JP4300101B2 - Optical element design method and apparatus - Google Patents

Description

  The present invention relates to an optical element design technique.

  Conventionally, when designing an optical element (for example, a lens) using laser light as an incident light source, a design method based on geometric optics (ray tracing) has been used. However, especially when the divergence angle is large, such as semiconductor laser light, in the design method based on geometric optics, only paraxial light is used in the design, so it is difficult to increase the light utilization efficiency. In addition, accurate design is difficult.

  On the other hand, the design method based on diffractive optics is designed based on a more precise expression of the propagation of laser light (an expression that gives the amplitude and phase distribution of light at an arbitrary point) and can be used. Since there is no restriction as described above for the light range, high utilization efficiency can be realized. In addition, more accurate design can be performed.

  In addition, by designing optical elements using holograms, design based on geometric optics, such as a single element that has multiple functions such as branching and condensing, and that functions for each of different incident wavelengths Optical elements that are impossible with this method can be designed.

For example, Joergen Bengtsson: Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method, Appl.Opt., 36-32, pp. 8435-8444 (1997). ) And Joergen Bengtsson; Kinoform designed to produce different fan-out patterns for two wavelengths, Appl. Opt., 37-1, p.2011-2020 (1998), called the Optimal Rotation Angle method (hereinafter referred to as the ORA method) A technique is disclosed. The ORA method is a phase modulation type CGH design method that designates the positions of a plurality of spots, calculates and outputs a computer generated hologram (CGH: Computer Generated Hologram) that generates light intensity that is approximately equal to the spot positions and that is as strong as possible. .
Joergen Bengtsson: Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method, Appl.Opt., 36-32, pp.8435-8444 (1997) Joergen Bengtsson; Kinoform designed to produce different fan-out patterns for two wavelengths, Appl.Opt., 37-1, p.2011-2020 (1998) Special Table 2002-526815 JP 2003-6181 A JP 2001-242414 A JP 9-512959 A

  However, in the above paper, only a plane wave and a simple spherical wave are assumed as the incident wave, and how to deal with an arbitrary incident wave such as a semiconductor laser beam having astigmatism is completely different. There is no disclosure or suggestion.

  Accordingly, an object of the present invention is to provide a technique for enabling the ORA method to cope with an arbitrary incident wave.

  An optical element design method according to a first aspect of the present invention is a method of designing an optical element for condensing incident light at a predetermined position, and the incident light at a plurality of positions defined by the optical element. Calculating the absolute value of the complex amplitude, calculating the partial differential value of the declination of the complex amplitude of the incident light at a plurality of positions defined by the optical element as a wave vector of the complex amplitude of the incident light, and optical It is specified in the optical element by using the absolute value of the complex amplitude of the incident light at a plurality of positions specified in the element, the wave vector of the complex amplitude of the incident light, and data on a predetermined position where the incident light is collected. Calculating phase modulation amounts at the plurality of positions.

  As will be described in detail below in the ORA method, the absolute value and wave number vector of the complex amplitude of the incident light at the pixels (small regions) at a plurality of positions defined by the optical element are required. In general, the wave number vector of arbitrary incident light cannot be easily obtained. However, from the novel and non-obvious finding by the inventor of the present invention that incident light can approximate a plane wave in a pixel that is a minute region. Thus, it was found that the wave vector can be obtained from the partial differential value of the deviation angle of the complex amplitude of the incident light. As a result, the ORA method can be adapted to any incident light.

により算出される。なお、本式はビームの径が波長に比べて十分大きいという前提条件の下に得られる。 Note that incident light beam diameter w _x in the x-axis direction at a wavelength lambda, when the beam diameter in the y-axis direction is a Gaussian beam of w _y, wave vector of the complex amplitudes of the incident light,

Is calculated by This equation is obtained under the precondition that the beam diameter is sufficiently larger than the wavelength.

  In the first aspect of the present invention, the phase modulation amount at the plurality of positions defined in the optical element and the refractive index of the material of the optical element are used, and the plurality of positions defined in the optical element are used. You may make it further include the step which calculates thickness. More specifically, the optical element can be designed.

  An optical element design method according to a second aspect of the present invention is a method of designing an optical element for condensing incident light at a predetermined position, and includes a plurality of predetermined positions and a plurality of optical elements defined by the optical element. Calculating a propagation coefficient of a diffracted wave obtained from a superimposed representation of a plurality of plane waves of incident light for each set of positions, and a phase modulation amount at a plurality of positions defined by the optical element; The phase modulation amounts at a plurality of positions defined in the optical element are set so that the complex amplitude of the diffracted wave at the predetermined position calculated from (2) or a value calculated from the complex amplitude satisfies a preset condition. Adjusting.

  As described above, the ORA method is considered only for application to plane waves or simple spherical waves, and is not considered for arbitrary incident light. According to the novel and non-obvious knowledge by the inventors of the present invention, if the incident light can be expressed as a superposition of a plurality of plane waves, the ORA method based on plane waves can be extended. At that time, if the processing as described above is performed, the phase modulation amount can be accurately calculated.

（但し、ｋ²−ｋ_x ²−ｋ_y ²＜０の場合、Ｆ（ｋ_x，ｋ_y）＝０）
により算出される。 The beam diameter in the x-axis direction in the incident light wavelength λ is w _x, a Gaussian beam having a beam diameter in the y-axis direction is w _y, a predetermined position _{(x m, y m, z} m), a plurality of positions defined in the optical element (x _c, y _c, 0), the number of samples n _x in the x-axis direction, the number of samples in the y-axis direction is n _y, z ₀ is the beam waist And the pixel size at a plurality of positions defined in the optical element is a × b, the propagation coefficient of the diffracted wave is

(However, in the case of _{^{k 2 -k x 2 -k y 2}} <0, F (k x, k y) = 0)
Is calculated by

  Further, in the second aspect of the present invention, the thicknesses at the plurality of positions defined by the optical element are calculated using the phase modulation amounts at the plurality of positions defined by the optical element and the refractive index of the material of the optical element. A step of calculating may be further included.

  Note that a program for causing a computer to execute the optical element design method according to the present invention can be created. This program can be a storage medium such as a flexible disk, a CD-ROM, a magneto-optical disk, a semiconductor memory, a hard disk, or the like. It is stored in a storage device. Moreover, it may be distributed as a digital signal via a network or the like. The intermediate processing result is temporarily stored in a storage device such as a memory.

  According to the present invention, the ORA method can be applied to any incident wave.

[First Embodiment]
1. FIG. 1 shows an optical system as a premise of the principle in the first embodiment. In FIG. 1, the CGH 3 is disposed at a position d ₁ away from the laser light source LD1 (beam waist), and the plane 5 including the focused spot is disposed at a position away from the CGH 3 by a distance d ₂ . This CGH3 is assumed to be parallel to the xy plane and disposed at a position of z = 0. Further, as shown in FIG. 2, the CGH 3 is divided into a plurality of pixels, and has a vertical size b and a horizontal size a of each pixel. The center coordinates of the pixel c are (x _c , y _c , 0). Also, the focused spot m, in the coordinate system (x _m, y _m, Z _m) has become.

In the conventional ORA method, a plane wave is assumed as incident light. The plane wave is expressed by the following formula, for example.
A · exp (−jk (X−X ₀ )) (1)
Incidentally, A is the amplitude, k is the wave number vector, X is an arbitrary position on CGH3, X ₀ represents a predetermined position on CGH3.

  On the other hand, if the ORA method is applied to arbitrary incident light, it is necessary to calculate the amplitude of the incident light and the wave number vector of the incident light. However, since arbitrary incident light does not have the form as shown in the equation (1), how to obtain the amplitude and the wave vector becomes a problem.

Here, the inventor of the present invention has arrived at a novel and non-obvious knowledge that arbitrary incident light can be approximated to a plane wave as expressed by the equation (1) in the vicinity of the center of the pixel in CGH3. In this case, if the incident light is ψ (X) in the vicinity of the center of the pixel, ψ (X) = A _c · exp (−jk _c (X−X _c )) can be set. Here, A _c is the amplitude at pixel c, k _c is the wave vector at pixel c, and X _c is the coordinate value of pixel c. Therefore, the amplitudes A _c = | ψ (X _c ) | and k _c = −∇∠ψ (X _c ). Note that ∠ represents a complex argument. Λ is the wavelength of incident light.

For example, consider the case of an elliptical cows beam in which the beam diameter (size at the beam waist) is w _{x in} the x-axis direction and w _{y in the} y-axis direction.

The complex amplitude distribution of light of wavelength λ that normally propagates in a three-dimensional free space is expressed as follows. Note that x (bold character) is a position expressed in an xyz orthogonal coordinate system (x, y, z).

Using a spatial spectrum (equation (3)) obtained by two-dimensional Fourier transform of u (x) in equation (2) with respect to the xy plane, equation (4) can be obtained.

By substituting equation (4) into equation (2), equation (5) can be obtained.

A wave traveling in the positive direction of the z-axis in equation (5) is given by equation (6).

ここで、ａ_x＝１／ｗ_x、ａ_y＝１／ｗ_yである。 Here, g (α, β) is an arbitrary function and is determined to give an initial condition of the amplitude distribution. As an initial condition, consider a case where the amplitude distribution u (x, y, −z ₀ ) at z = −z ₀ is given by a Gaussian distribution (equation (7)).

Here, a _x = 1 / w _x and a _y = 1 / w _y .

g (α, β) is given by Equation (8) using Equation (7) by substituting z = −z ₀ into Equation (6).

Substituting Equations (6) and (8) into Equation (4) yields Equation (9).

In order to calculate the complex amplitude of the incident light on the CGH, it is necessary to perform integration of equation (9). However, assuming that the approximation as in equation (10), that is, that the beam diameter is sufficiently larger than the wavelength, equation (11) is established and equation (12) is obtained by further solving the integral in equation (9). .

なお、ｗ_x＝ｗ_yであれば、ビーム形状が円形の場合を表す。（１２）式により表される入射光の複素振幅から、振幅、偏角及び波数ベクトル（＝偏角の偏微分値）を求めることができる。 The following formulas (13) to (15) are used.

If w _x = w _y , the beam shape is circular. From the complex amplitude of the incident light expressed by the equation (12), the amplitude, the declination, and the wave number vector (= the partial differential value of the declination) can be obtained.

なお、以下の（１９）式を用いる。

The following equation (19) is used.

2. Embodiment Hereinafter, a configuration when the principle in the first embodiment described above is implemented by a computer system will be described. FIG. 3 shows a functional block diagram of the computer system. The computer system prompts the user to input design parameters necessary for executing the ORA method in the present embodiment, receives an input of design parameters from the user, or reads a file storing the parameters, etc. 10, a design parameter storage unit 12 that stores data acquired by the input unit 10, a pixel center coordinate calculation unit 14 that reads out data stored in the design parameter storage unit 12 and calculates pixel center coordinates, and pixel center coordinate calculation Using the pixel center coordinate data storage unit 16 that stores the data of the pixel center coordinates calculated by the unit 14 and the data stored in the design parameter storage unit 12 and the pixel center coordinate data storage unit 16, for example, Amplitude and wave number vector are calculated according to equation (18) A wave vector calculation unit 18; an amplitude and wave vector storage unit 20 that stores amplitude and wave vector data calculated by the amplitude and wave vector calculation unit 18; a design parameter storage unit 12; a pixel center coordinate data storage unit 16; A propagation coefficient related data calculation unit 22 that calculates a propagation coefficient and related data using the data stored in the amplitude and wave vector storage unit 18, and a propagation that stores the data calculated by the propagation coefficient related data calculation unit 22 Calculated by the coefficient-related data storage unit 24, the ORA processing unit 26 that performs the process of the ORA method using the data stored in the design parameter storage unit 12 and the propagation coefficient-related data storage unit 24, and the ORA processing unit 26 Phase modulation amount storage for storing phase modulation amount data for all pixels of CGH3 28 and the relief shape for calculating the thickness (or height) of each pixel of the optical element to be created as the relief shape using the phase modulation amount data stored in the design parameter storage unit 12 and the phase modulation amount storage unit 28 The determination unit 30 includes a relief data storage unit 32 that stores data calculated by the relief shape determination unit 30. Furthermore, an output unit that reads data from the relief data storage unit 32 and outputs the data to an output device such as a display device, or an automatic creation device that automatically creates an optical element according to the relief data storage unit 32 may be further included.

  As shown in FIG. 4, the ORA processing unit 26 performs initialization processing of weight data and phase modulation amount data using data stored in the design parameter storage unit 12; A weight data storage unit 265 that stores weight data that is initialized and sequentially updated by the initialization processing unit 261, and a phase modulation amount storage unit 28 that stores the phase modulation amount that is initialized and sequentially updated by the initialization processing unit 261. The complex amplitude calculation unit 267 that calculates the complex amplitude or the like with reference to the propagation coefficient related data storage unit 24 and the phase modulation amount storage unit 28, and the complex amplitude calculation unit 267 stores the data such as the complex amplitude calculated. A convergence determination unit 271 that performs convergence determination with reference to the complex amplitude data storage unit 269, the complex amplitude data storage unit 269, and the propagation coefficient related data storage unit 24, and the convergence determination unit 2 The weight update processing unit updates the weight data stored in the weight data storage unit 265 using the data stored in the complex amplitude data storage unit 269 and the design parameter storage unit 12 in accordance with the determination result of the convergence determination unit 271 by 1. 273 and phase modulation for updating the phase modulation amount stored in the phase modulation amount storage unit 28 using the updated weight data and data stored in the complex amplitude data storage unit 269 and the propagation coefficient related data storage unit 24 A quantity update processing unit 275.

The processing flow of the computer system shown in FIGS. 3 and 4 will be described with reference to FIG. First, the input unit 10 prompts the user to input design parameters necessary for executing the ORA method, and receives input of design parameters from the user. Or, a file storing the design parameters is read. And the acquired design parameter is stored in the design parameter storage part 12 (FIG. 5: step S1). Design parameters include incident light wavelength λ, CGH x-axis pixel size a, CGH y-axis pixel size b, CGH x-axis pixel number Na, CGH y-axis pixel number Nb, The number M of the condensing spots, the coordinates (x _m , y _m , z _m ) of the condensing spot m (m is an integer from 1 to M), the desired light intensity I _m ^desired , and the light intensity at the condensing spot m , The refractive index n of the optical element substrate for realizing CGH3, the wave number k (= 2π / λ), and the total number of pixels N (= Na × Nb). Note that the wave number k and the total number N of pixels may be calculated.

  Next, the pixel center coordinate calculation unit 14 uses the pixel sizes a and b stored in the design parameter storage unit 12 to calculate the center coordinates of each pixel c (c is an integer from 1 to N) in the CGH 3. Then, it is stored in the pixel center coordinate data storage unit 16 (step S3). The center coordinates of each pixel c are (a / 2, b / 2, 0), (a / 2, -b / 2, 0), for example, when the z-axis is provided at the center of CGH3. , (−a / 2, b / 2, 0), (−a / 2, −b / 2, 0) to values obtained by changing an integer multiple of ± a for the x coordinate and an integer multiple of ± b for the y coordinate Have

Then, the amplitude and wave number vector calculation unit 18 uses the pixel center coordinate data of each pixel c stored in the pixel center coordinate data storage unit 16 to calculate the amplitude A _c and the wave vector k _c in the complex amplitude of the incident light. Calculated and stored in the amplitude and wave vector storage unit 20 (step S5). As described above, in the present embodiment, if the incident light is ψ (x), the amplitude A _c = | ψ (x _c ) |, k _c using the coordinate value x _c of each pixel _c. = −∇∠ψ (x _c ) ∠ represents the argument of a complex number. In addition, data stored in the design parameter storage unit 12 is used as necessary. In the case of a Gaussian beam whose beam shape is an ellipse, the amplitude and wave number vector are calculated for each pixel according to equations (16) and (18), and stored in the amplitude and wave vector storage unit 20. The first embodiment is most different from the prior art in the method of calculating the amplitude and wave number vector in the complex amplitude of the incident light.

なお、sincθ＝sinθ／θである。 Next, the propagation coefficient related data calculation unit 22 uses the data stored in the amplitude and wave vector storage unit 20, the pixel coordinate data storage unit 16, and the design parameter storage unit 12 for each focused spot m. Umc is calculated by equation (20), and the absolute value | Umc | and declination ∠Umc of the propagation coefficient Umc are calculated and stored in the propagation coefficient related data storage unit 24 (step S7). The equation (20) used in this step is as follows according to the conventional ORA method.

Note that sincθ = sinθ / θ.

  Thus, in this step, the propagation coefficient Umc and the like are calculated by the number of combinations of the focused spot m and the pixel c of CGH3.

The initialization processing unit 261 of the ORA processing unit 26 refers to the data stored in the design parameter storage unit 12 and sets the phase modulation amount φ _c for each pixel c of the CGH 3 to a value from 0 to 2π. Initialized with a random number, and further initialized with a weight w _m = I _m ^desired for each ^focused spot m, the phase modulation amount φ _c is stored in the phase modulation amount storage unit 28, and the weight w _m is stored in the weight data storage unit It stores in H.265 (step S9).

すなわち、全ピクセルの影響を集光スポットにつき重ね合わせる。 The complex amplitude calculation unit 267 of the URA processing unit 26 is realized based on CGH3 for each focused spot m using the data stored in the design parameter storage unit 12 and the phase modulation amount storage unit 28 according to the equation (24). that the complex amplitude Um diffracted wave by optical elements, and the light intensity I _m = can be determined from the complex amplitude Um | Um | calculates the argument ∠Um ² sequence complex amplitude Um, stored in the complex amplitude data storing unit 269 (Step S11).

That is, the influence of all pixels is superimposed on the focused spot.

When the processing is performed so far, the convergence determination unit 271 of the ORA processing unit 26 refers to the design parameter storage unit 12 and determines whether | I _m −I _m ^desired | <ε holds for all the ^focused spots m. (Step S13). If it is determined that the above condition is satisfied for all the condensed spots m, the process proceeds to step S19.

On the other hand, when it is determined that the above condition is not satisfied for any of the focused spots m, the weight update processing unit 273 of the ORA processing unit 26 sets the design parameter storage unit 12 and the complex amplitude data storage unit 269. The weight w _m for each focused spot m stored in the weight data storage unit 265 is updated and registered according to the equation (25) (step S15).

そしてステップＳ１１に戻る。 Further, the phase modulation amount update processing unit 275 of the ORA processing unit 26 uses the data stored in the weight data storage unit 265, the complex amplitude data storage unit 269, and the propagation coefficient related data storage unit 24, and uses the phase modulation amount storage unit The phase modulation amount is updated and registered for each pixel c stored in 28 according to the equations (26) to (29) (step S17).

Then, the process returns to step S11.

図６を用いてレリーフの説明をしておく。図６の例では、左から波長λの入射光が屈折率ｎの光学素子基板に入射される場合において、計算された位相変調量φ_cを用いて（３０）式によって、光学素子基板における凹凸の高さｈが決定される。 If it is determined in step S13 that the convergence condition is satisfied, the relief shape determination unit 30 is based on the phase modulation amount φ _c in each pixel c stored in the phase modulation amount storage unit 28. The height (thickness) h of the relief in the CGH 3 is calculated according to the equation (30) and stored in the relief data storage unit 32 (step S19).

The relief will be described with reference to FIG. In the example of FIG. 6, when incident light having a wavelength λ from the left is incident on an optical element substrate having a refractive index n, the unevenness on the optical element substrate is calculated by the equation (30) using the calculated phase modulation amount φ _c. The height h is determined.

For example, in FIG. 1, d ₁ = 1 mm, d ₂ = 30 mm, the pixel size of CGH 3 is 1 μm ² , the number of pixels is 250 ² , and the phase modulation amount is a continuous value in the range of 0 to 2π. Further, it is assumed that the wavelength λ of incident light is 650 nm, and the spot size at the light source is w _x = 4.6λ and w _y = 1.3λ. As shown in FIG. 7A, CGH3 is 0.25 mm in length and width from the number of pixels and the pixel size. Further, as shown in FIG. 7B, a condensing spot is arranged at the apex of a square of 0.4 mm square across the x axis and the y axis on the condensing surface xy. If it does so, CGH3 as shown to Fig.8 (a) can be obtained. In FIG. 8A, a bright part has a large phase modulation amount φ _c and a dark part has a small phase modulation amount φ _c . Such CGH3 is calculated by the processing as described above. On the other hand, on the condensing surface, a light intensity distribution as shown in FIG. 8B is calculated. For this light intensity distribution, separately from the processing described above, the light intensity on the condensing surface is calculated for each predetermined minute region based on the phase modulation amount φ _c .

  Although the first embodiment has been described above, the functional block diagram of FIG. 3 is shown for explaining the configuration of the computer system in the present embodiment, and is not necessarily a module such as a subroutine in the computer program. It does not correspond to. Further, it is necessary to determine in advance the expression such as the complex amplitude of the incident light.

[Second Embodiment]
1. Principle in the second embodiment In the first embodiment, the application range of the ORA method is expanded from the viewpoint that an arbitrary incident wave can approximate a plane wave in a minute region of the CGH3. However, this approximation may not always be appropriate.

  The second embodiment is a novel and non-obvious finding by the inventor of the present invention that if the arbitrary incident light can be expressed as a superposition of plane waves, the ORA method can be extended in an accurate form. based on.

  More specifically, consider the case of an elliptical Gaussian beam. In the first embodiment, a case has been described in which an approximation like the equation (10) is established in the equation (9). Here, equation (9) is replaced with an equation represented by superposition of plane waves, diffracted waves when the respective plane waves are incident on CGH 3 are combined to calculate the diffracted light of the Gaussian beam, and the ORA method is applied to obtain CGH 3 A case of creating a file will be described.

Expression (9) can be rewritten into a three-dimensional Fourier transform form like Expressions (31) and (32) by using Dirac's delta function δ.

Here, the vector k = (k _x , k _y , k _z ) is a wave vector. Further, dk _x dky _y dk _z is indicated as d ³ k. Expression (31) indicates that the incident light u (x) can be expressed by superposition of plane waves having an amplitude A (k) and a wave vector k. The center coordinates of CGH3 pixels placed between x _c, which allows the following such expressions to think about the.

Substituting equation (33) into equation (31) yields the following equation (34).

そして、これをＣＧＨ全体について重ね合わせることにより（３６）式に示すような回折波ｕ（ｘ_m）を求めている。

In the ORA method, the complex amplitude u _c (x _m ) of the diffracted light at the position x _m when the plane wave exp {jk · (x−x _c )} is incident on the pixel c having the center coordinate x _c and the size a × b. Is calculated by the following equation.

Then, the diffracted wave u (x _m ) as shown in the equation (36) is obtained by superimposing the entire CGH.

When exp {jk · (x−x _c )} in the equation (34) is replaced with the right side of the equation (35) and substituted into the equation (32), the diffracted light when the Gaussian beam is incident is expressed by the following equation (37): Given in.

但し、関数Ｆ（ｋ_x，ｋ_y）は、ｋ²−ｋ_x ²−ｋ_y ²＜０の場合はＦ（ｋ_x，ｋ_y）＝０となる。 _{Here, k z = (k-k} x 2 -k y 2) ^1/2. Integration range k _z is a real number, i.e., performed at ^{_{k x 2 + k y 2 ≦}} k 2 ranges C. A function F (k _x , k _y ) for calculating the above integral numerically is defined as the following equation (38).

However, the function F (k _x, k _y), if the ^{_{k 2 -k x 2 -k y 2}} <0 becomes _{F (k x, k y)} = 0.

Then, equation (37) can be rewritten as follows.

ｎ_x及びｎ_yについては、ｋ_x及びｋ_yのサンプリング回数を示している。このサンプリング回数を十分大きな値にすれば、積分値により近づく。 The integral of this equation is discretized and approximated by a finite sum as follows.

The n _x and n _y, shows a sampling frequency of k _x and k _y. If this number of times of sampling is set to a sufficiently large value, it will be closer to the integrated value.

  This equation (43) is used instead of the equation (20) in the first embodiment. In other words, in this embodiment, since a diffracted wave is derived after expressing an arbitrary incident wave as a superposition of plane waves, the wave number vector and amplitude of the incident wave are separately calculated as in the first embodiment. do not have to.

2. Embodiment Hereinafter, a configuration when the principle of the second embodiment described above is implemented by a computer system will be described. Note that the computer system according to the second embodiment has a form in which the amplitude and wave number vector calculation unit 18 and the amplitude and wave number vector storage unit 20 are removed from the functional block diagram shown in FIG. Therefore, step S5 is skipped also in the processing flow shown in FIG.

  The details of the processing in the present embodiment will be described below in accordance with the processing flow of FIG. 5 after correction as described above.

First, the input unit 10 prompts the user to input design parameters necessary for executing the ORA method, and receives input of design parameters from the user. Or, a file storing the design parameters is read. And the acquired design parameter is stored in the design parameter storage part 12 (step S1). Design parameters include incident light wavelength λ, CGH x-axis pixel size a, CGH y-axis pixel size b, CGH x-axis pixel number Na, CGH y-axis pixel number Nb, The number M of the condensing spots, the coordinates (x _m , y _m , z _m ) of the condensing spot m (m is an integer from 1 to M), the desired light intensity I _m ^desired , and the light intensity at the condensing spot m , The refractive index n of the optical element substrate for realizing CGH3, the wave number k (= 2π / λ), and the total number of pixels N (= Na × Nb). Note that the wave number k and the total number N of pixels may be calculated.

  Next, the pixel center coordinate calculation unit 14 uses the pixel sizes a and b stored in the design parameter storage unit 12 to calculate the center coordinates of each pixel c (c is an integer from 1 to N) in the CGH 3. Then, it is stored in the pixel center coordinate data storage unit 16 (step S3). The center coordinates of each pixel c are (a / 2, b / 2, 0), (a / 2, -b / 2, 0), for example, when the z-axis is provided at the center of CGH3. , (−a / 2, b / 2, 0), (−a / 2, −b / 2, 0) to values obtained by changing an integer multiple of ± a for the x coordinate and an integer multiple of ± b for the y coordinate Have

なお（３８）乃至（４１）を用いる。
本ステップでは、集光スポットｍとＣＧＨ３のピクセルｃとの組み合わせの個数だけ伝搬係数Ｕmc等が算出される。 Step S5 is skipped, and then the propagation coefficient related data calculation unit 22 uses the data stored in the amplitude and wave vector storage unit 20, the pixel coordinate data storage unit 16 and the design parameter storage unit 12 to perform each collection. For the light spot m, the propagation coefficient Umc is calculated by the equation (44), and the absolute value | Umc | and declination ∠Umc of the propagation coefficient Umc are calculated and stored in the propagation coefficient related data storage unit 24 (step S7). .

Note that (38) to (41) are used.
In this step, propagation coefficients Umc and the like are calculated for the number of combinations of the focused spot m and the pixel c of CGH3.

The initialization processing unit 261 of the ORA processing unit 26 refers to the data stored in the design parameter storage unit 12 and sets the phase modulation amount φ _c for each pixel c of the CGH 3 to a value from 0 to 2π. Initialized with a random number, and further initialized with a weight w _m = I _m ^desired for each ^focused spot m, the phase modulation amount φ _c is stored in the phase modulation amount storage unit 28, and the weight w _m is stored in the weight data storage unit It stores in H.265 (step S9).

The complex amplitude calculation unit 267 of the URA processing unit 26 is realized based on CGH3 for each focused spot m using the data stored in the design parameter storage unit 12 and the phase modulation amount storage unit 28 according to the equation (24). that the complex amplitude Um diffracted wave by optical elements, and the light intensity I _m = can be determined from the complex amplitude Um | Um | calculates the argument ∠Um ² sequence complex amplitude Um, stored in the complex amplitude data storing unit 269 (Step S11). In this way, the influence of all pixels is superimposed on the focused spot.

When the processing is performed so far, the convergence determination unit 271 of the ORA processing unit 26 refers to the design parameter storage unit 12 and determines whether | I _m −I _m ^desired | <ε holds for all the ^focused spots m. (Step S13). If it is determined that the above condition is satisfied for all the condensed spots m, the process proceeds to step S19.

On the other hand, when it is determined that the above condition is not satisfied for any of the focused spots m, the weight update processing unit 273 of the ORA processing unit 26 sets the design parameter storage unit 12 and the complex amplitude data storage unit 269. The weight w _m for each focused spot m stored in the weight data storage unit 265 is updated and registered according to the equation (25) (step S15).

  Further, the phase modulation amount update processing unit 275 of the ORA processing unit 26 uses the data stored in the weight data storage unit 265, the complex amplitude data storage unit 269, and the propagation coefficient related data storage unit 24, and uses the phase modulation amount storage unit For each pixel c stored in 28, the phase modulation amount is updated and registered according to equations (26) to (29) (step S17). Then, the process returns to step S11.

If it is determined in step S13 that the convergence condition is satisfied, the relief shape determination unit 30 is based on the phase modulation amount φ _c in each pixel c stored in the phase modulation amount storage unit 28. The height (thickness) h of the relief in the CGH 3 is calculated according to the equation (30) and stored in the relief data storage unit 32 (step S19).

  Although the processing according to the second embodiment has been described above, as described in the principle section, arbitrary incident light is expressed as a superposition of plane waves, and the expression of the diffracted wave is derived. It is necessary to carry out the process.

It is a schematic diagram of the optical system in this invention. It is a schematic diagram of CGH in the present invention. It is a functional block diagram of the computer system in the 1st and 2nd embodiment of this invention. It is a functional block of the ORA processing part in the 1st and 2nd embodiment of the present invention. An example of the processing flow in the 1st and 2nd embodiment of this invention is shown. It is a schematic diagram of a relief shape. (A) is size of CGH, (b) is a figure which shows positions, such as a condensing spot. (A) is an example of CGH, (b) is a figure which shows an example of a condensing state.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Input part 12 Design parameter storage part 14 Pixel center coordinate calculation part 16 Pixel center coordinate data storage part 18 Amplitude and wave number vector calculation part 20 Amplitude and wave number vector storage part 22 Propagation coefficient related data calculation part 24 Propagation coefficient related data storage part 26 ORA processing unit 28 phase modulation amount storage unit 30 relief shape determination unit 32 relief data storage unit 261 initialization processing unit 265 weight data storage unit 267 complex amplitude calculation unit 269 complex amplitude data storage unit 271 convergence determination unit 273 weight update processing unit 275 Phase modulation amount update processor

Claims (10)

A method of designing an optical element for condensing incident light at a predetermined position,
Calculating the absolute value of the complex amplitude of the incident light at a plurality of positions defined by the optical element;
Calculating a partial differential value of a deviation angle of the complex amplitude of the incident light at a plurality of positions defined by the optical element as a wave vector of the complex amplitude of the incident light;
Using the absolute value of the complex amplitude of the incident light at a plurality of positions defined by the optical element, the wave number vector of the complex amplitude of the incident light, and data on the predetermined position where the incident light is collected Calculating phase modulation amounts at the plurality of positions defined in the optical element;
An optical element design method including: The incident light, wavelength beam diameter in the x-axis direction λ is w _x, if the beam diameter in the y-axis direction is a Gaussian beam of w _y, wave vector of the complex amplitudes of the incident light,

The optical element design method according to claim 1, wherein the optical element design method is calculated by: Calculating the thickness at the plurality of positions defined by the optical element using the phase modulation amounts at the plurality of positions defined by the optical element and the refractive index of the material of the optical element; The optical element design method of Claim 1 or 2 containing. A method of designing an optical element for condensing incident light at a predetermined position,
Calculating a propagation coefficient of a diffracted wave obtained from a superimposed representation of a plurality of plane waves of the incident light for each set of the predetermined position and a plurality of positions defined in the optical element;
A complex amplitude of the diffracted wave for the predetermined position or a value calculated from the complex amplitude, which is calculated from the propagation coefficient and phase modulation amounts at a plurality of positions defined by the optical element, is preset. Adjusting a phase modulation amount at a plurality of positions defined in the optical element so as to satisfy a condition;
An optical element design method including: The beam diameter in the x-axis direction in the incident light wavelength λ is w _x, the beam diameter in the y-axis direction is a Gaussian beam of w _y, the predetermined position is _{(x m, y m, z} m) are, wherein the plurality of positions defined in the optical element is _{(x c, y c, 0} ), the x-axis direction of the sample number n _x, y-axis direction of the sample number n _y, z ₀ is the beam When it is the Z coordinate value of the waist and the pixel size at a plurality of positions defined in the optical element is a × b, the propagation coefficient of the diffracted wave is

(However, in the case of _{^{k 2 -k x 2 -k y 2}} <0, F (k x, k y) = 0)
The optical element design method according to claim 4, wherein the optical element design method is calculated by: Calculating the thickness at the plurality of positions defined by the optical element using the phase modulation amounts at the plurality of positions defined by the optical element and the refractive index of the material of the optical element; 6. The optical element design method according to claim 4 or 5. A program for designing an optical element for condensing incident light at a predetermined position,
Calculating the absolute value of the complex amplitude of the incident light at a plurality of positions defined by the optical element;
Calculating a partial differential value of a deviation angle of the complex amplitude of the incident light at a plurality of positions defined by the optical element as a wave vector of the complex amplitude of the incident light;
Using the absolute value of the complex amplitude of the incident light at a plurality of positions defined by the optical element, the wave number vector of the complex amplitude of the incident light, and data on the predetermined position where the incident light is collected Calculating phase modulation amounts at the plurality of positions defined in the optical element;
A program that causes a computer to execute. A program for designing an optical element for condensing incident light at a predetermined position,
Calculating a propagation coefficient of a diffracted wave obtained from a superimposed representation of a plurality of plane waves of the incident light for each set of the predetermined position and a plurality of positions defined in the optical element;
A complex amplitude of the diffracted wave for the predetermined position or a value calculated from the complex amplitude, which is calculated from the propagation coefficient and phase modulation amounts at a plurality of positions defined by the optical element, is preset. Adjusting a phase modulation amount at a plurality of positions defined in the optical element so as to satisfy a condition;
A program that causes a computer to execute. An optical element design apparatus for designing an optical element for condensing incident light at a predetermined position,
Means for calculating an absolute value of a complex amplitude of the incident light at a plurality of positions defined by the optical element;
Means for calculating a partial differential value of a deviation angle of the complex amplitude of the incident light at a plurality of positions defined by the optical element as a wave vector of the complex amplitude of the incident light;
Using the absolute value of the complex amplitude of the incident light at a plurality of positions defined by the optical element, the wave number vector of the complex amplitude of the incident light, and data on the predetermined position where the incident light is collected Means for calculating phase modulation amounts at the plurality of positions defined in the optical element;
An optical element design apparatus. An optical element design apparatus for designing an optical element for condensing incident light at a predetermined position,
Means for calculating a propagation coefficient of a diffracted wave obtained from a superimposed representation of a plurality of plane waves of the incident light for each set of the predetermined position and a plurality of positions defined by the optical element;
A complex amplitude of the diffracted wave for the predetermined position or a value calculated from the complex amplitude, which is calculated from the propagation coefficient and phase modulation amounts at a plurality of positions defined by the optical element, is preset. Means for adjusting phase modulation amounts at a plurality of positions defined in the optical element so as to satisfy a condition;
An optical element design apparatus.

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