the semiconductor substrate 10, and the clad layer 13 and the contact layer 14 are provided with the same conductive type as the semiconductor substrate 10. In one example, the semiconductor substrate 10 and the clad layer 11 are n-type, and the clad layer 13 and the contact layer 14 are p-type. The phase modulation layer 15 has the same conductive type as the semiconductor substrate 10 when it is provided between the active layer 12 and the clad layer 11, and the semiconductor when it is provided between the active layer 12 and the clad layer 13. It has a conductive type opposite to that of the substrate 10. The impurity concentration is, for example, 1 × 10 ¹⁷ to 1 × 10 ²¹ / cm ³ . The active layer 12 is intrinsic (i type) to which no impurities are intentionally added, and the impurity concentration thereof is 1 × 10 ¹⁵ / cm ³ or less. The impurity concentration of the phase modulation layer 15 may be true (i type) when it is necessary to suppress the influence of loss due to light absorption via the impurity level.

The thickness of the semiconductor substrate 10 is, for example, 150 μm. The thickness of the clad layer 11 is, for example, 2000 nm. The thickness of the active layer 12 is, for example, 175 nm. The thickness of the phase modulation layer 15 is, for example, 280 nm. The depth of the different refractive index region 15b is, for example, 200 nm. The thickness of the clad layer 13 is, for example, 2000 nm. The thickness of the contact layer 14 is, for example, 150 nm.

In the above structure, the different refractive index region 15b is a hole, but the different refractive index region 15b may be formed by embedding a semiconductor having a refractive index different from that of the basic layer 15a in the hole. In that case, for example, the pores of the basic layer 15a may be formed by etching, and the semiconductor may be embedded in the pores by using an organic metal vapor phase growth method, a sputtering method, or an epitaxial method. For example, when the basic layer 15a is made of GaAs, the different refractive index region 15b may be made of AlGaAs. Further, a semiconductor may be embedded in the pores of the basic layer 15a to form the different refractive index region 15b, and then the same semiconductor as the different refractive index region 15b may be further deposited therein. When the different refractive index region 15b is a vacancy, the vacant hole may be filled with an inert gas such as argon, nitrogen, or hydrogen, or air.

The antireflection film 19 is made of, for example, a dielectric single layer film such as silicon nitride (for example, SiN), a silicon oxide (for example, SiO ₂ ), or a dielectric multilayer film. Examples of the dielectric multilayer film include titanium oxide (TIM ₂ ), silicon dioxide (SiO ₂ ), silicon monoxide (SiO), niobium oxide (Nb ₂ O ₅ ), tantalum pentoxide (Ta ₂ O ₅ ), and foot. Dielectric layers such as magnesium oxide (MgF ₂ ), titanium oxide (TIO ₂ ), aluminum oxide (Al ₂ O ₃ ), cerium oxide (CeO ₂ ), indium oxide (In ₂ O ₃ ), zirconium oxide (ZrO ₂ ) A film in which two or more types of dielectric layers selected from the group are laminated can be used. For example, a film having a thickness of λ / 4 is laminated with an optical film thickness for light having a wavelength of λ. Further, the protective film 18 is an insulating film such as silicon nitride (for example, SiN) or silicon oxide (for example, SiO ₂ ). When the semiconductor substrate 10 and the contact layer 14 are made of a GaAs-based semiconductor, the electrode 16 can be made of a material containing at least one of Cr, Ti, and Pt and Au, for example, a Cr layer and an Au layer. Has a laminated structure of. The electrode 17 can be made of a material containing at least one of AuGe and Ni and Au, and has, for example, a laminated structure of an AuGe layer and an Au layer. The materials of the electrodes 16 and 17 are not limited to these ranges as long as ohmic contact can be realized.

In the above-mentioned structure, if the structure includes the active layer 12 and the phase modulation layer 15, the material system, the film thickness, and the layer structure can be changed in various ways. Here, the scaling law holds for the so-called square lattice photonic crystal laser when the perturbation from the virtual square lattice is 0. That is, when the wavelength becomes a constant α times, the same standing wave state can be obtained by multiplying the entire square lattice structure by α. Similarly, in this embodiment as well, the structure of the phase modulation layer 15 can be determined by the scaling law according to the wavelength. Therefore, it is also possible to realize the semiconductor light emitting element 1A that outputs visible light by using the active layer 12 that emits light such as blue, green, and red and applying the scaling rule according to the wavelength.

When manufacturing the semiconductor light emitting device 1A, the organic metal vapor phase growth (MOCVD) method or the molecular beam epitaxy (MBE) method is used for the growth of each compound semiconductor layer. In the production of the semiconductor light emitting element 1A using AlGaAs, the growth temperature of AlGaAs is 500 ° C. to 850 ° C., and 550 to 700 ° C. is adopted in the experiment. TMG (trimethylgallium) and TEG (triethylgallium) as gallium raw materials, AsH ₃ (arsine) as As raw materials, Si _{2H 6 (} disilane) as raw materials for n-type impurities, and DEZn (diethyl) as raw materials for p-type impurities. Zinc) is used. In the growth of GaAs, TMG and arsine are used, but TMA is not used. InGaAs is manufactured using TMG, TMI (trimethylindium) and arsine. The insulating film may be formed by sputtering a target using the constituent material as a raw material or by a PCVD (plasma CVD) method.

That is, the above-mentioned semiconductor light emitting device 1A first has an AlGaAs layer as an n-type clad layer 11 and an InGaAs / AlGaAs multiple quantum well structure as an active layer 12 on a GaAs substrate as an n-type semiconductor substrate 10. The GaAs layer as the basic layer 15a of the modulation layer 15 is sequentially epitaxially grown by using the MOCVD method or the MBE method.

Next, another resist is applied to the basic layer 15a, a two-dimensional fine pattern is drawn on the resist with an electron beam drawing device based on the alignment mark, and the two-dimensional fine pattern is formed on the resist by developing. .. Then, using the resist as a mask, the two-dimensional fine pattern is transferred onto the basic layer 15a by dry etching to form holes, and then the resist is removed. Before forming the resist, a SiN layer or a SiO ₂ layer is formed on the basic layer 15a by the PCVD method, a resist mask is formed on the basic layer 15a, and reactive ion etching (RIE) is used to form the SiN layer or the SiO ₂ layer. The fine pattern may be transferred, the resist may be removed, and then dry etching may be performed. In this case, the resistance to dry etching can be increased. The depth of the pores is, for example, 100 nm. These holes are set to the different refractive index region 15b, or the compound semiconductor (AlGaAs) to be the different refractive index region 15b is re-grown in these holes to the depth of the holes or more. When the hole has a different refractive index region 15b, a gas such as air, nitrogen, or argon may be sealed in the hole. In this way, the phase modulation layer 15 is formed. When the phase modulation layer 15 is provided between the active layer 12 and the clad layer 11, the phase modulation layer 15 may be formed on the clad layer 11 before the active layer 12 is formed.

Subsequently, the AlGaAs layer as the clad layer 13 and the GaAs layer as the contact layer 14 are sequentially formed by the MOCVD method or the MBE method, and the electrodes 16 and 17 are formed by the vapor deposition method or the sputtering method. Further, if necessary, the protective film 18 and the antireflection film 19 are formed by sputtering, a PCVD method, or the like. Through the above steps, the semiconductor light emitting device 1A of the present embodiment is manufactured.

FIG. 4 is a plan view of the phase modulation layer 15. As described above, the phase modulation layer 15 includes a basic layer 15a made of a first refractive index medium and a different refractive index region 15b made of a second refractive index medium having a refractive index different from that of the first refractive index medium. Here, a virtual square grid in the XY plane is set in the phase modulation layer 15. It is assumed that one side of the square lattice is parallel to the X-axis and the other side is parallel to the Y-axis. At this time, the square-shaped unit constituent region R centered on the grid point O of the square grid can be set two-dimensionally over a plurality of columns along the X-axis and a plurality of rows along the Y-axis. Assuming that the XY coordinates of each unit constituent area R are given at the center of gravity position of each unit constituent area R, this center of gravity position coincides with the grid point O of the virtual square grid. The plurality of different refractive index regions 15b are provided one by one in each unit constituent region R. The planar shape of the different refractive index region 15b is, for example, a circular shape. The lattice point O may be located outside the different refractive index region 15b, or may be included inside the different refractive index region 15b.

The ratio of the area S of the different refractive index region 15b to the unit constituent region R is referred to as a filling factor (FF). Assuming that the lattice spacing of the square lattice is a, the filling factor FF of the different refractive index region 15b is given as S / a ² . S is the area of the different refractive index region 15b in the XY plane, and is given as S = π (d / 2) ² using the diameter d of the perfect circle, for example, in the case of a perfect circle shape. Further, in the case of a square shape, it is given as S = LA ² using the length LA of one side of the square.

FIG. 5 is a diagram showing the positional relationship of the different refractive index region 15b in the phase modulation layer 15. As shown in FIG. 5, the center of gravity G of each different refractive index region 15b is arranged on the straight line D. The straight line D is a straight line that passes through the corresponding grid points O of each unit constituent region R and is inclined with respect to each side of the square grid. In other words, the straight line D is a straight line that is inclined with respect to both the X-axis and the Y-axis. The inclination angle of the straight line D with respect to one side (X-axis) of the square lattice is θ. The tilt angle θ is constant in the phase modulation layer 15. The inclination angle θ satisfies 0 ° <θ <90 °, and in one example, θ = 45 °. Alternatively, the inclination angle θ satisfies 180 ° <θ <270 °, and in one example, θ = 225 °. When the tilt angle θ satisfies 0 ° <θ <90 ° or 180 ° <θ <270 °, the straight line D extends from the first quadrant to the third quadrant of the coordinate plane defined by the X-axis and the Y-axis. Alternatively, the inclination angle θ satisfies 90 ° <θ <180 °, and in one example, θ = 135 °. Alternatively, the inclination angle θ satisfies 270 ° <θ <360 °, and in one example, θ = 315 °. When the tilt angle θ satisfies 90 ° <θ <180 ° or 270 ° <θ <360 °, the straight line D extends from the second quadrant to the fourth quadrant of the coordinate plane defined by the X-axis and the Y-axis. As described above, the inclination angle θ is an angle excluding 0 °, 90 °, 180 ° and 270 °. Here, the distance between the grid point O and the center of gravity G is r (x, y). x indicates the position of the x-th grid point on the X-axis, and y indicates the position of the y-th grid point on the Y-axis. When the distance r (x, y) is a positive value, the center of gravity G is located in the first quadrant (or the second quadrant). When the distance r (x, y) is a negative value, the center of gravity G is located in the third quadrant (or the fourth quadrant). When the distance r (x, y) is 0, the grid point O and the center of gravity G coincide with each other.

の範囲内である。なお、所望の光像から複素振幅分布を求める際には、ホログラム生成の計算時に一般的に用いられるGerchberg-Saxton（ＧＳ）法のような繰り返しアルゴリズムを適用することによって、ビームパターンの再現性が向上する。 The distance r (x, y) between the center of gravity G of each different refractive index region 15b and the corresponding lattice point O of each unit constituent region R shown in FIG. 4 is each different refractive index according to a desired optical image. It is set individually for each region 15b. The distribution of the distance r (x, y) has a specific value for each position determined by the values of x and y, but is not always expressed by a specific function. The distribution of the distance r (x, y) is determined from the complex amplitude distribution obtained by Fourier transforming the desired optical image from which the phase distribution is extracted. That is, when the phase P (x, y) at a certain coordinate (x, y) shown in FIG. 5 is P ₀ , the distance r (x, y) is set to 0, and the phase P (x, y) is set. When y) is π + P ₀ , the distance r (x, y) is set to the maximum value R ₀ , and when the phase P (x, y) is −π + P ₀ , the distance r (x, y) is set. Set to the minimum value -R ₀ . Then, for the intermediate phase P (x, y), the distance r (x, y) is such that r (x, y) = {P (x, y) −P ₀ } × R ₀ / π. ). Here, the initial phase P ₀ can be arbitrarily set. Assuming that the grid spacing of the square grid is a, the maximum value R ₀ of r (x, y) is, for example.

Is within the range of. When obtaining the complex amplitude distribution from the desired optical image, the reproducibility of the beam pattern can be improved by applying an iterative algorithm such as the Gerchberg-Saxton (GS) method, which is generally used when calculating hologram generation. improves.

FIG. 6 is a plan view showing an example in which the refractive index substantially periodic structure of FIG. 4 is applied only within a specific region of the phase modulation layer. In the example shown in FIG. 6, a substantially periodic structure (example: the structure of FIG. 4) for emitting a target beam pattern is formed inside the inner region RIN of the square. On the other hand, in the outer region ROUT surrounding the inner region RIN, a perfect circular different refractive index region where the position of the grid point of the square lattice and the position of the center of gravity coincide with each other is arranged. In the inner region RIN and the outer region ROUT, the grid spacing of the square grids virtually set is the same (= a). In the case of this structure, since the light is also distributed in the outer region ROUT, it is possible to suppress the generation of high frequency noise (so-called window function noise) generated by the sudden change in light intensity in the peripheral portion of the inner region RIN. can. In addition, light leakage in the in-plane direction can be suppressed, and a reduction in the threshold current can be expected.

FIG. 7 is a diagram for explaining the relationship between the optical image obtained as the output beam pattern of the semiconductor light emitting device 1A and the phase distribution P (x, y) in the phase modulation layer 15. The center Q of the output beam pattern is located on an axis perpendicular to the main surface 10a of the semiconductor substrate 10, and FIG. 7 shows four quadrants with the center Q as the origin. FIG. 7 shows a case where an optical image is obtained in the first quadrant and the third quadrant as an example, but it is also possible to obtain an image in the second quadrant and the fourth quadrant or all quadrants. In this embodiment, as shown in FIG. 7, a point-symmetrical optical image with respect to the origin is obtained. FIG. 7 shows, as an example, a case where the character “A” is obtained as the +1st-order diffracted light in the third quadrant, and the pattern obtained by rotating the character “A” by 180 degrees in the first quadrant is obtained as the -1st-order diffracted light. .. In the case of a rotationally symmetric optical image having the center Q as the origin (for example, a cross, a circle, a double circle, etc.), they are observed as one optical image overlapping.

The optical image obtained by forming the output beam pattern of the semiconductor light emitting device 1A is a spot, a straight line, a cross, a line art, a grid pattern, a photograph, a striped pattern, CG (computer graphics), and at least one of characters. Includes. Here, in order to obtain a desired optical image, the distribution of the distance r (x, y) in the different refractive index region 15b of the phase modulation layer 15 is determined by the following procedure.

First, as a first precondition, in the XYZ Cartesian coordinate system, it is composed of M1 (integer of 1 or more) × N1 (integer of 1 or more) unit constituent regions R each having a square shape on the XY plane. A virtual square grid is set. Next, as a second precondition, the coordinates (x, y, z) in the XYZ Cartesian coordinate system are, as shown in FIG. 8, the length r of the driving diameter and the inclination angle θ _tilt from the Z axis. , The rotation angle θ _rot from the X axis specified on the XY plane, and the spherical coordinates (r, θ _tilt , θ _rot ) defined by the following equations (10) to (12). Satisfy the relationship. Note that FIG. 8 is a diagram for explaining coordinate conversion from spherical coordinates (r, θ _tilt , θ _rot ) to coordinates (x, y, z) in the XYZ Cartesian coordinate system, and is a diagram for explaining coordinates (x, y, z) represents a design optical image on a predetermined plane set in a real space XYZ Cartesian coordinate system. When the beam pattern corresponding to the light image output from the semiconductor light emitting element is a set of bright spots in the directions defined by the angles θ _tilt and θ _rot , the angles θ _tilt and θ _rot are given by the following equation (13). The coordinate value k _x on the Kx axis, which is the standardized wave number specified in, and the Kx axis, which is the standardized wave number specified by the following equation (14), corresponds to the Y axis. It shall be converted into the coordinate value _ky on the orthogonal ky axis. The normalized wavenumber means the wavenumber standardized with the wavenumber corresponding to the grid spacing of the virtual square grid as 1.0. At this time, in the wavenumber space defined by the Kx axis and the Ky axis, the specific wavenumber range including the beam pattern corresponding to the optical image is square M2 (integer of 1 or more) × N2 (integer of 1 or more), respectively. ) Consists of image area FR. The integer M2 does not have to match the integer M1. Similarly, the integer N2 does not have to match the integer N1. Equations (13) and (14) also include, for example, Y. Kurosaka et al., "Effects of non-lasing band in two-dimensional photonic-crystal lasers clarified using omnidirectional band structure," Opt. Express 20, 21773-21783. It is disclosed in (2012).

上記第１～第４の前提条件の下、位相変調層１５は、以下の条件を満たすよう構成される。すなわち、格子点Ｏ（ｘ，ｙ）から対応する異屈折率領域１５ｂの重心Ｇまでの距離ｒ（ｘ，ｙ）が、
ｒ（ｘ，ｙ）＝Ｃ×（Ｐ（ｘ，ｙ）－Ｐ₀）
Ｃ：比例定数で例えばＲ₀／π
Ｐ₀：任意の定数であって例えば０
なる関係を満たすように、該対応する異屈折率領域１５ｂが単位構成領域Ｒ（ｘ，ｙ）内に配置される。すなわち、距離ｒ（ｘ，ｙ）は、或る座標（ｘ，ｙ）における位相Ｐ（ｘ，ｙ）がＰ₀である場合には０に設定され、位相Ｐ（ｘ，ｙ）がπ＋Ｐ₀である場合には最大値Ｒ₀に設定され、位相Ｐ（ｘ，ｙ）が－π＋Ｐ₀である場合には最小値－Ｒ₀に設定される。所望の光像を得たい場合、該光像を逆フーリエ変換して、その複素振幅の位相Ｐ（ｘ，ｙ）に応じた距離ｒ（ｘ，ｙ）の分布を、複数の異屈折率領域１５ｂに与えるとよい。位相Ｐ（ｘ，ｙ）と距離ｒ（ｘ，ｙ）とは、互いに比例してもよい。 As a third precondition, an image specified by the coordinate component k _x (integer of 1 or more and M2 or less) in the Kx axis direction and the coordinate component _ky (integer of 1 or more and N2 or less) in the Ky axis direction in the wave number space. Each region FR (k _{x, ky} ) is an XY plane specified by a coordinate component x in the X-axis direction (integer of 1 or more and M1 or less) and a coordinate component y in the Y-axis direction (integer of 1 or more and N1 or less). The complex amplitude F (x, y) obtained by performing a two-dimensional inverse Fourier transformation on the above unit constituent region R (x, y) is given by the following equation (15) with j as an imaginary unit. Further, this complex amplitude F (x, y) is defined by the following equation (16) when the amplitude term is A (x, y) and the phase term is P (x, y). Further, as a fourth precondition, the grid point O (x, y) in which the unit constituent region R (x, y) is parallel to the X-axis and the Y-axis and is the center of the unit constituent region R (x, y), respectively. It is defined by the s-axis and the t-axis that are orthogonal to each other in y).

Under the first to fourth preconditions, the phase modulation layer 15 is configured to satisfy the following conditions. That is, the distance r (x, y) from the lattice point O (x, y) to the center of gravity G of the corresponding different refractive index region 15b is.
r (x, y) = C × (P (x, y) -P ₀ )
C: Proportional constant, for example R ₀ / π
P ₀ : An arbitrary constant, for example, 0
The corresponding different refractive index regions 15b are arranged in the unit constituent region R (x, y) so as to satisfy the above relationship. That is, the distance r (x, y) is set to 0 when the phase P (x, y) at a certain coordinate (x, y) is P ₀ , and the phase P (x, y) is π + P ₀ . If is, the maximum value is set to R ₀ , and if the phase P (x, y) is −π + P ₀ , the minimum value is set to −R ₀ . When a desired optical image is desired, the optical image is subjected to an inverse Fourier transform to obtain a distribution of a distance r (x, y) corresponding to the phase P (x, y) of the complex amplitude in a plurality of different refractive index regions. It is good to give it to 15b. The phase P (x, y) and the distance r (x, y) may be proportional to each other.

The far-field image after Fourier transform of the laser beam has various shapes such as a single spot shape, a ring shape, a linear shape, a character shape, a double ring shape, or a Lager Gaussian beam shape. Can be taken. Since the beam direction can also be controlled, it is possible to realize, for example, a laser processing machine that electrically performs high-speed scanning by arranging the semiconductor light emitting elements 1A one-dimensionally or two-dimensionally. Since the beam pattern is represented by angle information in the distant field, if the target beam pattern is a bitmap image represented by two-dimensional position information, it is temporarily converted into angle information. Then, it is advisable to perform the reciprocal Fourier transform after converting to the wavenumber space.

As a method of obtaining the intensity distribution and the phase distribution from the complex amplitude distribution obtained by the inverse Fourier transform, for example, the intensity distribution I (x, y) is calculated by using the abs function of the numerical analysis software "MATLAB" of MathWorks. The phase distribution P (x, y) can be calculated by using the angular function of MATLAB.

Here, when the phase distribution P (x, y) is obtained from the inverse Fourier transform result of the optical image and the distance r (x, y) of each different refractive index region 15b is determined, a general discrete Fourier transform (or high speed) is used. Here are some points to keep in mind when calculating using the Fourier transform). The output beam pattern calculated from the complex amplitude distribution obtained by the inverse Fourier transform of FIG. 9 (a), which is a desired optical image, is as shown in FIG. 9 (b). When divided into four quadrants such as A1, A2, A3, and A4 as shown in FIGS. 9 (a) and 9 (b), the first quadrant of the output beam pattern of FIG. 9 (b) is shown in FIG. A pattern in which the first quadrant of a) is rotated 180 degrees and the third quadrant of FIG. 9 (a) are superimposed appears, and the second quadrant of FIG. 9 (a) is rotated 180 degrees in the second quadrant of the beam pattern. A pattern in which the fourth quadrant of FIG. 9 (a) is superimposed appears, and the third quadrant of FIG. 9 (a) is rotated 180 degrees and the third quadrant of FIG. 9 (a) is the third quadrant of the beam pattern. A pattern in which one quadrant is superimposed appears, and in the fourth quadrant of the beam pattern, a pattern in which the fourth quadrant of FIG. 9 (a) is rotated by 180 degrees and a pattern in which the second quadrant of FIG. 9 (a) is superimposed appear. At this time, the pattern rotated by 180 degrees is due to the -1st order light component.

Therefore, when an optical image (original optical image) before the Fourier transformation that has a value only in the first quadrant is used, the first quadrant of the original optical image appears in the third quadrant of the obtained beam pattern. , A pattern obtained by rotating the first quadrant of the original light image by 180 degrees appears in the first quadrant of the obtained beam pattern.

Here, FIG. 10A shows an example of a beam pattern (optical image) output from the semiconductor light emitting device 1A. The center of the figure corresponds to an axis line that intersects the light emitting surface of the semiconductor light emitting device 1A and is perpendicular to the light emitting surface. Further, FIG. 10B is a graph showing the light intensity distribution in the cross section including the axis. FIG. 10B is a far-field image acquired using an FFP optical system (A3267-12 manufactured by Hamamatsu Photonics), a camera (ORCA-05G manufactured by Hamamatsu Photonics), and a beam profiler (Lepas-12 manufactured by Hamamatsu Photonics). The vertical counts of the image data of dots × 1024 dots are integrated and plotted. The maximum count number in FIG. 10A is standardized at 255, and the central 0th-order light B0 is saturated in order to clearly indicate the intensity ratio of ± 1st-order light. From FIG. 10B, the difference in intensity between the primary light and the -1st light can be easily understood. Further, FIG. 11A is a diagram showing a phase distribution corresponding to the beam pattern shown in FIG. 10A. 11 (b) is a partially enlarged view of FIG. 11 (a). In FIGS. 11 (a) and 11 (b), the phase at each location in the phase modulation layer 15 is indicated by shading, and the dark part approaches the phase angle of 0 ° and the bright part approaches the phase angle of 360 °. However, since the center value of the phase angle can be set arbitrarily, the phase angle does not necessarily have to be set within the range of 0 ° to 360 °. As shown in FIGS. 10A and 10B, the semiconductor light emitting device 1A includes primary light including a first light image portion B1 output in a first direction inclined with respect to the axis. It is output in the second direction that is symmetric with respect to the first direction with respect to the axis, and outputs -1st order light including the first light image portion B1 and the second light image portion B2 that is rotationally symmetric with respect to the axis. Typically, the first light image portion B1 appears in the first quadrant in the XY plane and the second light image portion B2 appears in the third quadrant in the XY plane. Depending on the application, only one of the primary light and the -1st light may be used, and the other may not be used. In such a case, it is desirable that the amount of light of the other light is suppressed to be smaller than that of the one light. Therefore, in the present embodiment, as shown in FIG. 10 (b), the intensity difference is given to the primary light and the -1st order light.

FIG. 12 is a plan view conceptually showing the phase modulation layer 15. Now, the first region T1 and the second region T2 arranged in one grid point arrangement direction (X-axis direction) with the center point Q of the phase modulation layer in between, and the other grid with the center point Q of the phase modulation layer in between. A third region T3 and a fourth region T4 arranged in the point arrangement direction (Y-axis direction) are defined. That is, when the origin of the XY Cartesian coordinate system is made to coincide with the center point Q, the first region T1 is a region where the X-axis coordinates are positive, the second region T2 is a region where the X-axis coordinates are negative, and the third region T2. The region T3 is a region where the Y-axis coordinates are positive, and the fourth region T4 is a region where the Y-axis coordinates are negative. Therefore, the first region T1 and the third region T3 overlap each other in the first quadrant F1 in which the X-axis coordinates and the Y-axis coordinates are both positive. Further, the first region T1 and the fourth region T4 overlap each other in the second quadrant F2 in which the X-axis coordinates are positive and the Y-axis coordinates are negative. The second region T2 and the fourth region T4 overlap each other in the third quadrant F3 in which both the X-axis coordinate and the Y-axis coordinate are negative. The second region T2 and the third region T3 overlap each other in the fourth quadrant F4 in which the X-axis coordinates are negative and the Y-axis coordinates are positive.

In the phase modulation layer 15, which is the phase modulation layer of the square lattice type S-iPM laser, as shown in FIG. 12, basic traveling waves AU, AD, AR, and AL along the XY plane are generated. The traveling wave AR is a first traveling wave traveling in the direction (X-axis positive direction) from the second region T2 to the first region T1. The traveling wave AL is a second traveling wave traveling in the direction (X-axis negative direction) from the first region T1 to the second region T2. The traveling wave AU is a third traveling wave traveling in the direction (Y-axis positive direction) from the fourth region T4 to the third region T3. The traveling wave AD is a fourth traveling wave traveling in the direction (Y-axis negative direction) from the third region T3 to the fourth region T4.

As shown in FIG. 13, beam patterns in opposite directions can be obtained from traveling waves traveling in opposite directions. For example, a beam pattern BU containing only the second light image portion B2 can be obtained from the traveling wave AU, and a beam pattern BD containing only the first light image portion B1 can be obtained from the traveling wave AD. Similarly, the beam pattern BR containing only the second light image portion B2 is obtained from the traveling wave AR, and the beam pattern BL containing only the first light image portion B1 is obtained from the traveling wave AL. In other words, in the progressive waves traveling in opposite directions, one becomes the primary light and the other becomes the -1st order light. The beam pattern output from the semiconductor light emitting device 1A is a combination of these beam patterns BU, BD, BR, and BL.

Here, FIGS. 14 to 17 are graphs showing the intensity distributions of the traveling waves AU, AD, AR, and AL in the plane of the phase modulation layer 15. 14 shows the intensity distribution of the traveling wave AU, FIG. 15 shows the intensity distribution of the traveling wave AD, FIG. 16 shows the intensity distribution of the traveling wave AR, and FIG. 17 shows the intensity distribution of the traveling wave AL. Further, in FIGS. 14 to 17, (a) represents the intensity distributions of the traveling waves AU, AD, AR, and AL by equal intensity lines, the horizontal axis represents the position in the X-axis direction, and the vertical axis represents the position in the X-axis direction. Represents the position in the Y-axis direction. (B) is a three-dimensional representation of the intensity distribution of the traveling waves AU, AD, AR, and AL, and in addition to the X-axis direction position and the Y-axis direction position, the axis representing the intensity of the traveling wave is It is shown. As shown in these figures, the intensities of the traveling waves AU, AD, AR, and AL are unevenly distributed in the plane of the phase modulation layer 15.

Specifically, the intensity of the traveling wave AU traveling in the positive direction of the Y axis becomes stronger as the Y coordinate becomes larger, and becomes weaker as the Y coordinate becomes smaller. Further, the intensity of the traveling wave AD traveling in the negative direction of the Y axis becomes stronger as the Y coordinate becomes smaller, and becomes weaker as the Y coordinate becomes larger. Similarly, the intensity of the traveling wave AR traveling in the positive direction of the X-axis becomes stronger as the X-coordinate becomes larger, and becomes weaker as the X-coordinate becomes smaller. Further, the intensity of the traveling wave AL traveling in the negative direction of the X-axis becomes stronger as the X coordinate becomes smaller, and becomes weaker as the X coordinate becomes larger. In other words, the traveling waves AU and AR are strong in the first quadrant F1, the traveling waves AD and AR are strong in the second quadrant F2, the traveling waves AD and AL are strong in the third quadrant F3, and the traveling waves AD and AL are strong in the fourth quadrant F4. Has strong progressive waves AU and AL. When the inclination angle θ of the straight line D is 45 °, 135 °, 225 °, or 315 °, the maximum intensities of the traveling waves AU, AD, AR, and AL are equal to each other. When the inclination angle θ of the straight line D is 0 ° <θ <45 °, 135 ° <θ <225 °, or 315 ° <θ <360 °, the maximum intensity of the traveling waves AR and AL is the traveling wave. When the inclination angle θ of the straight line D is 45 ° <θ <135 ° or 225 ° <θ <315 °, which is larger than the maximum intensity of AU and AD, the maximum intensity of the traveling wave AU and AD is the traveling wave. It becomes larger than the maximum intensity of AR and AL.

In this embodiment, the intensity distributions of the above-mentioned traveling waves AU, AD, AR, and AL are used to give a difference in the amount of primary light and -1st order light, and one of them is reduced with respect to the other. do. Therefore, the arrangement of the different refractive index region 15b in the phase modulation layer 15 is designed by the following method. FIG. 18 is a flowchart showing a design method of the phase modulation layer 15 according to the present embodiment.

As shown in FIG. 18, in the first step S1, a plurality of complex amplitude distributions corresponding to the optical image are prepared for each of the traveling waves AU, AD, AR, and AL. First, the degree of deviation of the light intensity in the plane of the phase modulation layer 15 is predicted in advance, and the light images obtained by each of the traveling waves AU, AD, AR, and AL are separated from each other. As a result, four optical images corresponding to the traveling waves AU, AD, AR, and AL are obtained. Then, based on these optical images, the complex amplitude distribution EU (x, y) for the traveling wave AU, the complex amplitude distribution _ED (x, y) for the traveling wave _AD , and the complex amplitude distribution E for the traveling wave AR _R (x, y) and the complex amplitude distribution _EL (x, y) with respect to the traveling wave AL are calculated individually.

E _U (x, y) = A _U (x, y) exp {iP _U (x, y)}
_ED (x, y) = _AD (x, y) exp {iP _D (x, y)}
_{ER (x, y) = AR (x, y) exp {iP R ( x} , y)}
EL (x, y) = _AL (x, y) exp { _{iPL (} x, y)}
In addition, A _U (x, y), _AD (x, y), _AR (x, y), and _AL (x, y) are intensity distributions of the progressive waves AU, AD, AR, and AL, respectively. P _U (x, y), P _D (x, y), _PR (x, y), and _PL (x, y) are the phases of the progressive waves AU, AD, AR, and AL, respectively. It is a distribution. These complex amplitude distributions EU (x, y), _{ED (x, y), ER (x, y), and EL ( x ,} y) reverse Fourier each optical image as described above. Obtained by conversion. The calculation method of the complex amplitude distribution is described in, for example, WH Lee, "Sampled fourier transform hologram generated by computer", Appl, Opt, 9, 639-643 (1970).

Next, in the second step S2, the complex amplitude distributions EU (x, y), ED (x, y), _ER (x, _y ), and _E for each progressive wave AU, AD, AR, and AL. Correct _L (x, y). In the second step S2, the positive / negative of the phase term of the complex amplitude distribution for one of the traveling waves AR and AL is inverted, and the positive / negative of the phase term of the complex amplitude distribution for one of the traveling waves AU and AD is inverted. For example, the modified complex amplitude distributions _{E U} (x, y), ED (x, y), _ER (x, y), and _EL (x, y) are as follows, respectively.

E _U (x, y) = A _U (x, y) exp {-iP _U (x, y)}
_ED (x, y) = _AD (x, y) exp {iP _D (x, y)}
ER (x, y) = AR (x, y) exp { _{-iP R} (x, y) _}
EL (x, y) = _AL (x, y) exp { _{iPL (} x, y)}
In this example, the positive and negative of the phase terms of the traveling waves _AU (x, y) and _ER (x, y) are inverted, but the complex amplitude distribution ED related to the traveling waves _AD and AL. The positive and negative of the phase terms of (x, y) and _EL (x, y) may be inverted. Further, in this example, the inclination angle θ of the straight line D is 0 ° <θ <90 ° or 180 ° <θ <270 °, and the inclination angle θ of the straight line D is 90 ° <θ <180 °. Alternatively, when 270 ° <θ <360 °, it is preferable to invert the positive and negative of the phase term of the complex amplitude distribution with respect to the traveling wave AU, AL (or the traveling wave AD, AR).

Further, in the second step S2, as shown in the following formula, the complex amplitude distributions EU (x, y), ED (x, y), _ER (x, _y ), and _EL ( _x ). , Y) may be arbitrarily weighted. For example, the complex amplitude distributions EU (x, y) and ED (x, y) are multiplied by the same weight n, and the complex amplitude distributions _ER (x, _y ) and _EL (x, _y ) are multiplied by the same weight m. Multiply. Then, the weight n and the weight m are made different from each other.

E _U (x, y) = nA _U (x, y) exp {-iP _U (x, y)}
_{ED (x, y) = nA D (x, y) exp {iP D ( x} , y)}
ER (x, y) = mA _R (x, y) exp { _{-iP R (} x, y)}
_{EL (x, y) = mA L (} x, y) exp { _iPL (x, y)}
For example, the ratio (m / n) of the weight n to the weight m may be determined based on the inclination angle θ of the straight line D with respect to the square lattice. That is, when the inclination angle θ of the straight line D is 0 ° <θ <45 °, 135 ° <θ <225 °, or 315 ° <θ <360 °, the maximum of the traveling waves AR and AL is as described above. Since the intensity is higher than the maximum intensity of the traveling waves AU and AD, the ratio (m / n) is increased to increase the contribution of _{ER (x, y) and EL (} x, y). Further, when the inclination angle θ of the straight line D is 45 ° <θ <135 ° or 225 ° <θ <315 °, the maximum intensity of the traveling waves AU and AD is the maximum of the traveling waves AR and AL as described above. Since it is higher than the strength, the ratio (m / n) is reduced to increase the contribution of _EU (x, y) and _ED (x, y). In one embodiment, m = cosθ and n = sinθ may be set.

Subsequently, in the third step S3, as shown in the following mathematical formula (17), the complex amplitude distributions EU (x, y), _ED (x, y), _ER (x, _y ), and E. By superimposing (adding) _L (x, y) on each other, the total (final) complex amplitude distribution E _total (x, y) is obtained.

この第４ステップＳ４では、各異屈折率領域１５ｂの重心Ｇを直線Ｄ上に配置するとともに、各異屈折率領域１５ｂの重心Ｇと、対応する格子点Ｏとの距離ｒ（ｘ，ｙ）を、総合的な位相分布Ｐ_total（ｘ，ｙ）に基づいて決定する。 Finally, in the fourth step S4, as shown in the following mathematical formula (18), the comprehensive phase distribution P _total (x, y) is extracted from the comprehensive complex amplitude distribution E _total (x, y). , The position of the center of gravity G of each different refractive index region 15b is determined based on the total phase distribution P _total (x, y).

In the fourth step S4, the center of gravity G of each different refractive index region 15b is arranged on the straight line D, and the distance r (x, y) between the center of gravity G of each different refractive index region 15b and the corresponding lattice point O is Is determined based on the total phase distribution P _total (x, y).

In a square grid with a grid spacing a, where x and y are the unit vectors of Cartesian coordinates, the basic translation vector a ₁ = ax, a ₂ = ay, and the basic reciprocal lattice vector b with respect to the translation vectors a ₁ and a ₂ . ₁ = (2π / a) x, b ₂ = (2π / a) y. When the wave vector of the wave existing in the lattice is k = nb ₁ + mb ₂ (n and m are arbitrary integers), the wave number k exists at the Γ point, but the magnitude of the wave vector is basically the reverse. When it is equal to the magnitude of the lattice vector, a resonance mode (standing wave in the XY plane) in which the lattice spacing a is equal to the wavelength λ is obtained. In this embodiment, oscillation in such a resonance mode (standing wave state) can be obtained. At this time, considering the TE mode in which an electric field exists in a plane parallel to the square lattice, there are four modes in the standing wave state in which the lattice spacing and the wavelength are equal in this way due to the symmetry of the square lattice. In the present embodiment, a desired beam pattern can be obtained in the same manner when oscillating in any of the four standing wave modes.

In the semiconductor light emitting element 1A, the standing wave in the phase modulation layer 15 is scattered by the different refractive index region 15b, and the wavefront obtained in the direction perpendicular to the plane is phase-modulated to obtain a desired beam pattern. Therefore, a desired beam pattern can be obtained without a polarizing plate. This beam pattern is not only a pair of single peak beams (spots), but as described above, a character shape, two or more spots having the same shape, or a vector whose phase and intensity distribution are spatially non-uniform. It is also possible to use a beam or the like.

The refractive index of the basic layer 15a is preferably 3.0 to 3.5, and the refractive index of the different refractive index region 15b is preferably 1.0 to 3.4. Further, the average radius of each different refractive index region 15b is, for example, 20 nm to 120 nm in the case of the 940 nm band. The diffraction intensity in the Z-axis direction changes as the size of each different refractive index region 15b changes. This diffraction efficiency is proportional to the optical coupling coefficient κ1 represented by the first-order coefficient when the shape of the different refractive index region 15b is Fourier transformed. The photocoupling coefficient is described, for example, in K. Sakai et al., “Coupled-WaveTheory for Square-Lattice Photonic Crystal Lasers With TE Polarization, IEEE J.Q. E. 46, 788-795 (2010)”.

The effect obtained by the design method of the phase modulation layer 15 according to the present embodiment described above will be described. In the present embodiment, the phase modulation layer 15 optically coupled to the active layer 12 has a basic layer 15a and a plurality of different refractive index regions 15b having different refractive indexes from the basic layer 15a, and is a virtual square. The center of gravity G of each different refractive index region 15b is arranged on a straight line D that passes through the lattice point O of the lattice and is inclined with respect to the X-axis and the Y-axis of the square lattice. The distance r (x, y) between the center of gravity G of each different refractive index region 15b and the corresponding lattice point O is individually set according to the optical image. In such a case, the phase of the beam changes according to the distance between the grid point O and the center of gravity G. Therefore, the phase of the beam emitted from each different refractive index region 15b can be controlled only by changing the position of the center of gravity G, and the beam pattern formed as a whole can be made into a desired shape. That is, the semiconductor light emitting element 1A is an S-iPM laser, and according to such a structure, a conventional center of gravity G of each different refractive index region 15b has a rotation angle corresponding to an optical image around each lattice point O. Similar to the structure, it is possible to output an optical image having an arbitrary shape in a direction inclined with respect to a direction perpendicular to the main surface 10a of the semiconductor substrate 10.

Further, according to the study of the present inventor, in the conventional semiconductor light emitting device that rotates the different refractive index region around the lattice point, both traveling waves traveling in opposite directions due to the nature of the arrangement of the different refractive index region. Is always included. That is, in the conventional method, in any of the four progressive waves AU, AD, AR, and AL that form a standing wave, the same amount of primary light and -1st order light appear, and the radius of the rotating circle ( Depending on the distance between the center of gravity of the different refractive index region and the lattice point), 0th-order light is generated. Therefore, it is difficult in principle to give a difference in the amount of each of the primary light and the -1st order light, and it is difficult to selectively reduce one of them. Therefore, it is difficult to reduce the amount of -1st-order light relative to the amount of primary light.

を用いると、位相分布Φ（ｘ，ｙ）を級数展開することができ、０次光及び±１次光の各光量を説明することができる。このとき、位相分布Φ（ｘ，ｙ）の０次光成分はＪ₀（２πｒ／ａ）、１次光成分はＪ₁（２πｒ／ａ）、－１次光成分はＪ_-1（２πｒ／ａ）と表される。ところで、±１次のベッセル関数に関しては、Ｊ₁（ｘ）＝－Ｊ_-1（ｘ）の関係があるため、±１次光成分の大きさは等しくなる。ここでは、４つの進行波の１例としてＹ軸正方向の進行波ＡＵについて考えたが、他の３波（進行波ＡＤ，ＡＲ，ＡＬ）についても同様の関係が成立し、±１次光成分の大きさが等しくなる。以上の議論から、異屈折率領域１５ｂを格子点Ｏの周りで回転させる従来の方式では、±１次光成分の光量に差を与えることが原理的に困難となる。 Here, in the conventional method of rotating the different refractive index region 15b around the grid point O shown in FIG. 19A, it is possible to selectively reduce either the primary light or the -1st order light. Explain why it is difficult. As an example of the four traveling waves with respect to the design phase φ (x, y) at a certain position, consider the traveling wave AU in the positive direction of the Y axis shown in FIG. 19 (b). At this time, due to the geometrical relationship, the deviation from the lattice point O is r · sinφ (x, y) for the traveling wave AU, so the phase difference is (2π / a) r · sinφ (x). , Y). As a result, the phase distribution Φ (x, y) with respect to the traveling wave AU has a small influence on the size of the different refractive index region 15b, and if the influence can be ignored, Φ (x, y) = exp {j ( It is given by 2π / a) r · sinφ (x, y)}. The contribution of this phase distribution Φ (x, y) to the 0th-order light and the ± 1st-order light is n = 0 and n = ± when expanded by exp {jnΦ (x, y)} (n: integer). It is given by one component. By the way, a mathematical formula for the first-class Bessel function Jn (z) of degree n

Can be used to expand the phase distribution Φ (x, y) by series, and can explain the light quantities of the 0th-order light and the ± 1st-order light. At this time, the 0th-order light component of the phase distribution Φ (x, y) is J ₀ (2πr / a), the 1st-order light component is J ₁ (2πr / a), and the -1st-order light component is J _-1 (2πr / a). It is expressed as a). By the way, with respect to the ± 1st-order Bessel function, since there is a relationship of J ₁ (x) = −J _-1 (x), the magnitudes of the ± 1st-order optical components are equal. Here, the traveling wave AU in the positive direction of the Y-axis was considered as an example of the four progressive waves, but the same relationship holds for the other three waves (traveling waves AD, AR, AL), and ± primary light. The sizes of the components are equal. From the above discussion, in the conventional method of rotating the different refractive index region 15b around the grid point O, it is difficult in principle to give a difference in the amount of light of the ± primary light component.

On the other hand, according to the phase modulation layer 15 of the present embodiment, there is a difference in the amount of each of the primary light and the -1st order light for a single traveling wave, for example, the inclination angle θ is 45 °. In the case of 135 °, 225 ° or 315 °, the closer the shift amount R ₀ is to the upper limit of the above-mentioned equation (9), the more an ideal phase distribution can be obtained. As a result, the 0th-order light is reduced, and in each of the traveling waves AU, AD, AR, and AL, one of the primary light and the -1st-order light is selectively reduced. Therefore, in principle, it is possible to give a difference in the amount of primary light and -1st-order light by selectively reducing one of the traveling waves traveling in opposite directions.

で与えられる。この位相分布Φ（ｘ，ｙ）の０次光および±１次光への寄与は、ｅｘｐ｛ｎΦ（ｘ，ｙ）｝（ｎ：整数）で展開した場合の、ｎ＝０およびｎ＝±１の成分で与えられる。ところで、下記の数式（２１）によって表される関数ｆ（ｚ）

但し、

をＬａｕｒｅｎｔ級数展開すると、

なる数学公式が成り立つ。ここで、ｓｉｎｃ（ｘ）＝ｘ／ｓｉｎ（ｘ）である。この数学公式を用いると、位相分布Φ（ｘ，ｙ）を級数展開することができ、０次光及び±１次光の各光量を説明することができる。このとき、数学公式（２１）の指数項ｅｘｐ｛ｊπ（ｃ－ｎ）｝の絶対値が１である点に注意すると、位相分布Φ（ｘ，ｙ）の０次光成分の大きさは

と表され、１次光成分の大きさは

と表され、－１次光成分の大きさは

と表される。そして、数式（２４）～（２６）においては、

の場合を除いて、１次光成分以外に０次光および－１次光成分が現れる。しかしながら、±１次光成分の大きさは互いに等しくならない。 Here, in the method of the present embodiment in which the different refractive index region 15b moves on the straight line D which passes through the grid point O and is inclined with respect to the square grid, which is shown in FIG. 20A, the primary light and the -1st order are used. Explain why it is possible to selectively reduce any of the light. As an example of the four traveling waves with respect to the design phase φ (x, y) at a certain position, consider the traveling wave AU in the positive direction of the Y axis shown in FIG. 20 (b). At this time, due to the geometrical relationship, the deviation from the lattice point O is r · sin θ · {φ (x, y) −φ ₀ } / π for the traveling wave AU, so the phase difference is ( The relationship is 2π / a) r ・ sinθ ・ {φ (x, y) -φ ₀ } / π. Here, for the sake of simplicity, the inclination angle θ = 45 ° and the phase angle φ ₀ = 0 °. At this time, the phase distribution Φ (x, y) with respect to the traveling wave AU has a small influence on the size of the different refractive index region 15b, and if the influence can be ignored, the influence can be ignored.

Given in. The contribution of this phase distribution Φ (x, y) to the 0th-order light and the ± 1st-order light is n = 0 and n = ± when expanded by exp {nΦ (x, y)} (n: integer). It is given by one component. By the way, the function f (z) expressed by the following mathematical formula (21).

However,

When the Laurent series is expanded,

Mathematical formula holds. Here, sinc (x) = x / sin (x). Using this mathematical formula, the phase distribution Φ (x, y) can be expanded in series, and the light quantities of 0th-order light and ± 1st-order light can be explained. At this time, paying attention to the fact that the absolute value of the exponential term exp {jπ (cn)} of the mathematical formula (21) is 1, the magnitude of the 0th-order optical component of the phase distribution Φ (x, y) is.

The size of the primary light component is expressed as

The size of the -1st order light component is

It is expressed as. Then, in the mathematical formulas (24) to (26),

Except for the case of, 0th-order light and -1st-order light components appear in addition to the primary light component. However, the magnitudes of the ± primary light components are not equal to each other.

In the above explanation, the traveling wave AU in the positive direction of the Y-axis is considered as an example of the four progressive waves, but the same relationship is established for the other three waves (traveling waves AD, AR, AL), and the ± 1st order is established. There is a difference in the size of the light component. From the above discussion, according to the method of the present embodiment in which the different refractive index region 15b moves on the straight line D that passes through the grid point O and is inclined from the square grid, it is a principle that the amount of light of the ± primary light component is different. Is possible. Therefore, in principle, it is possible to selectively extract only the desired light image (first light image portion B1 or second light image portion B2) by reducing the -1st primary light or the primary light.

Therefore, in the design method of the present embodiment, in the second step S2 shown in FIG. 18, the phase of the complex amplitude distribution _ER (x, y) or _EL (x, y) with respect to one of the traveling waves AR and AL. The positive / negative of the term is inverted, and the positive / negative of the phase term of the complex amplitude distribution _EU (x, y) or ED (x, y) with respect to one of the traveling waves AU and _AD is inverted. If the beam pattern of the -1st order light is mainly obtained before the sign of the phase term is inverted, the beam pattern of the primary light is mainly obtained after the sign of the phase term is inverted. On the contrary, when the beam pattern of the primary light is mainly obtained before the sign of the phase term is inverted, the beam pattern of the -1st order light is mainly obtained after the sign of the phase term is inverted. Therefore, according to the design method of the present embodiment, the beam pattern of the primary light (or the -1st order light) can be mainly obtained from all the traveling waves AU, AD, AR, and AL, and the primary light and One of the -1st order lights can be dimmed with respect to the other light.

Further, as described above, in the second step S2, the complex amplitude distributions _EU (x, y), ED (x, y), _ER (x, y) for each of the traveling waves AU, _AD , AR, and AL. ), And _EL (x, y) may be weighted. As a result, the complex amplitude distribution _{E U} (x, y), ED (x, y), _ER (x, y), and _EL (x, y) are superposed to form a comprehensive complex amplitude distribution E _total . When finding (x, y), the complex amplitude distribution _{E U} (x, y), ED (x, y), ER (x, y) with respect to the comprehensive complex amplitude distribution _{E total} (x, y). , And the contribution of _EL (x, y) can be arbitrarily adjusted according to the intensity ratio of each progressive wave AU, AD, AR, and AL, and a desired optical image can be expressed more accurately. Further, when the intensity of the traveling wave AR, AL and the intensity of the traveling wave AU, AD are different from each other, as described above, the complex amplitude distributions _ER (x, y) and EL (x, y) regarding the traveling wave AR, _AL ( The weight m added to x, y) and the weight n added to the complex amplitude distributions _EU (x, y) and ED (x, y) with respect to the traveling waves AU and _AD may be different from each other. Since the ratio of the intensity of the traveling wave AR and AL to the intensity of the traveling wave AU and AD changes depending on the inclination angle θ of the straight line D with respect to the square grid, as described above, the ratio of the weight m and the weight n is the inclination angle. It may be determined based on θ.

Further, as in the present embodiment, the inclination angle θ of the straight line D with respect to the square lattice may be constant in the phase modulation layer 15. This makes it possible to easily design the arrangement of the center of gravity G in the different refractive index region 15b. Further, in this case, the inclination angle may be 45 °, 135 °, 225 ° or 315 °. As a result, the four fundamental waves (progressive waves AD, AR, AL) traveling along the square grid can contribute evenly to the optical image. Further, when the inclination angle θ is 45 °, 135 °, 225 ° or 315 °, the direction of the electromagnetic field on the straight line D is aligned in one direction by selecting an appropriate band end mode, so that linear polarization is performed. Obtainable. As an example of such a mode, non-patent literature C. Peng, et al., “Coupled-wave analysis for photonic-crystal surface-emitting laserson air holes with arbitrary crystals,” Optics Express Vol. 19, No. 24, pp. There are modes A and B shown in Fig. 3 of 24672-24686 (2011). When the inclination angle θ is 0 °, 90 °, 180 °, or 270 °, a pair of four traveling waves AU, AD, AR, and AL traveling in the Y-axis direction or the X-axis direction. Since the wave does not contribute to the primary light (signal light), it is difficult to improve the efficiency of the signal light.

Further, as in the present embodiment, the light emitting portion may be an active layer 12 provided on the semiconductor substrate 10. As a result, the light emitting unit and the phase modulation layer 15 can be easily optically coupled.

(First modification)
21 and 22 are plan views showing an example of the shape of the different refractive index region 15b in the XY plane. In the above embodiment, an example is shown in which the shape of the different refractive index region 15b in the XY plane is circular. However, the different refractive index region 15b may have a shape other than a circle. For example, the shape of the different refractive index region 15b in the XY plane may have mirror image symmetry (line symmetry). Here, the mirror image symmetry (line symmetry) is defined as the planar shape of the different refractive index region 15b located on one side of the straight line across a straight line along the XY plane and the other side of the straight line. It means that the planar shape of the located different refractive index region 15b can be mirror image symmetric (line symmetric) with each other. Examples of the shape having mirror image symmetry (line symmetry) include a perfect circle shown in FIG. 21 (a), a square shown in FIG. 21 (b), and a regular hexadecagon shown in FIG. 21 (c). The regular octagon shown in FIG. 21 (d), the regular hexadecagon shown in FIG. 21 (e), the rectangle shown in FIG. 21 (f), the ellipse shown in FIG. 21 (g), and the like are included. Can be mentioned. As described above, the shape of the different refractive index region 15b in the XY plane has mirror image symmetry (line symmetry). In this case, since each of the unit constituent regions R of the virtual square grid of the phase modulation layer 15 has a simple shape, the direction and position of the center of gravity G of the corresponding different refractive index region 15b from the grid point O can be accurately determined. Since it can be determined, patterning with high accuracy is possible.

Further, the shape of the different refractive index region 15b in the XY plane may be a shape having no rotational symmetry of 180 °. Such shapes include, for example, a regular triangle shown in FIG. 22 (a), a right-angled isosceles triangle shown in FIG. 22 (b), and a part of two circles or ellipses shown in FIG. 22 (c). The shape is deformed so that the dimension in the minor axis near one end along the long axis of the ellipse shown in FIG. 22 (d) is smaller than the dimension in the minor axis near the other end. Shape (ovate), a shape (tear shape) in which one end along the long axis of the ellipse shown in FIG. 22 (e) is deformed into a pointed end protruding along the long axis direction, FIG. 22. The isosceles triangle shown in (f), one side of the rectangle shown in FIG. 22 (g) is recessed in a triangular shape, and the opposite side is pointed in a triangular shape (arrow shape), as shown in FIG. 22 (h). The trapezoid shown, the pentagon shown in FIG. 22 (i), the shape in which parts of the two triangles shown in FIG. 22 (j) overlap each other, and the two triangles shown in FIG. 22 (k). Examples thereof include a shape in which parts overlap each other and do not have mirror image symmetry. As described above, since the shape of the different refractive index region 15b in the XY plane does not have the rotational symmetry of 180 °, higher light output can be obtained.

(Second modification)
FIG. 23 is a plan view of the phase modulation layer 15A according to the second modification of the above embodiment. The phase modulation layer 15A of this modification further has a plurality of different refractive index regions 15c different from the plurality of different refractive index regions 15b in addition to the configuration of the phase modulation layer 15 of the above embodiment (FIG. 4). Each different refractive index region 15c is composed of a second refractive index medium having a refractive index different from that of the first refractive index medium of the basic layer 15a. The different refractive index region 15c may be a hole or may be configured by embedding a compound semiconductor in the hole, as in the case of the different refractive index region 15b. Here, as shown in FIG. 24, in this modification, the center of gravity G, which is a combination of the center of gravity of each different refractive index region 15b and the center of gravity of each different refractive index region 15c, is arranged on the straight line D. .. Both the different refractive index regions 15b and 15c are included in the range of the unit constituent region R constituting the virtual square lattice. The unit constituent area R is an area surrounded by a straight line that bisects between the grid points of a virtual square lattice. The distance r (x, y) between the center of gravity G and the corresponding lattice point O of each unit constituent region R is individually set for each different refractive index region 15b according to a desired optical image. The distribution of the distance r (x, y) is determined from the complex amplitude distribution obtained by Fourier transforming the desired optical image from which the phase distribution is extracted. That is, when the phase P (x, y) at a certain coordinate (x, y) is P ₀ , the distance r (x, y) is set to 0, and the phase P (x, y) is π + P ₀ . In some cases, the distance r (x, y) is set to the maximum value R ₀ , and if the phase P (x, y) is −π + P ₀ , the distance r (x, y) is set to the minimum value −R ₀ . Set. Then, for the intermediate phase P (x, y), the distance r (x, y) is such that r (x, y) = {P (x, y) −P ₀ } × R ₀ / π. ). The initial phase P ₀ can be set arbitrarily.

The different refractive index regions 15c are provided in a one-to-one correspondence with the different refractive index regions 15b, respectively. The planar shape of the different refractive index region 15c is, for example, circular, but it may have various shapes like the different refractive index region 15b. 25 (a) to 25 (k) show examples of the shapes and relative relationships of the different refractive index regions 15b and 15c in the XY plane. 25 (a) and 25 (b) show a form in which the different refractive index regions 15b and 15c have a figure having the same shape. 25 (c) and 25 (d) show a form in which the different refractive index regions 15b and 15c have the same shape and a part of each overlaps with each other. FIG. 25 (e) shows a form in which the different refractive index regions 15b and 15c have the same shape, and the distance between the centers of gravity of the different refractive index regions 15b and 15c is arbitrarily set for each lattice point. FIG. 25 (f) shows a form in which the different refractive index regions 15b and 15c have figures having different shapes from each other. FIG. 25 (g) shows a form in which the different refractive index regions 15b and 15c have different shapes, and the distance between the centers of gravity of the different refractive index regions 15b and 15c is arbitrarily set for each lattice point.

Further, as shown in FIGS. 25 (h) to 25 (k), the different refractive index region 15b may be configured to include two regions 15b1 and 15b2 separated from each other. Then, the distance between the center of gravity of the regions 15b1 and 15b2 (corresponding to the center of gravity of a single different refractive index region 15b) and the center of gravity of the different refractive index region 15c may be arbitrarily set for each grid point. Further, in this case, as shown in FIG. 25 (h), the regions 15b1 and 15b2 and the different refractive index regions 15c may have shapes having the same shape as each other. Alternatively, as shown in FIG. 25 (i), two of the regions 15b1 and 15b2 and the different refractive index region 15c may be different from the others. Further, as shown in FIG. 25 (j), in addition to the angle of the straight line connecting the regions 15b1 and 15b2 with respect to the X-axis, the angle of the different refractive index region 15c with respect to the X-axis is arbitrarily set for each grid point. May be good. Further, as shown in FIG. 25 (k), the angle of the straight line connecting the regions 15b1, 15b2 with respect to the X axis is set for each grid point while the regions 15b1, 15b2 and the different refractive index regions 15c maintain the same relative angles. It may be set arbitrarily.

The shapes of the different refractive index regions in the XY plane may be the same among the grid points. That is, the different refractive index regions may have the same figure at all the lattice points, and may be superposed between the lattice points by a translation operation, or a translation operation and a rotation operation. In that case, it is possible to suppress the generation of noise light and 0th-order light that becomes noise in the beam pattern. Alternatively, the shape of the different refractive index region in the XY plane does not necessarily have to be the same between the grid points, and the shapes may differ from each other between the adjacent grid points, for example, as shown in FIG. 26. In any of FIGS. 21 to 26, the center of the straight line D passing through each grid point may be set so as to coincide with the grid point O.

For example, even with the configuration of the phase modulation layer as in the present modification, the effect of the above embodiment can be suitably exhibited.

(Third modification example)
FIG. 27 is a diagram showing the configuration of the light emitting device 1B according to the third modification. The light emitting device 1B includes a support substrate 6, a plurality of semiconductor light emitting elements 1A arranged one-dimensionally or two-dimensionally on the support substrate 6, and a drive circuit 4 for individually driving the plurality of semiconductor light emitting elements 1A. I have. The configuration of each semiconductor light emitting device 1A is the same as that of the above embodiment. However, the plurality of semiconductor light emitting elements 1A include a laser element that outputs an optical image in the red wavelength region, a laser element that outputs an optical image in the blue wavelength region, and a laser element that outputs an optical image in the green wavelength region. May be included. The laser element that outputs an optical image in the red wavelength region is composed of, for example, a GaAs-based semiconductor. The laser element that outputs an optical image in the blue wavelength region and the laser element that outputs an optical image in the green wavelength region are composed of, for example, a nitride semiconductor. The drive circuit 4 is provided on the back surface or the inside of the support substrate 6, and drives each semiconductor light emitting element 1A individually. The drive circuit 4 supplies a drive current to each semiconductor light emitting device 1A according to an instruction from the control circuit 7.

As in this modification, a module in which a plurality of semiconductor light emitting elements 1A individually driven are provided and a desired light image is taken out from each semiconductor light emitting element 1A, so that semiconductor light emitting elements corresponding to a plurality of patterns are arranged in advance. A head-up display or the like can be suitably realized by appropriately driving necessary elements. Further, the plurality of semiconductor light emitting elements 1A include a laser element that outputs an optical image in the red wavelength region, a laser element that outputs an optical image in the blue wavelength region, and a laser element that outputs an optical image in the green wavelength region. Therefore, a color head-up display or the like can be suitably realized.

(Second Embodiment)
FIG. 28 is a diagram showing a cross-sectional structure of the semiconductor light emitting device 1C according to the second embodiment. The semiconductor light emitting element 1C is a laser light source that forms a standing wave in the XY in-plane direction and outputs a phase-controlled plane wave in the Z direction, and is the main surface of the semiconductor substrate 10 as in the first embodiment. A two-dimensional arbitrary-shaped optical image including a direction perpendicular to 10a and a direction inclined with respect to the direction is output. However, the semiconductor light emitting device 1A of the first embodiment outputs an optical image transmitted through the semiconductor substrate 10 from the back surface, whereas the semiconductor light emitting device 1C of the present embodiment outputs the light image transmitted through the semiconductor substrate 10 from the front surface on the clad layer 13 side with respect to the active layer 12. Output an optical image.

The semiconductor light emitting device 1C includes a clad layer 11, an active layer 12, a clad layer 13, a contact layer 14, a phase modulation layer 15, a light reflection layer 20, and a current constriction layer 21. The clad layer 11 is provided on the semiconductor substrate 10. The active layer 12 is provided on the clad layer 11. The clad layer 13 is provided on the active layer 12. The contact layer 14 is provided on the clad layer 13. The phase modulation layer 15 is provided between the active layer 12 and the clad layer 13. The light reflecting layer 20 is provided between the active layer 12 and the clad layer 11. The current constriction layer 21 is provided in the clad layer 13. The configuration of each layer 11 to 15 (suitable material, band gap, refractive index, etc.) is the same as that of the first embodiment. The light reflecting layer 20 may be omitted if light absorption by the semiconductor substrate 10 is not a problem.

The structure of the phase modulation layer 15 is the same as the structure of the phase modulation layer 15 described in the first embodiment (see FIGS. 4 and 5). If necessary, an optical guide layer may be provided between the active layer 12 and the clad layer 13 and at least one of the active layer 12 and the clad layer 11. As shown in FIG. 29, the phase modulation layer 15 may be provided between the clad layer 11 and the active layer 12. The optical guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

The semiconductor light emitting device 1C further includes an electrode 23 provided on the contact layer 14 and an electrode 22 provided on the back surface 10b of the semiconductor substrate 10. The electrode 23 is in ohmic contact with the contact layer 14, and the electrode 22 is in ohmic contact with the semiconductor substrate 10. FIG. 30 is a plan view of the semiconductor light emitting device 1C as viewed from the electrode 23 side (front surface side). As shown in FIG. 30, the electrode 23 has a planar shape such as a frame shape (annular shape) and has an opening 23a. Although the square frame-shaped electrode 23 is exemplified in FIG. 30, the planar shape of the electrode 23 can be various shapes such as an annular shape. Further, the shape of the electrode 22 shown by the hidden line in FIG. 30 is similar to the shape of the opening 23a of the electrode 23, and is, for example, a square or a circle. The inner diameter of the opening 23a of the electrode 23 (the length of one side when the shape of the opening 23a is square) is, for example, 20 μm to 50 μm.

See FIG. 28 again. The contact layer 14 of the present embodiment has a planar shape similar to that of the electrode 23. That is, the central portion of the contact layer 14 is removed by etching to form an opening 14a, and the contact layer 14 has a planar shape such as a frame shape (annular shape). The light emitted from the semiconductor light emitting device 1C passes through the opening 14a of the contact layer 14 and the opening 23a of the electrode 23. By allowing light to pass through the opening 14a of the contact layer 14, it is possible to avoid light absorption in the contact layer 14 and improve the light emission efficiency. However, if light absorption in the contact layer 14 is acceptable, the contact layer 14 may cover the entire surface of the clad layer 13 without having an opening 14a. By passing the light through the opening 23a of the electrode 23, the light can be suitably emitted from the surface side of the semiconductor light emitting device 1C without being blocked by the electrode 23.

The surface of the clad layer 13 exposed from the opening 14a of the contact layer 14 (or the surface of the contact layer 14 when the opening 14a is not provided) is covered with the antireflection film 25. An antireflection film 25 may be provided on the outside of the contact layer 14. Further, the portion other than the electrode 22 on the back surface 10b of the semiconductor substrate 10 is covered with the protective film 24. The material of the protective film 24 is the same as that of the protective film 18 of the first embodiment. The material of the antireflection film 25 is the same as that of the antireflection film 19 of the first embodiment.

The light reflecting layer 20 reflects the light generated in the active layer 12 toward the surface side of the semiconductor light emitting device 1C. The light reflecting layer 20 is composed of, for example, a DBR (Disrtibuted Bragg Reflector) layer in which a plurality of layers having different refractive indexes are alternately laminated. Although the light reflecting layer 20 of the present embodiment is provided between the active layer 12 and the clad layer 11, the light reflecting layer 20 may be provided between the clad layer 11 and the semiconductor substrate 10. Alternatively, the light reflecting layer 20 may be provided inside the clad layer 11.

The clad layer 11 and the light reflecting layer 20 are provided with the same conductive type as the semiconductor substrate 10, and the clad layer 13 and the contact layer 14 are provided with the same conductive type as the semiconductor substrate 10. In one example, the semiconductor substrate 10, the clad layer 11 and the light reflecting layer 20 are n-type, and the clad layer 13 and the contact layer 14 are p-type. The phase modulation layer 15 has the same conductive type as the semiconductor substrate 10 when it is provided between the active layer 12 and the clad layer 11, and the semiconductor when it is provided between the active layer 12 and the clad layer 13. It has a conductive type opposite to that of the substrate 10. The impurity concentration is, for example, 1 × 10 ¹⁷ to 1 × 10 ²¹ / cm ³ . The active layer 12 is intrinsic (i type) to which no impurities are intentionally added, and the impurity concentration thereof is 1 × 10 ¹⁵ / cm ³ or less. The impurity concentration of the phase modulation layer 15 may be true (i type) when it is necessary to suppress the influence of loss due to light absorption via the impurity level.

The current constriction layer 21 has a structure that makes it difficult (or does not allow) the current to pass through, and has an opening 21a in the central portion. As shown in FIG. 30, the planar shape of the opening 21a is similar to the shape of the opening 23a of the electrode 23, and is, for example, a square or a circle. The current constriction layer 21 is, for example, an Al oxide layer formed by oxidizing a layer containing a high concentration of Al. Alternatively, the current constriction layer 21 may be a layer formed by injecting a proton (H ⁺ ) into the clad layer 13. Alternatively, the current constriction layer 21 may have a reverse pn junction structure in which a conductive semiconductor layer opposite to the semiconductor substrate 10 and a conductive semiconductor layer same as the semiconductor substrate 10 are sequentially laminated.

A dimensional example of the semiconductor light emitting device 1C of this embodiment will be described. The inner diameter of the opening 23a of the electrode 23 (the length of one side when the shape of the opening 23a is square) La is in the range of 5 μm to 100 μm, for example, 50 μm. The thickness ta of the phase modulation layer 15 is, for example, in the range of 100 nm to 400 nm, for example, 200 nm. The distance tb between the current constriction layer 21 and the contact layer 14 is in the range of 2 μm to 50 μm. In other words, the interval tb is in the range of 0.02La to 10La (for example, 0.1La) and in the range of 5.0ta to 500ta (for example, 25ta). Further, the thickness tc of the clad layer 13 is larger than the interval tb and is in the range of 2 μm to 50 μm. In other words, the thickness ct is in the range of 0.02La to 10La (for example, 0.1La) and in the range of 5.0ta to 500ta (for example, 25ta). The thickness td of the clad layer 11 is in the range of 1.0 μm to 3.0 μm (for example, 2.0 μm).

When a drive current is supplied between the electrode 22 and the electrode 23, the drive current reaches the active layer 12. At this time, the current flowing between the electrode 23 and the active layer 12 is sufficiently diffused in the thick clad layer 13 and passes through the opening 21a of the current constriction layer 21 so as to be uniform near the central portion of the active layer 12. Can spread to. Then, recombination of electrons and holes occurs in the active layer 12, and the active layer 12 emits light. The electrons and holes that contribute to this light emission, as well as the generated light, are efficiently confined between the clad layer 11 and the clad layer 13. The laser beam emitted from the active layer 12 enters the inside of the phase modulation layer 15 and forms a predetermined mode according to the lattice structure inside the phase modulation layer 15. The laser light emitted from the inside of the phase modulation layer 15 is reflected by the light reflecting layer 20, and is emitted from the clad layer 13 to the outside through the openings 14a and 23a.

(Specific example of the first embodiment)
The inventors examined the conditions under which the high-order mode does not occur with respect to the thickness and refractive index of the optical waveguide layer including the active layer and the thickness and refractive index of the contact layer. The examination process and results will be described below.

First, a specific structure of the semiconductor light emitting device 1A, which is the subject of study in this specific example, will be described. FIG. 31 is a table showing a layer structure when the semiconductor light emitting device 1A is made of a GaAs-based compound semiconductor (emission wavelength 940 nm band). The table of FIG. 31 shows the conductive type, composition, layer thickness, and refractive index of each layer. Note that layer number 1 indicates a contact layer 14, layer number 2 indicates an upper clad layer 13, layer number 3 indicates a phase modulation layer 15, layer number 4 indicates an optical guide layer and an active layer 12, and layer number 5 indicates a lower clad layer 11. .. FIG. 32 shows the refractive index distribution G21a and the mode distribution G21b of the semiconductor light emitting device 1A having the layer structure shown in FIG. The horizontal axis represents the position in the stacking direction (range is 2.5 μm). At this time, it can be seen that only the basic mode is generated and the higher-order mode is suppressed.

FIG. 33 is a table showing a layer structure when the semiconductor light emitting device 1A is made of an InP-based compound semiconductor (emission wavelength 1300 nm band). Layer number 1 indicates a contact layer 14, layer number 2 indicates an upper clad layer 13, layer number 3 indicates a phase modulation layer 15, layer number 4 indicates an optical guide layer and an active layer 12, and layer number 5 indicates a lower clad layer 11. FIG. 34 shows the refractive index distribution G22a and the mode distribution G22b of the semiconductor light emitting device 1A having the layer structure shown in FIG. 33. The horizontal axis represents the position in the stacking direction (range is 2.5 μm). At this time, it can be seen that only the basic mode is generated and the higher-order mode is suppressed.

FIG. 35 is a table showing a layer structure when the semiconductor light emitting device 1A is made of a nitride compound semiconductor (emission wavelength 405 nm band). Layer number 1 is the contact layer 14, layer number 2 is the upper clad layer 13, layer number 3 is the carrier barrier layer, layer number 4 is the active layer 12, layer number 5 is the optical guide layer, and layer number 6 is the phase modulation layer 15. Layer number 7 indicates the lower clad layer 11. FIG. 36 shows the refractive index distribution G23a and the mode distribution G23b of the semiconductor light emitting device 1A having the layer structure shown in FIG. 35. The horizontal axis represents the position in the stacking direction (range is 2.5 μm). At this time, it can be seen that only the basic mode is generated and the higher-order mode is suppressed.

In each of the above structures, the filling factor (FF) of the phase modulation layer 15 is 15%. The filling factor is the ratio of the area of the different refractive index region 15b to the unit constituent region R.

Next, the preconditions for the study will be described. In the following examination, TE mode was assumed. That is, the leak mode and the TM mode are not considered. Further, the lower clad layer 11 is sufficiently thick, and the influence of the semiconductor substrate 10 can be ignored. Further, the refractive index of the upper clad layer 13 is equal to or less than the refractive index of the lower clad layer 11. The active layer 12 (MQW layer) and the optical guide layer are regarded as one optical waveguide layer (core layer) having an average dielectric constant and a total film thickness, unless otherwise specified. Further, the dielectric constant of the phase modulation layer 15 is an average dielectric constant based on the filling factor.

The formulas for calculating the average refractive index and film thickness of the optical waveguide layer composed of the active layer 12 and the optical guide layer are as follows. That is, ε _core is the average permittivity of the optical waveguide layer and is defined by the following equation (28). ε _i is the dielectric constant of each layer, _{di is the thickness of each layer, and n i is} the refractive index of each layer. n _core is the average refractive index of the optical waveguide layer, and is defined by the following equation (29). The d _core is the film thickness of the optical waveguide layer and is defined by the following formula (30).

The formula for calculating the average refractive index of the phase modulation layer 15 is as follows. That is, n _PM is the average refractive index of the phase modulation layer 15, and is defined by the following equation (31). ε _PM is the dielectric constant of the phase modulation layer 15, n ₁ is the refractive index of the first refractive index medium, n ₂ is the refractive index of the second refractive index medium, and FF is the filling factor.

In the following studies, the waveguide structure was approximated by a 5-layer or 6-layer slab-type waveguide. 37 (a) and 37 (b) are a cross-sectional view and a refractive index distribution for explaining a case where the waveguide structure is approximated by a six-layer slab-type waveguide. 38 (a) and 38 (b) are a cross-sectional view and a refractive index distribution for explaining a case where the waveguide structure is approximated by a five-layer slab-type waveguide. As shown in FIGS. 37 (a) and 37 (b), when the refractive index of the phase modulation layer 15 is smaller than the refractive index of the lower clad layer 11, the phase modulation layer 15 does not have a waveguide function. An approximation was made for the 6-layer slab-type waveguide. That is, the optical waveguide layer has a structure including the active layer 12 and the optical guide layer, but does not include the lower clad layer 11, the upper clad layer 13, and the phase modulation layer 15. Such an approximation can be applied to, for example, the structures shown in FIGS. 33 and 35 (in P-based compound semiconductors or nitride-based compound semiconductors in this embodiment).

Further, as shown in FIGS. 38 (a) and 38 (b), when the refractive index of the phase modulation layer 15 is equal to or higher than the refractive index of the lower clad layer 11, the phase modulation layer 15 has a waveguide function. Therefore, an approximation was made for the five-layer slab-type waveguide. That is, the optical waveguide layer has a structure including the phase modulation layer 15 and the active layer 12, while not including the lower clad layer 11 and the upper clad layer 13. Such an approximation can be applied to, for example, the structure shown in FIG. 19 (GaAs-based compound semiconductor in this embodiment).

Further, in order to further simplify the calculation, the calculation range is limited to the peripheral portions of the optical waveguide layer and the contact layer having a refractive index higher than the equivalent refractive index of the semiconductor light emitting device 1A. That is, the optical waveguide layer and the upper and lower layers adjacent to the optical waveguide layer define a three-layer slab structure for the optical waveguide layer, and the contact layer 14 and the adjacent upper and lower layers form a three-layer slab structure for the contact layer 14. It is stipulated.

39 (a) and 39 (b) are cross sections for explaining a three-layer slab structure relating to an optical waveguide layer in a six-layer slab-type waveguide (see FIGS. 37 (a) and 37 (b)). Figure and refractive index distribution. In this case, the waveguide mode of the optical waveguide layer is calculated based on the refractive index distribution shown by the solid line in the refractive index distribution of FIG. 39 (b). Further, FIGS. 40 (a) and 40 (b) are for explaining a three-layer slab structure relating to the contact layer 14 in the six-layer slab-type waveguide (see FIGS. 37 (a) and 37 (b)). It is a cross-sectional view and a refractive index distribution of. In this case, the waveguide mode of the contact layer 14 is calculated based on the refractive index distribution shown by the solid line in FIG. 40 (b).

41 (a) and 41 (b) are cross-sectional views and refractive index distributions for explaining a three-layer slab structure relating to an optical waveguide layer in a five-layer slab-type waveguide (see FIG. 38). In this case, the waveguide mode of the optical waveguide layer is calculated based on the refractive index distribution shown by the solid line in FIG. 41 (b). 42 (a) and 42 (b) are cross-sectional views and refractive index distributions for explaining the three-layer slab structure with respect to the contact layer 14 in the five-layer slab-type waveguide (see FIG. 38). .. In this case, the waveguide mode of the contact layer 14 is calculated based on the refractive index distribution shown by the solid line in FIG. 42 (b).

In addition, in the above-mentioned approximation by the three-layer slab structure, the refractive index of the lower clad layer 11 is the equivalent refraction of the semiconductor light emitting device 1A in order to prevent the waveguide mode from leaking to the semiconductor substrate 10 via the lower clad layer 11. Must be less than or equal to the rate.

Here, the analysis formula of the three-layer slab structure will be described. 43 (a) and 43 (b) show a three-layer slab structure 30 composed of a lower clad layer 11, an optical waveguide layer 31, and an upper clad layer 13, and a refractive index distribution thereof. Here, the refractive index of the lower clad layer 11 is n ₂ , the refractive index of the optical waveguide layer 31 is n ₁ , and the refractive index of the upper clad layer 13 is n ₃ . Then, when the standardized waveguide width V ₁ of the optical waveguide layer 31 is defined by the above equation (1), if the solution of the standardized waveguide width V ₁ is within the range of only one, the waveguide mode is used. Is in basic mode only. However, when examining the waveguide mode of the above-mentioned 5-layer slab structure and 6-layer slab structure in the analysis formula of the 3-layer slab structure, it is necessary that the waveguide mode does not leak to the lower clad layer 11, so that the above formula (2) ) Must also be met at the same time.

Regarding the contact layer 14, in FIGS. 43 (a) and 43 (b), the lower clad layer 11 is replaced with the upper clad layer 13, the optical waveguide layer 31 is replaced with the contact layer 14, and the upper clad layer 13 is replaced with the air layer. It is good. Then, assuming that the refractive index of the contact layer 14 is n ₄ and the refractive index of the air layer is n ₅ , the above equation (5) regarding the normalized waveguide width V ₂ of the contact layer 14 is obtained. Then, as long as there is no solution for the normalized waveguide width V ₂ , the waveguide mode does not exist in the contact layer 14. However, when examining the waveguide mode of the above-mentioned 5-layer slab structure and 6-layer slab structure in the analysis formula of the 3-layer slab structure, it is necessary that the waveguide mode does not leak to the lower clad layer 11, so that the above formula (6). ) Must also be met at the same time.

By analyzing the waveguide mode generated by changing the film thickness of the upper clad layer 13, it was confirmed that the film thickness of the upper clad layer 13 does not affect the waveguide mode.

(When the semiconductor light emitting device 1A is made of a GaAs-based compound semiconductor)
FIG. 44 is a table showing an example of a five-layer slab structure when the semiconductor light emitting device 1A is made of a GaAs-based compound semiconductor. The range of film thicknesses of the optical waveguide layer (layer number 4) and the contact layer (layer number 2) in this five-layer slab structure is obtained by the following calculation.

FIG. 45 (a) is a table showing the refractive indexes n ₁ , n ₂ , and n ₃ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer 11 used in the calculation. In this case, the relationship between the normalized waveguide width V1 of the optical waveguide layer represented by the above equations ( ₁ ) and (2) and the normalized propagation coefficient b is shown in FIG. In FIG. 46, the graphs G31a to G31f show the case where the mode order N = 0 to 5, respectively. In this graph, the waveguide mode is only the basic mode (that is, N = 0) in the range where the solution of the normalized waveguide width V ₁ is one, and is inside the range H ₁ . In the range H ₁ , the lower limit is the value of the normalized waveguide width V ₁ corresponding to N = 0 when the normalized propagation coefficient b is 0, and N = 1 when the normalized propagation coefficient b is 0. It is a range in which the value of the normalized waveguide width V ₁ corresponding to is the upper limit value. FIG. 45B is a table showing the calculation results of such a lower limit value and an upper limit value.

Further, FIG. 47 (a) is a table showing the refractive indexes n ₄ , n ₅ , and n ₆ , the asymmetric parameter a', and the refractive index n _clad of the lower clad layer 11 used in the calculation. In this case, the relationship between the normalized waveguide width V2 of the contact layer 14 represented by the above equations (5) and ( ₆ ) and the normalized propagation coefficient b is shown in FIG. 48. In FIG. 48, the graphs G32a to G32f show the case where the mode order N = 0 to 5, respectively. In this graph, the waveguide mode caused by the contact layer 14 does not occur, and the waveguide mode of the semiconductor light emitting device 1A is _only the basic mode of the optical waveguide layer, as long as there is no solution of the normalized waveguide width V2. And is inside the range _H2 . In the range H ₂ , the lower limit value is 0, and the value of the normalized waveguide width V ₂ corresponding to N = 0 when the normalized propagation coefficient b is the value b ₁ corresponding to the refractive index of the lower clad layer 11 is set. This is the range to be the upper limit. FIG. 47B is a table showing the calculation result of such an upper limit value.

FIG. 49 shows the refractive index distribution G24a and the mode distribution G24b of the semiconductor light emitting device 1A having the layer structure shown in FIG. 44. It can be seen that only the basic mode is remarkably generated, and the higher-order mode is suppressed.

(When the semiconductor light emitting device 1A is made of an InP-based compound semiconductor)
FIG. 50 is a table showing an example of a 6-layer slab structure when the semiconductor light emitting device 1A is made of an InP-based compound semiconductor. The range of film thicknesses of the optical waveguide layer (layer number 5) and the contact layer (layer number 2) in this 6-layer slab structure is obtained by the following calculation.

FIG. 51 (a) is a table showing the refractive indexes n ₁ , n ₂ , and n ₃ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer 11 used in the calculation. In this case, the relationship between the normalized waveguide width V1 of the optical waveguide layer represented by the above equations ( ₁ ) and (2) and the normalized propagation coefficient b is shown in FIG. 52. In FIG. 52, the graphs G33a to G33f show the case where the mode order N = 0 to 5, respectively. In this graph, the waveguide mode is only the basic mode (that is, N = 0) in the range where the solution of the normalized waveguide width V ₁ is one, and is inside the range H ₁ . The definition of the range H ₁ is the same as that of the above-mentioned GaAs-based compound semiconductor. FIG. 51B is a table showing the calculation results of the lower limit value and the upper limit value.

Further, FIG. 53 (a) is a table showing the refractive indexes n ₄ , n ₅ , and n ₆ , the asymmetric parameter a', and the refractive index n _clad of the lower clad layer 11 used in the calculation. In this case, the relationship between the normalized waveguide width V ₂ of the contact layer 14 represented by the above equations (5) and (6) and the normalized propagation coefficient b is as shown in the graph shown in FIG. 54. In FIG. 54, graphs G34a to G34f show the case where the mode order N = 0 to 5, respectively. In this graph, the waveguide mode caused by the contact layer 14 does not occur, and the waveguide mode of the semiconductor light emitting device 1A is only the basic mode of the optical waveguide layer, as long as there is no solution of the normalized waveguide width V ₂ . And inside the range H ₂ . The definition of the range H ₂ is the same as that of the above-mentioned GaAs-based compound semiconductor. FIG. 53 (b) is a table showing the calculation result of such an upper limit value.

FIG. 55 shows the refractive index distribution G25a and the mode distribution G25b of the semiconductor light emitting device 1A having the layer structure shown in FIG. It can be seen that only the basic mode is remarkably generated, and the higher-order mode is suppressed.

(When the semiconductor light emitting device 1A is made of a nitride compound semiconductor)
FIG. 56 is a table showing an example of a 6-layer slab structure when the semiconductor light emitting device 1A is made of a nitride compound semiconductor. The range of film thicknesses of the optical waveguide layer (layer number 4) and the contact layer (layer number 2) in this 6-layer slab structure is obtained by the following calculation.

FIG. 57 (a) is a table showing the refractive indexes n ₁ , n ₂ , and n ₃ , the asymmetric parameter a'and the refractive index n _clad of the lower clad layer 11 used in the calculation. In this case, the relationship between the normalized waveguide width V ₁ of the optical waveguide layer represented by the above equations (1) and (2) and the normalized propagation coefficient b is shown in FIG. 58. In FIG. 58, the graphs G35a to G35f show the case where the mode order N = 0 to 5, respectively. In this graph, the waveguide mode is only the basic mode (that is, N = 0) in the range where the solution of the normalized waveguide width V ₁ is one, and is inside the range H ₁ . The range H ₁ has a lower limit value of the value of the normalized waveguide width V ₁ corresponding to N = 0 when the normalized propagation coefficient b is the value b ₁ , and the normalized propagation coefficient b is the value b ₁ . The upper limit is the value of the normalized waveguide width V ₁ corresponding to N = 1. FIG. 57B is a table showing the calculation results of the lower limit value and the upper limit value.

Further, FIG. 59 (a) is a table showing the refractive indexes n ₄ , n ₅ , and n ₆ , the asymmetric parameter a', and the refractive index n _clad of the lower clad layer 11 used in the calculation. In this case, the relationship between the normalized waveguide width V ₂ of the contact layer 14 represented by the above equations (5) and (6) and the normalized propagation coefficient b is shown in FIG. 60. In FIG. 60, the graphs G36a to G36f show the case where the mode order N = 0 to 5, respectively. In this graph, the waveguide mode caused by the contact layer 14 does not occur, and the waveguide mode of the semiconductor light emitting device 1A is only the basic mode of the optical waveguide layer, as long as there is no solution of the normalized waveguide width V ₂ . And inside the range H ₂ . The definition of the range H ₂ is the same as that of the above-mentioned GaAs-based compound semiconductor. FIG. 59 (b) is a table showing the calculation result of such an upper limit value.

FIG. 61 shows the refractive index distribution G26a and the mode distribution G26b of the semiconductor light emitting device 1A having the layer structure shown in FIG. It can be seen that only the basic mode is remarkably generated, and the higher-order mode is suppressed.

The light emitting device according to the present invention is not limited to the above-described embodiment, and various other modifications are possible. For example, in the above embodiment, a laser device made of a GaAs-based, InP-based, and nitride-based (particularly GaN-based) compound semiconductor is exemplified, but the present invention is applied to a laser device made of various semiconductor materials other than these. can.

Further, in the above embodiment, an example in which the active layer 12 provided on the semiconductor substrate 10 common to the phase modulation layer 15 is used as the light emitting portion has been described, but in the present invention, the light emitting portion is separated from the semiconductor substrate 10. It may be provided. As long as the light emitting unit is optically coupled to the phase modulation layer and supplies light to the phase modulation layer, the same effect as that of the above embodiment can be suitably exhibited even with such a configuration.

1A ... semiconductor light emitting element, 1B ... light emitting device, 1C ... semiconductor light emitting element, 4 ... drive circuit, 6 ... support substrate, 7 ... control circuit, 10 ... semiconductor substrate, 10a ... main surface, 10b ... back surface, 11, 13 ... Clad layer, 12 ... active layer, 14 ... contact layer, 14a ... opening, 15 ... phase modulation layer, 15a ... basic layer, 15b, 15c ... different refractive index regions, 16, 17, 22, 23 ... electrodes, 17a, 23a. ... Opening, 18 ... Protective film, 19 ... Antireflection film, 20 ... Light reflective layer, 21 ... Current constriction layer, 21a ... Opening, 24 ... Protective film, 25 ... Antireflection film, a ... Lattice spacing, AD, AL, AR, AU ... traveling wave, B1 ... first light image part, B2 ... second light image part, BD, BL, BR, BU ... beam pattern, D ... straight line, G ... center of gravity, O ... lattice point, R ... unit Constituent area, RIN ... inner area, ROUT ... outer area.

Claims (6)

It has a basic layer and a plurality of different refractive index regions having different refractive indexes from the basic layer, and is provided with a phase modulation layer provided on the substrate and optically coupled to a light emitting portion, and is provided on the main surface of the substrate. A method of designing the phase modulation layer of a light emitting device that outputs an optical image in a direction perpendicular to the direction and / or a direction inclined with respect to the direction.
A virtual square grid is set in a plane perpendicular to the thickness direction of the phase modulation layer , the X-axis is parallel to one side of the square grid, and the Y-axis is parallel to the other side of the square grid. When an XY Cartesian coordinate system whose origin coincides with the center point of the phase modulation layer is set , the first region in which the X-axis coordinates are positive, the second region in which the X-axis coordinates are negative, and Y When defining the third region where the axis coordinates are positive and the fourth region where the Y-axis coordinates are negative, the first traveling wave traveling in the positive direction of the X-axis and the second traveling traveling in the negative direction of the X axis . The first step of preparing a plurality of complex amplitude distributions corresponding to the optical image for each of the wave, the third traveling wave traveling in the positive direction of the Y axis, and the fourth traveling wave traveling in the negative direction of the Y axis.
The second step of modifying the complex amplitude distribution for each progressive wave,
The third step of superimposing the corrected complex amplitude distributions for each progressive wave to obtain a comprehensive complex amplitude distribution, and
The fourth step of extracting the phase distribution from the comprehensive complex amplitude distribution and determining the position of the center of gravity of each different refractive index region based on the phase distribution is included.
In the second step, whether the positive / negative of the phase term of the complex amplitude distribution regarding the first progressive wave is inverted and the positive / negative of the phase term of the complex amplitude distribution regarding the third progressive wave is inverted. Or, the positive / negative of the phase term of the complex amplitude distribution regarding the second progressive wave is inverted, and the positive / negative of the phase term of the complex amplitude distribution regarding the fourth progressive wave is inverted .
In the fourth step, the center of gravity of each different refractive index region passes through the grid points of the virtual square lattice and is tilted with respect to the X axis (a counterclockwise angle with 0 ° when parallel to the X axis). ) Arrange on a straight line where θ is 0 ° <θ <90 ° or 180 ° <θ <270 °, and the distance between the center of gravity of each different refractive index region and the corresponding lattice point is based on the phase distribution. The phase modulation layer design method to be determined. It has a basic layer and a plurality of different refractive index regions having different refractive indexes from the basic layer, and is provided with a phase modulation layer provided on the substrate and optically coupled to a light emitting portion, and is provided on the main surface of the substrate. A method of designing the phase modulation layer of a light emitting device that outputs an optical image in a direction perpendicular to the direction and / or a direction inclined with respect to the direction.
A virtual square grid is set in a plane perpendicular to the thickness direction of the phase modulation layer, the X-axis is parallel to one side of the square grid, and the Y-axis is parallel to the other side of the square grid. When an XY Cartesian coordinate system whose origin coincides with the center point of the phase modulation layer is set, the first region where the X-axis coordinates are positive, the second region where the X-axis coordinates are negative, and the Y-axis When defining the third region where the coordinates are positive and the fourth region where the Y-axis coordinates are negative, the first traveling wave traveling in the positive direction of the X-axis and the second traveling wave traveling in the negative direction of the X-axis. , The first step of preparing a plurality of complex amplitude distributions corresponding to the optical image for each of the third traveling wave traveling in the positive direction of the Y axis and the fourth traveling wave traveling in the negative direction of the Y axis.
The second step to modify the complex amplitude distribution for each progressive wave,
The third step of superimposing the corrected complex amplitude distributions for each progressive wave to obtain a comprehensive complex amplitude distribution, and
The fourth step of extracting the phase distribution from the comprehensive complex amplitude distribution and determining the position of the center of gravity of each different refractive index region based on the phase distribution is included.
In the second step, the positive / negative of the phase term of the complex amplitude distribution relating to the first progressive wave is inverted and the positive / negative of the phase term of the complex amplitude distribution relating to the fourth traveling wave is inverted, or the second step. The positive / negative of the phase term of the complex amplitude distribution regarding the traveling wave is inverted, and the positive / negative of the phase term of the complex amplitude distribution regarding the third traveling wave is inverted.
In the fourth step, the center of gravity of each different refractive index region passes through the grid points of the virtual square lattice and is tilted with respect to the X axis (counterclockwise angle with 0 ° when parallel to the X axis) θ. Is arranged on a straight line where 90 ° <θ <180 ° or 270 ° <θ <360 °, and the distance between the center of gravity of each different refractive index region and the corresponding lattice point is determined based on the phase distribution. How to design a phase modulation layer. The phase modulation layer design method according to claim 1 or 2 , wherein in the second step, the complex amplitude distribution for each traveling wave is weighted. The claim that the weight added to each complex amplitude distribution of the first traveling wave and the second traveling wave and the weight added to each complex amplitude distribution of the third traveling wave and the fourth traveling wave are different from each other. 3. The phase modulation layer design method according to 3. The ratio of the weight added to each complex amplitude distribution of the first traveling wave and the second traveling wave to the weight added to each complex amplitude distribution of the third traveling wave and the fourth traveling wave is taken with the straight line. The phase modulation layer design method according to claim 4 , which is determined based on the angle θ formed with the X axis . The phase modulation layer design method according to any one of claims 1 to 5 , wherein the light emitting unit is an active layer provided on the substrate.

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