Phase distribution design method, phase distribution design device, phase distribution design program, and recording medium

Abstract

To provide a phase distribution design method with which it is possible to synchronize the phases of a plurality of optical images with each other.SOLUTION: In a second step, a real-space function 213 after an amplitude distribution 211 is replaced with a target amplitude distribution 214 is converted by Fourier transform B6 into a wavenumber-space function 223 that includes an amplitude distribution 221 and a phase distribution 222. In a third step, the phase distribution 222 of the function 223 is aligned to the phase distribution 222 of a function 223 in one phase modulation region among two or more phase modulation regions, the amplitude distribution 221 of the function 223 is replaced with a target amplitude distribution 204, and the function 223 is converted by inverse-Fourier transform B2 into a real-space function 233 that includes an amplitude distribution 231 and a phase distribution 232. Hereafter, the second and third steps are repeated while replacing the function 213 in the second step with the function 233. The phase distribution 232 of the function 233 having been inverse-Fourier transformed by the last third step is taken as the phase distribution of each phase modulation region.SELECTED DRAWING: Figure 13

Description

[Technical Field]

[0001] The present disclosure relates to a phase distribution design method, a phase distribution design device, a phase distribution design program, and a recording medium. [Background technology]

[0002] Patent Document 1 describes a semiconductor light-emitting device including a phase modulation layer in which modified refractive index regions are distributed two-dimensionally. Light is supplied to the phase modulation layer from an active layer, and the light resonates in a plane perpendicular to the thickness direction of the phase modulation layer, thereby outputting an arbitrary optical image in a direction tilted with respect to the thickness direction of the phase modulation layer. Patent Document 1 also describes a method for designing the distribution of rotation angles of the centers of gravity of the modified refractive index regions around the lattice points of a square lattice, i.e., the phase distribution of the phase modulation layer, using the iterative Fourier method (GS method) based on a desired optical image. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2018-206921 [Non-patent literature]

[0004] [Non-Patent Document 1] Pengfei Qiao et al., "Recent advances in high -contrastmetastructures, metasurfaces, and photonic crystals", Advances in Opticsand Photonics, Volume 10, Issue 1, pp. 180-245 (2018) Summary of the Invention [Problem to be solved by the invention]

[0005] Devices that output arbitrary optical images by controlling the phase and intensity spectra of light emitted from multiple light-emitting points arranged in a two-dimensional array have been studied. Conventionally, such devices have been known to individually modulate the phase of light at multiple points distributed in a two-dimensional array. For example, a semiconductor light-emitting element known as an S-iPM (Static-Integrate Phase Modulating) laser has a structure including a phase modulation layer disposed on a substrate. The phase modulation layer includes a base layer and multiple modified refractive index areas, each of which has a refractive index different from that of the base layer. When a virtual square lattice is defined on a plane perpendicular to the thickness direction of the phase modulation layer, the modified refractive index areas are arranged so that each center of gravity is shifted from the corresponding lattice point of the square lattice in accordance with a phase distribution designed based on the optical image to be output. This semiconductor light-emitting element outputs light that forms an optical image of arbitrary shape in a direction inclined relative to the normal to the main surface of the substrate.

[0006] Conventionally, in such devices, the distribution of phase values ​​(phase distribution) at multiple points is designed based on a single optical image, as in the semiconductor light-emitting device described in Patent Document 1. Meanwhile, there is a technology for forming a hologram by overlapping multiple optical images in a single area and causing them to interfere. In such a technology, it is desirable for the phases of the multiple optical images to be synchronized with each other in order to produce a predetermined interference effect in the resulting hologram. However, when the phase distributions for generating each of the multiple optical images are individually designed, it is difficult to synchronize the phases of the multiple optical images with each other.

[0007] An object of the present disclosure is to provide a phase distribution design method, a phase distribution design device, a phase distribution design program, and a recording medium that are capable of synchronizing the phases of multiple optical images with each other. [Means for solving the problem]

[0008] A first phase distribution design method according to the present disclosure is a method for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. The first phase distribution design method includes a first step, a second step, and a third step. In the first step, a first function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space is set for each phase modulation region, and the first function is converted, for each phase modulation region, by an inverse Fourier transform into a second function including an amplitude distribution in real space and a phase distribution in real space. In the second step, the real-space amplitude distribution of the second function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in real space, and the second function after the replacement is converted, for each phase modulation region, by a Fourier transform into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space. In the third step, the phase distribution in wavenumber space of the third function in each phase modulation region is aligned with the phase distribution in wavenumber space of the third function in one of the two or more phase modulation regions, and the amplitude distribution in wavenumber space of the third function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space. Then, for each phase modulation region, the third function is converted into a fourth function including a real-space amplitude distribution and a real-space phase distribution by inverse Fourier transform. In the first phase distribution design method, after the first to third steps, the second and third steps are repeated while replacing the second function in the second step with the fourth function. Then, the real-space phase distribution of the fourth function converted in the final third step is set as the phase distribution of each phase modulation region.

[0009] A first phase distribution design device according to the present disclosure is a device for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. The first phase distribution design device includes a first processing unit, a second processing unit, and a third processing unit. The first processing unit sets a first function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space for each phase modulation region, and converts the first function, for each phase modulation region, into a second function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform. The second processing unit replaces the real-space amplitude distribution of the second function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in real space, and converts the replaced second function, for each phase modulation region, into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space by Fourier transform. The third processing unit aligns the phase distribution in wavenumber space of the third function in each phase modulation region with the phase distribution in wavenumber space of the third function in one of the two or more phase modulation regions, replaces the amplitude distribution in wavenumber space of the third function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space, and converts the third function, for each phase modulation region, into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform. In the first phase distribution design device, after the second processing unit and the third processing unit repeat operations while replacing the second function with the fourth function in the second processing unit, the real space phase distribution of the fourth function finally converted by the third processing unit is set as the phase distribution of each phase modulation region.

[0010] A first phase distribution design program according to the present disclosure is a program for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. The first phase distribution design program causes a computer to execute a first step, a second step, and a third step. In the first step, a first function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space is set for each phase modulation region, and the first function is converted, for each phase modulation region, by an inverse Fourier transform into a second function including an amplitude distribution in real space and a phase distribution in real space. In the second step, the real-space amplitude distribution of the second function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in real space, and the second function after the replacement is converted, for each phase modulation region, by a Fourier transform into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space. The third step aligns the wavenumber space phase distribution of the third function in each phase modulation region with the wavenumber space phase distribution of the third function in one of the two or more phase modulation regions, replaces the wavenumber space amplitude distribution of the third function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space, and converts the third function for each phase modulation region into a fourth function including a real-space amplitude distribution and a real-space phase distribution by inverse Fourier transform. The first phase distribution design program causes a computer to repeatedly execute the second and third steps after the first to third steps while replacing the second function of the second step with the fourth function. The real-space phase distribution of the fourth function converted in the final third step is then used as the phase distribution of each phase modulation region.

[0011] Conventionally, when designing the phase distribution of a single phase modulation region, after the above-mentioned first and second steps (or the operations of the first and second processing units), the amplitude distribution in wave number space of the third function is replaced with a target amplitude distribution based on a predetermined target intensity distribution in wave number space. Then, the replaced third function is converted into a fourth function including an amplitude distribution in real space and a phase distribution in real space by an inverse Fourier transform. Thereafter, the second and third steps (or the operations of the second and third processing units) are repeated while replacing the second function in the second step (second processing unit) with the fourth function. When a similar design method is applied individually (independently) to the phase distributions of multiple phase modulation regions, the phases of the multiple optical images output from the multiple phase modulation regions are not synchronized with each other.

[0012] Therefore, in the first phase distribution design method, the first phase distribution design device, and the first phase distribution design program, in the third step (third processing unit), the phase distribution in wave number space of the third function in each phase modulation region is aligned with the phase distribution in wave number space of the third function in one of the two or more phase modulation regions. This makes it possible to synchronize the phases of multiple optical images output from the multiple phase modulation regions. Therefore, it is possible to produce a predetermined interference effect in a hologram formed by superimposing multiple optical images in one region.

[0013] In the first phase distribution design method, the first phase distribution design device, and the first phase distribution design program, the one phase modulation region may be fixed when repeating the operation of the third step or the third processing unit. According to the simulation by the inventors, particularly in such a case, the phases of multiple optical images can be synchronized with high precision.

[0014] A second phase distribution design method according to the present disclosure is a method for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. The second phase distribution design method includes a first step, a second step, and a third step. In the first step, a first function including an initial value of the amplitude distribution in wavenumber space and an initial value of the phase distribution in wavenumber space is set for each phase modulation region, and the first function is converted, for each phase modulation region, by an inverse Fourier transform into a second function including an amplitude distribution in real space and a phase distribution in real space. In the second step, the real-space amplitude distribution of the second function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in real space, and the second function after the replacement is converted, for each phase modulation region, by a Fourier transform into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space. In the third step, the phase distribution in wavenumber space of the third function in each phase modulation region is replaced with a predetermined distribution that is the same across two or more phase modulation regions, or the amplitude distribution in wavenumber space of the third function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space, and the replaced third function is converted, for each phase modulation region, into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform. In this method, after the first to third steps described above, the second function in the second step is replaced with a fourth function while the second and third steps are repeated, and in this process, the replacement of the phase distribution in wavenumber space and the replacement of the amplitude distribution in wavenumber space are alternately performed in the third step. Then, the real-space phase distribution of the fourth function converted in the final third step is used as the phase distribution of each phase modulation region.

[0015] A second phase distribution design device according to the present disclosure is a device for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. The second phase distribution design device includes a first processing unit, a second processing unit, and a third processing unit. The first processing unit sets a first function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space for each phase modulation region, and converts the first function, for each phase modulation region, into a second function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform. The second processing unit replaces the real-space amplitude distribution of the second function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in real space, and converts the replaced second function, for each phase modulation region, into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space by Fourier transform. The third processing unit replaces the wavenumber space phase distribution of the third function in each phase modulation region with a predetermined distribution that is the same across two or more phase modulation regions, or replaces the wavenumber space amplitude distribution of the third function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space, and converts the replaced third function, for each phase modulation region, into a fourth function including a real-space amplitude distribution and a real-space phase distribution by inverse Fourier transform. In the second phase distribution design device, the second processing unit and the third processing unit repeat operations while the second processing unit replaces the second function with the fourth function. At that time, the third processing unit alternately replaces the wavenumber space phase distribution and the wavenumber space amplitude distribution. The real-space phase distribution of the fourth function finally converted by the third processing unit is used as the phase distribution of each phase modulation region.

[0016] A second phase distribution design program according to the present disclosure is a program for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. The second phase distribution design program causes a computer to execute a first step, a second step, and a third step. In the first step, a first function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space is set for each phase modulation region, and the first function is converted, for each phase modulation region, by an inverse Fourier transform into a second function including an amplitude distribution in real space and a phase distribution in real space. In the second step, the real-space amplitude distribution of the second function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in real space, and the second function after the replacement is converted, for each phase modulation region, by a Fourier transform into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space. In the third step, the phase distribution in wavenumber space of the third function in each phase modulation region is replaced with a predetermined distribution that is the same across two or more phase modulation regions, or the amplitude distribution in wavenumber space of the third function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space, and the replaced third function is converted, for each phase modulation region, into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform. The first phase distribution design program causes a computer to repeatedly execute the second and third steps after the first to third steps, while replacing the second function in the second step with a fourth function. In this process, in the third step, the replacement of the phase distribution in wavenumber space and the replacement of the amplitude distribution in wavenumber space are alternately performed. The real-space phase distribution of the fourth function converted in the final third step is then used as the phase distribution of each phase modulation region.

[0017] In the second phase distribution design method, the second phase distribution design device, and the second phase distribution design program, when the second step and the third step are repeated (or when the second processing unit and the third processing unit repeat their operations), the wavenumber space phase distribution of the third function in each phase modulation region is replaced with a predetermined distribution that is the same between two or more phase modulation regions during one of the two third step (or operations of the third processing unit). This allows the phases of multiple optical images output from the multiple phase modulation regions to be synchronized with each other. Therefore, a predetermined interference effect can be generated in a hologram formed by superimposing multiple optical images in one region.

[0018] In the second phase distribution design method, the second phase distribution design device, and the second phase distribution design program, the phase values ​​of multiple points in a predetermined distribution may be equal to each other. According to the simulations by the inventors, particularly in such cases, the phases of multiple optical images can be synchronized with high precision. In this case, the phase values ​​of multiple points in the predetermined distribution may be zero.

[0019] In the second phase distribution design method, the second phase distribution design device, and the second phase distribution design program, the predetermined distribution may remain unchanged for each repetition of the third step. According to the simulations conducted by the inventors, it is possible to precisely synchronize the phases of multiple optical images, particularly in such a case.

[0020] In the first and second phase distribution design methods, the first and second phase distribution design devices, and the first and second phase distribution design programs, the initial value of the amplitude distribution in wavenumber space may be set to a target amplitude distribution in wavenumber space. In this case, the optical image can be made to approach a predetermined target intensity distribution with high accuracy with a small number of iterations.

[0021] In the first and second phase distribution design methods, the first and second phase distribution design devices, and the first and second phase distribution design programs, the initial value of the phase distribution in wavenumber space may be set to a random distribution.

[0022] Another phase distribution design method according to the present disclosure is a method for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. This phase distribution design method includes a first step, a second step, and a third step. In the first step, a first function including an initial value of the amplitude distribution in wavenumber space and an initial value of the phase distribution in wavenumber space is set for each phase modulation region, and the first function is converted, for each phase modulation region, by an inverse Fourier transform into a second function including an amplitude distribution in real space and a phase distribution in real space. In the second step, the real-space amplitude distribution of the second function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in real space, and the second function after the replacement is converted, for each phase modulation region, by a Fourier transform into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space. In the third step, one or both of a first process, in which the wavenumber space phase distribution of the third function in each phase modulation region is replaced with a distribution that is the same across two or more phase modulation regions, and a second process, in which the wavenumber space amplitude distribution of the third function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space, are performed. Then, for each phase modulation region, the replaced third function is converted into a fourth function including a real-space amplitude distribution and a real-space phase distribution by inverse Fourier transform. In this method, after the first to third steps, the second and third steps are repeatedly performed while replacing the second function in the second step with a fourth function. In this case, if only one of the first and second processes is performed in each third step, the first and second processes are alternately performed for each repetition of the third step. The real-space phase distribution of the fourth function converted in the final third step is used as the phase distribution of each phase modulation region.

[0023] Another phase distribution design device according to the present disclosure is a device for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. This phase distribution design device includes a first processing unit, a second processing unit, and a third processing unit. The first processing unit sets a first function including an initial value of the amplitude distribution in wavenumber space and an initial value of the phase distribution in wavenumber space for each phase modulation region, and converts the first function, for each phase modulation region, into a second function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform. The second processing unit replaces the real-space amplitude distribution of the second function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in real space, and converts the replaced second function, for each phase modulation region, into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space by Fourier transform. The third processing unit performs one or both of a first process, which replaces the wavenumber space phase distribution of the third function in each phase modulation region with a distribution that is identical across two or more phase modulation regions, and a second process, which replaces the wavenumber space amplitude distribution of the third function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space. Then, for each phase modulation region, the replaced third function is converted by inverse Fourier transform into a fourth function including a real-space amplitude distribution and a real-space phase distribution. In this device, the second and third processing units repeat operations while replacing the second function of the second processing unit with the fourth function. In this case, if only one of the first and second processes is performed, the third processing unit alternates between the first and second processes with each repetition of the operation of the third processing unit. The real-space phase distribution of the fourth function finally converted by the third processing unit is used as the phase distribution of each phase modulation region.

[0024] Another phase distribution design program according to the present disclosure is a program for designing phase distributions of two or more phase modulation regions that individually modulate the phase of light at multiple points distributed two-dimensionally. This phase distribution design program causes a computer to execute a first step, a second step, and a third step. In the first step, for each phase modulation region, a first function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space is set, and for each phase modulation region, the first function is converted by inverse Fourier transform into a second function including an amplitude distribution in real space and a phase distribution in real space. In the second step, the real-space amplitude distribution of the second function in each phase modulation region is replaced with a target amplitude distribution based on a predetermined target intensity distribution in real space, and for each phase modulation region, the second function after the replacement is converted by Fourier transform into a third function including an amplitude distribution in wavenumber space and a phase distribution in wavenumber space. In the third step, one or both of a first process, which replaces the wavenumber space phase distribution of the third function in each phase modulation region with a distribution that is the same across two or more phase modulation regions, and a second process, which replaces the wavenumber space amplitude distribution of the third function in each phase modulation region with a target amplitude distribution based on a predetermined target intensity distribution in wavenumber space, are performed. For each phase modulation region, the replaced third function is converted into a fourth function including a real-space amplitude distribution and a real-space phase distribution by inverse Fourier transform. In this program, after the first to third steps, the second and third steps are repeatedly performed while replacing the second function in the second step with a fourth function. In this case, if only one of the first and second processes is performed in each third step, the first and second processes are alternately performed for each repetition of the third step. The real-space phase distribution of the fourth function converted in the final third step is used as the phase distribution of each phase modulation region.

[0025] A recording medium according to the present disclosure is a computer-readable recording medium on which any of the above phase distribution design programs is recorded. [Effects of the Invention]

[0026] According to the present disclosure, it is possible to provide a phase distribution design method, a phase distribution design device, a phase distribution design program, and a recording medium that are capable of synchronizing the phases of a plurality of optical images with each other. [Brief explanation of the drawings]

[0027] [Figure 1] FIG. 1 is a cross-sectional view showing the layered structure of a semiconductor light-emitting device to which the phase distribution design method of this embodiment is applied. [Figure 2] FIG. 2 is a plan view (viewed from the thickness direction) of the phase modulation layer. [Figure 3] FIG. 3 is an enlarged plan view showing a part of the phase modulation region. [Figure 4] FIG. 4 is an enlarged view of one unit constituent region. [Figure 5] FIG. 5 is a diagram for explaining coordinate transformation from spherical coordinates to coordinates in an XYZ orthogonal coordinate system. [Figure 6] FIG. 6 is an enlarged plan view showing a part of the connection region. [Figure 7] FIG. 7 is a diagram schematically showing the planar shapes of the first electrode and the second electrode, and a configuration for supplying current to the first electrode and the second electrode. [Figure 8] Fig. 8 shows the electromagnetic field distribution in the phase modulation region. Part (a) of Fig. 8 shows the electromagnetic field distribution in the resonant mode of symmetry A1 at point M1. Part (b) of Fig. 8 shows the electromagnetic field distribution in the resonant mode of symmetry B2 at point M1. [Figure 9] 9A and 9B are diagrams illustrating electromagnetic field distributions according to a comparative example. Part (a) of Fig. 9 shows the electromagnetic field distribution in a resonant mode with symmetry A1 at point M1. Part (b) of Fig. 9 shows the electromagnetic field distribution in a resonant mode with symmetry B2 at point M1. [Figure 10] FIG. 10 is a diagram conceptually showing an example of a plurality of optical images output from a plurality of phase modulation regions. [Figure 11] FIG. 11 is a diagram conceptually showing another example of a plurality of optical images output from a plurality of phase modulation regions. [Figure 12]FIG. 12 is a diagram conceptually showing yet another example of a plurality of optical images output from a plurality of phase modulation regions. [Figure 13] FIG. 13 is a diagram conceptually showing the first design method. [Figure 14] FIG. 14 is a diagram showing a phase modulation layer having a total of four phase modulation regions arranged in two columns in the X direction and two rows in the Y direction. [Figure 15] FIG. 15 is a diagram showing a phase modulation layer in which two phase modulation regions included in the first row have phase distribution pattern B and two phase modulation regions included in the second row have phase distribution pattern A. [Figure 16] FIG. 16 is a diagram conceptually showing a method for designing phase distribution patterns A and B. In FIG. [Figure 17] FIG. 17 is a diagram showing a phase modulation layer having a total of m×n phase modulation regions with m columns in the X direction and n rows in the Y direction. [Figure 18] FIG. 18 is a diagram conceptually showing a method for designing m×n phase distribution patterns. [Figure 19] Part (a) of Fig. 19 is a block diagram showing a hardware configuration of a phase distribution design device capable of performing the first design method, and part (b) of Fig. 19 is a functional block diagram of a phase distribution design device capable of performing the first design method. [Figure 20] FIG. 20 is a diagram conceptually showing the second design method. [Figure 21] FIG. 21 is a diagram conceptually showing a method for designing phase distribution patterns A and B. In FIG. [Figure 22] FIG. 22 is a diagram conceptually showing a method for designing m×n phase distribution patterns. [Figure 23] FIG. 23 is a block diagram showing the configuration of a phase distribution design device that can perform the second design method. [Figure 24] FIG. 24 is a diagram conceptually showing the third design method as a comparative example. [Figure 25]Part (a) of Fig. 25 shows a desired optical image in the irradiation area (far field) set when designing phase distribution pattern A. Part (b) of Fig. 25 shows the optical image shown in part (a) converted into wave number space, i.e., the target amplitude distribution in wave number space. Part (c) of Fig. 25 shows phase distribution pattern A calculated based on the target amplitude distribution shown in part (b). [Figure 26] Part (a) of Fig. 26 shows a desired optical image in the irradiation region (far field) set when designing phase distribution pattern B. Part (b) of Fig. 26 shows the optical image shown in part (a) converted into wave number space, i.e., the target amplitude distribution in wave number space. Part (c) of Fig. 26 shows phase distribution pattern B calculated based on the target amplitude distribution shown in part (b). [Figure 27] Part (a) of Fig. 27 is a diagram showing a state in which two phase modulation regions located on one diagonal line are each given a phase distribution pattern A, and two phase modulation regions located on the other diagonal line are each given a phase distribution pattern B. Part (b) of Fig. 27 is a diagram conceptually showing the difference in light intensity between two phase modulation regions located on one diagonal line and two phase modulation regions located on the other diagonal line, which is achieved by individually controlling the current of each electrode portion. [Figure 28] Figure 28 shows the final optical image that is expected when optical images emitted from two phase modulation regions having phase distribution pattern A and optical images emitted from two phase modulation regions having phase distribution pattern B are made to interfere with each other. [Figure 29] Part (a) of Fig. 29 shows the final optical image obtained by the first design method, part (b) of Fig. 29 shows the final optical image obtained by the second design method, and part (c) of Fig. 29 shows the final optical image obtained by the third design method as a comparative example. [Figure 30]Part (a) of Fig. 30 shows a desired optical image in the irradiation region (far field) set when designing phase distribution pattern A. Part (b) of Fig. 30 shows the optical image shown in part (a) converted into wave number space, i.e., the target amplitude distribution in wave number space. Part (c) of Fig. 30 shows phase distribution pattern A calculated based on the target amplitude distribution shown in part (b). [Figure 31] Part (a) of Fig. 31 shows a desired optical image in the irradiation region (far field) set when designing phase distribution pattern B. Part (b) of Fig. 31 shows the optical image shown in part (a) converted into wave number space, i.e., the target amplitude distribution in wave number space. Part (c) of Fig. 31 shows phase distribution pattern B calculated based on the target amplitude distribution shown in part (b). [Figure 32] Part (a) of Fig. 32 is a diagram showing a state in which two phase modulation regions located on one diagonal line are each given a phase distribution pattern A, and two phase modulation regions located on the other diagonal line are each given a phase distribution pattern B. Part (b) of Fig. 32 is a diagram conceptually showing the difference in light intensity between two phase modulation regions located on one diagonal line and two phase modulation regions located on the other diagonal line, which is achieved by individually controlling the current of each electrode portion. [Figure 33] Figure 33 shows the final optical image that is expected when an optical image emitted from a phase modulation area having phase distribution pattern A and an optical image emitted from a phase modulation area having phase distribution pattern B are made to interfere with each other. [Figure 34] FIG. 34 is a diagram showing the final optical image obtained by the simulation. [Figure 35] FIG. 35 is a diagram showing the final optical image obtained by the simulation. DETAILED DESCRIPTION OF THE INVENTION

[0028] Specific examples of the phase distribution design method, phase distribution design device, phase distribution design program, and recording medium of the present disclosure will be described below with reference to the drawings. Note that the present invention is not limited to these examples, but is defined by the claims, and is intended to include all modifications within the meaning and scope equivalent to the claims. In the following description, the same elements in the drawings will be given the same reference numerals, and duplicate explanations will be omitted.

[0029] FIG. 1 is a cross-sectional view showing the layered structure of a semiconductor light-emitting element 1 to which the phase distribution design method of this embodiment is applied. In FIG. 1, an XYZ Cartesian coordinate system is defined, with the axis extending in the thickness direction of the semiconductor light-emitting element 1 as the Z axis. The semiconductor light-emitting element 1 is a laser light source that forms standing waves in the XY plane direction and outputs phase-controlled plane waves in a direction intersecting the thickness direction. The semiconductor light-emitting element 1 is an Si-iPM laser, and can output an optical image of any shape in a direction perpendicular to the main surface 10a of the semiconductor substrate 10, i.e., the Z direction, or in a direction tilted relative to the Z direction, or in a direction including both.

[0030] The semiconductor light emitting element 1 includes a semiconductor substrate 10. The semiconductor substrate 10 has a main surface 10a and a back surface 10b. The normal direction to the main surface 10a and the back surface 10b and the thickness direction of the semiconductor substrate 10 are along the Z direction. The semiconductor substrate 10 is made of a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor.

[0031] The semiconductor light-emitting element 1 further includes a semiconductor stack 20. The semiconductor stack 20 is provided on the principal surface 10a of the semiconductor substrate 10. The stacking direction of the semiconductor stack 20 is along the Z direction. The semiconductor stack 20 has a stacked structure including a cladding layer 11, an active layer 12, a cladding layer 13, a contact layer 14, and a phase modulation layer 15 between a first surface 20a and a second surface 20b. The second surface 20b of the semiconductor stack 20 faces the principal surface 10a of the semiconductor substrate 10. In the illustrated example, the cladding layer 11 is provided on the principal surface 10a of the semiconductor substrate 10, the active layer 12 is provided on the cladding layer 11, the phase modulation layer 15 is provided on the active layer 12, the cladding layer 13 is provided on the phase modulation layer 15, and the contact layer 14 is provided on the cladding layer 13. That is, the active layer 12 and the phase modulation layer 15 are sandwiched between the cladding layers 11 and 13. In the illustrated example, the phase modulation layer 15 is provided between the active layer 12 and the cladding layer 13, but the phase modulation layer 15 may be provided between the cladding layer 11 and the active layer 12. An optical guide layer may be provided, if necessary, between the active layer 12 and the cladding layer 13 and / or between the active layer 12 and the cladding layer 11. The optical guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

[0032] The cladding layer 11, the active layer 12, the cladding layer 13, and the contact layer 14 are made of a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor. The active layer 12 has, for example, a multiple quantum well structure. The energy band gaps of the cladding layer 11 and the cladding layer 13 are larger than the energy band gap of the active layer 12. The thickness directions of the cladding layer 11, the active layer 12, the cladding layer 13, and the contact layer 14 coincide with the Z-axis direction.

[0033] The phase modulation layer 15 is optically coupled to the active layer 12. The thickness direction of the phase modulation layer 15 coincides with the Z-axis direction. FIG. 2 is a plan view (viewed from the thickness direction) of the phase modulation layer 15. As shown in FIGS. 1 and 2, the phase modulation layer 15 has a plurality of phase modulation regions 151 and a connection region 152. The planar shape of the connection region 152 as viewed from the stacking direction of the semiconductor stack 20 is, for example, a lattice shape. Each of the multiple phase modulation regions 151 is provided in a corresponding one of a plurality of openings 152a of the connection region 152 formed in a lattice shape.

[0034] The planar shape of each of the multiple phase modulation regions 151 is, for example, a square or a rectangle. The multiple phase modulation regions 151 are arranged two-dimensionally along a virtual plane P perpendicular to the thickness direction of the phase modulation layer 15 (in other words, parallel to the XY plane) and are optically coupled to one another. In the illustrated example, the multiple phase modulation regions 151 are arranged along the X and Y directions. Note that in the illustrated example, the multiple phase modulation regions 151 are arranged two-dimensionally, but the multiple phase modulation regions 151 may also be arranged one-dimensionally. In the illustrated example, the multiple phase modulation regions 151 are provided at intervals from one another. The connection region 152 includes a portion 152b provided between adjacent phase modulation regions 151 and a frame-shaped portion 152c that collectively surrounds the multiple phase modulation regions 151.

[0035] As shown in FIG. 1, each of the multiple phase modulation regions 151 includes a base region 15a and multiple modified refractive index regions 15b. Similarly, the connection region 152 also includes a base region 15a and multiple modified refractive index regions 15b. The base region 15a is made of a first refractive index medium. The base region 15a is made of a compound semiconductor, such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor. The multiple modified refractive index regions 15b are made of a second refractive index medium having a refractive index different from that of the first refractive index medium and are present within the base region 15a. The modified refractive index regions 15b are, for example, cavities. The modified refractive index regions 15b are covered by a cap region 15c provided on the base region 15a. The cap region 15c constitutes part of the phase modulation layer 15 and is made of, for example, the same material as the base region 15a.

[0036] The multiple modified refractive index regions 15b are distributed two-dimensionally along the imaginary plane P. In each phase modulation region 151, the multiple modified refractive index regions 15b include a lattice-like, approximately periodic structure. If the equivalent refractive index of the mode is n and the lattice spacing is a, the wavelength λ0 selected by each phase modulation region 151 is expressed as λ0 = (√2)a × n, for example, in the case of M1-point oscillation. This wavelength λ0 is included in the emission wavelength range of the active layer 12. Each phase modulation region 151 can select a band edge wavelength near the wavelength λ0 from the emission wavelengths of the active layer 12 and output it to the outside. Light incident on each phase modulation region 151 from the active layer 12 forms a predetermined mode in accordance with the arrangement of the modified refractive index regions 15b in each phase modulation region 151 and is output as laser light L from the back surface 10b of the semiconductor substrate 10 to the outside of the semiconductor light emitting element 1.

[0037] FIG. 3 is an enlarged plan view of a portion of the phase modulation region 151. While FIG. 3 shows only one phase modulation region 151, the other phase modulation regions 151 have a similar configuration. As described above, the phase modulation region 151 includes a basic region 15a and multiple modified refractive index regions 15b. In FIG. 3, a virtual square lattice is defined for the phase modulation region 151 along a virtual plane P. One side of the square lattice is parallel to the X-axis, and the other side is parallel to the Y-axis. Square unit constituent regions R, each centered on a lattice point O of the square lattice, are two-dimensionally arranged across multiple columns along the X-axis and multiple rows along the Y-axis. The X and Y coordinates of each unit constituent region R are determined by the center of gravity of the respective unit constituent region R. These center of gravity positions coincide with the lattice point O of the virtual square lattice. For example, one modified refractive index region 15b is provided within each unit constituent region R. The planar shape of the modified refractive index region 15b is, for example, circular. The lattice point O may be located outside the modified refractive index area 15b, or may be included inside the modified refractive index area 15b.

[0038] FIG. 4 is an enlarged view of one unit constituent region R. As shown in the figure, each modified refractive index region 15b has a center of gravity G. The center of gravity G of the modified refractive index region 15b is located on a straight line D set for each lattice point O. The straight line D passes through the lattice point O corresponding to each unit constituent region R and is inclined with respect to each side of the square lattice. In other words, the straight line D is inclined with respect to both the X-axis and the Y-axis. The inclination angle of the straight line D with respect to one side of the square lattice, in other words, with respect to the X-axis, is β.

[0039] The tilt angle β is the same for all straight lines D within the phase modulation region 151. The tilt angle β is also the same for multiple phase modulation regions 151. The tilt angle β satisfies 0°<β<90°, and in one example, β=45°. Alternatively, the tilt angle β satisfies 180°<β<270°, and in one example, β=225°. When the tilt angle β satisfies 0°<β<90° or 180°<β<270°, the straight line D extends from the first quadrant to the third quadrant of the coordinate plane defined by the X-axis and Y-axis. The tilt angle β satisfies 90°<β<180°, and in one example, β=135°. Alternatively, the tilt angle β satisfies 270°<β<360°, and in one example, β=315°. When the tilt angle β satisfies 90°<β<180° or 270°<β<360°, the straight line D extends from the second quadrant to the fourth quadrant of the coordinate plane defined by the X-axis and the Y-axis. Thus, the tilt angle β is an angle excluding 0°, 90°, 180°, and 270°.

[0040] Here, the distance between lattice point O and center of gravity G is r(x,y). x is the position of the xth lattice point on the X axis, and y is the position of the yth lattice point on the Y axis. When the distance r(x,y) is a positive value, center of gravity G is located in the first or second quadrant. When the distance r(x,y) is a negative value, center of gravity G is located in the third or fourth quadrant. When the distance r(x,y) is 0, lattice point O and center of gravity G coincide with each other. The tilt angles are preferably 45°, 135°, 225°, or 275°. With these tilt angles, only two of the four wave vectors forming the standing wave at point M, for example, the in-plane wave vectors (±π / a, ±π / a), are phase-modulated, and the other two are not. Therefore, a stable standing wave can be formed.

[0041] The distance r(x, y) is set individually for each modified refractive index area 15b according to the phase distribution φ(x, y) corresponding to the optical image to be output from each phase modulation area 151. That is, when the phase φ(x, y) at a certain coordinate (x, y) is φ0, the distance r(x, y) is set to 0. When the phase φ(x, y) is π+φ0, the distance r(x, y) is set to the maximum value R0. When the phase φ(x, y) is -π+φ0, the distance r(x, y) is set to the minimum value -R0. For intermediate phases φ(x, y), the distance r(x, y) is set so that r(x, y) = {φ(x, y) - φ0} × R0 / π. When the lattice spacing of the virtual square lattice is a, the maximum value R0 of r(x, y) falls within the range of, for example, the following formula (1).

number

[0042] By determining the distribution of the distances r(x, y) of the modified refractive index areas 15b in each of the multiple phase modulation areas 151, a desired optical image can be output from each of the multiple phase modulation areas 151. Each phase modulation area 151 is configured to satisfy the following conditions.

[0043] As a first prerequisite, a virtual square lattice consisting of M1×N1 square unit constituent regions R is set on the XY plane, where M1 and N1 are integers of 1 or greater.

[0044] As shown in Figure 5, the length of the moving radius r and the tilt angle θ from the Z axis tilt and the rotation angle θ from the X-axis specified on the XY plane rot and the spherical coordinates (r,θ rot ,θ tilt The second prerequisite is that the coordinates (ξ,η,ζ) in the XYZ Cartesian coordinate system are defined as spherical coordinates (r,θ rot ,θ tilt ) satisfy the relationships shown in the following equations (2) to (4). rot ,θ tilt ) to coordinates (ξ,η,ζ) in the XYZ Cartesian coordinate system. The coordinates (ξ,η,ζ) represent a designed light image on a predetermined plane set in the XYZ Cartesian coordinate system, which is real space.

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[0045] The light emitted from each phase modulation region 151 is irradiated at an angle θ tilt and θ rot The set of bright points facing the direction defined by the angle θ tilt and θ rotis converted into coordinate values ​​kx and ky. The coordinate value kx is a normalized wave number defined by the following equation (5), and corresponds to the X axis. x The coordinate value ky is a normalized wave number defined by the following equation (6), and corresponds to the Y axis and is also on the K axis. x perpendicular to the axis K y The normalized wave number is the wave number normalized with the wave number 2π / a, which corresponds to the lattice spacing of a virtual square lattice, set to 1.0. In this case, K x axis and K y In the wavenumber space defined by the axes, a specific wavenumber range including a beam pattern corresponding to a light image is composed of M2 × N2 image regions FR, each of which is square. M2 and N2 are integers equal to or greater than 1. The integer M2 does not have to match the integer M1. The integer N2 does not have to match the integer N1. Equations (5) and (6) are disclosed in, for example, Non-Patent Document 1.

number

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[0046] In wavenumber space, the image domain FR(kx,ky) is x Axial coordinate components kx and K yThe coordinate component kx is an integer between 0 and M2-1 inclusive. The coordinate component ky is an integer between 0 and N2-1 inclusive. A unit constituent region R(x,y) on the XY plane is specified by the coordinate component x in the X-axis direction and the coordinate component y in the Y-axis direction. The coordinate component x is an integer between 0 and M1-1 inclusive. The coordinate component y is an integer between 0 and N1-1 inclusive. As a third prerequisite, the complex amplitude CA(x,y) obtained by performing a two-dimensional inverse discrete Fourier transform of each image region FR(kx,ky) into the unit constituent region R(x,y) is given by the following equation (7), where j is the imaginary unit. The complex amplitude CA(x,y) is defined by the following equation (8), where the amplitude term is A(x,y) and the phase term is φ(x,y). As a fourth prerequisite, the unit constituent region R(x,y) is defined by the s-axis and the t-axis. The s-axis and t-axis are parallel to the X-axis and Y-axis, respectively, and are orthogonal to each other at the lattice point O(x,y) which is the center of the unit constituent area R(x,y). CA(x,y) shown in equations (7) and (8) is A1e in Figures 16 and 21. iφ1 and A2e iφ2 , and A in Figs. 18 and 22 1,1 e φ1,1 ~A m,n e φm,n It corresponds to.

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[0047] Under the above-mentioned first to fourth prerequisites, each phase modulation area 151 is configured to satisfy the following condition: That is, the corresponding modified refractive index area 15b is arranged within the unit constituent area R(x, y) so that the distance r(x, y) from the lattice point O(x, y) to the center of gravity G of the corresponding modified refractive index area 15b satisfies the following relationship: r(x,y)=C×(φ(x,y)-φ0) C: proportionality constant, e.g. R0 / π φ0: an arbitrary constant, e.g., 0 To obtain a desired optical image, the optical image is subjected to an inverse Fourier transform, and a distribution of distances r(x, y) according to the phases φ(x, y) of the complex amplitudes is provided to the multiple modified refractive index areas 15b. The phases φ(x, y) and the distances r(x, y) may be proportional to each other.

[0048] FIG. 6 is an enlarged plan view of a portion of the connection region 152. While FIG. 6 shows only a portion of the connection region 152, the other portions of the connection region 152 have a similar configuration. As described above, the connection region 152 also includes a basic region 15a and multiple modified refractive index regions 15b. A virtual square lattice similar to that shown in FIG. 3 is also set in the connection region 152. One side of the square lattice is parallel to the X-axis, and the other side is parallel to the Y-axis. The lattice constant a of the square lattice is equal to the lattice constant a of the phase modulation region 151. In the connection region 152, the centers of gravity G of the multiple modified refractive index regions 15b are located at the lattice points of the square lattice. In other words, the positions of the centers of gravity G of the multiple modified refractive index regions 15b coincide with the positions of the lattice points of the square lattice. Therefore, in the connection region 152, the multiple modified refractive index regions 15b are periodically arranged along the X-axis and the Y-axis.

[0049] Referring again to FIG. 1 , the semiconductor light-emitting element 1 further includes an electrode 16 (first electrode) and an electrode 17 (second electrode). The electrode 16 is provided to face the first surface 20a of the semiconductor stack 20, and in the illustrated example, the electrode 16 is provided on the first surface 20a, i.e., on the contact layer 14. The electrode 16 forms ohmic contact with the contact layer 14. The electrode 17 is provided to face the second surface 20b of the semiconductor stack 20, and in the illustrated example, the electrode 17 is provided on the back surface 10b of the semiconductor substrate 10. The electrode 17 forms ohmic contact with the semiconductor substrate 10.

[0050] FIG. 7 is a diagram schematically illustrating the planar shapes of the electrodes 16 and 17 and a configuration for supplying current to the electrodes 16 and 17. As shown in FIG. 7, the electrode 17 has multiple openings 17a. Each opening 17a corresponds one-to-one with a corresponding phase modulation region 151. When viewed from the thickness direction of the semiconductor stack 20, the openings 17a overlap with their corresponding phase modulation regions 151. The planar shape of each opening 17a is, for example, a square or rectangle. The electrode 16 includes multiple electrode portions 161. The multiple electrode portions 161 are arranged with gaps between them and are electrically isolated from one another. Note that the electrode portions being electrically isolated from one another means that there is no other electrical connection path except for the path via the semiconductor stack 20. Each electrode portion 161 corresponds one-to-one with a corresponding phase modulation region 151. When viewed from the thickness direction of the semiconductor stack 20, the electrode portions 161 overlap with their corresponding phase modulation regions 151. The planar shape of each electrode portion 161 is, for example, square or rectangular.

[0051] Each of the multiple electrode portions 161 is electrically connected to the drive circuit 31 individually via a respective one of multiple wirings 33. Furthermore, the electrode 17 is electrically connected to the drive circuit 31 via wiring 34. The drive circuit 31 is electrically connected to the power supply circuit 32 via wiring 35. The drive circuit 31 receives power from the power supply circuit 32 and supplies a drive current between the multiple electrode portions 161 and the electrode 17. The drive circuit 31 can freely change the magnitude of the drive current for each electrode portion 161. The magnitude of the drive current to each electrode portion 161 is set independently for each electrode portion 161.

[0052] Referring again to FIG. 1 , the contact layer 14 is etched away except for the portions overlapping with the electrode portions 161 to limit the current range. Therefore, the contact layer 14 is divided into a plurality of portions corresponding to the electrode portions 161. The gaps between the contact layer 14 portions are filled with a protective film 18. This protects the surface of the semiconductor stack 20 exposed from the electrode 16. The protective film 18 is made of an inorganic insulator such as silicon nitride (e.g., SiN) or silicon oxide (e.g., SiO2). The contact layer 14 does not need to be removed except for the portions overlapping with the electrode portions 161. In this case, the protective film 18 is provided on the contact layer 14 in the gaps between the electrode portions 161.

[0053] The back surface 10b of the semiconductor substrate 10, excluding the region where the electrode 17 is provided, is covered with an anti-reflection film 19, including the inside of the opening 17a. The anti-reflection film 19 in the region excluding the opening 17a may be removed. The anti-reflection film 19 is made of a single-layer or multi-layer dielectric film such as silicon nitride (e.g., SiN) or silicon oxide (e.g., SiO2). The dielectric multi-layer film may be a film formed by stacking two or more dielectric layers selected from the group consisting of titanium oxide (TiO2), silicon dioxide (SiO2), silicon monoxide (SiO), niobium oxide (Nb2O5), tantalum pentoxide (Ta2O5), magnesium fluoride (MgF2), titanium oxide (TiO2), aluminum oxide (Al2O3), cerium oxide (CeO2), indium oxide (In2O3), and zirconium oxide (ZrO2). The dielectric multilayer film is formed by stacking a plurality of films, each having an optical film thickness of λ / 4 for light of wavelength λ, for example.

[0054] In this embodiment, the electrode 16 facing the first surface 20a includes multiple electrode portions 161. However, instead of or in addition to this configuration, the electrode 17 facing the second surface 20b may also include multiple electrode portions. In this case, like the multiple electrode portions 161, the multiple electrode portions of the electrode 17 are also arranged with gaps between them and electrically isolated from one another. Each electrode portion of the electrode 17 corresponds one-to-one to each phase modulation region 151. When viewed from the thickness direction of the semiconductor stack 20, each electrode portion of the electrode 17 overlaps with the corresponding phase modulation region 151. The planar shape of each electrode portion of the electrode 17 is, for example, a rectangular frame shape including an opening 17a. Each of the multiple electrode portions of the electrode 17 is electrically connected to the drive circuit 31 individually via multiple wirings. The drive circuit 31 freely changes the magnitude of the drive current for each electrode portion of the electrode 17.

[0055] In the semiconductor light emitting device 1, when a driving current is supplied between the electrode portion 161 and the electrode 17, recombination of electrons and holes occurs in a portion of the active layer 12 located directly below the electrode portion 161, and light is output from that portion of the active layer 12. At this time, the electrons and holes that contribute to light emission, as well as the light output from the active layer 12, are efficiently confined between the cladding layer 11 and the cladding layer 13.

[0056] The light output from the corresponding portion of the active layer 12 enters the phase modulation region 151 facing the corresponding portion, resonates in the phase modulation region 151 along the imaginary plane P, and forms a predetermined mode corresponding to the arrangement of the multiple modified refractive index regions 15b. A portion of the laser light L output from the phase modulation region 151 is directly output from the back surface 10b through the opening 17a to the outside of the semiconductor light emitting element 1. The remainder of the laser light L output from the phase modulation region 151 is reflected by the electrode 16 and then output from the back surface 10b through the opening 17a to the outside of the semiconductor light emitting element 1. At this time, the signal light contained in the laser light L is output in a direction intersecting both the first surface 20a and the second surface 20b of the semiconductor stack 20. In other words, the signal light contained in the laser light L is output in any direction, including a direction perpendicular to the back surface 10b and a direction inclined relative to the direction perpendicular to the back surface 10b. The light output from the semiconductor light emitting element 1 is composed of the signal light. The signal light is primarily 1st-order diffracted light or -1st-order diffracted light of the laser light, or both. Hereinafter, the 1st-order diffracted light will be referred to as 1st-order light, and the -1st-order diffracted light will be referred to as -1st-order light.

[0057] The laser light L output from each of the multiple phase modulation regions 151 is irradiated as an optical image according to the arrangement of the multiple modified refractive index regions 15b onto a common irradiation region (far field) located in a direction intersecting both the first surface 20a and the second surface 20b of the semiconductor stack 20. The multiple modified refractive index regions 15b included in at least two of the multiple phase modulation regions 151 have different arrangements for each phase modulation region 151. Therefore, the optical images output from each of the multiple phase modulation regions 151 interfere with each other to form a final optical image.

[0058] In order to obtain a final optical image by causing the optical images output from the multiple phase modulation regions 151 to interfere with each other, these optical images are phase-synchronized with each other. In this embodiment, to synchronize these optical images with each other, a connection region 152 is provided between adjacent phase modulation regions 151. Since the resonance modes of adjacent phase modulation regions 151 are shared via the connection region 152, the phases of the laser light L resonating in each phase modulation region 151 can be synchronized with each other. Note that the connection region 152 may be eliminated and adjacent phase modulation regions 151 may be placed adjacent to each other. Even in such a case, the phases of the laser light L resonating in each phase modulation region 151 can be synchronized with each other. Note that in order to synchronize the phases of multiple optical images with each other, this must be taken into consideration when designing the phase distribution φ(x, y) of each phase modulation region 151. Designing the phase distribution φ(x, y) taking phase synchronization into consideration will be described later.

[0059] Furthermore, in order to obtain a desired optical image by causing the optical images output from each of the multiple phase modulation regions 151 to interfere with each other, it is desirable that the polarization directions of these optical images be aligned. In this embodiment, the center of gravity G of the modified refractive index region 15b is located on a straight line D set for each lattice point O. The tilt angle β of the straight line D is the same for all lattice points O in the phase modulation region 151, and is also the same for each of the multiple phase modulation regions 151.

[0060] FIG. 8 is a diagram showing the electromagnetic field distribution in the phase modulation region 151. Part (a) of FIG. 8 shows the electromagnetic field distribution in the resonance mode of symmetry A1 at point M1. Part (b) of FIG. 8 shows the electromagnetic field distribution in the resonance mode of symmetry B2 at point M1. In FIG. 8, the arrows represent the magnitude and direction of the electric field, and the shades of color represent the magnitude of the magnetic field. When the center of gravity G of the modified refractive index region 15b is positioned on the straight line D as in this embodiment (the figure shows a schematic representation of the change in the position of the central modified refractive index region 15b), it is expected that the polarization direction will be consistent in any electromagnetic field distribution, regardless of the distance between the center of gravity G of the modified refractive index region 15b and the lattice point O (in other words, regardless of the phase value realized by each modified refractive index region 15b).

[0061] On the other hand, FIG. 9 shows, as a comparative example, an electromagnetic field distribution in a case where the center of gravity G of the modified refractive index area 15b is located at a fixed distance from the lattice point O, and the rotation angle of the vector connecting the lattice point O to the center of gravity G around the lattice point O is set for each modified refractive index area 15b according to the phase distribution φ(x, y). Part (a) of FIG. 9 shows the electromagnetic field distribution in a resonance mode with symmetry A1 at point M1. Part (b) of FIG. 9 shows the electromagnetic field distribution in a resonance mode with symmetry B2 at point M1. In FIG. 9 as well, the arrows represent the magnitude and direction of the electric field, and the shades of color represent the magnitude of the magnetic field. In this comparative example, in each electromagnetic field distribution, the polarization direction changes depending on the rotation angle of the modified refractive index area 15b around the lattice point O. Therefore, it is almost impossible to expect the polarization directions to be aligned. For these reasons, a configuration in which the center of gravity G of the modified refractive index area 15b is located on a straight line D, as in this embodiment, and the distance between the center of gravity G and the lattice point O changes depending on the phase, is desirable.

[0062] As described above, the semiconductor light emitting element 1 of this embodiment irradiates a common irradiation area with multiple optical images output from multiple phase modulation regions 151, and forms a final optical image (hologram) by overlapping and interfering the multiple optical images. FIG. 10 is a conceptual diagram showing an example of multiple optical images output from multiple phase modulation regions 151. In FIG. 10, a total of 64 optical images LA are shown, arranged in eight columns in the X direction and eight rows in the Y direction, with the lower the optical intensity, the darker the image, and the higher the optical intensity, the lighter the image. These optical images are output from the 64 phase modulation regions 151 arranged in eight columns in the X direction and eight rows in the Y direction. In this example, the optical intensity distribution of the optical images LA output from each of the multiple phase modulation regions 151 includes a sinusoidal distribution whose period in two mutually orthogonal directions (X direction and Y direction) differs for each phase modulation region 151. Such optical images LA can be used, for example, as a basis image for a discrete cosine transform (DCT). That is, the final optical image can be realized by performing a discrete cosine transform on the light intensity distribution of the final optical image and outputting the resulting base images from the phase modulation regions 151. Furthermore, by changing the magnitude of the drive currents of the electrode portions 161 corresponding to the phase modulation regions 151, the contribution of each base image to the final optical image can be individually adjusted, thereby presenting a dynamic optical image that changes over time.

[0063] 11 is a conceptual diagram illustrating another example of multiple optical images output from multiple phase modulation regions 151. This example shows multiple optical images LA used as basis images for a discrete wavelet transform (DWT). As in this example, the final optical image can also be realized by performing a discrete wavelet transform on the light intensity distribution of the final optical image and outputting the resulting multiple basis images from the multiple phase modulation regions 151, respectively. Furthermore, by changing the magnitude of the drive currents of the multiple electrode portions 161 corresponding to the multiple phase modulation regions 151, the contribution of each basis image to the final optical image can be individually adjusted, thereby presenting a dynamic optical image that changes over time.

[0064] Note that the transform is not limited to the discrete cosine transform and the discrete wavelet transform, and for example, the basis images of a collection of multiple optical images to be displayed in the far field may be learned by machine learning (principal component analysis, dictionary learning, etc.). In addition, in the example shown in Fig. 10, the periods in two mutually orthogonal directions (X direction and Y direction) are different for each phase modulation region 151, but the period in one direction (X direction or Y direction) may be different for each phase modulation region 151. FIG. 12 is a conceptual diagram showing yet another example of multiple light images output from multiple phase modulation regions 151. FIG. 12 shows a total of four light images LA, arranged in two columns in the X direction and two rows in the Y direction. These are light images output from the four phase modulation regions 151, arranged in two columns in the X direction and two rows in the Y direction. In this example, the light intensity distribution of the light image LA output from each of the phase modulation regions 151 includes a sinusoidal distribution that changes periodically along the Y direction. The phase in the Y direction of the sinusoidal light intensity distribution of the light image LA output from each of the two phase modulation regions 151 located on one diagonal line is different from the phase in the Y direction of the sinusoidal light intensity distribution of the light image LA output from each of the two phase modulation regions 151 located on the other diagonal line. In this example, the phase of the sinusoidal light intensity distribution presented in the final optical image can be freely changed by changing the ratio between the magnitude of the drive current of the two electrode portions 161 corresponding to the two phase modulation regions 151 located on one diagonal line and the magnitude of the drive current of the two electrode portions 161 corresponding to the two phase modulation regions 151 located on the other diagonal line. As shown in the example in FIG. 12, the phases in one direction (Y direction) of the sinusoidal light intensity distribution of the optical image LA output from each of the at least two phase modulation regions 151 may be different from each other. Note that the light intensity distribution of the optical image LA output from each of the phase modulation regions 151 may include a sinusoidal distribution that changes periodically along two directions (X direction and Y direction). In this case, the phases in two directions (X direction and Y direction) of the sinusoidal light intensity distribution of the optical image LA output from each of the at least two phase modulation regions 151 may be different from each other.

[0065] Next, a detailed description will be given of a phase distribution design method of this embodiment, which takes into consideration the mutual phase synchronization of the optical images output from each of the multiple phase modulation regions 151. In the following description, the multiple modified refractive index regions 15b may be referred to as "multiple points." In other words, the method described below is a method for designing phase distributions φ(x, y) of two or more phase modulation regions 151 that individually modulate the phase of light at multiple points distributed two-dimensionally. In the following description, "real space" refers to the space of the phase modulation region 151, and "wave number space" refers to the space of the optical image (also called a beam pattern) in the irradiation region. [First design method]

[0066] FIG. 13 is a diagram conceptually showing the first design method. First, as a first step, an initial condition is set (arrow B1 in the diagram). For each phase modulation region 151, a first function 203 is set, which is a complex amplitude distribution function including an initial value 201 of the amplitude distribution in wave number space and an initial value 202 of the phase distribution in wave number space. When the initial value 201 of the amplitude distribution in wave number space is F0(kx,ky) and the initial value 202 of the phase distribution in wave number space is θ0(kx,ky), the first function 203 is F0(kx,ky)·e iθ0(kx,ky) In this case, the initial value 201 of the amplitude distribution in the wave number space may be set to a predetermined target amplitude distribution 204 in the wave number space. If the target amplitude distribution 204 in the wave number space is F0(kx,ky), the light intensity distribution (i.e., the desired light image) is expressed as F0 2 (kx, ky). In addition, the initial value 202 of the phase distribution in wave number space may be set to a random phase distribution 205.

[0067] Furthermore, in the first step, for each phase modulation region 151, the first function 203 is transformed into a second function 213, which is a complex amplitude distribution function including a real space amplitude distribution 211 and a real space phase distribution 212, by an inverse Fourier transform such as an Inverse Fast Fourier Transform (IFFT) (arrow B2 in the figure). When the real space amplitude distribution 211 is A(x, y) and the real space phase distribution 212 is φ(x, y), the second function 213 is A(x, y)·e iφ(kx,ky) It is expressed as:

[0068] Next, in the second step, the amplitude distribution 211 of the second function 213 in each phase modulation region 151 is replaced with a target amplitude distribution 214 based on a predetermined target intensity distribution in real space (arrows B3 and B4 in the figure). For example, if the predetermined target intensity distribution is A0 2 (x,y), the target amplitude distribution is given as A0(x,y). In one example, the predetermined target intensity distribution A0 2 (x, y) is constant regardless of x and y, and the target amplitude distribution A0(x, y) is also constant regardless of x and y. At this time, the phase distribution 212 of the second function 213 in each phase modulation region 151 is maintained as is (arrow B5 in the figure). Then, for each phase modulation region 151, the second function 213 after replacement is converted into a third function 223, which is a complex amplitude distribution function including an amplitude distribution 221 in wave number space and a phase distribution 222 in wave number space, by a Fourier transform such as a Fast Fourier Transform (FFT) (arrow B6 in the figure). When the amplitude distribution 221 in wave number space is F(kx, ky) and the phase distribution 222 in wave number space is θ(kx, ky), the third function 223 is expressed as F(kx, ky)·e iθ(kx,ky) It is expressed as:

[0069] Next, in a third step, the phase distribution 222 of the third function 223 in each phase modulation region 151 is aligned with the phase distribution 222 of the third function 223 in one of the multiple phase modulation regions 151 (arrow B7 in the figure). At this time, one phase modulation region 151 that serves as a reference for aligning the phase distributions 222 is arbitrarily determined. Also in this third step, the amplitude distribution 221 of the third function 223 in each phase modulation region 151 is replaced with a target amplitude distribution 204 (arrows B8 and B9 in the figure). Then, for each phase modulation region 151, the replaced third function 223 is converted into a fourth function 233, which is a complex amplitude distribution function including a real space amplitude distribution 231 and a real space phase distribution 232, by an inverse Fourier transform such as IFFT (arrow B2 in the figure). If the amplitude distribution 231 in real space is A(x,y) and the phase distribution 232 in real space is φ(x,y), the fourth function 233 is A(x,y)·e iφ(kx,ky) It is expressed as:

[0070] Thereafter, the second step and the third step are repeated while replacing the second function 213 in the second step with the fourth function 233. Note that each time the third step is repeated, the position of one phase modulation region 151, which serves as a reference for aligning the phase distributions 222, may be fixed without being changed. Then, the phase distribution 232 of the fourth function 233 converted in the final third step is set as the phase distribution φ(x, y) of each phase modulation region 151 (arrow B10 in the figure).

[0071] As an example, consider a phase modulation layer 15 having a total of four phase modulation regions 151 arranged in two columns in the X direction and two rows in the Y direction, as shown in Fig. 14. Two of the phase modulation regions 151 located on a diagonal line have phase distribution pattern A, and two phase modulation regions 151 located on the opposite diagonal line have phase distribution pattern B. Alternatively, as shown in Fig. 15, two phase modulation regions 151 in the first row may have phase distribution pattern B, and two phase modulation regions 151 in the second row may have phase distribution pattern A. Fig. 16 is a diagram conceptually showing a method for designing phase distribution patterns A and B.

[0072] First, as a first step, an initial value is set (arrow B11 in the figure). That is, for the phase distribution pattern A, the first function F1(kx,ky)·e, which is a complex amplitude distribution function including the initial value of the amplitude distribution F1(kx,ky) in the wave number space and the initial value of the phase distribution θ1(kx,ky) in the wave number space, is set. iθ1(kx,ky) Set (hereinafter, F1e iθ1 For the phase distribution pattern B, the first function F2(kx,ky)·e is a complex amplitude distribution function that includes the initial value of the amplitude distribution F2(kx,ky) in the wave number space and the initial value of the phase distribution θ2(kx,ky) in the wave number space. iθ2(kx,ky) Set (hereinafter, F2e iθ2 Then, the first function F1·e of the phase distribution pattern A iθ1 By performing an inverse Fourier transform such as IFFT, the second function A1(x,y)·e is obtained, which is a complex amplitude distribution function including the amplitude distribution A1(x,y) in real space and the phase distribution φ1(x,y) in real space. iφ1(x,y) (arrow B12 in the figure. Below, A1·e iφ1 Similarly, the first function F2(x,y) e of the phase distribution pattern B iθ2(x,y) By performing an inverse Fourier transform such as IFFT, the second function A2(x,y)·e is obtained, which is a complex amplitude distribution function including the amplitude distribution A2(x,y) in real space and the phase distribution φ2(x,y) in real space. iφ2(x,y) (arrow B13 in the figure. Below, A2·e iφ2 abbreviated as ).

[0073] Next, as the second step, the second function A1·e iφ1 The amplitude distribution A1 is converted into a target amplitude distribution A1 based on a predetermined target intensity distribution in real space. ’ Similarly, the second function A2·e iφ2 The amplitude distribution A2 is converted into a target amplitude distribution A2 based on a predetermined target intensity distribution in real space. ’ (arrow B14 in the figure). At this time, the phase distribution φ1 and the phase distribution φ2 are maintained as they are. Then, the second function A1 after the replacement ’ ·e iφ1By applying a Fourier transform such as FFT, the third function F1·e, which is a complex amplitude distribution function including the amplitude distribution F1 in wave number space and the phase distribution θ1 in wave number space, can be obtained. iθ1 (arrow B15 in the figure). Similarly, the second function A2 after the substitution ’ ·e iφ2 By applying a Fourier transform such as FFT, the third function F2·e, which is a complex amplitude distribution function including the amplitude distribution F2 in wave number space and the phase distribution θ2 in wave number space, can be obtained. iθ2 (arrow B16 in the figure).

[0074] Next, in the third step, the third function F2·e iθ2 The phase distribution θ2 of the third function F1·e iθ1 The phase distribution θ1 of the third function F1·e iθ1 The amplitude distribution F1 and the third function F2·e iθ2 The amplitude distribution F2 is set to the target amplitude distribution F1 ’ and F2 ’ (arrow B17 in the figure). Then, the third function F1 ’ ·e iθ1 By performing an inverse Fourier transform such as IFFT, the fourth function A1·e, which is a complex amplitude distribution function including the amplitude distribution A1 in real space and the phase distribution φ1 in real space, is obtained. iφ1 (arrow B18 in the figure). Similarly, the third function F2 ’ ·e iθ1 By performing an inverse Fourier transform such as IFFT, the fourth function A2·e, which is a complex amplitude distribution function including the amplitude distribution A2 in real space and the phase distribution φ2 in real space, is obtained. iφ2 (arrow B19 in the figure).

[0075] From now on, the second function A1·e iφ1 and the second function A2·e iφ2 The fourth function A1·e iφ1 and the fourth function A2·e iφ2 The second and third steps are repeated while replacing the fourth function A1·e with the fourth function A1·e (arrow B20 in the figure). iφ1The phase distribution φ1 of the phase distribution pattern A is defined as the phase distribution φ(x,y) of the phase distribution pattern A. In addition, the fourth function A2·e iφ2 The phase distribution φ2 of the phase distribution pattern B is defined as the phase distribution φ(x, y).

[0076] As another example, consider the phase modulation layer 15 shown in Fig. 17, which has a total of m x n phase modulation regions 151 with m columns in the X direction and n rows in the Y direction. The m x n phase modulation regions 151 have different phase distribution patterns. Fig. 18 is a diagram conceptually showing a method for designing m x n phase distribution patterns.

[0077] First, as a first step, an initial value is set (arrow B41 in the figure). That is, for the m×n phase modulation regions 151, the amplitude distribution F in the wave number space is 1,1 (kx,ky)~F m,n The first function F is a complex amplitude distribution function that includes the initial values ​​of (kx,ky) and the initial values ​​of the phase distributions θ1,1(kx,ky) to θm,n(kx,ky) in wavenumber space. 1,1 (kx,ky)·e iθ1,1(kx,ky) ~F m,n (kx,ky)·e iθm,n(kx,ky) Set (hereinafter, F 1,1 e iθ1,1 ~F m,n e iθm,n Then, for each phase modulation region 151, a first function F 1,1 e iθ1,1 ~F m,n e iθm,n By performing an inverse Fourier transform such as IFFT, the amplitude distribution A 1,1 (x,y)~A m,n (x,y) and the second function A, which is a complex amplitude distribution function containing the real-space phase distributions φ1,1(x,y) to φm,n(x,y), respectively. 1,1 (x,y) e iφ1,1(x,y) ~A m,n (x,y) e iφm,n(x,y) (arrow group B42 in the figure. Hereafter, A 1,1 e iφ1,1 ~A m,n e iφm,n abbreviated as ).

[0078] Next, as a second step, for each phase modulation region 151, a second function A 1,1 e iφ1,1 ~A m,n e iφm,n Amplitude distribution A 1,1 ~A m,n is a target amplitude distribution A based on a predetermined target intensity distribution in real space. ’ 1,1 ~A ’ m,n (arrow B43 in the figure). At this time, the phase distributions φ1,1 to φm,n are maintained as they are. Then, the second function A after the replacement ’ 1,1 e iφ1,1 ~A ’ m,n e iφm,n For each phase modulation region 151, the amplitude distribution F 1,1 ~F m,n and the third function F, which is a complex amplitude distribution function including the phase distributions θ1,1 to θm,n in wavenumber space. 1,1 e iθ1,1 ~F m,n e iθm,n (arrow group B44 in the figure).

[0079] Next, as the third step, we use the third function F 1,1 e iθ1,1 ~F m,n e iθm,n All phase distributions θ1,1 to θm,n are expressed as a third function F 1,1 e iθ1,1 The phase distribution θ1,1 is also aligned with the third function F 1,1 e iθ1,1 ~F m,n e iθm,n The amplitude distribution of F 1,1 ~F m,n , the target amplitude distribution F ’ 1,1 ~F ’ m,n (arrow B45 in the figure). Then, the third function F ’ 1,1 e iθ1,1 ~F ’ m,n eiθ1,1 By performing an inverse Fourier transform such as IFFT, the amplitude distribution A 1,1 ~A m,n and the fourth function A, which is a complex amplitude distribution function including the phase distributions φ1,1 to φm,n in real space. 1,1 e iφ1,1 ~A m,n e iφm,n (arrow group B46 in the figure).

[0080] From now on, the second function A in the second step 1,1 e iφ1,1 ~A m,n e iφm,n the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n The second and third steps are repeated while replacing the fourth function A with the fourth function B (arrow B47 in the figure). 1,1 e iφ1,1 ~A m,n e iφm,n The phase distributions φ1,1 to φm,n are defined as the phase distributions φ(x,y) of the phase modulation regions 151, respectively.

[0081] The configuration of a phase distribution design device for executing the above-described phase distribution design method will be described. Part (a) of FIG. 19 is a block diagram showing the hardware configuration of a phase distribution design device 300 capable of performing the above-described first design method. The phase distribution design device 300 is a device for designing phase distributions of two or more phase modulation regions 151 that individually modulate the phase of light at multiple points distributed two-dimensionally. The phase distribution design device 300 is a computer having a processor, such as a personal computer, a smart device such as a smartphone or a tablet terminal, or a cloud server. As shown in part (a) of FIG. 19, the phase distribution design device 300 can be physically configured as a typical computer including a processor (CPU) 301, a main storage device such as a ROM 302 and a RAM 303, an input device 304 such as a keyboard, a mouse, or a touch screen, an output device 305 such as a display (including a touch screen), a communication module 306 such as a network card for transmitting and receiving data to and from other devices, an auxiliary storage device 307 such as a hard disk, and a device for reading data recorded on a recording medium 308.

[0082] 19(b) is a functional block diagram of a phase distribution design device 300 capable of performing the first design method described above. The phase distribution design device 300 includes a first processing unit 310, a second processing unit 320, and a third processing unit 330. That is, the processor of the computer provided in the phase distribution design device 300 realizes the function of the first processing unit 310, the function of the second processing unit 320, and the function of the third processing unit 330. The respective functions may be realized by the same processor or by different processors.

[0083] The first processing unit 310 performs the first step of the first design method. That is, the first processing unit 310 sets a first function 203 including an initial value 201 of the amplitude distribution in wave number space and an initial value 202 of the phase distribution in wave number space for each phase modulation region 151. Thereafter, the first processing unit 310 converts the first function 203 for each phase modulation region 151 by inverse Fourier transform into a second function 213 including an amplitude distribution 211 in real space and a phase distribution 212 in real space.

[0084] The second processing unit 320 performs the second step of the first design method. That is, the second processing unit 320 replaces the amplitude distribution 211 of the second function 213 in each phase modulation region 151 with a target amplitude distribution 214 based on a predetermined target intensity distribution in real space. At this time, the second processing unit 320 maintains the phase distribution 212 of the second function 213 in each phase modulation region 151 as is. Thereafter, the second processing unit 320 converts, by Fourier transform, the replaced second function 213 for each phase modulation region 151 into a third function 223, which is a complex amplitude distribution function including an amplitude distribution 221 in wavenumber space and a phase distribution 222 in wavenumber space.

[0085] The third processing unit 330 performs the third step of the first design method. That is, the third processing unit 330 aligns the phase distribution 222 of the third function 223 in each phase modulation region 151 with the phase distribution 222 of the third function 223 in one of the multiple phase modulation regions 151. In addition, the third processing unit 330 replaces the amplitude distribution 221 of the third function 223 in each phase modulation region 151 with the target amplitude distribution 204. Thereafter, the third processing unit 330 converts the replaced third function 223 for each phase modulation region 151 by an inverse Fourier transform into a fourth function 233, which is a complex amplitude distribution function including a real space amplitude distribution 231 and a real space phase distribution 232, by

[0086] Thereafter, the operations of the second processing unit 320 and the third processing unit 330 are repeated while replacing the second function 213 of the second processing unit 320 with the fourth function 233. Then, the phase distribution 232 of the fourth function 233 converted by the final operation of the third processing unit 330 is set as the phase distribution φ(x, y) of each phase modulation region 151.

[0087] The processor 301 of the computer can realize each of the above functions by means of a phase distribution design program. Therefore, the phase distribution design program causes the processor 301 of the computer to operate as a first processing unit 310, a second processing unit 320, and a third processing unit 330 in the phase distribution design device 300. The phase distribution design program is stored in a main storage device (ROM 302) or an auxiliary storage device 307 inside the computer. Alternatively, the phase distribution design program may be acquired via a communication line and then stored in the main storage device or the auxiliary storage device 307, or may be read from a computer-readable recording medium 308 and stored in the main storage device or the auxiliary storage device 307. Examples of the recording medium 308 include a flexible disk, a CD-ROM, a DVD-ROM, a BD-ROM, a semiconductor memory, and a cloud server. [Second design method]

[0088] 20 is a diagram conceptually showing the second design method. Note that the first and second steps are the same as those in the first design method described above, and therefore a description thereof will be omitted.

[0089] In the first third step, the phase distribution 222 of the third function 223 in each phase modulation region 151 is replaced with a predetermined phase distribution that is the same in multiple phase modulation regions 151 (arrow B21 in the figure). The phase values ​​of multiple points (kx, ky) in the predetermined phase distribution may be equal to each other. In this case, the phase values ​​of multiple points (kx, ky) in the predetermined phase distribution may be zero (0 rad). At this time, the amplitude distribution 221 is maintained as is (arrow B22 in the figure). Then, the third function 223 is transformed into a fourth function 233 by an inverse Fourier transform such as IFFT (arrow B2 in the figure).

[0090] The second step is performed again by replacing the second function 213 with the fourth function 233, and in the subsequent (second) third step, the amplitude distribution 221 of the third function 223 is replaced with the target amplitude distribution 204 (arrows B23 and B24 in the figure). At this time, the phase distribution 222 is maintained as is (arrow B25 in the figure). Then, the replaced third function 223 is transformed into the fourth function 233 by an inverse Fourier transform such as IFFT (arrow B2 in the figure).

[0091] Thereafter, the second step and the third step are repeated while replacing the second function 213 in the second step with the fourth function 233. In this case, in the third step, the phase distribution 222 is replaced with a predetermined phase distribution and the amplitude distribution 221 is replaced with the target amplitude distribution 204 alternately. The predetermined phase distribution may be fixed without change each time the third step is repeated. The phase distribution 232 of the fourth function 233 converted in the final third step is set as the phase distribution φ(x, y) of each phase modulation region 151 (arrow B10 in the figure).

[0092] As an example, consider the phase modulation layer 15 shown in Fig. 14 or 15, which has a total of four phase modulation regions 151 arranged in two columns in the X direction and two rows in the Y direction. Two of the phase modulation regions 151 have phase distribution pattern A, and the other two phase modulation regions 151 have phase distribution pattern B. Fig. 21 is a diagram conceptually showing a method for designing phase distribution patterns A and B. Note that the first and second steps are similar to the first design method described above, and therefore their explanation will be omitted.

[0093] In the first third step, the third function F1·e iθ1 The phase distribution θ1 of the iθ2 The phase distribution θ2 of the phase distribution pattern A is replaced with a predetermined phase distribution θ' common to both the phase distribution pattern A and the phase distribution pattern B (arrow B31 in the figure). At this time, the amplitude distribution F1 and the amplitude distribution F2 are maintained as they are. Then, the third function F1·e iθ’ and the third function F2·e iθ’ By performing an inverse Fourier transform such as IFFT, the fourth function A1·e iφ1 and the fourth function A2·e iφ2(arrows B32 and B33 in the figure).

[0094] The second function A1·e iφ1 and the second function A2·e iφ2 The fourth function A1·e iφ1 and the fourth function A2·e iφ2 The second step is repeated (arrows B34 to B36 in the figure), and then in the third step (the second time), the third function F1·e iθ1 The amplitude distribution F1 and the third function F2·e iθ2 The amplitude distribution F2 is set to the target amplitude distribution F1 ’ and F2 ’ (arrow B37 in the figure). Then, the third function F1 ’ ·e iθ1 and the third function F2 ’ ·e iθ2 By performing an inverse Fourier transform such as IFFT, the fourth function A1·e iφ1 and the fourth function A2·e iφ2 (arrows B38 and B39 in the figure).

[0095] From now on, the second function A1·e iφ1 and the second function A2·e iφ2 The fourth function A1·e iφ1 and the fourth function A2·e iφ2 The second and third steps are repeated while replacing the phase distributions θ1 and θ2 (arrow B31 in the figure) with the amplitude distributions F1 and F2 (arrow B37 in the figure) in the third step. Then, the fourth function A1·e iφ1 The phase distribution φ1 of the phase distribution pattern A is defined as the phase distribution φ(x,y) of the phase distribution pattern A. In addition, the fourth function A2·e iφ2 The phase distribution φ2 of the phase distribution pattern B is defined as the phase distribution φ(x, y).

[0096] As another example, consider a phase modulation layer 15 having a total of m×n phase modulation regions 151 with m columns in the X direction and n rows in the Y direction, as shown in Fig. 17. The m×n phase modulation regions 151 have different phase distribution patterns. Fig. 22 is a diagram conceptually showing a method for designing m×n phase distribution patterns. Note that the first and second steps are similar to the first design method described above, and therefore description thereof will be omitted.

[0097] In the first third step, the third function F 1,1 e iθ1,1 ~F m,n e iθm,n All the phase distributions θ1,1 to θm,n are replaced with a common and predetermined phase distribution θ′ (arrow B51 in the figure). At this time, the amplitude distribution F 1,1 ~F m,n is kept as it is. And the third function F 1,1 e iθ’ ~F m,n e iθ’ By performing an inverse Fourier transform such as IFFT, the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n (arrow group B52 in the figure).

[0098] Second function A 1,1 e iφ1,1 ~A m,n e iφm,n the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n and the second step is performed again (arrow B53 and arrow group B54 in the figure), and then in the (second) third step, the third function F 1,1 e iθ1,1 ~F m,n e iθm,n The amplitude distribution of F 1,1 ~F m,n , the target amplitude distribution F ’ 1,1 ~F ’ m,n (arrow B55 in the figure). Then, the third function F ’ 1,1 e iθ1,1~F ’ m,n e iθm,n By performing an inverse Fourier transform such as IFFT, the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n (arrow group B56 in the figure).

[0099] From now on, the second function A in the second step 1,1 e iφ1,1 ~A m,n e iφm,n the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n The second and third steps are repeated while replacing the phase distributions θ1,1 to θm,n (arrow B51 in the figure) with the amplitude distribution F 1,1 ~F m,n (arrow B55 in the figure) and the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n The phase distributions θ1,1 to θm,n are defined as the phase distributions φ(x,y) of the phase modulation regions 151, respectively.

[0100] The configuration of a phase distribution design device for executing the above-described phase distribution design method will be described. FIG. 23 is a functional block diagram of a phase distribution design device 400 capable of performing the above-described second design method. The phase distribution design device 400 is a device for designing the phase distribution of two or more phase modulation regions 151 that individually modulate the phase of light at multiple points distributed two-dimensionally. The phase distribution design device 400 has the same hardware configuration as the above-described phase distribution design device 300. The phase distribution design device 400 includes a first processing unit 410, a second processing unit 420, and a third processing unit 430. That is, the processor of a computer provided in the phase distribution design device 400 realizes the functions of the first processing unit 410, the second processing unit 420, and the third processing unit 430. The respective functions may be realized by the same processor or different processors.

[0101] The function of the first processing unit 410 is similar to that of the first processing unit 310 of the above-described phase distribution design device 300. The function of the second processing unit 420 is similar to that of the second processing unit 320 of the above-described phase distribution design device 300.

[0102] The third processing unit 430 performs the third step of the second design method. That is, the third processing unit 430 replaces the phase distribution 222 of the third function 223 in each phase modulation region 151 with a predetermined phase distribution that is the same in multiple phase modulation regions 151, or replaces the amplitude distribution 221 of the third function 223 with a target amplitude distribution 204. Thereafter, the third processing unit 430 converts the third function 223 into a fourth function 233 by an inverse Fourier transform.

[0103] Thereafter, the second step and the third step are repeated while replacing the second function 213 of the second step with the fourth function 233. During this process, in the third step, the phase distribution 222 is replaced with a predetermined phase distribution and the amplitude distribution 221 is replaced with the target amplitude distribution 204 alternately. The phase distribution 232 of the fourth function 233 converted in the final third step is set as the phase distribution φ(x, y) of each phase modulation region 151.

[0104] The computer processor can realize each of the above functions by the phase distribution design program. Therefore, the phase distribution design program causes the computer processor to operate as the first processing unit 410, the second processing unit 420, and the third processing unit 430 in the phase distribution design device 400. The phase distribution design program is stored in a main storage device or an auxiliary storage device inside the computer. Alternatively, the phase distribution design program may be acquired via a communication line and then stored in the main storage device or the auxiliary storage device, or may be read from a computer-readable recording medium and stored in the main storage device or the auxiliary storage device. Examples of recording media include a flexible disk, a CD-ROM, a DVD-ROM, a BD-ROM, a semiconductor memory, a cloud server, etc.

[0105] The effects obtained by the phase distribution design method, phase distribution design device, phase distribution design program, and recording medium of this embodiment explained above will be explained. FIG. 24 is a diagram conceptually showing a third design method as a comparative example. The first and second steps of the third design method are the same as the first and second steps of the first design method described above (arrows B11 to B16 in the figure). Then, in the third step, the third function F1·e iθ1 The amplitude distribution F1 and the third function F2·e iθ2 The amplitude distribution F2 is set to the target amplitude distribution F1 ’ and F2 ’ (arrow B37 in the figure). Then, the third function F1 ’ ·e iθ1 and the third function F2 ’ ·e iθ2 By performing an inverse Fourier transform such as IFFT, the fourth function A1·e iφ1 and the fourth function A2·e iφ2 (arrows B38 and B39 in the figure).

[0106] From now on, the second function A1·e iφ1 and the second function A2·e iφ2 The fourth function A1·e iφ1 and the fourth function A2·e iφ2The second and third steps are repeated while replacing the fourth function A1·e with the fourth function A1·e (arrow B20 in the figure). iφ1 The phase distribution φ1 of the phase distribution pattern A is defined as the phase distribution φ(x,y) of the phase distribution pattern A. In addition, the fourth function A2·e iφ2 The phase distribution φ2 of the phase distribution pattern B is defined as the phase distribution φ(x, y).

[0107] When this third design method is applied individually (independently) to the phase distributions of the multiple phase modulation regions 151, the phases of the multiple optical images output from the multiple phase modulation regions 151 are not synchronized with each other. Therefore, in the first design method, the phase distribution design device 300, and its program, in the third step and the third processing unit 330, the phase distribution 222 in the wave number space of the third function 223 in each phase modulation region 151 is aligned with the phase distribution 222 in the wave number space of the third function 223 in one of the two or more phase modulation regions 151 (arrow B7 in FIG. 13). For example, in the example shown in FIG. 16, as shown by arrow B17, the third function F2(kx,ky)·e iθ2(kx,ky) The phase distribution θ2(kx,ky) of the third function F1(kx,ky)·e iθ1(kx,ky) In the example shown in FIG. 18, as shown by the arrow B45, the third function F 1,1 e iθ1,1 ~F m,n e iθm,n All phase distributions θ1,1 to θm,n are expressed as a third function F 1,1 e iθ1,1 This aligns the phase distribution θ1,1 of the multiple optical images output from the multiple phase modulation regions 151. This makes it possible to synchronize the phases of the multiple optical images output from the multiple phase modulation regions 151. Therefore, it is possible to produce a predetermined interference effect in a hologram formed by superimposing multiple optical images in one region.

[0108] In the second design method, the phase distribution design device 400, and its program, when the third step or the operation of the third processing unit 430 is repeated, one of two times the phase distribution 222 in the wave number space of the third function 223 in each phase modulation region 151 is replaced with a predetermined phase distribution that is the same between two or more phase modulation regions 151. For example, in the example shown in FIG. 21, as indicated by the arrow B31, the third function F1(kx,ky)·e iθ1(kx,ky) The phase distribution θ1(kx,ky) of the iθ2(kx,ky) 22, the phase distribution θ2(kx,ky) of the phase distribution pattern A is replaced with a predetermined phase distribution θ′(kx,ky) that is common to the phase distribution pattern A and the phase distribution pattern B. In addition, in the example shown in FIG. 22, as indicated by the arrow B45, the third function F 1,1 e iθ1,1 ~F m,n e iθm,n All of the phase distributions θ1,1 to θm,n in the phase modulation regions 151 are replaced with a common and predetermined phase distribution θ'. This makes it possible to synchronize the phases of the multiple optical images output from the multiple phase modulation regions 151. Therefore, it is possible to produce a predetermined interference effect in a hologram formed by superimposing multiple optical images in one region.

[0109] As described above, in the first and second design methods, the phase distribution design devices 300 and 400, and the programs thereof, the initial value 201 of the amplitude distribution in wavenumber space may be set to the target amplitude distribution 204. In this case, the optical image can be made to approach a predetermined target intensity distribution with high accuracy with a small number of iterations. In the first and second design methods, the phase distribution design devices 300 and 400, and the programs thereof, the initial value 202 of the phase distribution in wave number space may be set to a random phase distribution 205, as described above.

[0110] As described above, in the first design method, the phase distribution design device 300, and its program, the position of one phase modulation region 151 serving as a reference for aligning the phase distribution 222 may be fixed without being changed each time the third step or the operation of the third processing unit 330 is repeated. According to the simulation by the inventor, the phases of multiple optical images can be synchronized with high precision, particularly in such a case.

[0111] In the second design method, the phase distribution design device 400, and its program, as described above, when the phase distribution 222 of the third function 223 is replaced with a predetermined phase distribution, the phase values ​​of the multiple points (kx, ky) in the predetermined phase distribution may be equal to each other. According to the simulation by the inventor, particularly in such a case, the phases of the multiple optical images can be synchronized with high precision. In this case, the phase values ​​of the multiple points (kx, ky) in the predetermined phase distribution may be zero (0 rad).

[0112] As described above, in the second design method, the phase distribution design device 400, and its program, the predetermined phase distribution may be fixed without change for each repetition of the third step or the operation of the third processing unit 430. According to the simulations by the inventors, it is possible to synchronize the phases of multiple optical images with high precision, particularly in such cases. [First Example]

[0113] The inventors performed a phase distribution design simulation using the phase distribution design method of the above embodiment for a phase modulation layer 15 having four phase modulation regions 151 shown in FIG. 14. Part (a) of FIG. 25 shows a desired light image in the irradiation region (far field) set when designing phase distribution pattern A. In part (a) of FIG. 25, the lighter the color, the higher the light intensity, and the darker the color, the lower the light intensity. As shown in part (a) of FIG. 25, for phase distribution pattern A, a light image having a sinusoidal light intensity distribution in which the light intensity changes periodically along one direction was targeted. Part (b) of FIG. 25 shows the light image shown in part (a) transformed into wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of FIG. 25 shows phase distribution pattern A calculated based on the target amplitude distribution shown in part (b). In part (c) of FIG. 25, the lighter the color, the closer to 2π (rad), and the darker the color, the closer to 0 (rad).

[0114] Part (a) of Figure 26 shows the desired light image in the irradiation area (far field) set when designing phase distribution pattern B. In part (a) of Figure 26, the light intensity increases as the color becomes lighter, and the light intensity decreases as the color becomes darker. As shown in part (a) of Figure 26, for phase distribution pattern B, a light image having a sinusoidal light intensity distribution in which the light intensity periodically changes along a direction perpendicular to the direction of change in light intensity in part (a) of Figure 25 was targeted. However, the period of the sine wave was the same as in part (a) of Figure 25. Part (b) of Figure 26 shows the light image shown in part (a) transformed into wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 26 shows phase distribution pattern B calculated based on the target amplitude distribution shown in part (b). In part (c) of Figure 26, the lighter the color, the closer it is to 2π (rad), and the darker the color, the closer it is to 0 (rad).

[0115] Part (a) of Figure 27 is a diagram showing a state in which a phase distribution pattern A is applied to each of two phase modulation regions 151 located on one diagonal line, and a phase distribution pattern B is applied to each of two phase modulation regions 151 located on the other diagonal line. Part (b) of Figure 27 is a diagram conceptually showing the difference in light intensity between two phase modulation regions 151 located on one diagonal line and two phase modulation regions 151 located on the other diagonal line, which is achieved by individually controlling the current of each electrode portion 161. In part (b) of Figure 27, the lighter the color, the greater the light intensity, and the darker the color, the lower the light intensity.

[0116] 28 is a diagram showing a final optical image that is expected when an optical image (see part (a) of FIG. 25) emitted from two phase modulation regions 151 having phase distribution pattern A and an optical image (see part (a) of FIG. 26) emitted from two phase modulation regions 151 having phase distribution pattern B are made to interfere with each other. When these optical images are made to interfere with each other, the peaks of the optical intensity reinforce each other and the troughs of the optical intensity weaken each other, and it is expected that a checkerboard-like optical intensity distribution will be obtained.

[0117] FIG. 29 shows the final optical image obtained by this simulation. Part (a) of FIG. 29 shows the optical image obtained by the first design method of the above embodiment. Part (b) of FIG. 29 shows the optical image obtained by the second design method of the above embodiment. Part (c) of FIG. 29 shows the optical image obtained by the third design method as a comparative example. Comparing these figures, it can be seen that the checkerboard pattern obtained by the second design method is clearer than that obtained by the third design method. It can also be seen that the checkerboard pattern obtained by the first design method is even clearer than that obtained by the second design method. In this simulation, the clearer the checkerboard pattern, the better the phase synchronization is performed and the more accurate the interference between the optical images. Therefore, it was revealed that the first or second design method can synchronize the phases of the multiple optical images output from the multiple phase modulation regions 151 with each other, compared to the third design method, and can produce a predetermined interference effect in the hologram formed by superimposing multiple optical images in a single region. It was also revealed that this effect is more pronounced with the first design method than with the second design method. [Second Example]

[0118] Next, the inventors performed another phase distribution design simulation using the first design method of the above embodiment for the phase modulation layer 15 having four phase modulation regions 151 shown in FIG. 14. Part (a) of FIG. 30 shows a desired light image in the irradiation region (far field) set when designing phase distribution pattern A. In part (a) of FIG. 30, the lighter the color, the higher the light intensity, and the darker the color, the lower the light intensity. As shown in part (a) of FIG. 30, for phase distribution pattern A, a light image having a sinusoidal light intensity distribution in which the light intensity changes periodically along one direction was targeted. Part (b) of FIG. 30 shows the light image shown in part (a) transformed into wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of FIG. 30 shows phase distribution pattern A calculated based on the target amplitude distribution shown in part (b). In part (c) of FIG. 30, the lighter the color, the closer to 2π (rad), and the darker the color, the closer to 0 (rad).

[0119] Part (a) of Figure 31 shows a desired light image in the irradiation area (far field) set when designing phase distribution pattern B. In part (a) of Figure 31, lighter colors indicate higher light intensity, while darker colors indicate lower light intensity. As shown in part (a) of Figure 31, similar to phase distribution pattern A, the target light image for phase distribution pattern B was a sinusoidal light intensity distribution in which the light intensity periodically changes along one direction. However, the period of the sine wave was the same as that of the desired light image when designing phase distribution pattern A, and the phase of the sine wave was shifted relative to that of the desired light image when designing phase distribution pattern A. Part (b) of Figure 31 shows the light image shown in part (a) converted into wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 31 shows phase distribution pattern B calculated based on the target amplitude distribution shown in part (b). In part (c) of FIG. 31, the lighter the color, the closer it is to 2π (rad), and the darker the color, the closer it is to 0 (rad).

[0120] Part (a) of Figure 32 is a diagram showing a state in which a phase distribution pattern A is applied to each of two phase modulation regions 151 located on one diagonal line, and a phase distribution pattern B is applied to each of two phase modulation regions 151 located on the other diagonal line. Part (b) of Figure 32 is a diagram conceptually showing the difference in light intensity between two phase modulation regions 151 located on one diagonal line and two phase modulation regions 151 located on the other diagonal line, which is achieved by individually controlling the current of each electrode portion 161. In part (b) of Figure 32, the lighter the color, the greater the light intensity, and the darker the color, the lower the light intensity.

[0121] 33 is a diagram showing a final optical image that is expected when an optical image (see part (a) of FIG. 30) emitted from two phase modulation regions 151 having phase distribution pattern A and an optical image (see part (a) of FIG. 31) emitted from two phase modulation regions 151 having phase distribution pattern B are made to interfere with each other. When these optical images are made to interfere with each other, it is expected that a sinusoidal optical intensity distribution having a phase corresponding to the ratio of the optical intensity of the optical image emitted from the two phase modulation regions 151 having phase distribution pattern A to the optical intensity of the optical image emitted from the two phase modulation regions 151 having phase distribution pattern B will be obtained.

[0122] 34 and 35 are diagrams showing the final optical images obtained by this simulation. Fig. 34 shows a case where the phase difference between the optical image output from the phase modulation region 151 having phase distribution pattern A (see part (a) of Fig. 30) and the optical image output from the phase modulation region 151 having phase distribution pattern B (see part (a) of Fig. 31) is 45°. Fig. 35 shows a case where the phase difference between these optical images is 135°. When the optical intensity of the optical image output from the phase modulation region 151 having phase distribution pattern A is PA and the optical intensity of the optical image output from the phase modulation region 151 having phase distribution pattern B is PB, the optical intensity ratio is expressed as (PA / PB). To facilitate understanding of the phase change in response to changes in the light intensity ratio, Figures 34 and 35 show the final light images when the light intensity ratio (PA / PB) is set to 0 / 1.00, 0.25 / 0.75, 0.50 / 0.50, 0.75 / 0.25, and 1.00 / 0, arranged in a direction intersecting the direction of change in light intensity.

[0123] As shown in these figures, according to the phase distribution design method of the above embodiment, by dynamically changing the light intensity ratio of the light images emitted from multiple phase modulation regions 151 having mutually different phase distribution patterns, it is possible to realize a sinusoidal light intensity distribution whose phase can be dynamically changed.

[0124] The phase distribution design method, phase distribution design device, phase distribution design program, and recording medium according to the present disclosure are not limited to the above-described embodiments, and various modifications are possible. For example, in the first design method of the above-described embodiment, the position of one phase modulation region 151 serving as a reference for aligning the phase distribution 222 is fixed each time the third step is repeated. However, the position of the one phase modulation region 151 may be changed each time the third step is repeated. Furthermore, in the second design method of the above-described embodiment, when the phase distribution 222 of the third function 223 is replaced with a predetermined phase distribution in the third step, the phase values ​​of multiple points in the predetermined phase distribution are made equal to each other. However, the phase values ​​of at least two points may be different from each other. Furthermore, when the phase values ​​of multiple points are equal to each other, the phase values ​​are not limited to zero. [Explanation of symbols]

[0125] 1...semiconductor light emitting element, 10...semiconductor substrate, 10a...main surface, 10b...rear surface, 11...cladding layer, 12...active layer, 13...cladding layer, 14...contact layer, 15...phase modulation layer, 15a...basic region, 15b...modified refractive index region, 15c...cap region, 16...electrode (first electrode), 17...electrode (second electrode), 17a...opening, 18...protective film, 19...anti-reflection film, 20...semiconductor stack, 20a...first surface, 20b...second surface, 31...drive circuit, 32...power supply circuit, 33-35...wiring, 151...phase modulation region, 152...connection region, 152a...opening, 152b, 152c...portion, 161...electrode portion, 201...initial value of amplitude distribution in wave number space , 202...initial value of phase distribution in wavenumber space, 203...first function, 204...target amplitude distribution, 205...random phase distribution, 211...amplitude distribution in real space, 212...phase distribution in real space, 213...second function, 214...target amplitude distribution, 221...amplitude distribution in wavenumber space, 222...phase distribution in wavenumber space, 223...third function, 231...amplitude distribution in real space, 232...phase distribution in real space, 233...fourth function, 300,400...phase distribution design device, 310,410...first processing unit, 320,420...second processing unit, 330,430...third processing unit, D...straight line, G...center of gravity, L...laser light, LA...light image, O...lattice point, P...virtual plane, R...unit configuration area.

Claims

1. A method for designing a phase distribution of two or more phase modulation regions included in a phase modulation layer of a semiconductor light-emitting element that outputs an optical image, each phase modulation region including a basic region and a plurality of modified refractive index regions different from the refractive index of the basic region, the plurality of modified refractive index regions respectively corresponding to a plurality of points distributed two-dimensionally, and the positions of the modified refractive index regions being determined so as to individually modulate the phase of light at each of the plurality of points, a first step of setting a first function, which is a complex amplitude distribution function including an initial value of an amplitude distribution in wave number space and an initial value of a phase distribution in wave number space, for each of the phase modulation regions, and converting the first function into a second function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform for each of the phase modulation regions; a second step of replacing the amplitude distribution in the real space of the second function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents a desired optical image in the real space, and converting the second function after the replacement into a third function including an amplitude distribution in a wave number space and a phase distribution in the wave number space by a Fourier transform, for each phase modulation region; a third step of aligning a phase distribution in wavenumber space of the third function in each phase modulation region with a phase distribution in wavenumber space of the third function in one of the two or more phase modulation regions, and replacing an amplitude distribution in wavenumber space of the third function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents the desired optical image in wavenumber space, and converting the third function into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform for each phase modulation region; thereafter, the second step and the third step are repeated while replacing the second function in the second step with the fourth function, and then the phase distribution in the real space of the fourth function converted in the final third step is set as the phase distribution of each phase modulation region.

2. The phase distribution design method according to claim 1 , wherein the one phase modulation region is not changed when the third step is repeated.

3. A method for designing a phase distribution of two or more phase modulation regions included in a phase modulation layer of a semiconductor light-emitting element that outputs an optical image, each phase modulation region including a basic region and a plurality of modified refractive index regions different from the refractive index of the basic region, the plurality of modified refractive index regions respectively corresponding to a plurality of points distributed two-dimensionally, and the positions of the modified refractive index regions being determined so as to individually modulate the phase of light at each of the plurality of points, a first step of setting a first function, which is a complex amplitude distribution function including an initial value of an amplitude distribution in wave number space and an initial value of a phase distribution in wave number space, for each of the phase modulation regions, and converting the first function into a second function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform for each of the phase modulation regions; a second step of replacing the amplitude distribution in the real space of the second function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents a desired optical image in the real space, and converting the second function after the replacement into a third function including an amplitude distribution in a wave number space and a phase distribution in the wave number space by a Fourier transform, for each phase modulation region; a third step of replacing the phase distribution in the wave number space of the third function in each phase modulation region with a predetermined distribution that is the same between the two or more phase modulation regions, or replacing the amplitude distribution in the wave number space of the third function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents the desired optical image in wave number space, and converting the third function after replacement into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform, for each phase modulation region; Including, Thereafter, the second step and the third step are repeatedly performed while replacing the second function in the second step with the fourth function, and at this time, the replacement of the phase distribution in the wave number space and the replacement of the amplitude distribution in the wave number space are alternately performed in the third step; and a phase distribution design method for designing a phase distribution, wherein the phase distribution in the real space of the fourth function converted in the last third step is set as the phase distribution of each phase modulation region.

4. The phase distribution design method according to claim 3 , wherein the phase values ​​of the plurality of points in the predetermined distribution are equal to each other.

5. The phase distribution design method according to claim 4 , wherein the phase value is zero.

6. 6. The phase distribution design method according to claim 3, wherein the predetermined distribution remains unchanged for each repetition of the third step.

7. 7. The phase distribution design method according to claim 1, wherein an initial value of the amplitude distribution in the wave number space is set to the target amplitude distribution in the wave number space.

8. The phase distribution design method according to any one of claims 1 to 7, wherein an initial value of the phase distribution in the wave number space is set to a random distribution.

9. An apparatus for designing the phase distribution of two or more phase modulation regions included in a phase modulation layer of a semiconductor light-emitting element that outputs an optical image, each phase modulation region including a basic region and a plurality of modified refractive index regions different from the refractive index of the basic region, the plurality of modified refractive index regions respectively corresponding to a plurality of points distributed two-dimensionally, and the positions of the modified refractive index regions being determined so as to individually modulate the phase of light at each of the plurality of points, a first processing unit that sets a first function, which is a complex amplitude distribution function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space, for each of the phase modulation regions, and converts the first function into a second function including an amplitude distribution in real space and a phase distribution in real space by an inverse Fourier transform for each of the phase modulation regions; a second processing unit that replaces the amplitude distribution in the real space of the second function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents a desired optical image in real space, and converts the second function after the replacement into a third function that includes an amplitude distribution in a wave number space and a phase distribution in the wave number space by a Fourier transform, for each phase modulation region; a third processing unit that aligns a phase distribution in wavenumber space of the third function in each phase modulation region with a phase distribution in wavenumber space of the third function in one of the two or more phase modulation regions, replaces an amplitude distribution in wavenumber space of the third function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents the desired optical image in wavenumber space, and converts the third function into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform, for each phase modulation region; Equipped with a phase distribution design device in which the second processing unit and the third processing unit repeat operations while replacing the second function with the fourth function in the second processing unit, and then the phase distribution in the real space of the fourth function finally converted by the third processing unit is set as the phase distribution of each phase modulation region.

10. An apparatus for designing the phase distribution of two or more phase modulation regions included in a phase modulation layer of a semiconductor light-emitting element that outputs an optical image, each phase modulation region including a basic region and a plurality of modified refractive index regions different from the refractive index of the basic region, the plurality of modified refractive index regions respectively corresponding to a plurality of points distributed two-dimensionally, and the positions of the modified refractive index regions being determined so as to individually modulate the phase of light at each of the plurality of points, a first processing unit that sets a first function, which is a complex amplitude distribution function including an initial value of an amplitude distribution in wavenumber space and an initial value of a phase distribution in wavenumber space, for each of the phase modulation regions, and converts the first function into a second function including an amplitude distribution in real space and a phase distribution in real space by an inverse Fourier transform for each of the phase modulation regions; a second processing unit that replaces the amplitude distribution in the real space of the second function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents a desired optical image in real space, and converts the second function after the replacement into a third function that includes an amplitude distribution in a wave number space and a phase distribution in the wave number space by a Fourier transform, for each phase modulation region; a third processing unit that replaces the phase distribution in the wave number space of the third function in each phase modulation region with a predetermined distribution that is the same between the two or more phase modulation regions, or replaces the amplitude distribution in the wave number space of the third function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents the desired optical image in wave number space, and converts the third function after replacement into a fourth function that includes an amplitude distribution in real space and a phase distribution in real space by an inverse Fourier transform, for each phase modulation region; Equipped with The second processing unit and the third processing unit repeat operations while replacing the second function with the fourth function in the second processing unit, and at that time, the third processing unit alternately replaces the phase distribution in the wave number space and the amplitude distribution in the wave number space, a phase distribution design device that sets the phase distribution in the real space of the fourth function finally converted by the third processing unit as the phase distribution of each phase modulation region.

11. A program for designing the phase distribution of two or more phase modulation regions included in a phase modulation layer of a semiconductor light-emitting element that outputs an optical image, each phase modulation region including a basic region and a plurality of modified refractive index regions different from the refractive index of the basic region, the plurality of modified refractive index regions respectively corresponding to a plurality of points distributed two-dimensionally, and the positions of the modified refractive index regions being determined so as to individually modulate the phase of light at each of the plurality of points, a first step of setting a first function, which is a complex amplitude distribution function including an initial value of an amplitude distribution in wave number space and an initial value of a phase distribution in wave number space, for each of the phase modulation regions, and converting the first function into a second function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform for each of the phase modulation regions; a second step of replacing the amplitude distribution in the real space of the second function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents a desired optical image in the real space, and converting the second function after the replacement into a third function including an amplitude distribution in a wave number space and a phase distribution in the wave number space by a Fourier transform, for each phase modulation region; a third step of aligning a phase distribution in wavenumber space of the third function in each phase modulation region with a phase distribution in wavenumber space of the third function in one of the two or more phase modulation regions, and replacing an amplitude distribution in wavenumber space of the third function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents the desired optical image in wavenumber space, and converting the third function into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform for each phase modulation region; and thereafter, the second step and the third step are repeatedly executed by the computer while replacing the second function in the second step with the fourth function, and then the phase distribution in the real space of the fourth function converted by the final third step is set as the phase distribution of each phase modulation region.

12. A program for designing a phase distribution of two or more phase modulation regions included in a phase modulation layer of a semiconductor light-emitting element that outputs an optical image, each phase modulation region including a basic region and a plurality of modified refractive index regions different from the refractive index of the basic region, the plurality of modified refractive index regions respectively corresponding to a plurality of points distributed two-dimensionally, and the positions of the modified refractive index regions being determined so as to individually modulate the phase of light at each of the plurality of points, a first step of setting a first function, which is a complex amplitude distribution function including an initial value of an amplitude distribution in wave number space and an initial value of a phase distribution in wave number space, for each of the phase modulation regions, and converting the first function into a second function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform for each of the phase modulation regions; a second step of replacing the amplitude distribution in the real space of the second function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents a desired optical image in the real space, and converting the second function after the replacement into a third function including an amplitude distribution in a wave number space and a phase distribution in the wave number space by a Fourier transform, for each phase modulation region; a third step of replacing the phase distribution in the wave number space of the third function in each phase modulation region with a predetermined distribution that is the same between the two or more phase modulation regions, or replacing the amplitude distribution in the wave number space of the third function in each phase modulation region with a target amplitude distribution that is the square root of an arbitrary target intensity distribution that represents the desired optical image in wave number space, and converting the third function after replacement into a fourth function including an amplitude distribution in real space and a phase distribution in real space by inverse Fourier transform, for each phase modulation region; and thereafter, the second step and the third step are repeatedly executed by the computer while replacing the second function in the second step with the fourth function, and at this time, the replacement of the phase distribution in the wave number space and the replacement of the amplitude distribution in the wave number space are alternately performed in the third step; and a phase distribution design program for determining the phase distribution in the real space of the fourth function converted by the last third step as the phase distribution of each phase modulation region.

13. A computer-readable recording medium on which the phase distribution design program according to claim 11 or 12 is recorded.

Images