JP3479449B2 - Method of manufacturing reflection type diffractive optical element - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for manufacturing a diffractive optical element that functions as a hologram having a light phase modulation function, and more particularly to a method for manufacturing a reflective diffractive optical element.

[0002]

2. Description of the Related Art A diffractive optical element is a lens element for deflecting or condensing a light beam in an arbitrary direction. This diffractive optical element is an optical element that uses a phase modulation function of light and has a stepwise shape similar to a Fresnel lens that can achieve desired optical characteristics without inviting a large size and weight like a shaped lens. .

A computer is generally used to manufacture the diffractive optical element. In the manufacturing method using this computer, the optical path difference function ρ (x, y) = ΣC _N x ^m y ⁿ (where n and m are positive integers and N = {(M + n) ² + m + 3
The coefficient in each polynomial (i.e., n} / 2 holds), that is, the optical path difference coefficient C _N is obtained. Obtained optical path difference coefficient C _N
By substituting into the computer program, the conditions of the mask for photolithography necessary for obtaining a desired shape by photolithography, that is, the number of masks and the pattern of each mask are generated. A mask is manufactured according to this mask condition, and a diffractive optical element having a desired shape is formed by a photolithography method using this mask.

[0004]

By the way, in the conventional manufacturing method as described above, regarding the polynomial that gives the shape of the lens exhibiting the desired optical characteristic, the optical characteristic can be obtained for each optical characteristic. A belief polynomial is calculated according to each situation, each optical path difference coefficient C _N is obtained from the calculation result, and a mask obtained by computer processing with this optical path difference coefficient C _N is generated.

Along with the computer processing of this optical path difference coefficient C _N , the optical path difference coefficient C which is the calculation result by the computer
The optical characteristic of the optical path difference function including _N is simulated, the polynomial that gives the initial shape is modified based on the result, and the mask condition is calculated again using the modified optical path difference coefficient C _N based on the modified polynomial. In order to process.

By such trial and error work, a mask for forming a diffractive optical element exhibiting desired optical characteristics is determined, and by photolithography using this mask, selective etching processing is performed on the lens material. Then, a diffractive optical element having desired optical characteristics was formed. Therefore, the manufacturing efficiency of the diffractive optical element exhibiting desired optical characteristics is extremely low, and particularly, the designing and manufacturing of a large number of lenses such as an optical wiring of an optoelectronic circuit which requires a large number of lens groups exhibiting different optical characteristics are included. It has been desired to improve the manufacturing efficiency of the diffractive optical element.

In particular, if the reflection type diffractive optical element has the same etching depth as compared with the transmission type diffractive optical element,
Since it is possible to increase the minimum width dimension of the mask pattern of the etching mask and to easily manufacture it, it has been strongly desired to improve the manufacturing efficiency of this reflective diffractive optical element.

[0008]

SUMMARY OF THE INVENTION The present invention has the basic concept of replacing an optical path difference function satisfying desired optical characteristics with an approximate expression of Taylor expansion in order to obtain each coefficient of a polynomial to be inputted to a computer. In order to solve the above-mentioned conventional problems, the following configuration is adopted. <Structure> The present invention is necessary for forming a reflection type diffractive optical element having a shape specified by the optical path difference function by photolithography by giving each coefficient of the polynomial in the optical path difference function expressed by the polynomial. the method of manufacturing a reflection type diffractive optical element comprising a step of obtaining a mask condition by the execution of a computer program for determining the a mask conditions, to determine the optical path difference function satisfying predetermined optical characteristics as the following general formula, lights obtained path A general expression of the difference function is Taylor expanded to obtain an approximate expression, and the coefficient of each term of the approximate expression obtained by the Taylor expansion is stored in the computer program.
Each coefficient of the given polynomial is input to a computer program, the mask condition is determined by executing the program, a mask of the required condition is manufactured, and a lens material is selectively selected by a photolithography method using the mask. Forming a reflective film on the surface of the lens material after performing various etching processes, thereby producing a reflective diffractive optical element .

In the manufacturing method according to the present invention, an optical path difference function satisfying predetermined optical characteristics of the reflection type diffractive optical element is obtained by a general formula, and this general formula is subjected to Taylor expansion to approximate the desired optical path difference function. A Taylor expansion formula is required. By obtaining the coefficient of each term of the Taylor expansion equation, which is an approximate expression, and inputting each coefficient into the computer program for obtaining the mask condition, the influence of the error is strongly exerted without going through trial and error work. It is possible to obtain the mask condition extremely quickly without using the mask condition.

As one specific example of the optical characteristics of the reflection-type diffractive optical element according to the present invention, an incident light having a refractive index n with respect to a light beam converted from a point light source into a parallel light flux having an arbitrary deflection angle and reflected There is an optical characteristic in the side medium. Optical path difference function ρ showing the optical characteristics of this reflective diffractive optical element
The general formula of (x, y) is as follows: ρ (x, y) = (n / 2) · {(X−x) ² + (Y−
y) ² + Z ² } ¹ / 2- (nL / 2)-(n / 2) ・
{(Αx + βy) / (α ² + β ² + γ ² ) ^1/2 }
Is expressed by (A), and the coefficient of each term of the above two-dimensional Taylor expansion equation is input to the computer program (corresponding to claim 1 ). Here, (X, Y, Z) represents the coordinate position of the point light source.

Further, as a specific example of other optical characteristics,
There is an optical property in the incident light side medium having a refractive index n for a light beam in which a parallel light beam having an arbitrary deflection angle is focused on an image point and reflected. The general formula of the optical path difference function ρ (x, y) showing the optical characteristics of this reflective diffractive optical element is as follows: ρ (x, y) = (n / 2) · {(X−x) ² + ( Y-
y) ² + Z ² } ^1/2 − (nL / 2) + (n / 2) ·
{(Αx + βy) / (α ² + β ² + γ ² ) ^1/2 }
... (B) (corresponding to claim 2 ). Where (X, Y,
Z) represents the image point position.

Furthermore, as one specific example of other optical characteristics, regarding the image formation from an object point to an image point and a reflected ray,
There is an optical characteristic in the incident light side medium having a refractive index n. Optical path difference function ρ showing the optical characteristics of this reflective diffractive optical element
The general formula of (x, y) is the following formula ρ (x, y) = (n / 2) · {(X ₁ −x) ² + (Y ₁
-Y) ² + Z ₁ ² } ₁ /2-(nL ^1/2 ) + (n /
2) · {(X ₂ −x) ² + (Y ₂ −y) ² + Z ₂ ² }
^1/2 - _(nL 2/2) represented by ... (C) (corresponding to claim 3). Where (X ₁ ,
Y ₁ , Z ₁ ) represents the coordinate position of the point light source, and (X ₂ ,
Y ₂ , Z ₂ ) represents the image point position.

Further, as another specific example of other optical characteristics, incident light having a refractive index n with respect to a light beam in which a parallel light beam having an arbitrary deflection angle is deflected and reflected by a parallel light beam having an arbitrary deflection angle. There is an optical characteristic in the side medium. The optical path difference function ρ (x, y) indicating the optical characteristics of this reflection type diffractive optical element is defined as the vector component of light passing through the origin parallel to the incident parallel light flux (α ₁ , β ₁ , γ ₁ ), and the exit parallel light flux. The vector component of the light passing through the origin parallel to is (α ₂ , β ₂ ,
γ ₂ ), the general formula is as follows: ρ (x, y) = (n / 2) · (α ₁ x + β ₁ y) / (α
₁ ² + β ₁ ² + γ ₁ ² ) ^1/2 − (n / 2) · (α ₂ x
+ Β ₂ y) / (α ₂ ² + β ₂ ² + γ ₂ ² ) ^1/2 ...
It is represented by (D) (corresponding to claim 4 ).

[0014]

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, the present invention will be described in detail with reference to the illustrated embodiments. <Specific Example> FIG. 1 is a flow chart showing the procedure of a method for manufacturing a reflective diffractive optical element according to the present invention. First, as a lens design, optical characteristics such as a focal length, a deflection angle, an aperture ratio, an object point position and an image point position of a reflection type diffractive optical element to be obtained are determined. (Step S1). Next, the optical path difference function ρ (x, y) that satisfies the desired optical characteristic determined in step S1 is obtained as a general expression (step S2). Then, an approximate expression of this optical path difference function is obtained by Taylor expansion of this optical path difference function (step S3). The term coefficient of the approximate expression obtained by the Taylor expansion is input to the CAD program as the optical path difference coefficient of the program (step S4).

This CAD program is a mask pattern such as the number of masks and mask patterns used for producing a reflection type diffractive optical element having an optical path difference function expressed by a polynomial expression that gives a desired shape by photolithography. Output the data. The two-dimensional optical path difference function ρ (x, y) is
Ρ (x, y) = ΣC _N x ^m y ⁿ (1) N = {(m + n) ² + m + 3n} / 2 (2) where m and n are positive integers. is there.

Data of a mask pattern used in photolithography can be obtained by inputting each coefficient in a polynomial giving a desired shape, that is, the optical path difference coefficient C _N to this CAD program. CA like this
An example of the D program is CghC manufactured by NIPT Inc. of San Diego, California, USA.
There is AD. In this CghCAD, although it will be described in detail later in the formulas (1) and (2) due to the data capacity, there is a limitation that m + n is 10 or less and N is 65 or less. However, it does not affect the essence of the present invention.

In order to manufacture a mask pattern in accordance with the mask pattern data obtained in step S4, for example, electron beam drawing similar to the conventional one can be used, and a mask pattern is generated by this electron beam drawing ( Step S5). By a well-known photolithography method using this mask pattern, the lens material is selectively etched, and then a metal film such as aluminum is deposited as a reflective film on the surface of the lens material, As a result, a reflective diffractive optical element having desired optical characteristics is formed (step S6).

In the method for manufacturing a diffractive optical element according to the present invention, a general expression of the optical path difference function satisfying desired optical characteristics is Taylor-expanded, and the coefficient of each term of this approximate expression is used as a computer program for obtaining the mask condition. By inputting into, it is possible to obtain the mask condition extremely quickly without undergoing trial and error work and without being strongly influenced by the error. Therefore, the method of the present invention is suitable for manufacturing an optical device that requires a large number of reflective diffractive optical elements.

Further, in the reflection type diffractive optical element to which the present invention is applied, the minimum width dimension of the mask pattern of the etching mask is increased as long as the etching depth is equal to that of the transmission type diffractive optical element. It can be easily manufactured. That is, the respective etching depths T _Reflection and T _Transmission in the reflective diffractive optical element and the transmissive diffractive optical element according to the present invention are the same as the optical depth of the two-phase (binary) diffractive optical element using one etching mask. When the wavelength is λ, they are respectively expressed by the following equations.

T _Transmission = λ / (2 | n ₁ −n ₂ |) (E) T _Reflection = λ / (4n ₁ ) (F) where n ₁ is the refractive index of the incident side medium. Yes, n ₂ is the refractive index of the exit side medium.

As is clear from the comparison between the two expressions (E) and (F), the etching depth T in the transmission type is
_Transmission is the refractive index n ₁ of both the incident side medium and the outgoing side medium
And whereas associated with n _2, the reflection type, the etching depth T _Reflection is related only to the refractive index n ₁ of the incident side medium.

As a result, in general, the required etching depth T in the etching process applied to the lens material using the etching mask is shallower in the reflective diffractive optical element than in the transmissive type. Its manufacture becomes easy. As an example, when a binary diffractive optical element for handling infrared light of 1.5 μm is obtained, when quartz having a refractive index n ₁ of 1.5 is used as a lens material, the need for the reflective diffractive optical element is increased. And a similar etching depth T is 0.26 μm and a silicon substrate having a refractive index n ₁ of 3.5 is used as the lens material, the same etching depth T is 0.1
1 μm, and etching depths of 1.5 μm and 0.3 μ, respectively, when a similar element is manufactured by a transmission type diffraction optical element.
While the etching depth is m, the etching depth becomes shallow, which makes a large practical contribution.

Further, if the etching depth is equivalent, the reflection type diffractive optical element can set a larger deflection angle than that of the transmission type diffractive optical element, and the optical device in which the optical elements are combined can be made compact. Above, reflective diffractive optical elements are extremely advantageous.

In the method of manufacturing the reflective diffractive optical element according to the present invention, as described in steps S1 to S3 of FIG. 1, the optical path difference function ρ (x,
After y) is obtained as a general expression, an approximate expression of this optical path difference function is obtained by Taylor expansion. The Taylor expansion formula of this optical path difference function ρ (x, y) up to the 10th order polynomial is
This is shown as the equation (3) in FIG. Δ shown in the second term on the right side of the equation (3) indicates a surplus term when Taylor expansion is performed, and is usually small enough to be ignored.

In the expression (3), the reason why the polynomial order is limited to 10th order is that in CghCAD, (m + n) indicating the polynomial order is 10 or less, and the number of terms of the optical path difference coefficient is shown. If N is 65 or less, and if the Taylor expansion is obtained up to 10th order polynomial, all 6 required
It is based on the fact that the coefficient of term 5 can be obtained. Therefore, if an optical path difference coefficient exceeding 65 terms is required in relation to the CAD program, the Taylor expansion equations up to 11 or higher multi-order terms can be applied.

After the optical path difference function satisfying the desired optical characteristics is obtained in step S2, an approximate expression by the Taylor expansion is obtained in step S3. As a preparation for obtaining this approximate expression, Expression (3) is expanded to a 10th order polynomial, and the coefficient of each term is used as a relational expression of the general expression ρ (x, y) of the optical path difference function.
~ Represented in Figure 9. 3 to 9 are arranged such that the coefficient of each term obtained by expanding Expression (3) up to a 10th degree polynomial, that is, each optical path difference coefficient, as a relational expression of the general expression ρ (x, y) of the optical path difference function. FIG.

Therefore, the general expression ρ (x, y) of the optical path difference function obtained in step 2 is expressed by the expression (4-) shown in FIGS.
0) to (4-65) are substituted into ρ (x, y), and each expression (4
By executing the operations of −0) to (4-65), each coefficient of the power series term is obtained by Taylor expansion of the general formula.

<First Specific Example> FIG. 10 is an explanatory diagram showing the optical characteristics of the reflective diffractive optical element according to the first specific example of the present invention. FIG. 10 shows a reflective diffractive optical element 10 according to the present invention as a reflective computer generated hologram that converts a divergent spherical wave from a point light source s into a parallel light flux and reflects it. The point light source s exists at a position separated from the origin by a distance L. In order to simplify the description, the reflective diffractive optical element 10
Is a vector component of the light passing through the origin, which lies in a plane passing through the origin and including the X axis and the Y axis, and which is parallel to the traveling direction of the parallel light flux converted and reflected by the reflective diffractive optical element 10. α, β, γ).

In the first specific example, the reflective diffractive optical element 1 is used.
The refractive index of the incident light side medium in which the point light source s for 0 is located is shown by n. Further, in this example, the point light source s is not limited to the Z axis, and the coordinate position of the point light source is (X, Y,
Z), and the thickness dimension of the diffractive optical element shows a sufficiently small value that can be ignored.

The optical path difference function ρ (x, y) of the reflective diffractive optical element 10 showing the optical characteristics shown in the first specific example is
It is given by the following formula.

Ρ (x, y) = (n / 2) · {(X-
x) ² + (Y-y) ² + Z ² } ¹ /2-(nL / 2)-
(N / 2) · {(αx + βy) / (α ² + β ² + γ ² ).
^1/2 } (5) Here, L is the distance from the point light source to the origin, and is represented by the following equation: L = (X ² + Y ² + Z ² ) ^1/2 (6).

The first and second terms of equation (5) are the point source s
2 in the reflective diffractive optical element 10 in the spherical wave from
Dimensional optical path difference. Further, the third term of Expression (5) represents the optical path difference of the parallel light flux (α, β, γ) in the traveling direction after being reflected by the diffractive optical element 10.

The optical path difference function ρ (x,
For each optical path difference coefficient by Taylor expansion for y), Expression (5) is substituted into Expressions (4-0) to (4-65) of FIGS. 3 to 9 which are obtained in advance, and the respective calculations are executed. It is required. 11 to 16 show the calculation results for each term C _{N in} the form of Expression (7-0) to Expression (7-65).

The optical path difference coefficient C _N shown in the equation (1) of the CAD program is defined by using the respective values of C _{0 to} C ₆₅ shown in the equations (7-0) to (7-65) as the optical path difference coefficients. 10 is executed and the program is executed (even if the term of C ₀ is substituted, since this term is a constant term, it does not substantially affect the change of the lens shape, etc.). Data of the mask pattern having the shown optical characteristics and necessary for forming the reflective diffractive optical element 10 represented by the formula (5) can be obtained.

The lens material is selectively etched by the photolithography method (step S6) using the mask pattern (step S5) generated by the mask pattern data, and then the surface of the lens material is made of, for example, aluminum. A metal material such as is vapor-deposited, thereby forming a reflective film. As a result, FIG.
Finally, the reflective diffractive optical element 10 represented by the formula (5) having the optical characteristics shown in FIG.

This reflective diffractive optical element can be used in combination with a conventional bulk lens. In designing such an optical system, the CAD program can be combined with an optical CAD simulation program called, for example, "CodeV" for reducing and optimizing aberrations and the like. In such a case, it is necessary to appropriately change each of the optical path difference coefficients C _N assigned to the CAD program and execute the calculation for each change.

Next, regarding the first specific example, an error caused by adopting an approximate expression by Taylor expansion will be examined using Expressions (8) and (9) shown in FIG. A diverging spherical wave from a point light source s separated by a distance L from the origin is reflected by the reflection type diffractive optical element 10 having the optical path difference function expressed by the equation (5), so that the diffractive optical element is substantially divided into two. It is transmitted once, and as a result, it is converted into a plane wave represented by the equation (8) parallel to the vector (α, β, γ). On the other hand, in the approximate expression of the Taylor-expanded optical path difference function, the divergent spherical wave is expressed by Expression (9).

As is clear from the comparison of the right sides of both equations (8) and (9), the approximation equation by Taylor expansion substantially includes the aberration of exp {i (2π / λ) Δ}. This aberration corresponds to a higher-order optical path difference coefficient after C _{65, and} since the optical path difference coefficient C ₆₅ is generally on the order of 10 ⁻⁸ , the relative error Δ corresponding to this is also It is in the order of 10 ^-8 . Therefore, by Taylor expansion up to the tenth coefficient,
It can be judged that sufficient accuracy has been obtained.

<Second Specific Example> FIG. 18 is an explanatory diagram showing the optical characteristics of a reflective diffractive optical element 10 according to a second specific example of the present invention. In the second specific example, as in the first specific example shown in FIG. 10, for simplification of description, the reflective diffractive optical element 10 shown as a computer generated hologram according to the present invention passes through the origin. It lies in a plane including the X axis and the Y axis.

The reflective diffractive optical element 10 in the second specific example converts a parallel light flux having a vector component passing through the origin and having an arbitrary deflection angle represented by (α, β, γ) into a spherical wave and reflects the spherical wave. Accordingly, an example of a reflection type diffractive optical element 10 that condenses on condensing point position. The refractive index of the incident light side medium to the reflection type diffractive optical element 10 is indicated by n, and the coordinate position of the image point which is the condensing point is indicated by (X, Y, Z).

The optical path difference function ρ (x, y) of the reflective diffractive optical element 10 showing the optical characteristics shown in the second specific example is given by the following equation.

Ρ (x, y) = (n / 2) · {(X−
x) ² + (Y−y) ² + Z ² } ^1/2 − (nL / 2) +
(N / 2) · {(αx + βy) / (α ² + β ² + γ ² ).
^1/2 } (10) Here, L is the distance from the origin to the image point (focus point) , and is represented by the following equation: L = (X ² + Y ² + Z ² ) ^1/2 (11) Be done.

Expression (10) is replaced by Expression (4-0) to Expression (4-6).
5), the calculation result of each optical path difference coefficient by the same Taylor expansion as described above for the optical path difference function ρ (x, y) obtained by substituting it into Equation (12-0) to FIG. It is shown for each term C _{N in} the form of equation (12-65).

By using the respective values of C _{0 to} C ₆₅ shown in the equations (12-0) to (12-65) as the optical path difference coefficient C _N , the CAD program similar to the above is executed to obtain the equation (1
Data of the mask pattern required for forming the reflective diffractive optical element 10 represented by 0) can be obtained.

Also in the second specific example, regarding the error caused by using the approximate expression by Taylor expansion, the expressions (13) and (1) shown in FIG. 25, which are similar to those shown in FIG. 17, are used.
Consider using 4). The plane wave traveling parallel to the vector (α, β, γ) is reflected by the reflective diffractive optical element 10 having the optical path difference function represented by the equation (10), so that it is substantially transmitted through the diffractive optical element twice. As a result, the light is converted into a plane wave that is condensed at a condensing point d separated by a distance L from the origin as represented by the equation (13). On the other hand, in the approximate expression of the Taylor-expanded optical path difference function, the divergent spherical wave is expressed by Expression (14).

As is clear from the comparison of the right sides of both equations (13) and (14), the approximate equation by Taylor expansion is:
The same value as in the first specific example, exp {i (2π /
λ) Δ} aberration is included. Regarding this aberration,
As described along with the specific example, since the relative error Δ of the optical path difference is about 10 ⁻⁸ , it can be judged that sufficient accuracy is obtained in fact.

<Third Specific Example> FIG. 26 is an explanatory diagram showing optical characteristics of the reflective diffractive optical element 10 according to the third specific example of the present invention. The reflection-type computer generated hologram shown in FIG. 26, that is, the reflection-type diffractive optical element 10 forms an image from the point light source s to the condensing point d and reflects it. For simplification of description, the diffractive optical element 10 is
It is in the plane that passes through the origin and includes the X axis and the Y axis, and the refractive index of the incident light side medium is indicated by n. Further, the coordinate positions of the point light source and the condensing point that is the image point are indicated by (X ₁ , Y ₁ , Z ₁ ) and (X ₂ , Y ₂ , Z ₂ ), respectively.

The optical path difference function ρ (x, y) of the reflection type diffractive optical element 10 showing the optical characteristics shown in the third example is given by the following equation.

Ρ (x, y) = (n / 2) · {(X ₁ -x) ² + (Y ₁ -y) ² + Z ₁ ² } ₁ /2-(nL ^1/2 ) + (n _{/ 2) · {(X 2} -x) 2 + (Y 2 -y) 2 + Z 2 2} 1/2 - (nL 2/2) ... (15) where the distance from the origin to the point light source L ₁ and the distance L ₂ from the origin to the image point are respectively expressed by the following equations. L ₁ = (X ₁ ² + Y ₁ ² + Z ₁ ² ) ^1/2 (16) L ₂ = (X ₂ ² + Y ₂ ² + Z ₂ ² ) ^1/2 (17)

The right side of the equation (15), the first term and the second term, are the two-dimensional optical path differences in the reflective diffractive optical element 10 in the spherical wave from the point light source s spaced by the distance L ₁ from the origin. Represent Further, the right side, the third term, and the fourth term of the equation represent the two-dimensional optical path difference in the reflective diffractive optical element 10 in the spherical wave focused on the image point separated by the distance L ₂ from the origin.

Expression (15) is replaced with Expression (4-0) to Expression (4-6).
5), the calculation result of each optical path difference coefficient by the Taylor expansion similar to the above regarding the optical path difference function ρ (x, y) obtained is substituted into equations (18-0) to (38-0) in FIGS. It is shown for each term C _{N in} the form of equation (18-65).

By using the respective values of C _{0 to} C ₆₅ shown in the equations (18-0) to (18-65) as the optical path difference coefficient C _N , the CAD program similar to the above is executed to obtain the equation (1
Data of the mask pattern necessary for forming the reflective diffractive optical element 10 represented by 5) can be obtained.

Also in the third specific example, an error caused by using an approximate expression by Taylor expansion will be examined.
Equation (19) in FIG. 39 shows that the divergent spherical wave from the point light source (X ₁ , Y ₁ , Z ₁ ) passes through the reflection-type computer generated hologram represented by equation (15) and the image point (X ₂ , Y ₂ , Z 1 ₂ ) Represents a spherical wave focused on. On the other hand, the equation (20) in the figure shows an approximate equation by Taylor expansion of the similar spherical wave of the equation (15).

As is clear from the comparison of the right sides of both equations (19) and (20), the approximate equation by Taylor expansion is
Exp with the same value as in the first and second examples
The aberration of {i (2π / λ) Δ} is included. This aberration is a value that can be substantially ignored, as in the first and second specific examples, and it can be judged that sufficient accuracy is obtained in fact.

<Fourth Concrete Example> The example shown in FIG. 40 is a reflection type diffractive optical element 10 having the optical characteristic of deflecting and reflecting a parallel light beam having an arbitrary deflection angle into a parallel light beam having an arbitrary deflection angle. It is an example and serves the same function as a reflective prism. The incident parallel light flux is parallel to the vector components (α ₁ , β ₁ , γ ₁ ) of the light passing through the origin, and the reflected outgoing parallel light flux is the vector components (α ₂ , β ₂ , γ ₂ ) passing through the origin. Parallel to. The incident light side medium has a refractive index n. The general formula of the optical path difference function ρ (x, y) is

Ρ (x, y) = (n / 2) · (α ₁ x + β ₁ y) / (α ₁ ² + β ₁ ² + γ ₁ ² ) ^1/2 − (n / 2) · ( α ₂ x + β ₂ y) / (α ₂ ² + β ₂ ² + γ ₂ ² ) ^1/2 (21)

Expression (21) is replaced with Expression (4-0) to Expression (4-6).
By substituting into 5), the calculation result of each optical path difference coefficient for the optical path difference function ρ (x, y) can be obtained. For this calculation, since the equation (21) is a linear expression of x and y, the term obtained by the partial differentiation thereof is as shown in FIG.
As shown in Formula (22-0) to Formula (22-2),
It is only the terms C ₀ -C ₂ .

By using the respective values of C _{0 to} C ₂ shown in the equations (22-0) to (22-2) as the optical path difference coefficient C _N , the CAD program similar to that described above is executed to obtain the equation (2
The mask pattern data necessary for forming the reflective diffractive optical element 10 represented by 1) can be obtained.

With respect to the fourth specific example, an error caused by using an approximate expression by Taylor expansion will be examined. Figure 4
The equation (23) of ₂ is a vector (α ₂ , β ₂ ) obtained by converting the incident plane wave parallel to the vector (α ₁ , β ₁ , γ ₁ ) through the reflective diffractive optical element 10 shown by the equation (21). , Γ ₂ ) of the emitted plane wave parallel to. On the other hand, the equation (24) in the figure is
An approximate expression by Taylor expansion of a similar plane wave of Expression (21) is shown.

Unlike the other specific examples, in the fourth specific example, the Taylor expansion has only the linear term as described above, and as is apparent from the fact that the right sides of the equations (23) and (24) are the same. , The effect of aberration due to approximation does not occur at all.

FIG. 43 shows an application example of the reflection type diffractive optical element 10 according to the present invention. In an optical device 11 shown in FIG. 15, IC chips 13 and 14 each having a light emitting element s and a light receiving element d on one surface 12a of a glass substrate 12 are mutually bonded by a flip chip bonding method using a bump 15. Spaced and positioned.

In the IC chip 13 provided with the light emitting element s, the first condenser lens 16 for converting the divergent light from the light emitting element s into a parallel light flux and guiding it into the substrate 12.
a is incorporated. Further, the IC chip 14 provided with the light receiving element d incorporates a second condenser lens 16b for guiding the parallel light flux from the substrate 12 to the light receiving element d.

Further, the substrate 12 defines a zigzag path 17 for guiding the parallel light flux guided into the substrate 12 through the first condenser lens 16a to the second condenser lens 16b. Reflective films 18a and 18b, a pair of deflection lenses 19a and 19b, and a pair of relay lenses 20a and 20b are incorporated.

The pair of deflecting lenses 19a and 19b and the pair of relay lenses 20a and 20b are respectively composed of the reflective diffractive optical element (10) according to the present invention. That is, the deflection lenses 19a and 19b
Is composed of the reflective diffractive optical element 10 having the prism function of the fourth specific example shown in FIG. Further, the relay lenses 20a and 20b are composed of the reflective diffractive optical element (10) having the image forming function of the third specific example shown in FIG.

The light emitted from the light emitting element s of the IC chip 13 and guided into the substrate 12 by the first condenser lens 16a reflects the reflection films 18a and 18b, the pair of deflection lenses 19a and 19b, and the pair of deflection lenses 19a and 19b. Relay lens 20a
And zigzag path 17 defined by 20b,
The light is guided to the second condenser lens 16b, and is transmitted to the light receiving element d of the IC chip 14 via the condenser lens 16b.

The reflection type diffractive optical element has a width dimension P of a mask used for its manufacture as compared with the transmission type diffractive optical element.
With the same size, a large deflection angle can be obtained.
From this, by using as a reflection type lens for defining the zigzag path 17 as shown in FIG.
The total reflection angle at which reflection loss theoretically becomes zero
The zigzag path 17 can be formed between the chips 13 and 14, and the reflection type diffractive optical element is extremely effective for such an optical device 11 for optical wiring.

The present invention can be applied not only to the above-mentioned optical characteristics, but also to other optical characteristic elements, and can also be applied to the manufacture of an optical device in which these optical elements are variously combined.

[0068]

According to the manufacturing method of the present invention, a reflection type diffractive optical element having a desired shape is obtained based on an approximate expression obtained by Taylor expansion of a general expression representing an optical path difference function satisfying predetermined optical characteristics. Since the mask condition for
It is possible to obtain the mask condition extremely promptly without undergoing the trial and error work as in the past and without being strongly influenced by the error. Therefore, according to the present invention, it is possible to efficiently manufacture a reflection-type diffractive optical element with a precision that is high enough to ignore an error due to an approximate expression.

[Brief description of drawings]

FIG. 1 is a manufacturing process diagram of a reflective diffractive optical element according to the present invention.

FIG. 2 is an explanatory diagram of a Taylor expansion type.

FIG. 3 is an explanatory diagram (No. 1) showing an optical path difference coefficient according to a Taylor expansion formula.

FIG. 4 is an explanatory view (No. 2) showing an optical path difference coefficient by Taylor expansion formula.

FIG. 5 is an explanatory diagram (No. 3) showing the optical path difference coefficient by the Taylor expansion formula.

FIG. 6 is an explanatory view (No. 4) showing the optical path difference coefficient according to the Taylor expansion formula.

FIG. 7 is an explanatory view (No. 5) showing the optical path difference coefficient according to the Taylor expansion formula.

FIG. 8 is an explanatory view (No. 6) showing the optical path difference coefficient according to the Taylor expansion formula.

FIG. 9 is an explanatory view (No. 7) showing the optical path difference coefficient according to the Taylor expansion formula.

FIG. 10 is an explanatory diagram showing optical characteristics of the reflective diffractive optical element according to the first example.

FIG. 11 is an explanatory diagram (No. 1) showing the optical path difference coefficient of the first specific example.

FIG. 12 is an explanatory view (No. 2) showing the optical path difference coefficient of the first specific example.

FIG. 13 is an explanatory diagram (No. 3) showing the optical path difference coefficient of the first specific example.

FIG. 14 is an explanatory view (No. 4) showing the optical path difference coefficient of the first specific example.

FIG. 15 is an explanatory view (No. 5) showing the optical path difference coefficient of the first specific example.

FIG. 16 is an explanatory diagram (No. 6) showing the optical path difference coefficient of the first specific example.

FIG. 17 is an explanatory diagram of an error due to Taylor expansion of the first specific example.

FIG. 18 is an explanatory diagram showing optical characteristics of a reflective diffractive optical element according to a second specific example.

FIG. 19 is an explanatory diagram (Part 1) of the optical path difference coefficient according to the second specific example.

FIG. 20 is an explanatory diagram (No. 2) showing the optical path difference coefficient according to the second specific example.

FIG. 21 is an explanatory diagram (part 3) of the optical path difference coefficient according to the second specific example.

FIG. 22 is an explanatory view (No. 4) showing the optical path difference coefficient according to the second specific example.

FIG. 23 is an explanatory view (No. 5) showing the optical path difference coefficient according to the second specific example.

FIG. 24 is an explanatory view (No. 6) showing the optical path difference coefficient according to the second specific example.

FIG. 25 is an explanatory diagram of an error due to Taylor expansion of the second specific example.

FIG. 26 is an explanatory diagram showing optical characteristics of a reflective diffractive optical element according to a third specific example.

FIG. 27 is an explanatory diagram (Part 1) of the optical path difference coefficient according to the third specific example.

FIG. 28 is an explanatory diagram (part 2) of the optical path difference coefficient according to the third specific example.

FIG. 29 is an explanatory diagram (part 3) of the optical path difference coefficient according to the third specific example.

FIG. 30 is an explanatory diagram (Part 4) of the optical path difference coefficient according to the third specific example.

FIG. 31 is an explanatory diagram (5) of the optical path difference coefficient according to the third specific example.

FIG. 32 is an explanatory diagram (Part 6) of the optical path difference coefficient according to the third specific example.

FIG. 33 is an explanatory view (No. 7) showing the optical path difference coefficient according to the third specific example.

FIG. 34 is an explanatory view (No. 8) showing the optical path difference coefficient according to the third specific example.

FIG. 35 is an explanatory diagram (9) of the optical path difference coefficient according to the third specific example.

FIG. 36 is an explanatory view (No. 10) showing the optical path difference coefficient according to the third specific example.

FIG. 37 is an explanatory diagram (Part 11) of the optical path difference coefficient according to the third specific example.

FIG. 38 is an explanatory diagram (Part 12) of the optical path difference coefficient according to the third specific example.

FIG. 39 is an explanatory diagram of an error due to Taylor expansion of the third specific example.

FIG. 40 is an explanatory diagram showing optical characteristics of the reflective diffractive optical element according to the fourth specific example.

FIG. 41 is an explanatory diagram showing optical path difference coefficients according to a fourth specific example.

FIG. 42 is an explanatory diagram of an error due to Taylor expansion of the fourth specific example.

FIG. 43 is a sectional view of an optical device showing an application example of the reflective diffractive optical element according to the present invention.

[Explanation of symbols]

10 Diffractive Optical Element 11 Optical Lens Device ρ (x, y) Optical Path Difference Function C _N Optical Path Difference Coefficient

Claims (4)

(57) [Claims] 1. A reflection-type diffractive optical element having a shape specified by the optical path difference function is obtained by giving each coefficient of the polynomial expression in the optical path difference function expressed by the polynomial expression that indicates a desired optical characteristic of the reflection-type diffractive optical element. A method for manufacturing a reflective diffractive optical element, including the step of determining a mask condition by executing a computer program for determining a mask condition necessary for forming an optical element by a photolithography method, wherein the optical characteristic is a point. A flat light source with an arbitrary deflection angle
Refraction of the rays that are converted into the line bundle and reflected
Optical characteristics in the incident light side medium having a ratio n,
The coordinate position of (X, Y, Z) is orthogonal to the X and Y axes.
The distance from the origin on the Z axis to the light source is L, the converted parallel
The vector component of the light passing through the origin parallel to the light flux is (α, β,
γ) respectively, the optical path difference function ρ (x, y)
Of general formula, ρ (x, y) = (n / 2) · {(X-x) 2+ (Y-
y) 2 + Z2} 1 / 2- (nL / 2)-(n / 2) ・
Be determined as {(αx + βy) / ( α2 + β2 + γ2) 1/2}, a general formula of the optical path difference function obtained by Taylor expansion,
Obtaining the approximation formula, the coefficient of each term of the approximation formula obtained by Taylor expansion is
Each coefficient of the polynomial given to the computer program
Enter into the computer program as
Gram is used to determine the mask conditions, a mask with the required conditions is manufactured, and the lens material is selectively etched by the photolithography method using the mask. A method of manufacturing a reflective diffractive optical element, which comprises forming a reflective film. 2. A reflection-type diffractive optical element having a shape specified by the optical path difference function is provided by giving each coefficient of the polynomial expression in the optical path difference function expressed by the polynomial expression that indicates a desired optical characteristic of the reflection-type diffractive optical element. A method for manufacturing a reflective diffractive optical element, including the step of determining a mask condition by executing a computer program for determining a mask condition necessary for forming an optical element by a photolithography method, wherein the optical characteristic is arbitrary. Is the optical characteristic of the incident light side medium having the refractive index n for the light rays that are focused and reflected by the parallel light beam having the deflection angle of, and the image point position is (X, Y, Z), X When the distance from the origin on the Z axis orthogonal to the axis and the Y axis to the condensing point is L, and the vector component of light passing through the origin parallel to the incident parallel light flux is (α, β, γ), the optical path difference is Seki The general formula of the number ρ (x, y) is expressed as ρ (x, y) = (n / 2) · {(X−x) ² + (Y−
y) ² + Z ² } ^1/2 − (nL / 2) + (n / 2) ·
{(Αx + βy) / (α ² + β ² + γ ² ) ^1/2 }, Taylor expansion of the obtained general formula of the optical path difference function,
Obtaining the approximate expression, inputting the coefficient of each term of the approximate expression obtained by Taylor expansion as each coefficient of the polynomial to be given to the computer program, and obtaining the mask condition by executing the program. That is, the method includes producing a mask under the required conditions, performing a selective etching process on the lens material by a photolithography method using the mask, and then forming a reflective film on the surface of the lens material. Manufacturing method of reflective diffractive optical element. 3. A reflection type diffractive optical element having a shape specified by the optical path difference function by giving each coefficient of the polynomial expression in the optical path difference function expressed by a polynomial expression showing a desired optical characteristic of the reflection type diffractive optical element. A method for manufacturing a reflection-type diffractive optical element, which includes a step of determining a mask condition by executing a computer program for determining a mask condition necessary for forming an optical element by a photolithography method, wherein the optical characteristic is an object. It is an optical characteristic of an incident light side medium having a refractive index n with respect to an image formed from a point to an image point and a reflected ray, and the coordinate position of the point light source is (X ₁ , Y ₁ ,
Z ₁ ), the distance from the origin to the point light source is L ₁ , the image point position is (X ₂ , Y ₂ , Z ₂ ), and the distance from the origin to the image point is L ₂ , respectively, the optical path difference function ρ The general formula of (x, y) is expressed by ρ (x, y) = (n / 2) · {(X ₁ −x) ² + (Y ₁
-Y) ² + Z ₁ ² } ₁ /2-(nL ^1/2 ) + (n /
2) · {(X ₂ −x) ² + (Y ₂ −y) ² + Z ₂ ² }
^1/2 - _(nL 2/2) be found as a general formula of the optical path difference function obtained by Taylor expansion,
Obtaining the approximate expression, inputting the coefficient of each term of the approximate expression obtained by Taylor expansion as each coefficient of the polynomial to be given to the computer program, and obtaining the mask condition by executing the program. That is, the method includes producing a mask under the required conditions, performing a selective etching process on the lens material by a photolithography method using the mask, and then forming a reflective film on the surface of the lens material. Manufacturing method of reflective diffractive optical element. 4. A reflection type diffractive optical element having a shape specified by the optical path difference function by giving each coefficient of the polynomial expression in the optical path difference function expressed by a polynomial expression showing a desired optical characteristic of the reflection type diffractive optical element. A method for manufacturing a reflective diffractive optical element, including the step of determining a mask condition by executing a computer program for determining a mask condition necessary for forming an optical element by a photolithography method, wherein the optical characteristic is arbitrary. Is the optical characteristic of the incident light side medium having the refractive index n for the light beam that is deflected and reflected by the parallel light flux having the deflection angle of The vector component of the light passing through is (α ₁ , β ₁ , γ ₁ ), and the vector component of the light passing through the origin parallel to the output parallel light flux is (α ₂ , β ₂ , γ ₂ ).
, Respectively, the general formula of the optical path difference function ρ (x, y) is expressed by ρ (x, y) = (n / 2) · (α ₁ x + β ₁ y) / (α
₁ ² + β ₁ ² + γ ₁ ² ) ^1/2 − (n / 2) · (α ₂ x
+ Β ₂ y) / (α ₂ ² + β ₂ ² + γ ₂ ² ) ^1/2 , the Taylor expansion of the obtained general formula of the optical path difference function,
Obtaining the approximate expression, inputting the coefficient of each term of the approximate expression obtained by Taylor expansion as each coefficient of the polynomial to be given to the computer program, and obtaining the mask condition by executing the program. That is, the method includes producing a mask under the required conditions, performing a selective etching process on the lens material by a photolithography method using the mask, and then forming a reflective film on the surface of the lens material. Manufacturing method of reflective diffractive optical element.