JP4238573B2 - Lamella type diffraction grating and design method thereof - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a diffraction grating that is a wavelength dispersion / wavelength selection element used in a spectroscope or a demultiplexer, and more particularly to a lamellar diffraction grating having a rectangular groove cross-sectional shape and a method for designing the diffraction grating. .
[0002]
[Prior art]
A diffraction grating (grating) is one of wavelength separation / selection elements used in spectroscopes, duplexers, and the like. Diffraction gratings are classified into several types according to the material of the grating, the shape of the grating surface, the shape of the grating grooves, and the like. For example, when attention is paid to the shape of the lattice grooves, as shown in FIG. 3 (A), the groove cross-sectional shape is an sawet type, and as shown in FIG. 3 (B), the groove cross-sectional shape is a rectangular shape ( It may be called a laminar type). Such diffraction gratings are classified into reflection diffraction gratings and transmission diffraction gratings depending on whether reflection diffraction light or transmission diffraction light is used.
[0003]
Conventionally, lamellar diffraction gratings are often used for short-wavelength spectroscopy such as radiation, and Escheret diffraction gratings are often used for spectrometers for ultraviolet to near infrared light. . However, when a manufacturing process such as holographic exposure or mechanical engraving, which has a relatively low manufacturing cost, is employed, it is easier for the lamellar type to reduce the manufacturing accuracy error than the echelette type. For this reason, it is expected that the use of lamellar diffraction gratings will increase in the future even in a relatively long wavelength region that has been rarely used.
[0004]
By the way, in free space, light is a transverse wave of an electromagnetic wave, and its orientation (wave number vector orientation), electric field, and magnetic field are orthogonal to each other. In natural light, the vibration direction of the electric and magnetic fields changes irregularly, but all plane waves are stretched by two polarization components. Originally, the behavior of the two polarization components in the boundary region of the grating groove surface of the diffraction grating is different. Therefore, it is customary that the electric field vector of light incident on the diffraction grating oscillates parallel to the grating groove direction (TE (Polarized light) and vertically oscillating component (TM polarized light), and the appearance on the surface of the diffraction grating groove is analyzed for each polarized component to obtain, for example, diffraction efficiency.
[0005]
However, when the wavelength used is sufficiently small with respect to the groove period of the diffraction grating, only the intensity of the light, that is, the diffraction groove's frown foreground, is analyzed without dividing the electric field vector of the incident light into two components. It is known that just by calculating the diffraction efficiency by integrating the contributions from all diffraction grating grooves for the fa diffraction (such a calculation theory is called scalar diffraction theory), a calculation result that is quite in agreement with the actual one can be obtained. It has been. More specifically, a region where the grating period / wavelength> 10 is called a scalar region, and the diffraction efficiency can be calculated by integrating Fraunhofer diffraction contributed by individual diffraction grating grooves. In this region, the difference in spectral shape due to polarized light is small.
[0006]
On the other hand, the region of the grating period / wavelength <10 can be classified into a resonance region (Resonance Domain), a sub-wavelength region (a region where the diffraction mode is only 0th order light), and an effective refractive index region. Diffraction theory does not hold. In particular, in the resonance region and sub-wavelength region, the action at the boundary region of the grating groove surface differs depending on the polarization component, so the light incident on the diffraction grating is regarded as a vector quantity and the appearance on the diffraction grating groove surface is strictly determined. Although it is necessary to obtain the diffraction efficiency by analysis, the amount of calculation is very large.
[0007]
[Non-Patent Document 1]
Thomas Gaylord et al., “Analysis and Application of Optical Diffraction by Gratings”, Proceedings of the IEEE, Vol. 73, No. 5, May 1985 (Thomas K. Gayload etal "Analysis and Applicationa of Optical Diffraction by Gratings" Proceedings of The IEEE, Vol.73, No.5, May 1985)
[Non-Patent Document 2]
Satoshi Sato, “Examination for speeding up exact coupled wave analysis”, 29th Electromagnetic Theory Symposium ET-00-69 25 (2000)
[0008]
[Problems to be solved by the invention]
In recent years, the use of diffraction gratings in the field of communication using a wavelength band centered on the near infrared region has increased overwhelmingly. In such applications, the wavelength used and the grating period are almost the same. Use in a certain resonance region. However, as described above, the calculation of the diffraction efficiency of the diffraction grating in the resonance region is very complicated, and a method for designing a groove cross-sectional shape that can realize high diffraction efficiency has not yet been established. For this reason, in the past, in designing such optical elements, an inefficient work of searching for an optimal or close cross-sectional shape by performing extensive calculations by trial and error has been performed, and such work is also performed by the designer. The reality is that we often rely on experience and intuition.
[0009]
Further, as described above, in the resonance region, the action in the boundary region of the grating groove surface differs depending on the polarization component. Therefore, if this is used, diffraction with the polarization component selected can be performed. That is, this is a polarization discrimination diffraction grating that selectively diffracts only one polarization component with high efficiency. Although such elements have been proposed in the past, the conventional polarization discriminating diffraction grating utilizes optical anisotropy due to a fine structure, and requires a complicated design technique and high-cost fine processing technology. It was poor in practicality. Therefore, conventionally, in order to perform diffraction with polarization selected, it has been common to combine a non-polarization diffraction grating and a polarizer. Therefore, it is structurally a general lamellar grating, and if the polarization discriminating diffraction grating can be realized by setting only the parameters appropriately, it is considered that the utility value is very high.
[0010]
Furthermore, when a reflection type diffraction grating cannot be used due to the configuration of the apparatus, etc., glass or MgF₂The transmission type diffraction grating made of a dielectric material such as the above is used, but also in such a transmission type diffraction grating, the groove of the transmission type polarization discrimination diffraction grating that enables the diffraction with the polarization selected as described above is possible. The shape design method has not been established yet, and it has been difficult to stably obtain high diffraction efficiency.
[0011]
The present invention has been made in view of the above problems, and the object of the present invention is to achieve a high diffraction efficiency in a lamellar diffraction grating having a rectangular groove cross-sectional shape that is easy to design. It is an object of the present invention to provide a reflection type non-polarization diffraction grating and a design method thereof.
[0012]
In addition, another object of the present invention is a reflection type that is easy to design and can achieve high diffraction efficiency according to polarization in a lamellar diffraction grating having a rectangular groove cross-sectional shape. It is an object to provide a polarization discrimination diffraction grating and a design method thereof.
[0013]
Furthermore, another object of the present invention is a lamellar diffraction grating having a rectangular groove cross-sectional shape, which is easy to design and can achieve high diffraction efficiency according to polarization. It is an object of the present invention to provide a type polarizing diffraction grating and a design method thereof.
[0014]
[Means for Solving the Problems]
The lamellar diffraction grating according to the first invention made to solve the above problems is a lamellar reflection diffraction grating having a rectangular groove cross-sectional shape.
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. Under
Focusing on the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in rigorous coupled wave analysis (= RCWA), first, the imaginary part of the propagation constant is non-zero from near zero for TE polarized light. Search for the duty ratio of the grating period that shifts to a zero value, and then set the duty ratio of the grating period to the vicinity thereof, and within the groove depth range that increases the diffraction efficiency of TE-polarized light, TM polarization By determining the groove depth at which the diffraction efficiency increases, the duty ratio of the grating period and the groove depth are determined.
[0015]
Further, the design method of the lamellar diffraction grating according to the second invention is a method of designing a lamellar reflection diffraction grating whose groove cross-sectional shape is rectangular,
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. To determine the grating period duty ratio and groove depth of the diffraction grating,
Focusing on the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in RCWA, first search for the duty ratio of the grating period such that the imaginary part of the propagation constant changes from near zero to non-zero for TE polarized light And steps to
Next, by setting the duty ratio of the grating period in the vicinity thereof, and finding the groove depth at which the diffraction efficiency of the TM polarized light becomes high within the groove depth range where the diffraction efficiency of the TE polarized light becomes high;
It is characterized by having.
[0016]
A lamellar diffraction grating according to a third aspect of the present invention for solving the above-described problems is a lamellar diffraction grating having a rectangular groove cross-sectional shape and having a polarization selectivity. ,
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. Under
Focusing on the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in RCWA, first search for the duty ratio of the grating period such that the imaginary part of the propagation constant changes from near zero to non-zero for TE polarized light Then, after setting the duty ratio of the grating period to a value sufficiently larger than the searched duty ratio, and finding the groove depth at which the diffraction efficiency of TM polarized light becomes higher, the duty ratio of the grating period and the groove It is characterized by having determined the depth.
[0017]
The method for designing a lamellar diffraction grating according to the fourth aspect of the invention is a method for designing a reflection type polarization discriminating diffraction grating that is a lamellar type having a rectangular groove cross section and has polarization selectivity. And
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. To determine the grating period duty ratio and groove depth of the diffraction grating,
Focusing on the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in RCWA, first search for the duty ratio of the grating period such that the imaginary part of the propagation constant changes from near zero to non-zero for TE polarized light And steps to
Next, after setting the duty ratio of the grating period to a value sufficiently larger than the searched duty ratio, finding the groove depth at which the diffraction efficiency of TM polarized light is increased;
It is characterized by having.
[0018]
A lamellar diffraction grating according to a fifth aspect of the present invention to solve the above problems is a lamellar diffraction grating having a rectangular groove cross-sectional shape and having a polarization selectivity. In
When light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only 0th-order light and -1st-order light, and the wave vector tangent of the -1st-order diffracted light is opposite in polarity to that of the incident wave. Under the condition that it is transmitted in the direction
Paying attention to the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in RCWA, first search for the duty ratio of the grating period so that the magnitude relationship between the first and second order propagation constants is reversed for TM polarization, The duty ratio of the grating period and the groove depth are determined by setting the duty ratio of the grating period in the vicinity thereof and finding the groove depth at which the diffraction efficiency of TE-polarized light is increased.
[0019]
The method for designing a lamellar diffraction grating according to the sixth aspect of the invention is a method for designing a transmission type polarization discrimination diffraction grating that is a lamellar type having a rectangular groove cross section and that has polarization selectivity. And
When light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only 0th-order light and -1st-order light, and the wave vector tangent of the -1st-order diffracted light is opposite in polarity to that of the incident wave. In order to determine the duty ratio and groove depth of the grating period of the diffraction grating under the condition that the light is transmitted in such a direction,
Focusing on the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in RCWA, first search for the duty ratio of the grating period so that the magnitude relationship between the first and second order propagation constants is reversed for TM polarization,
Next, setting the grating period duty ratio in the vicinity thereof to find the groove depth at which the diffraction efficiency of TE-polarized light is increased;
It is characterized by having.
[0020]
DETAILED DESCRIPTION OF THE INVENTION
Conventionally, a technique called rigorous coupling wave analysis (RCWA) is known as one of optical characteristic analysis techniques for diffraction gratings (see, for example, Non-Patent Document 1). This RCWA is conventionally used to calculate diffraction efficiency from the structural parameters of the diffraction grating and the incident conditions.
[0021]
The inventor of the present application, in the process of repeatedly studying the optical characteristics analysis of a diffraction grating using RCWA (for example, see Non-Patent Document 2), a calculation formula that expresses the electromagnetic field inside the periodic structure of the diffraction grating as superposition of plane waves in RCWA It is found that a plurality of propagation constants included in the crystal exhibit a specific change depending on the duty ratio of the grating groove depending on the polarization component, the duty ratio dependence of the relationship between the propagation constant and the diffraction efficiency, and the groove depth. From the relationship between the diffraction efficiency and the diffraction efficiency, the inventors decided to determine the duty ratio and groove depth of the grating grooves. In particular, by determining the duty ratio and groove depth so that the diffraction efficiency is good for both TE-polarized light and TM-polarized light, an unpolarized diffraction grating that can achieve high diffraction efficiency regardless of polarization. Obtainable. In addition, after setting the conditions so that the diffraction efficiency for one polarization becomes very small, the polarization ratio is selected by determining the duty ratio and groove depth so that the diffraction efficiency for the other polarization is good. Thus, it is possible to obtain a polarization discrimination diffraction grating that can achieve high diffraction efficiency.
[0022]
【The invention's effect】
According to the design method of the lamellar diffraction grating according to the first invention and the lamellar diffraction grating according to the second invention, it is not a trial-and-error procedure that relies on the experience and intuition of a skilled person as in the prior art, but is a typical one. In the procedure, it is possible to determine the grating groove duty ratio and the groove depth so that the diffraction efficiency becomes the best or close to that. Therefore, the design efficiency of the diffraction grating can be greatly improved.
[0023]
In addition, according to the design method of the lamellar diffraction grating according to the third invention and the lamellar diffraction grating according to the fourth invention, it is not a trial and error procedure that relies on the experience and intuition of a skilled person as in the prior art, but a fixed pattern. With a typical procedure, it is possible to determine the grating groove duty ratio and groove depth so that one polarization component is hardly diffracted and the diffraction efficiency for the other polarization component is at or near the best. Therefore, the design efficiency of the polarization discriminating diffraction grating can be greatly improved, and polarization discrimination can be performed without using a polarizer, so that the configuration of the optical system can be easily reduced in cost.
[0024]
Further, according to the design method of the lamellar diffraction grating according to the fifth invention and the lamellar diffraction grating according to the sixth invention, the transmission polarization discriminating diffraction grating also relies on the experience and intuition of a skilled person as in the past. The grating groove duty ratio is such that it is not a trial-and-error procedure but a standard procedure that hardly diffracts one polarization component and the transmission diffraction efficiency for the other polarization component is at or near the best. And the groove depth can be determined. Accordingly, the design efficiency of the transmission type polarization discriminating diffraction grating can be greatly improved, and polarization discrimination can be performed without using a polarizer, so that the configuration of the optical system is simplified and the cost can be reduced.
[0025]
【Example】
First, the principle of the method for designing a lamellar diffraction grating according to the present invention will be described. Here, a Littrow arrangement as depicted in FIG. 1 is assumed as a light incident condition on the lamellar diffraction grating. That is, when light of wavelength λ is incident on the grating groove surface of the lamellar diffraction grating 1 having a rectangular cross-sectional shape, zero-order diffracted light is generated so that the grating groove surface is specularly reflected, and incident light In this state, the first-order diffracted light is reflected so as to face directly. Under this condition, no diffracted light other than the 0th order light and the −1st order light is generated.
[0026]
Now, consider the (x, y, z) coordinate system as shown in FIG. That is, the direction along the groove direction on the groove surface of the lamellar diffraction grating 1 is x, the direction orthogonal to x in the groove surface is y, and the direction orthogonal to both x and y is z. The groove depth is represented by h, and the grating period is represented by Λ. Using such a coordinate system, RCWA can express the electromagnetic field inside the periodic structure of the diffraction grating as a superposition of plane waves as shown in the following equation (1).
E (r) = Σexp (-iσ⁽ⁿ⁾y) ・ Σ [e₊ ^{(n, n ')}exp (-iK^{(n ')}z) + e_- ^{(n, n ' )}exp (iK^{(n ')}z)]… (1)
(In Equation (1), the first Σ is the sum for n, and the second Σ is the sum for n ′)
[0027]
In equation (1), e₊ ^{(n, n ')}And e_- ^{(n, n ')}Is the amplitude of the forward and backward waves, K⁽ⁿ⁾ Corresponds to the propagation constant of the plane wave component. N and n 'are mode indexes (in the diffraction grating, n corresponds to the diffraction order). Furthermore, σ⁽ⁿ⁾Is Bloch wave number k_y (Interface projection component of incident wave number) and reciprocal lattice G_y= [Lambda] / 2 [pi] ([Lambda] is a lattice period) is expressed by the following equation (2) as a linear combination.
σ⁽ⁿ⁾= K_y+ NG_y       … (2)
In equation (1), if n and n ′ are summed over (−∞, ∞), the convergence of the propagation constant is guaranteed mathematically, but the required accuracy can be obtained in actual numerical calculations. N can be cut off.
[0028]
When the diffraction grating 1 is made of metal, all propagation constants K⁽ⁿ⁾Is the imaginary part Im {K⁽ⁿ⁾} Is generally a non-zero value, the greater the value, the greater the attenuation (extinction), and the smaller the contribution to propagation and diffraction within the grating. Therefore, the propagation constant K⁽ⁿ⁾Imaginary part Im {K⁽ⁿ⁾} In small order, only the first few are substantially involved in the optical properties of the diffraction grating, and others can be ignored. Furthermore, here, as described above, conditions are set such that there are only two diffracted waves of the 0th and −1st order. Under this condition, the propagation constant K⁽ⁿ⁾Imaginary part Im {K⁽ⁿ⁾}, It can be considered that the first two plane wave components with the smallest} contribute dominantly to the diffraction characteristics.
[0029]
The groove sectional shape of the lamellar diffraction grating as shown in FIGS. 1 and 2 can be defined by the grating groove duty ratio Λ1 / Λ and the groove depth h. Therefore, here, attention is paid to the dependency on the duty ratio, which differs for each polarization component, for the two propagation constants determined by the RCWA as described above, which are dominant in the diffraction characteristics of the plane wave mode. Then, in the reflection-type non-polarization diffraction grating and the reflection-type polarization discrimination diffraction grating, the preferable requirements are considered, and the design procedure is constructed so as to satisfy the requirements.
[0030]
(1) Reflective non-polarized diffraction grating
The requirement of the reflection-type non-polarization diffraction grating is that the diffraction efficiency of reflection is as high as possible for both TE-polarized light and TM-polarized light. When the diffraction grating is made of metal, it is expected that the smaller the duty ratio, the larger the proportion of air and the smaller the attenuation, and conversely, the larger the duty ratio, the larger the proportion of the metal and the larger the attenuation. In fact, as will be described later, in the TE polarization, when the duty ratio is gradually increased, the duty ratio (hereinafter, referred to as the duty ratio) showing a remarkable rise so that the imaginary part of all the propagation constants becomes much larger than 0. This duty ratio is called “transition point.” Near the transition point, the diffraction efficiency of TE-polarized light has a very low dependence on the groove depth, and a high diffraction efficiency is achieved regardless of the groove depth. A range of groove depths that can be formed exists with an appropriate width.
[0031]
Therefore, as a design procedure, as shown in FIG. 4, first, a duty ratio that becomes a transition point is searched (step S11). At the transition point, as described above, high diffraction efficiency is obtained in TE polarization, and the high efficiency is maintained even if the groove depth is changed within a certain range. Therefore, after fixing the duty ratio at the transition point (step S12), the TM polarized light diffraction efficiency is analyzed in a wide groove depth range in which high diffraction efficiency is maintained for the TE polarized light. Since TM polarized light has a propagating mode even at the transition point, its diffraction efficiency varies depending on the groove depth, and it is possible to find a groove depth that gives high diffraction efficiency to TM polarized light. I can do it. Therefore, the groove depth at which the diffraction efficiency of TM polarized light reaches a peak (maximum) within the range of the groove depth is searched (step S13). Thereby, the duty ratio and the groove depth are determined (step S14), and high diffraction efficiency can be achieved for both polarized lights. That is, non-polarization blazing can be realized, and a reflection-type non-polarization diffraction grating with a wider high reflection range can be obtained.
[0032]
(2) Reflective polarization discriminating diffraction grating
The requirement of the reflective polarization discriminating grating is that the diffraction efficiency of reflection of one polarization is as high as possible and the diffraction efficiency of reflection of the other polarization is as low as possible. Therefore, as a design procedure, as shown in FIG. 5, first, a transition point is searched for in the same manner as in the case of designing non-polarized blazed (step S21). When the duty ratio becomes larger than the transition point, the propagating mode disappears in TE polarized light, and the diffraction efficiency gradually approaches zero. Therefore, after finding the transition point, a duty ratio as large as possible is selected from the transition point in consideration of a desired extinction ratio (TE polarization diffraction efficiency / TM polarization diffraction efficiency) and manufacturing limitations (step S22). ). Even when the duty ratio is close to 1, the TM polarized light has a propagation mode. Therefore, the diffraction efficiency of TM polarized light varies depending on the groove depth, and a groove depth that gives high diffraction efficiency should be found. Therefore, by searching for the groove depth at which the diffraction efficiency of TM polarized light reaches a peak (step S23), and determining the duty ratio and groove depth (step S24), only the TM polarized light can be blazed.
[0033]
(3) Transmission type polarization discriminating diffraction grating
In the above description, the diffraction grating is assumed to be a reflection type and made of metal. However, when the diffraction grating is a transmission type, a dielectric such as glass is considered as a material having a high light transmittance. When the diffraction grating is made of a dielectric, the propagation constant K in the above equation (1)⁽ⁿ⁾Is either a real number or a pure imaginary number. When it is a real number, it is a mode capable of propagating, and when it is an imaginary number, it is a non-propagating mode and decays. The decaying mode has little effect on the optical characteristics of the diffraction grating, and the optical characteristics are defined by the modes that can be propagated. When the wavelength and the grating period are substantially equal and there are only two diffraction modes, there are often two modes that can be propagated.
[0034]
Here, as in the case of the reflection type, attention is paid to the dependency on the duty ratio, which differs for each polarization component, with respect to two propagation constants determined by RCWA, which are dominant in the diffraction characteristics of the plane wave mode. In this case, the proportion of air (refractive index = 1) increases as the duty ratio of the grating grooves decreases, so the propagation constant decreases. Conversely, the proportion of dielectric (refractive index> 1) increases as the duty ratio increases. Therefore, the propagation constant is expected to increase. This is because the propagation constant of the plane wave is proportional to the refractive index in the case of the bulk. Actually, as will be described in detail later, the dependency of the propagation constant on the duty ratio varies greatly depending on the polarization. That is, in the TE polarization, the magnitude relationship between the first and second propagation constants is maintained as it is, but in the TM polarization, the magnitude relationship is switched at a certain duty ratio. In other words, a peculiar phenomenon that there is a degenerate point can be found. At this time, TM polarized light has a characteristic optical characteristic that it does not diffract at all regardless of the groove depth.
[0035]
Therefore, as a design procedure, as shown in FIG. 6, first, a duty ratio in which the magnitude relationship between the propagation constants of the first order and the second order is switched in TM polarization is searched (step S31), and the duty ratio is set there. It is fixed (step S32). At this time, the diffraction of TM polarized light is almost zero, while the diffraction efficiency of TE polarized light varies depending on the groove depth. Therefore, the groove depth that gives high diffraction efficiency should be found. Therefore, by searching for the groove depth at which the diffraction efficiency of TE-polarized light reaches its peak (step S33) and determining the duty ratio and groove depth (step S34), only the TE-polarized light can be blazed.
[0036]
Next, among the lamellar diffraction gratings according to the present invention, the reflection-type non-polarization diffraction grating and the reflection-type polarization discrimination diffraction grating will be described with specific design examples.
A metal diffraction grating generally uses aluminum mainly for the reason of easy replication. Therefore, here, the propagation constant and the optical characteristics of the reflective diffraction grating were calculated under the conditions shown in FIG.
[0037]
8A and 8B show the duty ratio dependence of the propagation constants of TE polarized light and TM polarized light, respectively. The propagation constant has a higher priority as the imaginary part is smaller, and focuses on the top two. Therefore, K1 and K2 in FIG. 8 are the first and second propagation constants (eigenvalues), respectively, and Re {Kn} and Im {Kn} (where n = 1 or 2) are the real parts, respectively. Represents the imaginary part. A mode with a large imaginary part is evanescent and extinguishes rapidly as the distance from the interface between the lattice and the free space increases, so that optical characteristics are hardly affected. Therefore, there is no problem even if it is excluded from consideration here.
[0038]
9, 10 and 11 are graphs showing the dependency of the diffraction efficiency on the groove depth when the duty ratio is 0.1, 0.27 and 0.8, respectively. R (-1) and R (0) in FIGS. 9 to 11 mean -1st order and 0th order diffraction efficiencies, respectively.
[0039]
When the duty ratio is 0.1 (see FIG. 9), for TE polarized light, the imaginary part of the highest-order propagation constant is close to zero and is one wave (hereinafter referred to as a sufficiently long distance without attenuation). Since there are n plane wave components that can be propagated, it is said to be n-wave), and therefore, sinusoidal modulation is shown with respect to the groove depth. On the other hand, with respect to TM polarization, since the imaginary part of the highest order and second order propagation constants is close to zero and has two waves, it is not a monotone sinusoidal modulation with respect to the groove depth. It shows a curve (for example, what is called a bump or a shoulder) as if these modes were synthesized.
[0040]
When the duty ratio increases to about 0.27 (see FIG. 10), TE polarized light is zero-wave and gradually becomes insensitive to the groove depth, and a state that seems to be a saturation phenomenon is observed. On the other hand, the TM polarized light has a single wave shape, and changes to a sinusoidal modulation with respect to the groove depth although there is an overall undulation.
[0041]
When the duty ratio is further increased to 0.8 (see FIG. 11), TE polarized light hardly diffracts regardless of the groove depth. In other words, the presence of the grating grooves is not reflected in the diffraction, and the behavior is almost equivalent to the specular reflection. On the other hand, TM polarized light maintains a one-wave state and exhibits sinusoidal modulation with respect to the groove depth.
[0042]
Thus, it can be seen that there is a clear duty ratio that causes a phase transition of the optical characteristics, and the behavior of the diffracted light is divided at this boundary. FIG. 12 shows this comprehensively. FIG. 12 is a diagram in which the maximum points of diffraction efficiency are plotted on a plane having the duty ratio and groove depth as axes orthogonal to each other. From this result, an important conclusion can be obtained as a guideline in designing the diffraction grating as follows.
[0043]
(1) Reflective non-polarized diffraction grating
As can be seen from FIG. 12, in the vicinity of the duty ratio (0.27 here) as the transition point, the curve connecting the maximum points of TE polarized light rises so as to be parallel to the vertical axis (groove depth). That is, this means that a high-efficiency reflection band can be formed when the groove depth dependency that exhibits high diffraction efficiency is taken. On the other hand, a TM polarized peak exists in this reflection band. Therefore, by searching for a groove depth that satisfies this condition, both polarizations can be made highly efficient.
[0044]
(2) Reflective polarization discriminating diffraction grating
At a duty ratio sufficiently larger than the transition point (here, 0.8), TE polarized light is hardly reflected. On the other hand, TM polarized light modulates in a sinusoidal shape with respect to the groove depth, and therefore has a maximum point with the highest efficiency. By searching for this condition, it is possible to obtain a reflective polarization discrimination grating in which only TM polarized light is diffracted.
[0045]
It should be noted that there are a plurality of solutions that satisfy the above conditions, not unique. However, considering that the wavelength and incident angle are fluctuated in the vicinity, it is desirable to select a groove depth that is as shallow as possible because the reflection band is wider as the groove depth is shallower. In addition, the shallower the groove depth, the easier the production of the diffraction grating.
[0046]
FIGS. 13 and 14 show the wavelength dependence of diffraction efficiency when the duty ratio is 0.27 and the groove depth is 2.5 [μm] and 1.1 [μm], respectively. As can be seen from these, the reflection band increases as the groove depth decreases. These phenomena are true in all cases.
[0047]
Next, among the lamellar diffraction gratings according to the present invention, a transmission type polarization discrimination diffraction grating will be described with a specific design example.
Typical materials for the dielectric used in the transmissive diffraction grating include glass and semiconductors in the near infrared region. Here, glass is taken as an example, and propagation constants and optical characteristics were calculated under the diffraction conditions shown in FIG.
[0048]
FIG. 16 shows the duty ratio dependency of the propagation constants of TE polarized light and TM polarized light. In the case of glass, since the dielectric constant is a real number, the propagation constant is divided into a real number and a pure imaginary number. Under this condition, there are only two propagation constants that are real numbers, and these are plotted. As a characteristic phenomenon in this case, when the duty ratio is 0.282 for TM polarized light, the eigenvalues of the first mode and the second mode are degenerated (have the same value).
[0049]
FIG. 17 is a diagram showing the relationship between the groove depth and the diffraction efficiency at this time (duty ratio = 0.282). T (-1) and T (0) in FIG. 17 mean -1st order and 0th order diffraction efficiency (transmittance), respectively (the same applies to the following). At this time, it is understood that TM polarized light is not diffracted at all. Such a phenomenon is presumed to be because the two plane wave components cancel each other out due to the interference effect and the diffraction amplitude becomes zero regardless of the groove depth. On the other hand, TE polarized light shows sinusoidal modulation with respect to the groove depth, and has a maximum diffraction efficiency when the groove depth is about 1.8 [μm] and 6.0 [μm]. At this time, it is understood that TE polarized light functions as a diffraction grating for selecting polarized light without diffracting high-efficiency diffraction and TM polarized light. In this way, an appropriate duty ratio and groove depth can be determined.
[0050]
Note that the maximum point of TE polarized light that satisfies the above conditions is not unique and there are a plurality of local maximum points. However, considering that the wavelength and incident angle are fluctuated in the vicinity, it is desirable to select a groove depth that is as shallow as possible because the reflection band is wider as the groove depth is shallower. In addition, the shallower the groove depth, the easier it is to manufacture the diffraction grating.
[0051]
18 and 19 show the wavelength dependence of diffraction efficiency when the duty ratio is 0.282 and the groove depth is 1.8 [μm] and 6.0 [μm], respectively. As can be seen from these, the reflection band increases as the groove depth decreases. These phenomena are true in all cases.
[0052]
It should be noted that the above embodiment is merely an example of the present invention, and it is obvious that the present invention is encompassed by the present invention even if appropriate modifications, corrections, or additions are made within the scope of the present invention.
[Brief description of the drawings]
FIG. 1 is a conceptual diagram showing a Littrow arrangement assumed in a lamellar diffraction grating according to the present invention.
FIG. 2 is a diagram showing an (x, y, z) coordinate system on a grating groove surface of a lamellar diffraction grating.
FIG. 3 is a sectional view of a groove of a diffraction grating.
FIG. 4 is a flowchart showing a design procedure for a reflective non-polarized diffraction grating.
FIG. 5 is a flowchart showing a design procedure for a reflective polarization discrimination diffraction grating.
FIG. 6 is a flowchart showing a design procedure of a transmission type polarization discrimination diffraction grating.
FIG. 7 is a diagram showing an example of diffraction conditions of a reflective diffraction grating.
FIG. 8 is a diagram showing duty ratio dependency of propagation constants of TE-polarized light and TM-polarized light in a reflective diffraction grating.
FIG. 9 is a diagram showing the groove depth dependence of diffraction efficiency when the duty ratio is 0.1.
FIG. 10 is a diagram showing the groove depth dependence of diffraction efficiency when the duty ratio is 0.27.
FIG. 11 is a diagram showing the groove depth dependence of diffraction efficiency when the duty ratio is 0.8.
FIG. 12 is a diagram in which the maximum point of diffraction efficiency is plotted on a plane with the duty ratio and groove depth as axes orthogonal to each other.
FIG. 13 is a diagram showing the wavelength dependence of diffraction efficiency when the duty ratio is 0.27 and the groove depth is 2.5 [μm].
FIG. 14 is a diagram showing the wavelength dependence of diffraction efficiency when the duty ratio is 0.27 and the groove depth is 1.1 [μm].
FIG. 15 is a diagram showing an example of diffraction conditions of a transmission diffraction grating.
FIG. 16 is a diagram showing the duty ratio dependency of propagation constants of TE-polarized light and TM-polarized light in a transmissive diffraction grating.
FIG. 17 is a graph showing the relationship between the groove depth and the diffraction efficiency when the duty ratio is 0.282.
FIG. 18 is a diagram showing the wavelength dependence of diffraction efficiency when the duty ratio is 0.282 and the groove depth is 1.8 [μm].
FIG. 19 is a diagram showing the wavelength dependence of diffraction efficiency when the duty ratio is 0.282 and the groove depth is 6.0 [μm].
[Explanation of symbols]
1 ... Lamellar diffraction grating

Claims (6)

In the lamellar reflective diffraction grating where the groove cross-sectional shape is rectangular,
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. Under
Paying attention to the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in the rigorous coupled wave analysis, first the duty of the grating period such that the imaginary part of the propagation constant changes from near zero value to non-zero value for TE polarized light Search for the ratio, and then set the grating period duty ratio in the vicinity to find the groove depth that increases the TM polarized light diffraction efficiency within the groove depth range where the TE polarized light diffraction efficiency increases. A lamellar diffraction grating characterized in that the duty ratio of the grating period and the groove depth are determined by A method of designing a lamellar reflective diffraction grating having a rectangular groove cross-sectional shape,
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. In order to determine the duty cycle of the grating period and the groove depth of the reflective lamellar diffraction grating,
Paying attention to the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in the rigorous coupled wave analysis, first the duty of the grating period such that the imaginary part of the propagation constant changes from near zero value to non-zero value for TE polarized light Searching for a ratio;
Next, by setting the duty ratio of the grating period in the vicinity thereof, and finding the groove depth at which the diffraction efficiency of the TM polarized light becomes high within the groove depth range where the diffraction efficiency of the TE polarized light becomes high;
A method for designing a lamellar diffraction grating, comprising: In the reflection type polarization discriminating diffraction grating having a lamellar type in which the groove cross-sectional shape is rectangular and having polarization selectivity,
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. Under
Paying attention to the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in the rigorous coupled wave analysis, first the duty of the grating period such that the imaginary part of the propagation constant changes from near zero value to non-zero value for TE polarized light By searching for the ratio, and then setting the grating period duty ratio to a value sufficiently larger than the searched duty ratio, and finding the groove depth at which the diffraction efficiency of TM polarized light is increased, the grating period duty is determined. A lamellar diffraction grating characterized in that the ratio and groove depth are determined. A method of designing a reflection type polarization discriminating diffraction grating having a lamellar type whose groove cross-sectional shape is rectangular and having polarization selectivity,
The condition that when the light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only the 0th order light and the −1st order light, and the −1st order diffracted light is reflected in the direction facing the incident wave. To determine the grating period duty ratio and groove depth of the diffraction grating,
Paying attention to the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in the rigorous coupled wave analysis, first the duty of the grating period such that the imaginary part of the propagation constant changes from near zero value to non-zero value for TE polarized light Searching for a ratio;
Next, after setting the duty ratio of the grating period to a value sufficiently larger than the searched duty ratio, finding the groove depth at which the diffraction efficiency of TM polarized light is increased;
A method for designing a lamellar diffraction grating, comprising: In the transmission type polarization discriminating diffraction grating which is a lamellar type whose groove cross-sectional shape is rectangular and has polarization selectivity,
When light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only 0th-order light and -1st-order light, and the wave vector tangent of the -1st-order diffracted light is opposite in polarity to that of the incident wave. Under the condition that it is transmitted in the direction
Focusing on the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in rigorous coupled wave analysis, first search for the duty ratio of the grating period so that the magnitude relationship between the first and second order propagation constants is reversed for TM polarized light Then, the duty ratio of the grating period and the groove depth are determined by setting the duty ratio of the grating period in the vicinity thereof and finding the groove depth at which the diffraction efficiency of TE-polarized light is increased. Lamella type diffraction grating. A method of designing a transmission type polarization discriminating diffraction grating having a rectangular lamellar cross-sectional shape and having a polarization selectivity,
When light of a predetermined wavelength is incident on the grating groove surface at a predetermined incident angle, the diffracted wave is only 0th-order light and -1st-order light, and the wave vector tangent of the -1st-order diffracted light is opposite in polarity to that of the incident wave. In order to determine the duty ratio and groove depth of the grating period of the diffraction grating under the condition that the light is transmitted in such a direction,
Focusing on the propagation constant of the plane wave component of the electromagnetic field inside the periodic structure in the rigorous coupled wave analysis, first search for the duty ratio of the grating period so that the magnitude relationship between the first and second order propagation constants is reversed for TM polarization. And
Next, setting the grating period duty ratio in the vicinity thereof to find the groove depth at which the diffraction efficiency of TE-polarized light is increased;
A method for designing a lamellar diffraction grating, comprising:

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