PHASE DISTRIBUTION DESIGN METHOD, PHASE DISTRIBUTION DESIGN DEVICE, PHASE DISTRIBUTION DESIGN PROGRAM, AND RECORDING MEDIUM

Abstract

In a second processing, a second function in a real space after an amplitude distribution has been replaced with a target amplitude distribution is converted to a third function in a wave number space including an amplitude distribution and a phase distribution through a Fourier transform. In a third processing, the phase distribution of the third function is made the same as the phase distribution of the third function in one of two or more phase modulation areas, the amplitude distribution of the third function is replaced with a target amplitude distribution, and the third function is converted to a fourth function in the real space including an amplitude distribution and a phase distribution through an inverse Fourier transform. Thereafter, the second processing and the third processing are repeated while replacing the second function of the second processing with the fourth function.

Claims

1. A phase distribution design method of designing phase distributions of two or more phase modulation areas for individually modulating phases of light at a plurality of points which are distributed in a two-dimensional shape, the phase distribution design method comprising: performing a first processing of setting a first function including an initial value of an amplitude distribution in a wave number space and an initial value of a phase distribution in the wave number space for each of the two or more phase modulation areas and converting the first function to a second function including an amplitude distribution in a real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area; performing a second processing of replacing the amplitude distribution in the real space of the second function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the real space and converting the second function subjected to replacement to a third function including an amplitude distribution in the wave number space and a phase distribution in the wave number space through a Fourier transform for each phase modulation area; and performing a third processing of making the phase distribution in the wave number space of the third function in each of the two or more phase modulation areas same as the phase distribution in the wave number space of the third function in one phase modulation area of the two or more phase modulation areas, replacing the amplitude distribution in the wave number space of the third function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the wave number space, and converting the third function to a fourth function including an amplitude distribution in the real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area, wherein the second processing and the third processing are then repeated while replacing the second function of the second processing with the fourth function, and then the phase distribution in the real space of the fourth function finally subjected to conversion in the third processing is set as the phase distribution of each of the two or more phase modulation areas.

2. The phase distribution design method according to claim 1, wherein the one phase modulation area is fixed at repetition of the third processing.

3. A phase distribution design method of designing phase distributions of two or more phase modulation areas for individually modulating phases of light at a plurality of points which are distributed in a two-dimensional shape, the phase distribution design method comprising: performing a first processing of setting a first function including an initial value of an amplitude distribution in a wave number space and an initial value of a phase distribution in the wave number space for each of the two or more phase modulation areas and converting the first function to a second function including an amplitude distribution in a real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area; performing a second processing of replacing the amplitude distribution in the real space of the second function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the real space and converting the second function subjected to replacement to a third function including an amplitude distribution in the wave number space and a phase distribution in the wave number space through a Fourier transform for each phase modulation area; and performing a third processing of performing a first procedure of replacing the phase distribution in the wave number space of the third function in each of the two or more phase modulation areas with a predetermined distribution which is same in the two or more phase modulation areas or a second procedure of replacing the amplitude distribution in the wave number space of the third function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the wave number space and converting the third function subjected to replacement to a fourth function including an amplitude distribution in the real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area, wherein the second processing and the third processing are then repeated while replacing the second function of the second processing with the fourth function, the first procedure and the second procedure being alternately performed in repetition of the third processing, and wherein the phase distribution in the real space of the fourth function finally subjected to conversion in the third processing is set as the phase distribution of each of the two or more phase modulation areas.

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

5. The phase distribution design method according to claim 4, wherein the phase values are zero.

6. The phase distribution design method according to claim 3, wherein the predetermined distribution is fixed in repetition of the third processing.

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

8. The phase distribution design method according to claim 1, wherein the initial value of the phase distribution in the wave number space has a random distribution.

9. A phase distribution design device for designing phase distributions of two or more phase modulation areas for individually modulating phases of light at a plurality of points which are distributed in a two-dimensional shape, the phase distribution design device comprising a processor executing: a first processing of setting a first function including an initial value of an amplitude distribution in a wave number space and an initial value of a phase distribution in the wave number space for each of the two or more phase modulation areas and converting the first function to a second function including an amplitude distribution in a real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area; a second processing of replacing the amplitude distribution in the real space of the second function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the real space and converting the second function subjected to replacement to a third function including an amplitude distribution in the wave number space and a phase distribution in the wave number space through a Fourier transform for each phase modulation area; and a third processing of making the phase distribution in the wave number space of the third function in each of the two or more phase modulation areas same as the phase distribution in the wave number space of the third function in one phase modulation area of the two or more phase modulation areas, to replace the amplitude distribution in the wave number space of the third function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the wave number space, and converting the third function to a fourth function including an amplitude distribution in the real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area, wherein the second processing and the third processing are then repeated while replacing the second function of the second processing with the fourth function, and then the phase distribution in the real space of the fourth function finally subjected to conversion in the third processing is set as the phase distribution of each of the two or more phase modulation areas.

10. A phase distribution design device for designing phase distributions of two or more phase modulation areas for individually modulating phases of light at a plurality of points which are distributed in a two-dimensional shape, the phase distribution design device comprising a processor executing: a first processing of setting a first function including an initial value of an amplitude distribution in a wave number space and an initial value of a phase distribution in the wave number space for each of the two or more phase modulation areas and converting the first function to a second function including an amplitude distribution in a real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area; a second processing of replacing the amplitude distribution in the real space of the second function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the real space and converting the second function subjected to replacement to a third function including an amplitude distribution in the wave number space and a phase distribution in the wave number space through a Fourier transform for each phase modulation area; and a third processing of performing a first procedure of replacing the phase distribution in the wave number space of the third function in each of the two or more phase modulation areas with a predetermined distribution which is same in the two or more phase modulation areas or a second procedure of replacing the amplitude distribution in the wave number space of the third function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the wave number space and converting the third function subjected to replacement to a fourth function including an amplitude distribution in the real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area, wherein the second processing and the third processing are then repeated while replacing the second function of the second processing with the fourth function, the first procedure and the second procedure being alternately performed in repetition of operation of the third processing, and wherein the phase distribution in the real space of the fourth function finally subjected to conversion in the third processing is set as the phase distribution of each of the two or more phase modulation areas.

11. A phase distribution design program for designing phase distributions of two or more phase modulation areas for individually modulating phases of light at a plurality of points which are distributed in a two-dimensional shape, the phase distribution design program causing a computer to perform: a first processing of setting a first function including an initial value of an amplitude distribution in a wave number space and an initial value of a phase distribution in the wave number space for each of the two or more phase modulation areas and converting the first function to a second function including an amplitude distribution in a real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area; a second processing of replacing the amplitude distribution in the real space of the second function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the real space and converting the second function subjected to replacement to a third function including an amplitude distribution in the wave number space and a phase distribution in the wave number space through a Fourier transform for each phase modulation area; and a third processing of making the phase distribution in the wave number space of the third function in each of the two or more phase modulation areas same as the phase distribution in the wave number space of the third function in one phase modulation area of the two or more phase modulation areas, replacing the amplitude distribution in the wave number space of the third function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the wave number space, and converting the third function to a fourth function including an amplitude distribution in the real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area, wherein the computer is then caused to repeatedly perform the second processing and the third processing while replacing the second function of the second processing with the fourth function, and then the phase distribution in the real space of the fourth function finally subjected to conversion in the third processing is set as the phase distribution of each of the two or more phase modulation areas.

12. A phase distribution design program for designing phase distributions of two or more phase modulation areas for individually modulating phases of light at a plurality of points which are distributed in a two-dimensional shape, the phase distribution design program causing a computer to perform: a first processing of setting a first function including an initial value of an amplitude distribution in a wave number space and an initial value of a phase distribution in the wave number space for each of the two or more phase modulation areas and converting the first function to a second function including an amplitude distribution in a real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area; a second processing of replacing the amplitude distribution in the real space of the second function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the real space and converting the second function subjected to replacement to a third function including an amplitude distribution in the wave number space and a phase distribution in the wave number space through a Fourier transform for each phase modulation area; and a third processing of performing a first procedure of replacing the phase distribution in the wave number space of the third function in each of the two or more phase modulation areas with a predetermined distribution which is same in the two or more phase modulation areas or a second procedure of replacing the amplitude distribution in the wave number space of the third function in each of the two or more phase modulation areas with a target amplitude distribution based on a predetermined target intensity distribution in the wave number space and converting the third function subjected to replacement to a fourth function including an amplitude distribution in the real space and a phase distribution in the real space through an inverse Fourier transform for each phase modulation area, wherein the computer is then caused to repeatedly perform the second processing and the third processing while replacing the second function of the second processing with the fourth function, the first procedure and the second procedure being alternately performed in repetition of the third processing, and wherein the phase distribution in the real space of the fourth function finally subjected to conversion in the third processing is set as the phase distribution of each of the two or more phase modulation areas.

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

Description

BRIEF DESCRIPTION OF DRAWINGS

[0027] FIG. 1 is a sectional view illustrating a stacked structure of a semiconductor light-emitting device to which a phase distribution design method according to an embodiment is applied.

[0028] FIG. 2 is a plan view of a phase modulation layer (when seen in a thickness direction thereof).

[0029] FIG. 3 is an enlarged plan view of a part of a phase modulation area.

[0030] FIG. 4 is an enlarged view of a single unit constituent area.

[0031] FIG. 5 is a diagram illustrating coordinate transformation from spherical coordinates to coordinates in an XYZ orthogonal coordinate system.

[0032] FIG. 6 is a partially enlarged plan view of a connection area.

[0033] FIG. 7 is a diagram schematically illustrating planar shapes of a first electrode and a second electrode and a configuration for supplying a current to the first electrode and the second electrode.

[0034] FIG. 8 is a diagram illustrating an electromagnetic field distribution in phase modulation areas, where part (a) of FIG. 8 illustrates an electromagnetic field distribution in a resonance mode with symmetry A.sub.1 at M.sub.1 points and part (b) of FIG. 8 illustrates an electromagnetic field distribution in a resonance mode with symmetry B.sub.2 at M.sub.1 points.

[0035] FIG. 9 is a diagram illustrating an electromagnetic field distribution according to a comparative example, where part (a) of FIG. 9 illustrates an electromagnetic field distribution in a resonance mode with symmetry A.sub.1 at M.sub.1 points and part (b) of FIG. 9 illustrates an electromagnetic field distribution in a resonance mode with symmetry B.sub.2 at M.sub.1 points.

[0036] FIG. 10 is a diagram conceptually illustrating an example of a plurality of light images output from a plurality of phase modulation areas.

[0037] FIG. 11 is a diagram conceptually illustrating another example of a plurality of light images output from a plurality of phase modulation areas.

[0038] FIG. 12 is a diagram conceptually illustrating another example of a plurality of light images output from a plurality of phase modulation areas.

[0039] FIG. 13 is a diagram conceptually illustrating a first design method.

[0040] FIG. 14 is a diagram illustrating a phase modulation layer including a total of four phase modulation areas of two columns in an X direction and two rows in a Y direction.

[0041] FIG. 15 is a diagram illustrating a phase modulation layer in which two phase modulation areas included in a first row have phase distribution pattern B and two phase modulation areas included in a second row have phase distribution pattern A.

[0042] FIG. 16 is a diagram conceptually illustrating a design method of phase distribution patterns A and B.

[0043] FIG. 17 is a diagram illustrating a phase modulation layer including a total of mn phase modulation areas of m columns in the X direction and n rows in the Y direction.

[0044] FIG. 18 is a diagram conceptually illustrating a method of designing mn phase distribution patterns.

[0045] Part (a) of FIG. 19 is a block diagram illustrating a hardware configuration of a phase distribution design device that can perform the first design method, and part (b) of FIG. 19 is a functional block diagram illustrating the phase distribution design device that can perform the first design method.

[0046] FIG. 20 is a diagram conceptually illustrating a second design method.

[0047] FIG. 21 is a diagram conceptually illustrating a design method of phase distribution patterns A and B.

[0048] FIG. 22 is a diagram conceptually illustrating a method of designing mn phase distribution patterns.

[0049] FIG. 23 is a block diagram illustrating a configuration of a phase distribution design device that can perform the second design method.

[0050] FIG. 24 is a diagram conceptually illustrating a third design method according to a comparative example.

[0051] Part (a) of FIG. 25 is a diagram illustrating a desired light image in an irradiation area (a far field) which is set when phase distribution pattern A is designed, part (b) of FIG. 25 is a diagram illustrating a light image obtained by converting the light image illustrated in part (a) of FIG. 25 to a wave number space, that is, a target amplitude distribution in the wave number space, and part (c) of FIG. 25 is a diagram illustrating phase distribution pattern A which is calculated on the basis of the target amplitude distribution illustrated in part (b) of FIG. 25.

[0052] Part (a) of FIG. 26 is a diagram illustrating a desired light image in an irradiation area (a far field) which is set when phase distribution pattern B is designed, part (b) of FIG. 26 is a diagram illustrating a light image obtained by converting the light image illustrated in part (a) of FIG. 26 to a wave number space, that is, a target amplitude distribution in the wave number space, and part (c) of FIG. 26 is a diagram illustrating phase distribution pattern B which is calculated on the basis of the target amplitude distribution illustrated in part (b) of FIG. 26.

[0053] Part (a) of FIG. 27 is a diagram illustrating an example in which phase distribution pattern A is applied to two phase modulation areas located on one diagonal and phase distribution pattern B is applied to two phase modulation areas located on the other diagonal, and part (b) of FIG. 27 is a diagram conceptually illustrating a difference between a light intensity of two phase modulation areas located on one diagonal and a light intensity of two phase modulation areas located on the other diagonal which is realized by individually controlling currents of electrode parts.

[0054] FIG. 28 is a diagram illustrating a final light image which is supposed when light images output from two phase modulation areas with phase distribution pattern A and light images output from two phase modulation areas with phase distribution pattern B are caused to interfere with each other.

[0055] Part (a) of FIG. 29 illustrates a final light image obtained using the first design method, part (b) of FIG. 29 illustrates a final light image obtained using the second design method, and part (c) of FIG. 29 illustrates a final light image obtained using a third design method according to a comparative example.

[0056] Part (a) of FIG. 30 is a diagram illustrating a desired light image in an irradiation area (a far field) which is set when phase distribution pattern A is designed, part (b) of FIG. 30 is a diagram illustrating a light image obtained by converting the light image illustrated in part (a) of FIG. 30 to a wave number space, that is, a target amplitude distribution in the wave number space, and part (c) of FIG. 30 is a diagram illustrating phase distribution pattern A which is calculated on the basis of the target amplitude distribution illustrated in part (b) of FIG. 30.

[0057] Part (a) of FIG. 31 is a diagram illustrating a desired light image in an irradiation area (a far field) which is set when phase distribution pattern B is designed, part (b) of FIG. 31 is a diagram illustrating a light image obtained by converting the light image illustrated in part (a) of FIG. 31 to a wave number space, that is, a target amplitude distribution in the wave number space, and part (c) of FIG. 31 is a diagram illustrating phase distribution pattern B which is calculated on the basis of the target amplitude distribution illustrated in part (b) of FIG. 31.

[0058] Part (a) of FIG. 32 is a diagram illustrating an example in which phase distribution pattern A is applied to two phase modulation areas located on one diagonal and phase distribution pattern B is applied to two phase modulation areas located on the other diagonal, and part (b) of FIG. 32 is a diagram conceptually illustrating a difference between a light intensity of two phase modulation areas located on one diagonal and a light intensity of two phase modulation areas located on the other diagonal which is realized by individually controlling currents of electrode parts.

[0059] FIG. 33 is a diagram illustrating a final light image which is supposed when light images output from a phase modulation area with phase distribution pattern A and light images output from a phase modulation area with phase distribution pattern B are caused to interfere with each other.

[0060] FIG. 34 is a diagram illustrating a final light image obtained by simulation.

[0061] FIG. 35 is a diagram illustrating a final light image obtained by simulation.

DESCRIPTION OF EMBODIMENTS

[0062] Specific examples of a phase distribution design method, a phase distribution design device, a phase distribution design program, and a recording medium according to the present disclosure will be described below with reference to the accompanying drawings. The present disclosure is not limited to such examples and is intended to be represented by the appended claims and to include all modifications with meanings and scopes equivalent to the claims. In the following description, the same elements in description with reference to the drawings will be referred to by the same reference signs, and description thereof will be omitted.

[0063] FIG. 1 is a sectional view illustrating a stacked structure of a semiconductor light-emitting device 1 to which a phase distribution design method according to an embodiment is applied. In FIG. 1, an XYZ orthogonal coordinate system with an axis extending in a thickness direction of the semiconductor light-emitting device 1 as a Z axis is defined. The semiconductor light-emitting device 1 is a laser light source that forms a standing wave in the XY plane direction and outputs a planar wave of which a phase has been controlled in a direction crossing the thickness direction. The semiconductor light-emitting device 1 is an S-iPM laser and can output an arbitrary-shaped light image in a direction perpendicular to a main surface 10a of a semiconductor substrate 10, that is, in the Z direction, a direction oblique to the Z direction, or a direction including both thereof.

[0064] The semiconductor light-emitting device 1 includes semiconductor substrate 10. The semiconductor substrate 10 includes a main surface 10a and a rear surface 10b. A normal direction of the main surface 10a and the rear surface 10b and the thickness direction of the semiconductor substrate 10 are along the Z direction. The semiconductor substrate 10 is formed of, for example, a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor.

[0065] The semiconductor light-emitting device 1 further includes a semiconductor stacked layer 20. The semiconductor stacked layer 20 is provided on the main surface 10a of the semiconductor substrate 10. A stacking direction of the semiconductor stacked layer 20 is along the Z direction. The semiconductor stacked layer 20 has a stacked structure in which a clad layer 11, an active layer 12, a clad layer 13, a contact layer 14, and a phase modulation layer 15 are included between a first face 20a and a second face 20b. The second face 20b of the semiconductor stacked layer 20 is opposite to the main surface 10a of the semiconductor substrate 10. In the illustrated example, the clad layer 11 is provided on the main surface 10a of the semiconductor substrate 10, the active layer 12 is provided on the clad layer 11, the phase modulation layer 15 is provided on the active layer 12, the clad layer 13 is provided on the phase modulation layer 15, and the contact layer 14 is provided on the clad layer 13. That is, the clad layers 11 and 13 have the active layer 12 and the phase modulation layer 15 interposed therebetween. In the illustrated example, the phase modulation layer 15 is provided between the active layer 12 and the clad layer 13, but the phase modulation layer 15 may be provided between the clad layer 11 and the active layer 12. A light guide layer may be provided in one or both of a layer between the active layer 12 and the clad layer 13 and a layer between the active layer 12 and the clad layer 11 according to necessity. The light guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

[0066] The clad layer 11, the active layer 12, the clad layer 13, and the contact layer 14 are formed of, for example, 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 multi-quantum well structure. An energy bandgap of the clad layer 11 and an energy bandgap of the clad layer 13 are larger than an energy bandgap of the active layer 12. The thickness directions of the clad layer 11, the active layer 12, the clad layer 13, and the contact layer 14 coincide with the Z-axis direction.

[0067] 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 of the phase modulation layer 15 (a view in the thickness direction). As illustrated in FIGS. 1 and 2, the phase modulation layer 15 includes a plurality of phase modulation areas 151 and a connection area 152. A planar shape of the connection area 152 when seen in the stacking direction of the semiconductor stacked layer 20 is, for example, a lattice shape. The plurality of phase modulation areas 151 are provided at a plurality of openings 152a of the connection area 152 formed in the lattice shape.

[0068] A planar shape of each of the plurality of phase modulation areas 151 is, for example, square or rectangular. The plurality of phase modulation areas 151 are two-dimensionally arranged on a virtual plane P perpendicular to the thickness direction of the phase modulation layer 15 (that is, parallel to the XY plane) and are optically coupled to each other. In the illustrated example, the plurality of phase modulation areas 151 are arranged in the X direction and the Y direction. In the illustrated example, the plurality of phase modulation areas 151 are two-dimensionally arranged, but the plurality of phase modulation areas 151 may be one-dimensionally arranged. In the illustrated example, the plurality of phase modulation areas 151 are arranged with intervals therebetween. The connection area 152 includes a part 152b provided between the neighboring phase modulation areas 151 and a frame-shaped part 152c surrounding the plurality of phase modulation areas 151 together.

[0069] As illustrated in FIG. 1, each of the plurality of phase modulation areas 151 includes a basic region 15a and a plurality of different-refractive-index regions 15b. Similarly, the connection area 152 also includes a basic region 15a and a plurality of different-refractive-index regions 15b. The basic region 15a is formed of a first refractive-index medium. The basic region 15a is formed of, for example, a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor. The plurality of different-refractive-index regions 15b are formed of a second refractive-index medium of which the refractive index is different from that of the first refractive-index medium and are present in the basic region 15a. The different-refractive-index regions 15b are, for example, voids. The different-refractive-index regions 15b are covered by a cap region 15c provided on the basic region 15a. The cap region 15c constitutes a part of the phase modulation layer 15 and is formed of, for example, the same material as the basic region 15a.

[0070] The plurality of different-refractive-index regions 15b are distributed in a two-dimensional shape on a virtual plane P. In each phase modulation area 151, the plurality of different-refractive-index regions 15b include a substantially periodical structure of a lattice shape. When an equivalent refractive index of a mode is n and a lattice spacing is a, a wavelength .sub.0 selected by each phase modulation area 151 is expressed by .sub.0=(2)an, for example, in a case of M.sub.1-point oscillation. This wavelength .sub.0 is included in an emission wavelength range of the active layer 12. Each phase modulation area 151 selects a band end wavelength near the wavelength .sub.0 out of emission wavelengths of the active layer 12 and outputs the selected band end wavelength to the outside. Light incident on each phase modulation area 151 from the active layer 12 forms a predetermined mode based on the arrangement of the different-refractive-index regions 15b in each phase modulation area 151 and is output as laser light L from the rear surface 10b of the semiconductor substrate 10 to the outside of the semiconductor light-emitting device 1.

[0071] FIG. 3 is an enlarged plan view of a part of the phase modulation area 151. Only one phase modulation area 151 is illustrated in FIG. 3, and the other phase modulation areas 151 have the same configuration. As described above, each phase modulation area 151 includes the basic region 15a and the plurality of different-refractive-index regions 15b. In FIG. 3, virtual tetragonal lattices on the virtual plane P are set for the phase modulation area 151. One side of each tetragonal lattice is parallel to the X axis, and the other side is parallel to the Y axis. Unit constituent areas R with a square shape centered on lattice points O of the tetragonal lattice are two-dimensionally arranged in a plurality of columns along the X axis and a plurality of rows along the Y axis. XY coordinates of each unit constituent area R are defined by a position of the centroid of the corresponding unit constituent area R. The positions of the centroids match the lattice points O of the virtual tetragonal lattice. For example, one different-refractive-index region 15b is provided in each unit constituent area R. A planar shape of the different-refractive-index region 15b is, for example, circular. The lattice point O may be located outside of the different-refractive-index region 15b or may be located inside of the different-refractive-index region 15b.

[0072] FIG. 4 is an enlarged view of one unit constituent area R. As illustrated in the drawing, each different-refractive-index region 15b has the centroid G. The centroid G of the different-refractive-index region 15b is disposed on a straight line D which is set for each lattice point O. The straight line D is a straight line which passes through the lattice point O corresponding to the corresponding unit constituent area R and which is oblique to the sides of the tetragonal lattice. That is, the straight line D is a straight line which is oblique to both the X axis and the Y axis. A tilt angle of the straight line D with respect to one side of the tetragonal lattice, that is, the X axis, is .

[0073] The tilt angle is the same for all the straight lines D in the phase modulation area 151. The tilt angle is the same for all of the plurality of phase modulation areas 151. The tilt angle satisfies 0<<90 and is, for example, 45. Alternatively, the tilt angle satisfies 180<<270 and is, for example, =225. When the tilt angle satisfies 0<<90 or 180<<270, the straight line D extends from the first quadrant to the third quadrant of a coordinate plane which is defined by the X axis and the Y axis. The tilt angle satisfies 90<<180 and is, for example, =135. Alternatively, the tilt angle satisfies 270<<360 and is, for example, =315. When the tilt angle satisfies 90<<180 or 270<<360, the straight line D extends from the second quadrant to the fourth quadrant of the coordinate plane which is defined by the X axis and the Y axis. In this way, the tilt angle is an angle other than 0, 90, 180, and 270.

[0074] Here, it is assumed that a distance between the lattice point O and the centroid G is r(x, y). Here, x is a position of an x-th lattice point on the X axis, and y is a position of a y-th lattice point on the Y axis. When the distance r(x, y) has a positive value, the centroid G is located in the first quadrant or the second quadrant. When the distance r(x, y) has a negative value, the centroid G is located in the third quadrant or the fourth quadrant. When the distance r(x, y) is 0, the lattice point O and the centroid G match each other. The tilt angle is preferably 45, 135, 225, or 275. With these tilt angles, only two out of four wave number vectors forming a standing wave at M points, for example, in-plane wave number vectors (+/a, +/a), are modulated in phase, and the other two wave number vectors are not modulated in phase. Accordingly, it is possible to form a stable standing wave.

[0075] The distance r(x, y) is individually set for each different-refractive-index region 15b according to a phase distribution (x, y) corresponding to a light image to be output from each phase modulation area 151. That is, when a phase (x, y) at certain coordinates (x, y) is .sub.0, the distance r(x, y) is set to 0. When the phase (x, y) is +.sub.0, the distance r(x, y) is set to a maximum value R.sub.0. When the phase (x, y) is +.sub.0, the distance r(x, y) is set to a minimum value R.sub.0. For an intermediate phase (x, y) therebetween, the distance r(x, y) is set to satisfy r(x, y)={(x, y).sub.0}R.sub.0/. When a lattice spacing of a virtual tetragonal lattice is defined as a, the maximum value R.sub.0 of the distance r(x, y) falls within, for example, the range of Formula (1).

[00001]$\begin{array}{cc}\left[\mathrm{Formula}1\right]& \\ 0R_0\frac{a}{\sqrt{2}}& \left(1\right)\end{array}$

[0076] The initial phase .sub.0 can be arbitrarily set. The distribution of the phase (x, y) and the distribution of the distance r(x, y) have specific values for each position which is determined by the values of x and y, but cannot be said to be expressed by a specific function.

[0077] By determining the distribution of the distance r(x, y) of the different-refractive-index regions 15b of the plurality of phase modulation areas 151, it is possible to output a desired light image from each of the plurality of phase modulation areas 151. The phase modulation areas 151 are configured to satisfy the following conditions.

[0078] As a first precondition, a virtual tetragonal lattice including M.sub.1N.sub.1 unit constituent areas R having a square shape is set on the XY plane. M.sub.1 and N.sub.1 are integers equal to or greater than 1.

[0079] As illustrated in FIG. 5, spherical coordinates (r, .sub.rot, .sub.tilt) are defined by a length r of a radius vector, a tilt angle .sub.tilt from the Z axis, and a rotation angle .sub.rot from the X axis which is identified on the XY plane. As a second precondition, it is assumed that coordinates (, , ) in the XYZ orthogonal coordinate system satisfy the relationships represented by Formulas (2) to (4) with respect to the spherical coordinates (r, .sub.rot, .sub.tilt). FIG. 5 is a diagram illustrating coordinate transformation from the spherical coordinates (r, .sub.rot, .sub.tilt) to coordinates (, , ) in the XYZ orthogonal coordinate system. A light image in design on a predetermined plane set in the XYZ orthogonal coordinate system which is a real space is represented by the coordinates (, , ).

[00002]$\begin{array}{cc}\left[\mathrm{Formula}2\right]& \\ =r\sin {}_{\mathrm{tilt}}\cos {}_{\mathrm{rot}}& \left(2\right)\end{array}$$\begin{array}{cc}\left[\mathrm{Formula}3\right]& \\ =r\sin {}_{\mathrm{tilt}}\sin {}_{\mathrm{rot}}& \left(3\right)\end{array}$$\begin{array}{cc}\left[\mathrm{Formula}4\right]& \\ =r\cos {}_{\mathrm{tilt}}& \left(4\right)\end{array}$

[0080] Light emitted from each phase modulation area 151 is a set of bright spots in a direction which is defined by the angles .sub.tilt and .sub.rot. In this case, the angles .sub.tilt and .sub.rot are converted to coordinate values kx and ky. The coordinate value kx is a standardized wave number defined by Formula (5) and is a coordinate value on a K.sub.x axis corresponding to the X axis. The coordinate value ky is a standardized wave number defined by Formula (6) and is a coordinate value on a K.sub.y axis corresponding to the Y axis and perpendicular to the K.sub.x axis. The standardized wave number is a wave number which is standardized with a wave number 2/a corresponding to the lattice spacing of the virtual tetragonal lattice as 1.0. In this case, in the wave number space defined by the K.sub.x axis and the K.sub.y axis, a specific wave number range including a beam pattern corresponding to a light image includes M.sub.2N.sub.2 image areas FR with a square shape. M.sub.2 and N.sub.2 are integers equal to or greater than 1. The integer M.sub.2 does not need to be equal to the integer M.sub.1. The integer N.sub.2 does not need to be equal to the integer N.sub.1. Formulas (5) and (6) are disclosed in, for example, Non Patent Literature 1.

[00003]$\begin{array}{cc}\left[\mathrm{Formula}5\right]& \\ k_x=\frac{a}{}\sin {}_{\mathrm{tilt}}\cos {}_{\mathrm{rot}}& \left(5\right)\end{array}$$\begin{array}{cc}\left[\mathrm{Formula}6\right]& \\ k_y=\frac{a}{}\sin {}_{\mathrm{tilt}}\sin {}_{\mathrm{rot}}& \left(6\right)\end{array}$ [0081] a: a lattice constant of the virtual tetragonal lattice [0082] : an emission wavelength of the semiconductor light-emitting device 1

[0083] In the wave number space, an image area FR(kx, ky) is identified by a coordinate component kx in the K.sub.x-axis direction and a coordinate component ky in the K.sub.y-axis direction. The coordinate component kx is an integer equal to or greater than 0 and equal to or less than M.sub.21. The coordinate component ky is an integer equal to or greater than 0 and equal to or less than N.sub.21. A unit constituent area R(x, y) on the XY plane is identified by a coordinate component x in the X-axis direction and a coordinate component y in the Y-axis direction. The coordinate component x is an integer equal to or greater than 0 and equal to or less than M.sub.11. The coordinate component y is an integer equal to or greater than 0 and equal to or less than N.sub.11. As a third precondition, a complex amplitude CA(x, y) which is obtained by performing a two-dimensional inverse discrete Fourier transform on the image area FR(kx, ky) to the unit constituent area R(x, y) is represented by Formula (7) with j as an imaginary unit. The complex amplitude CA(x, y) is defined by Formula (8), where an amplitude term is defined as A(x, y) and a phase term is defined as (x, y). As a fourth precondition, the unit constituent area R(x, y) is defined by an s axis and a t axis. The s axis and the taxis are parallel to the X axis and the Y axis, respectively, and are orthogonal at a lattice point O(x, y) which is the center of the unit constituent area R(x, y). The complex amplitudes CA(x, y) represented by Formulas (7) and (8) correspond to A.sub.1e.sup.i1 and A.sub.2e.sup.i2 in FIGS. 16 and 21 and A.sub.1,1e.sup.1,1 to A.sub.m,ne.sup.m,n in FIGS. 18 and 22.

[00004]$\begin{array}{cc}\left[\mathrm{Formula}7\right]& \\ \mathrm{CA}\left(x,y\right)=\underset{k_x=0}{\overset{M2-1}{.Math.}}\underset{k_y=0}{\overset{N2-1}{.Math.}}\mathrm{FR}\left(k_x,k_y\right)\exp \left[j2\left(\frac{k_x}{M2}x+\frac{k_y}{N2}y\right)\right]& \left(7\right)\end{array}$$\begin{array}{cc}\left[\mathrm{Formula}8\right]& \\ \mathrm{CA}\left(x,y\right)=A\left(x,y\right)\exp \left[j\left(x,y\right)\right]& \left(8\right)\end{array}$

[0084] In the first to fourth preconditions, the phase modulation areas 151 are configured to satisfy the following conditions. That is, the corresponding different-refractive-index region 15b is disposed in the unit constituent area R(x, y) such that a distance r(x, y) from the lattice point O(x, y) to the centroid G of the corresponding different-refractive-index region 15b satisfies the following relationship.

[00005]$r\left(x,y\right)=C\left(\left(x,y\right)-{}_0\right)$ [0085] C: a proportion coefficient, for example, R.sub.0/ [0086] .sub.0: an arbitrary coefficient, for example, 0

[0087] When it is intended to acquire a desired light image, the light image can be subjected to an inverse Fourier transform, and a distribution of the distance r(x, y) corresponding to the phase (x, y) of a complex amplitude thereof can be applied to the plurality of different-refractive-index regions 15b. The phase (x, y) and the distance r(x, y) may be proportional to each other.

[0088] FIG. 6 is a partially enlarged plan view of the connection area 152. Only a part of the connection area 152 is illustrated in FIG. 6, and the configuration of the other parts of the connection area 152 is the same. As described above, the connection area 152 also includes a basic region 15a and a plurality of different-refractive-index regions 15b. In the connection area 152, the same virtual tetragonal lattice as in FIG. 3 is set. One side of the tetragonal lattice is parallel to the X axis, and the other side is parallel to the Y axis. The lattice constant a of the tetragonal lattice is the same as the lattice constant a of the tetragonal lattice of the phase modulation area 151. In the connection area 152, the centroids G of the plurality of different-refractive-index regions 15b are located at the lattice points of the tetragonal lattice. In other words, the positions of the centroids G of the plurality of different-refractive-index regions 15b match the positions of the lattice points of the tetragonal lattice. Accordingly, in the connection area 152, the plurality of different-refractive-index regions 15b are arranged periodically along the X axis and the Y axis.

[0089] Description will be continued with reference back to FIG. 1. The semiconductor light-emitting device 1 further includes an electrode 16 (a first electrode) and an electrode 17 (a second electrode). The electrode 16 is provided to face the first face 20a of the semiconductor stacked layer 20, and the electrode 16 is provided on the first face 20a, that is, the contact layer 14, in the illustrated example. The electrode 16 forms an ohmic contact with the contact layer 14. The electrode 17 is provided to face the second face 20b of the semiconductor stacked layer 20, and the electrode 17 is provided on the rear surface 10b of the semiconductor substrate 10 in the illustrated example. The electrode 17 forms an ohmic contact with the semiconductor substrate 10.

[0090] FIG. 7 is a diagram schematically illustrating planar shapes of the electrodes 16 and 17 and the configuration for supplying currents to the electrodes 16 and 17. As illustrated in FIG. 7, the electrode 17 includes a plurality of openings 17a. The openings 17a correspond to the phase modulation areas 151 in a one-to-one manner. When seen in the thickness direction of the semiconductor stacked layer 20, the openings 17a overlap the corresponding phase modulation areas 151. The planar shape of each opening 17a is, for example, a square shape or a rectangular shape. The electrode 16 includes a plurality of electrode parts 161. The plurality of electrode parts 161 are arranged with intervals therebetween and are electrically isolated from each other. When it is mentioned that the electrode parts are electrically isolated from each other, it means that there is no other electrical path except for a path passing through the semiconductor stacked layer 20. The electrode parts 161 correspond to the phase modulation areas 151 in a one-to-one manner. When seen in the thickness direction of the semiconductor stacked layer 20, the electrode parts 161 overlap the corresponding phase modulation areas 151. The planar shape of each electrode part 161 is, for example, a square shape or a rectangular shape.

[0091] The plurality of electrode parts 161 are individually electrically connected to a drive circuit 31 via a plurality of lines 33. The electrode 17 is electrically connected to the drive circuit 31 via a line 34. The drive circuit 31 is electrically connected to a power supply circuit 32 via a line 35. The drive circuit 31 is supplied with electric power from the power supply circuit 32 and supplies driving currents to the plurality of electrode parts 161 and the electrode 17. The drive circuit 31 can change the magnitude of the driving current for each electrode part 161. The magnitude of the driving current to the electrode parts 161 is independently set for each electrode part 161.

[0092] Description will be continued with reference back to FIG. 1. Parts other than parts of the contact layer 14 overlapping the electrode parts 161 are removed by etching in order to limit a current range. Accordingly, the contact layer 14 is divided to a plurality of parts respectively corresponding to the plurality of electrode parts 161. Gaps between the plurality of parts of the contact layer 14 are filled with a protection film 18. Accordingly, the surface of the semiconductor stacked layer 20 exposed from the electrode 16 is protected. The protection film 18 is formed of, for example, an inorganic insulator such as a silicon nitride (for example, SiN) or a silicon oxide (for example, SiO.sub.2). Parts of the contact layer 14 other than the parts overlapping the electrode parts 161 may not be removed but be left. In this case, the protection film 18 is provided on the contact layer 14 of the gaps between the plurality of electrode parts 161.

[0093] On the rear surface 10b of the semiconductor substrate 10, an area that includes the insides of the openings 17a other than the area in which the electrode 17 is provided is covered with an antireflection film 19. The antireflection film 19 provided in an area other than the openings 17a may be removed. The antireflection film 19 is formed of, for example, a single-layered film or a multi-layered film such as a silicon nitride (for example, SiN) or a silicon oxide (for example, SiO.sub.2). As the multi-layered film of a dielectric, for example, a film in which two or more types of dielectric layers selected from a dielectric layer group consisting of titanium oxide (TiO.sub.2), silicon dioxide (SiO.sub.2), silicon monoxide (SiO), niobium oxide (Nb.sub.2O.sub.5), tantalum pentoxide (Ta.sub.2O.sub.5), magnesium fluoride (MgF.sub.2), titanium oxide (TiO.sub.2), aluminum oxide (Al.sub.2O.sub.3), cerium oxide (CeO.sub.2), indium oxide (In.sub.2O.sub.3), and zirconium oxide (ZrO.sub.2) can be used. The multi-layered film of a dielectric is formed, for example, by stacking a plurality of films of which an optical thicknesses with respect to light of a wavelength is /4.

[0094] In this embodiment, the electrode 16 facing the first face 20a includes a plurality of electrode parts 161, but the electrode 17 facing the second face 20b may include a plurality of electrode parts instead of the configuration or in addition to the configuration. In this case, similarly to the plurality of electrode parts 161, the plurality of electrode parts of the electrode 17 are arranged with gaps therebetween and electrically isolated from each other. The electrode parts of the electrode 17 correspond to the phase modulation areas 151 in a one-to-one manner. When seen in the thickness direction of the semiconductor stacked layer 20, the electrode parts of the electrode 17 overlap the corresponding phase modulation areas 151. The planar shape of each electrode part of the electrode 17 is, for example, a rectangular frame shape including an opening 17a. The plurality of electrode parts of the electrode 17 are individually electrically connected to the drive circuit 31 via a plurality of lines. The drive circuit 31 freely changes the magnitude of a driving current for each electrode part of the electrode 17.

[0095] In the semiconductor light-emitting device 1, when driving current supplied between each electrode part 161 and the electrode 17, recombination of electrons and holes is caused in a part of the active layer 12 located just below the corresponding electrode part 161, and light is output from the corresponding part of the active layer 12. At this time, electrons and holes contributing to emission of light and light output from the active layer 12 are efficiently confined between the clad layer 11 and the clad layer 13.

[0096] Light output from the corresponding part of the active layer 12 is input into the phase modulation area 151 facing the part. Then, the light oscillates along the virtual plane P in the phase modulation area 151 and forms a predetermined mode based on the arrangement of the plurality of different-refractive-index regions 15b. A part of laser light L output from the corresponding phase modulation area 151 is directly output to the outside of the semiconductor light-emitting device 1 from the rear surface 10b via the opening 17a. The remaining part of the laser light L output from the phase modulation area 151 is reflected by the electrode 16 and is then output to the outside of the semiconductor light-emitting device 1 from the rear surface 10b via the opening 17a. At this time, signal light included in the laser light L exits in a direction crossing both the first face 20a and the second face 20b of the semiconductor stacked layer 20. In other words, signal light included in the laser light L exits in an arbitrary direction including a direction perpendicular to the rear surface 10b and a direction oblique to the direction perpendicular to the rear surface 10b. Exit light from the semiconductor light-emitting device 1 includes signal light. The signal light is mainly one or both of 1st-order diffracted light or 1 st-order diffracted light of the laser light. In the following description, 1st-order diffracted light is referred to as 1st-order light, and 1st-order diffracted light is referred to as 1st-order light.

[0097] Laser light L output from the plurality of phase modulation areas 151 is applied as light images based on the arrangement of the plurality of different-refractive-index regions 15b to a common irradiation area (a far field) which is located in a direction crossing both the first face 20a and the second face 20b of the semiconductor stacked layer 20. A plurality of different-refractive-index regions 15b included in at least two phase modulation areas 151 out of the plurality of phase modulation areas 151 have arrangements which are different for the phase modulation areas 151. Accordingly, a plurality of light images output from the plurality of phase modulation areas 151 interfere with each other to form a final light image.

[0098] In order to acquire a final light image by causing a plurality of light images output from the plurality of phase modulation areas 151 to interfere with each other, these light images are synchronized in phase with each other. In order to synchronize phases the light images with each other, in this embodiment, the connection area 152 is provided between neighboring phase modulation areas 151. Since the resonance modes in the neighboring phase modulation areas 151 are shared via the connection area 152, the phases of laser light L oscillating in the phase modulation areas 151 can be synchronized between the plurality of phase modulation areas 151. The connection area 152 may be removed to make the neighboring phase modulation areas 151 adjacent to each other. In this case, the phases of laser light L oscillating in the phase modulation areas 151 can be synchronized with each other between the plurality of phase modulation areas 151. In order to synchronize phases a plurality of light images with each other, phase synchronization needs to be considered when the phase distribution (x, y) of the phase modulation areas 151 is designed. Design of the phase distribution (x, y) in consideration of phase synchronization will be described later.

[0099] In order to acquire a desired light image by causing the light images output from the plurality of phase modulation areas 151 to interfere with each other, it is preferable that polarization directions of the light images be aligned. In this embodiment, the centroids G of the different-refractive-index regions 15b are disposed on the straight line D set for the corresponding lattice points O. The tilt angles of the straight lines D are the same at all the lattice points O in the phase modulation area 151 and are the same in the plurality of phase modulation areas 151.

[0100] FIG. 8 is a diagram illustrating an electromagnetic field distribution in the phase modulation area 151. Part (a) of FIG. 8 illustrates an electromagnetic field distribution in a resonance mode with symmetry A.sub.1 at M.sub.1 points. Part (b) of FIG. 8 illustrates an electromagnetic field distribution in a resonance mode with symmetry B.sub.2 at M.sub.1 points. In FIG. 8, arrows indicate magnitudes and directions of an electric field, and color gradation indicates a magnitude of a magnetic field. In this embodiment, the centroid G of each different-refractive-index region 15b is disposed on the straight line D. In the drawing, a change in arrangement of the central different-refractive-index regions 15b is schematically illustrated. In this case, in any electromagnetic field distribution, the polarization directions are expected to be aligned regardless of the distance between the centroid G of the different-refractive-index region 15b and the lattice point O, that is, regardless of the phase values realized by the different-refractive-index regions 15b.

[0101] On the other hand, FIG. 9 is a diagram illustrating an electromagnetic field distribution according to a comparative example. In this example, the centroids G of the different-refractive-index regions 15b are disposed at a constant distance from the lattice point O, and an azimuth angle (a rotation angle) of a vector connecting the lattice point O to the centroid G about the lattice point is set for each different-refractive-index region 15b according to the phase distribution (x, y). Part (a) of FIG. 9 illustrates an electromagnetic field distribution in the resonance mode with symmetry A.sub.1 at M.sub.1 points. Part (b) of FIG. 9 illustrates an electromagnetic field distribution in the resonance mode with symmetry B.sub.2 at M.sub.1 points. In FIG. 9, an arrow indicates a magnitude and a direction of an electric field, and color gradation indicates a magnitude of a magnetic field. In this comparative example, in any electromagnetic field distribution, the polarization direction changes according to the rotation angle of the different-refractive-index region 15b around the lattice point O. Accordingly, it cannot be expected that the polarization directions are aligned. In this regard, it is preferable that the centroid G of the different-refractive-index regions 15b be disposed on the straight line D and the distance between the centroid G and the lattice point O change according to the phase as in this embodiment.

[0102] As described above, the semiconductor light-emitting device 1 according to this embodiment irradiates a common irradiation area with a plurality of light images output from the plurality of phase modulation areas 151. A final one light image (a hologram) is formed by causing the plurality of light images to overlap and interfere with each other. FIG. 10 is a diagram conceptually illustrating an example of a plurality of light images output from the plurality of phase modulation areas 151. In FIG. 10, a total of 64 light images LA of 8 columns in the X direction and 8 rows in the Y direction become darker as the light intensity thereof becomes smaller and become lighter as the light intensity thereof becomes larger. These are light images output from a total of 64 phase modulation areas 151 of 8 columns in the X direction and 8 rows in the Y direction. In this example, a light intensity distribution of the light images LA output from the plurality of phase modulation areas 151 includes a distribution of a sinusoidal wave shape. In the distribution of a sinusoidal wave shape, periods in two directions perpendicular to each other (the X direction and the Y direction) differ for each phase modulation area 151. These light images LA can be used, for example, as base images of a discrete cosine transform (DCT). That is, by converting a target final light intensity distribution using the discrete cosine transform and outputting the acquired plurality of base images from the plurality of phase modulation areas 151, the final light image can be realized. By changing the magnitude of the driving current of the plurality of electrode parts 161 corresponding to the plurality of phase modulation areas 151, it is also possible to individually adjust degrees of contribution of the base images to the final light image and to present a dynamic light image varying with time.

[0103] FIG. 11 is a diagram conceptually illustrating another example of the plurality of light images output from the plurality of phase modulation areas 151. This example employs a plurality of light images LA which are used as base images of a discrete wavelet transform (DWT). Like this example, by converting a target final light intensity distribution using the discrete wavelet transform and outputting the acquired plurality of base images from the plurality of phase modulation areas 151, the final light image can also be realized. By changing the magnitude of the driving current of the plurality of electrode parts 161 corresponding to the plurality of phase modulation areas 151, it is also possible to individually adjust degrees of contribution of the base images to the final light image and to present a dynamic light image varying with time.

[0104] As well as the discrete cosine transform and the discrete wavelet transform, the base images may be learned, for example, from a group of a plurality of light images to be displayed in a far field through machine learning (such as main component analysis or dictionary learning). In the example illustrated in FIG. 10, the periods in two directions perpendicular to each other (the X direction and the Y direction) differ for each phase modulation area 151, but the period in only one direction (the X direction or the Y direction) may differ for each phase modulation area 151.

[0105] FIG. 12 is a diagram conceptually illustrating another example of the plurality of light images output from the plurality of phase modulation areas 151. A total of 4 light images LA of 2 columns in the X direction and 2 rows in the Y direction are illustrated in FIG. 12. These are light images which are output from a total of 4 phase modulation areas 151 of 2 columns in the X direction and 2 rows in the Y direction. In this example, the light intensity distribution of the light images LA output from the phase modulation areas 151 includes a distribution with a sinusoidal wave shape which varies periodically in the Y direction. The phase in the Y direction of the sinusoidal distribution of the light images LA output from two phase modulation areas 151 located on one diagonal is different from the phase in the Y direction of the sinusoidal light intensity distribution of the light images LA output from two phase modulation areas 151 located on the other diagonal. In this example, by changing a ratio of the magnitude of the driving current of two electrode parts 161 corresponding to the two phase modulation areas 151 located on one diagonal and the magnitude of the driving current of two electrode parts 161 corresponding to the two phase modulation areas 151 located on the other diagonal, it is possible to freely change the phase of the light intensity distribution with a sinusoidal wave shape presented in the final light image. As in the example illustrated in FIG. 12, the phases in only one direction (the Y direction) of the sinusoidal light intensity distribution of the light images LA output from at least two phase modulation areas 151 may be different from each other. The light intensity distribution of the light images LA output from at least two phase modulation areas 151 may include a distribution with a sinusoidal wave shape which varies periodically in two directions (the X direction and the Y direction). In this case, the phase in each direction of the light intensity distribution with a sinusoidal shape of at least two light images LA output from at least two phase modulation areas 151 may differ between the light images LA.

[0106] A phase distribution design method according to this embodiment in consideration of phase synchronization of light images output from a plurality of phase modulation areas 151 will be described below in detail. In the following description, a plurality of different-refractive-index regions 15b may be referred to as a plurality of points. That is, the method described below is a method of designing a phase distribution (x, y) of two or more phase modulation areas 151 for individually modulating phases of light at a plurality of points which are distributed in a two-dimensional shape. In the following description, a real space refers to a space of the phase modulation areas 151, and a wave number space refers to a space of light images (also referred to as beam patterns) in an irradiation area.

[First Design Method]

[0107] FIG. 13 is a diagram conceptually illustrating a first design method. First, in a first step, initial conditions are set (an arrow B.sub.1 in the drawing). A first function 203 which is a complex amplitude distribution function including an initial value 201 of the amplitude distribution in the wave number space and an initial value 202 of the phase distribution in the wave number space is set for each phase modulation area 151. When the initial value 201 of the amplitude distribution in the wave number space is F.sub.0(kx, ky) and the initial value 202 of the phase distribution in the wave number space is 0(kx, ky), the first function 203 is expressed as F.sub.0(kx, ky).Math.e.sup.i0(kx,ky). At this time, the initial value 201 of the amplitude distribution in the wave number space may be a predetermined target amplitude distribution 204 in the wave number space. When the target amplitude distribution 204 in the wave number space is F.sub.0(kx, ky), a light intensity distribution (that is, a desired light image) is given as F.sub.0.sup.2(kx, ky). The initial value 202 of the phase distribution in the wave number space may be a random phase distribution 205.

[0108] In the first step, for each phase modulation area 151, the first function 203 is converted to a second function 213 which is a complex amplitude distribution function including an amplitude distribution 211 in the real space and a phase distribution 212 in the real space, for example, using an inverse Fourier transform such as an inverse fast Fourier transform (IFFT) (an arrow B2 in the drawing). When the amplitude distribution 211 in the real space is A(x, y) and the phase distribution 212 in the real space is (x, y), the second function 213 is expressed as A(x, y).Math.e.sup.i(kx,ky).

[0109] Then, in a second step, the amplitude distribution 211 of the second function 213 in each phase modulation area 151 is replaced with a target amplitude distribution 214 based on a predetermined target intensity distribution in the real space (arrows B.sub.3 and B.sub.4 in the drawing). For example, when the predetermined target intensity distribution is A.sub.0.sup.2(x, y), the target amplitude distribution is given as A.sub.0(x, y). For example, the predetermined target intensity distribution A.sub.0.sup.2(x, y) is constant regardless of x and y, and the target amplitude distribution A.sub.0(x, y) is also constant regardless of x and y. In this case, the phase distribution 212 of the second function 213 in each phase modulation area 151 is held without any change (an arrow B5 in the drawing). Then, for each phase modulation area 151, the second function 213 subjected to the replacement is converted to a third function 223 which is a complex amplitude distribution function including an amplitude distribution 221 in the wave number space and a phase distribution 222 in the wave number space, for example, using a Fourier transform such as a fast Fourier transform (FFT) (an arrow B6 in the drawing). When the amplitude distribution 221 in the wave number space is F(kx, ky) and the phase distribution 222 in the wave number space is (kx, ky), the third function 223 is expressed as F(kx, ky).Math.e.sup.i(kx,ky).

[0110] Then, in a third step, the phase distributions 222 of the third function 223 in the phase modulation areas 151 are made the same as the phase distribution 222 of the third function 223 in one phase modulation area 151 out of the plurality of phase modulation areas 151 (an arrow B7 in the drawing). In this case, the one phase modulation area 151 serving as a reference for making the phase distributions 222 the same is arbitrarily determined. In the third step, the amplitude distribution 221 of the third function 223 in each phase modulation area 151 is replaced with the target amplitude distribution 204 (arrows B8 and B9 in the drawing). Then, for each phase modulation area 151, the third function 223 subjected to the replacement is converted to a fourth function 233 which is a complex amplitude distribution function including an amplitude distribution 231 in the real space and a phase distribution 232 of the real space using an inverse Fourier transform such as an IFFT (an arrow B2 in the drawing). When the amplitude distribution 231 in the real space is A(x, y) and the phase distribution 232 in the real space is (x, y), the fourth function 233 is expressed as A(x, y).Math.e.sup.i(kx,ky).

[0111] 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. Whenever the third step is repeated, the position of one phase modulation area 151 serving as a reference for making the phase distribution 222 the same may be fixed without being changed. Then, the phase distribution 232 of the fourth function 233 finally subjected to the conversion in the third step is set as the phase distribution (x, y) of the phase modulation areas 151 (an arrow B10 in the drawing).

[0112] For example, as illustrated in FIG. 14, a phase modulation layer 15 including a total of 4 phase modulation areas 151 of 2 columns in the X direction and 2 rows in the Y direction is considered. Among these, it is assumed that two phase modulation areas 151 located on one diagonal have a phase distribution pattern A and two phase modulation areas 151 located on the other diagonal have a phase distribution pattern B. Alternatively, as illustrated in FIG. 15, two phase modulation areas 151 included in the first row have a phase distribution pattern B, and two phase modulation areas 151 included in the second row may have a phase distribution pattern A. FIG. 16 is a diagram conceptually illustrating a method of designing phase distribution patterns A and B.

[0113] First, in the first step, initial values are set (an arrow B11 in the drawing). That is, a first function F.sub.1(kx, ky).Math.e.sup.i1(kx,ky) (hereinafter abbreviated to F.sub.1.Math.e.sup.i1) which is a complex amplitude distribution function including an initial value of an amplitude distribution F.sub.1(kx, ky) in the wave number space and an initial value of a phase distribution 1(kx, ky) in the wave number space is set for the phase distribution pattern A. A first function F.sub.2(kx, ky).Math.e.sup.i2(kx,ky) (hereinafter abbreviated to F.sub.2.Math.e.sup.i2) which is a complex amplitude distribution function including an initial value of an amplitude distribution F.sub.2(kx, ky) in the wave number space and an initial value of a phase distribution 2(kx, ky) in the wave number space is set for the phase distribution pattern B. Then, the first function F.sub.1.Math.e.sup.i1 of the phase distribution pattern A is converted to a second function A.sub.1(x, y).Math.e.sup.i1(x,y) (hereinafter abbreviated to A.sub.1e.sup.i1) which is a complex amplitude distribution function including an amplitude distribution A.sub.1(x, y) in the real space and a phase distribution 1(x, y) in the real space through an inverse Fourier transform such as an IFFT (an arrow B12 in the drawing). Similarly, the first function F.sub.2(x, y).Math.e.sup.i2(x,y) of the phase distribution pattern B is converted to a second function A.sub.2(x, y).Math.e.sup.i2(x,y) (hereinafter abbreviated to A.sub.2.Math.e.sup.i2) which is a complex amplitude distribution function including an amplitude distribution A.sub.2(x, y) in the real space and a phase distribution 2(x, y) in the real space through an inverse Fourier transform such as an IFFT (an arrow B13 in the drawing).

[0114] Then, in the second step, the amplitude distribution A.sub.1 of the second function A.sub.1.Math.e.sup.i1 is replaced with a target amplitude distribution A.sub.1 based on a predetermined target intensity distribution in the real space. Similarly, the amplitude distribution A.sub.2 of the second function A.sub.2.Math.e.sup.i2 is replaced with a target amplitude distribution A.sub.2 based on a predetermined target intensity distribution in the real space (an arrow B14 in the drawing). At this time, the phase distribution 1 and the phase distribution 2 are held without any change. Then, the second function A.sub.1.Math.e.sup.i1 subjected to the replacement is converted to a third function F.sub.1.Math.e.sup.i1 which is a complex amplitude distribution function including an amplitude distribution F.sub.1 in the wave number space and a phase distribution 1 in the wave number space, for example, through a Fourier transform such as an FFT (an arrow B15 in the drawing). Similarly, the second function A.sub.2.Math.e.sup.i2 subjected to the replacement is converted to a third function F.sub.2.Math.e.sup.i2 which is a complex amplitude distribution function including an amplitude distribution F.sub.2 in the wave number space and a phase distribution 2 in the wave number space, for example, through a Fourier transform such as an FFT (an arrow B16 in the drawing).

[0115] Then, in the third step, the phase distribution 2 of the third function F.sub.2.Math.e.sup.i2 is made the same as the phase distribution 1 of the third function F.sub.1.Math.e.sup.i1. The amplitude distribution F.sub.1 of the third function F.sub.1.Math.e.sup.i1 and the amplitude distribution F.sub.2 of the third function F.sub.2.Math.e.sup.i2 are replaced with the target amplitude distributions F.sub.1 and F.sub.2 (an arrow B17 in the drawing). Then, the third function F.sub.1.Math.e.sup.i1 is converted to a fourth function A.sub.1.Math.e.sup.i1 which is a complex amplitude distribution function including the amplitude distribution A.sub.1 in the real space and the phase distribution 1 in the real space through inverse Fourier transform such as an IFFT (an arrow B18 in the drawing). Similarly, the third function F.sub.2.Math.e.sup.i1 is converted to a fourth function A.sub.2.Math.e.sup.i 2 which is a complex amplitude distribution function including the amplitude distribution A.sub.2 in the real space and the phase distribution 2 in the real space through inverse Fourier transform such as an IFFT (an arrow B19 in the drawing).

[0116] Thereafter, the second step and the third step are repeated while replacing the second function A.sub.1.Math.e.sup.i1 and the second function A.sub.2.Math.e.sup.i2 in the second step with the fourth function A.sub.1.Math.e.sup.i1 and the fourth function A.sub.2.Math.e.sup.i2, respectively (an arrow B20 in the drawing). Then, the phase distribution .sub.1 of the fourth function A.sub.1.Math.e.sup.i1 finally subjected to the conversion in the third step is set as the phase distribution (x, y) with the phase distribution pattern A. The phase distribution 2 of the fourth function A.sub.2.Math.e.sup.i2 finally subjected to the conversion in the third step is set as the phase distribution (x, y) with the phase distribution pattern B.

[0117] As another example, as illustrated in FIG. 17, a phase modulation layer 15 including a total of mn phase modulation areas 151 of m columns in the X direction and n rows in the Y direction is considered. The mn phase modulation areas 151 have different phase distribution patterns. FIG. 18 is a diagram conceptually illustrating a method of designing mn phase distribution patterns.

[0118] First, in the first step, initial values are set (an arrow B41 in the drawing). That is, first functions F.sub.1,1(kx, ky).Math.e.sup.i1,1(kx, ky) to F.sub.m,n(kx, ky).Math.e.sup.im,n(kx,ky) (hereinafter abbreviated to F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n) which are complex amplitude distribution functions including initial values of amplitude distributions F.sub.1,1(kx, ky) to F.sub.m,n(kx, ky) in the wave number space and initial values of phase distributions 1,1(kx, ky) to m,n(kx, ky) in the wave number space are set for the mn phase modulation areas 151. For each phase modulation area 151, the first functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are converted to second functions A.sub.1,1(x, y).Math.e.sup.i1,1(x,y) to A.sub.m,n(x, y).Math.e.sup.im,n(x,y) (hereinafter abbreviated to A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n) which are complex amplitude distribution functions including amplitude distributions A.sub.1,1(x, y) to A.sub.m,n(x, y) in the real space and phase distributions 1,1(x, y) to m,n(x, y) in the real space through an inverse Fourier transform such as an IFFT (an arrow B42 in the drawing).

[0119] Then, in the second step, for each phase modulation area 151, the amplitude distributions A.sub.1,1 to A.sub.m,n of the second functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n are replaced with target amplitude distributions A.sub.1,1 to A.sub.m,n based on a predetermined target intensity distribution in the real space (an arrow B43 in the drawing). At this time, the phase distributions 1,1 to m,n are held without any change. Then, for each phase modulation area 151, the second functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n subjected to the replacement are converted to third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n which are complex amplitude distribution functions including amplitude distributions F.sub.1,1 to F.sub.m,n in the wave number space and phase distributions 1,1 to m,n in the wave number space, for example, through a Fourier transform such as an FFT (an arrow B44 in the drawing).

[0120] Then, in the third step, all the phase distributions 1,1 to m,n of the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are made the same as the phase distribution 1,1 of the third function F.sub.1,1.Math.e.sup.i1,1. The amplitude distributions F.sub.1,1 to F.sub.m,n of the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are replaced with target amplitude distributions F.sub.1,1 to F.sub.m,n (an arrow B45 in the drawing). Then, the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.i1,1 are converted to fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n which are complex amplitude distribution functions including the amplitude distributions A.sub.1,1 to A.sub.m,n in the real space and the phase distributions 1,1 to m,n in the real space through an inverse Fourier transform such as an IFFT (an arrow B46 in the drawing).

[0121] Thereafter, the second step and the third step are repeated while replacing the second functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n in the second step with the fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n (an arrow B47 in the drawing). Then, the phase distributions 1,1 to m,n of the fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n finally subjected to the conversion in the third step are set as the phase distributions (x, y) of the phase modulation areas 151.

[0122] A configuration of a phase distribution design device for performing the phase distribution design method will be described below. Part (a) of FIG. 19 is a block diagram illustrating a hardware configuration of a phase distribution design device 300 that can perform the first design method. The phase distribution design device 300 is a device that designs phase distributions of two or more phase modulation areas 151 for individually modulating phases of light at a plurality of points distributed in a two-dimensional shape. The phase distribution design device 300 is, for example, a computer including a processor such as a personal computer, a smart device such as a smartphone or a table terminal, or a cloud server. As illustrated in part (a) of FIG. 19, the phase distribution design device 300 can be physically constituted as a normal 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, and a touch screen, an output device 305 such as a display (which includes a touch screen), a communication module 306 such as a network card for transmitting and receiving data to and from another device, an auxiliary storage device 307 such as a hard disk, and a device for reading data recorded in a recording medium 308.

[0123] Part (b) of FIG. 19 is a functional block diagram of the phase distribution design device 300 that can perform the first design method. 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, a processor of a 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 functions may be realized by the same processor or may be realized by different processors.

[0124] The first processing unit 310 performs the first step of the first design method. That is, the first processing unit 310 sets the first function 203 including the initial value 201 of the amplitude distribution in the wave number space and the initial value 202 of the phase distribution in the wave number space for each phase modulation area 151. Thereafter, the first processing unit 310 converts the first function 203 to the second function 213 including the amplitude distribution 211 in the real space and the phase distribution 212 in the real space through an inverse Fourier transform for each phase modulation area 151.

[0125] 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 area 151 to the target amplitude distribution 214 based on the predetermined target intensity distribution in the real space. At this time, the second processing unit 320 holds the phase distribution 212 of the second function 213 in each phase modulation area 151 without any change. Thereafter, for each phase modulation area 151, the second processing unit 320 converts the second function 213 subjected to the replacement to the third function 223 which is a complex amplitude distribution function including the amplitude distribution 221 in the wave number space and the phase distribution 222 in the wave number space through a Fourier transform.

[0126] The third processing unit 330 performs the third step of the first design method. That is, the third processing unit 330 makes the phase distribution 222 of the third function 223 in each phase modulation area 151 the same as the phase distribution 222 of the third function 223 in one phase modulation area 151 out of the plurality of phase modulation areas 151. In addition, the third processing unit 330 replaces the amplitude distribution 221 of the third function 223 in each phase modulation area 151 to the target amplitude distribution 204. Thereafter, the third processing unit 330 converts the third function 223 subjected to the replacement to the fourth function 233 which is a complex amplitude distribution function including the amplitude distribution 231 in the real space and the phase distribution 232 in the real space through an inverse Fourier transform for each phase modulation area 151.

[0127] Thereafter, the second processing unit 320 and the third processing unit 330 repeatedly perform the operations 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 finally subjected to the conversion with the operation of the third processing unit 330 is set as the phase distribution (x, y) of each phase modulation area 151.

[0128] The processor 301 of the computer can realize the functions using a phase distribution design program. Accordingly, the phase distribution design program causes the processor 301 of the computer to serve as the first processing unit 310, the second processing unit 320, and the third processing unit 330 of the phase distribution design device 300. The phase distribution design program is stored in the main storage device (the ROM 302) or the auxiliary storage device 307 in 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 the phase distribution design program stored in a computer-readable recording medium 308 may be read and stored in the main storage device or the auxiliary storage device 307. A flexible disk, a CD-ROM, a DVD-ROM, a BD-ROM, a semiconductor memory, a cloud server, or the like can be used as the recording medium 308.

[Second Design Method]

[0129] FIG. 20 is a diagram conceptually illustrating a second design method. The first step and the second step are the same as in the first design method, and thus description thereof will be omitted.

[0130] In the third step of the first time, the phase distribution 222 of the third function 223 in each phase modulation area 151 is replaced with a predetermined phase distribution which is the same in the plurality of phase modulation areas 151 (a first procedure, an arrow B21 in the drawing). The phase values of a plurality of points (kx, ky) in the predetermined phase distribution may be the same. In this case, the phase values of the plurality of points (kx, ky) in the predetermined phase distribution may be zero (0 rad). At this time, the amplitude distribution 221 is held without any change (an arrow B22 in the drawing). Then, the third function 223 is converted to the fourth function 233 through an inverse Fourier transform such as an IFFT (an arrow B2 in the drawing).

[0131] The second function 213 is replaced with the fourth function 233 and the second step is performed again. Thereafter, in the third step (of the second time), the amplitude distribution 221 of the third function 223 is replaced with the target amplitude distribution 204 (a second procedure, arrows B23 and B24 in the drawings). At this time, the phase distribution 222 is held without any change (an arrow B25 in the drawing). Then, the third function 223 subjected to the replacement is converted to the fourth function 233 through an inverse Fourier transform such as an IFFT (an arrow B2 in the drawing).

[0132] Thereafter, the second step and the third step are repeatedly performed while replacing the second function 213 of the second step with the fourth function 233. At that time, in repetition of the third step, replacement of the phase distribution 222 with the predetermined phase distribution (the first procedure) and replacement of the amplitude distribution 221 with the target amplitude distribution 204 (the second procedure) are alternately performed. In the first procedure in which the third steps are repeated, the predetermined phase distribution may be fixed without being changed. The phase distribution 232 of the fourth function 233 finally subjected to the replacement in the third step is set as the phase distribution (x, y) of each phase modulation area 151 (an arrow B10 in the drawing).

[0133] For example, as illustrated in FIG. 14 or 15, the phase modulation layer 15 including a total of 4 phase modulation areas 151 of 2 columns in the X direction and 2 rows in the Y direction is considered. Among these, two phase modulation areas 151 have a phase distribution pattern A and two phase modulation areas 151 have a phase distribution pattern B. FIG. 21 is a diagram conceptually illustrating a method of designing the phase distribution patterns A and B. The first step and the second step are the same as in the first design method, and thus description thereof will be omitted.

[0134] In the third step of the first time, the phase distribution 1 of the third function F.sub.1.Math.e.sup.i1 and the phase distribution 2 of the third function F.sub.2.Math.e.sup.i2 are replaced with a predetermined phase distribution common to the phase distribution pattern A and the phase distribution pattern B (an arrow B31 in the drawing). At that time, the amplitude distribution F.sub.1 and the amplitude distribution F.sub.2 are held without any change. Then, the third function F.sub.1.Math.e.sup.i and the third function F.sub.2.Math.e.sup.i are converted to the fourth function A.sub.1.Math.e.sup.i1 and the fourth function A.sub.2.Math.e.sup.i2, respectively, through an inverse Fourier transform such as an IFFT (arrows B32 and B33 in the drawing).

[0135] The second step is performed again while replacing the second function A.sub.1.Math.e.sup.i1 and the second function A.sub.2.Math.e.sup.i2 with the fourth function A.sub.1.Math.e.sup.i1 and the fourth function A.sub.2.Math.e.sup.i 2, respectively (arrows B34 to B36 in the drawing). Thereafter, in the third step (of the second time), the amplitude distribution F.sub.1 of the third function F.sub.1.Math.e.sup.i1 and the amplitude distribution F.sub.2 of the third function F.sub.2.Math.e.sup.i2 are replaced with the target amplitude distributions F.sub.1 and F.sub.2, respectively (an arrow B37 in the drawing). Then, the third function F.sub.1.Math.e.sup.i1 and the third function F.sub.2.Math.e.sup.i2 are converted to the fourth function A.sub.1.Math.e.sup.i1 and the fourth function A.sub.2.Math.e.sup.i2, respectively, through an inverse Fourier transform such as an IFFT (arrows B38 and B39 in the drawing).

[0136] Thereafter, the second step and the third step are repeated while replacing the second function A.sub.1.Math.e.sup.i1 and the second function A.sub.2.Math.e.sup.i2 in the second step with the fourth function A.sub.1.Math.e.sup.i1 and the fourth function A.sub.2.Math.e.sup.i 2, respectively (an arrow B20 in the drawing). At that time, in repetition of the third step, replacement of the phase distributions 1 and 2 (the first procedure, an arrow B31 in the drawing) and replacement of the amplitude distributions F.sub.1 and F.sub.2 (the second procedure, an arrow B37 in the drawing) are alternately performed. Then, the phase distribution 1 of the fourth function A.sub.1.Math.e.sup.i1 finally subjected to the conversion in the third step is set as the phase distribution (x, y) with the phase distribution pattern A. The phase distribution 2 of the fourth function A.sub.2.Math.e.sup.i2 finally subjected to the conversion in the third step is set as the phase distribution (x, y) with the phase distribution pattern B.

[0137] As another example, as illustrated in FIG. 17, the phase modulation layer 15 including a total of mn phase modulation areas 151 of m columns in the X direction and n rows in the Y direction is considered. The mn phase modulation areas 151 have different phase distribution patterns. FIG. 22 is a diagram conceptually illustrating a method of designing the mn phase distribution patterns. The first step and the second step are the same as in the first design method, and thus description thereof will be omitted.

[0138] In the third step of the first time, all the phase distributions 1,1 to m,n of the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are replaced with a predetermined common phase distribution (the first procedure, an arrow B51 in the drawing). At this time, amplitude distributions F.sub.1,1 to F.sub.m,n are held without any change. Then, the third functions F.sub.1,1.Math.e.sup.i to F.sub.m,n.Math.e.sup.i are converted to the fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n, respectively, through an inverse Fourier transform such as an IFFT (an arrow B52 in the drawing).

[0139] The second step is performed again after replacing the second functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n with the fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n, respectively (arrows B53 and B54 in the drawing). Thereafter, in the third step (of the second time), the amplitude distributions F.sub.1,1 to F.sub.m,n of the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are replaced with the target amplitude distributions F.sub.1,1 to F.sub.m,n, respectively (an arrow B55 in the drawing). Then, the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are converted to the fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n, respectively, through an inverse Fourier transform such as an IFFT (a group of arrows B56 in the drawing).

[0140] Thereafter, the second step and the third step are repeated while replacing the second functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n in the second step with the fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n, respectively (an arrow B47 in the drawing). At that time, in repetition of the third step, replacement of the phase distributions 1,1 to m,n (the first procedure, an arrow B51 in the drawing) and replacement of the amplitude distributions F.sub.1,1 to F.sub.m,n (the second procedure, an arrow B55 in the drawing) are alternately performed. Then, the phase distributions 1,1 to m,n of the fourth functions A.sub.1,1.Math.e.sup.i1,1 to A.sub.m,n.Math.e.sup.im,n finally subjected to the conversion in the third step are set as the phase distributions (x, y) of the phase modulation areas 151.

[0141] A configuration of a phase distribution design device for performing the phase distribution design method will be described below. FIG. 23 is a functional block diagram illustrating of a phase distribution design device 400 that can perform the second design method. The phase distribution design device 400 is a device that designs phase distributions of two or more phase modulation areas 151 for individually modulating phases of light at a plurality of points distributed in a two-dimensional shape. The phase distribution design device 400 has the same hardware configuration as the 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, a processor of a computer provided in the phase distribution design device 400 realizes the function of the first processing unit 410, the function of the second processing unit 420, and the function of the third processing unit 430. The functions may be realized by the same processor or may be realized by different processors.

[0142] The function of the first processing unit 410 is the same as the first processing unit 310 of the phase distribution design device 300. The function of the second processing unit 420 is the same as the second processing unit 320 of the phase distribution design device 300.

[0143] The third processing unit 430 performs the third step of the second design method. That is, the third processing unit 430 makes the phase distribution 222 of the third function 223 in each phase modulation area 151 the same as a predetermined phase distribution which is the same in the plurality of phase modulation areas 151 (the first procedure) or replaces the amplitude distribution 221 of the third function 223 with the target amplitude distribution 204 (the second procedure). Thereafter, the third processing unit 430 converts the third function 223 to the fourth function 233 through an inverse Fourier transform.

[0144] Thereafter, the second processing unit 420 and the third processing unit 430 repeatedly perform the operations while replacing the second function 213 of the second processing unit 420 with the fourth function 233. At that time, in repetition of the operation of the third processing unit 430, replacement of the phase distribution 222 with the predetermined phase distribution (the first procedure) and replacement of the amplitude distribution 221 with the target amplitude distribution 204 (the second procedure) are alternately performed. Then, the phase distribution 232 of the fourth function 233 finally subjected to the conversion with the operation of the third processing unit 430 is set as the phase distribution (x, y) of each phase modulation area 151.

[0145] The processor of the computer can realize the functions using a phase distribution design program. Accordingly, the phase distribution design program causes the processor of the computer to serve as the first processing unit 410, the second processing unit 420, and the third processing unit 430 of the phase distribution design device 400. The phase distribution design program is stored in the main storage device or the auxiliary storage device in 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 the phase distribution design program stored in a computer-readable recording medium may be read and stored in the main storage device or the auxiliary storage device. A flexible disk, a CD-ROM, a DVD-ROM, a BD-ROM, a semiconductor memory, a cloud server, or the like can be used as the recording medium.

[0146] Advantageous effects obtained from the phase distribution design methods, the phase distribution design devices, the phase distribution design programs, and the recording media according to the embodiments described above will be described below. FIG. 24 is a diagram conceptually illustrating a third design method as a comparative example. The first step and the second step of the third design method are the same as the first step and the second step of the first design method (arrows B11 to B16 in the drawing). In the third step, the amplitude distribution F.sub.1 of the third function F.sub.1.Math.e.sup.i1 and the amplitude distribution F.sub.2 of the third function F.sub.2.Math.e.sup.i2 are replaced with the target amplitude distributions F.sub.1 and F.sub.2, respectively (an arrow B37 in the drawing). Then, the third function F.sub.1.Math.e.sup.i1 and the third function F.sub.2.Math.e.sup.i2 are converted to the fourth function A.sub.1.Math.e.sup.i1 and the fourth function A.sub.2.Math.e.sup.i2, respectively, through an inverse Fourier transform such as an IFFT (arrows B38 and B39 in the drawing).

[0147] Thereafter, the second step and the third step are repeated while replacing the second function A.sub.1.Math.e.sup.i1 and the second function A.sub.2.Math.e.sup.i2 in the second step with the fourth function A.sub.1.Math.e.sup.i1 and the fourth function A.sub.2.Math.e.sup.i 2, respectively (an arrow B20 in the drawing). Then, the phase distribution 1 of the fourth function A.sub.1.Math.e.sup.i1 finally subjected to the conversion in the third step is set as the phase distribution (x, y) with the phase distribution pattern A. The phase distribution 2 of the fourth function A.sub.2.Math.e.sup.i 2 finally subjected to the conversion in the third step is set as the phase distribution (x, y) with the phase distribution pattern B.

[0148] When the third design method is individually (independently) applied to the phase distributions of the plurality of phase modulation areas 151, the phases of the plurality of light images output from the plurality of phase modulation areas 151 are not synchronized with each other. Therefore, with the first design method, the phase distribution design device 300, and the program, in the third step and the third processing unit 330, the phase distributions 222 in the wave number space of the third function 223 in the phase modulation areas 151 are made the same as the phase distribution 222 in the wave number space of the third function 223 in one phase modulation area 151 out of two or more phase modulation areas 151 (an arrow B.sub.7 in FIG. 13). For example, in the example illustrated in FIG. 16, the phase distribution 2 (kx, ky) of the third function F.sub.2(kx, ky).Math.e.sup.i2(kx,ky) is made the same as the phase distribution 1(kx, ky) of the third function F.sub.1(kx, ky).Math.e.sup.i1(kx, ky) as indicated by the arrow B17. In the example illustrated in FIG. 18, all the phase distributions 1,1 to m,n of the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are made the same as the phase distribution 1,1 of the third function F.sub.1,1.Math.e.sup.i1,1 as indicated by the arrow B45. Accordingly, it is possible to synchronize a plurality of light images output from the plurality of phase modulation areas 151 with each other. As a result, it is possible to cause a predetermined interference effect in a hologram that is formed by overlapping the plurality of light images on one area.

[0149] With the second design method, the phase distribution design device 400, and the program, in one of two times the third step or the operation of the third processing unit 430 is repeated, the phase distribution 222 in the wave number space of the third function 223 in each phase modulation area 151 is replaced with a predetermined phase distribution which is the same in two or more phase modulation areas 151. For example, in the example illustrated in FIG. 21, the phase distribution 1(kx, ky) of the third function F.sub.1(kx, ky).Math.e.sup.i1(kx, ky) and the phase distribution 2(kx, ky) of the third function F.sub.2(kx, ky).Math.e.sup.i2(kx,ky) are replaced with a predetermined phase distribution (kx, ky) which is common to the phase distribution pattern A and the phase distribution pattern B as indicated by the arrow B31. In the example illustrated in FIG. 22, all the phase distributions 1,1 to m,n of the third functions F.sub.1,1.Math.e.sup.i1,1 to F.sub.m,n.Math.e.sup.im,n are replaced with the predetermined common phase distribution as indicated by the arrow B51. Accordingly, it is possible to synchronize a plurality of light images output from the plurality of phase modulation areas 151 with each other. As a result, it is possible to cause a predetermined interference effect in a hologram that is formed by overlapping the plurality of light images on one area.

[0150] With 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 the wave number space may be the target amplitude distribution 204 as described above. In this case, it is possible to cause light images to accurately approach a predetermined target intensity distribution with a small number of repetitions.

[0151] With 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 the wave number space may be a random phase distribution 205 as described above.

[0152] With the first design method, the phase distribution design device 300, and the program thereof, as described above, the position of one phase modulation area 151 serving as a reference for making the phase distribution 222 the same may be fixed without being changed while the third step or the operation of the third processing unit 330 is repeated. According to the inventor's simulation, it is possible to accurately synchronize the phases of a plurality of light images particularly in this case.

[0153] With the second design method, the phase distribution design device 400, and the program thereof, as described above, the phase values at a plurality of points (kx, ky) in the predetermined phase distribution when the phase distribution 222 of the third function 223 is replaced with a predetermined phase distribution may be the same. According to the inventor's simulation, it is possible to accurately synchronize the phases of a plurality of light images particularly in this case. In this case, the phase values at the plurality of points (kx, ky) in the predetermined phase distribution may be zero (0 rad).

[0154] With the second design method, the phase distribution design device 400, and the program thereof, as described above, the predetermined phase distribution may be fixed without being changed while the third step or the operation of the third processing unit 430 is repeated. According to the inventor's simulation, it is possible to accurately synchronize the phases of a plurality of light images particularly in this case.

First Example

[0155] The inventor performed phase distribution design simulation by employing the phase distribution design method according to the embodiment for the phase modulation layer 15 including four phase modulation areas 151 illustrated in FIG. 14. Part (a) of FIG. 25 illustrates a desired light image in an irradiation area (a far field) which was set when the phase distribution pattern A was designed. In part (a) of FIG. 25, the light intensity becomes larger as the color becomes lighter, and the light intensity becomes smaller as the color becomes darker. As illustrated in part (a) of FIG. 25, a goal of the phase distribution pattern A is to form a light image having a light intensity distribution with a sinusoidal wave shape in which a light intensity changes periodically in only one direction. Part (b) of FIG. 25 illustrates a distribution obtained by converting the light image illustrated in part (a) to the wave number space, that is, a target amplitude distribution in the wave number space. Part (c) of FIG. 25 is a diagram illustrating the phase distribution pattern A which was calculated on the basis of the target amplitude distribution illustrated in part (b). In part (c) of FIG. 25, the phase becomes closer to 2 (rad) as the color becomes lighter, and the phase becomes closer to 0 (rad) as the color becomes darker.

[0156] Part (a) of FIG. 26 illustrates a desired light image in an irradiation area (a far field) which was set when the phase distribution pattern B was designed. In part (a) of FIG. 26, the light intensity becomes larger as the color becomes lighter, and the light intensity becomes smaller as the color becomes darker. As illustrated in part (a) of FIG. 26, a goal of the phase distribution pattern B was to form a light image having a light intensity distribution with a sinusoidal wave shape in which a light intensity changes periodically in only a direction perpendicular to a changing direction of the light intensity in part (a) of FIG. 25. Here, the period of the sinusoidal wave was set to the same as in part (a) of FIG. 25. Part (b) of FIG. 26 illustrates a distribution obtained by converting the light image illustrated in part (a) to the wave number space, that is, a target amplitude distribution in the wave number space. Part (c) of FIG. 26 is a diagram illustrating a phase distribution pattern B which was calculated on the basis of the target amplitude distribution illustrated in part (b). In part (c) of FIG. 26, the phase becomes closer to 2 (rad) as the color becomes lighter, and the phase becomes closer to 0 (rad) as the color becomes darker.

[0157] Part (a) of FIG. 27 is a diagram illustrating an example in which the phase distribution pattern A was applied to two phase modulation areas 151 located on one diagonal and the phase distribution pattern B was applied to two phase modulation areas 151 located on the other diagonal. Part (b) of FIG. 27 is a diagram conceptually illustrating a difference between a light intensity in the two phase modulation areas 151 located on one diagonal and a light intensity in the two phase modulation areas 151 located on the other diagonal which is realized by individually controlling currents of the electrode parts 161. In part (b) of FIG. 27, the light intensity becomes larger as the color become lighter, and the light intensity becomes smaller as the color becomes darker.

[0158] FIG. 28 is a diagram illustrating a final light image which is supposed when a light image emitted from two phase modulation areas 151 having the phase distribution pattern A (see part (a) of FIG. 25) and a light image emitted from two phase modulation areas 151 having the phase distribution pattern B (see part (a) of FIG. 26) are caused to interfere with each other. When these light images are caused to interfere with each other, peaks of the light intensities mutually strengthen each other and bottoms of the light intensities mutually weaken each other, and thus it is expected to obtain a light intensity distribution like a checkboard pattern.

[0159] FIG. 29 is a diagram illustrating a final light image acquired through this simulation. Part (a) of FIG. 29 illustrates a light image which is acquired using the first design method according to the embodiment. Part (b) of FIG. 29 illustrates a light image which is acquired using the second design method according to the embodiment. Part (c) of FIG. 29 illustrates a light image which is acquired using the third design method according to the comparative example. Through comparison of these diagrams, it can be seen that the checkboard pattern based on the second design method is clearer than that based on the third design method. It can be seen that the checkboard pattern based on the first design method is clearer than that based on the second design method. In this simulation, when the checkboard pattern becomes clearer, it represents that phase synchronization is more appropriately performed and the light images interfere with each other more accurately. Accordingly, with the first design method or the second design method, in comparison with the third design method, it was found that the phases of a plurality of light images output from the plurality of phase modulation areas 151 can be synchronized with each other and a predetermined interference effect can be caused in a hologram formed by overlapping the plurality of light images on one area. It was found that this effect of the first design method is more remarkable than that of the second design method.

Second Example

[0160] The inventor performed other phase distribution design simulation by employing the first design method for the phase modulation layer 15 including four phase modulation areas 151 illustrated in FIG. 14. Part (a) of FIG. 30 illustrates a desired light image in an irradiation area (a far field) which was set when the phase distribution pattern A was designed. In part (a) of FIG. 30, the light intensity becomes larger as the color becomes lighter, and the light intensity becomes smaller as the color becomes darker. As illustrated in part (a) of FIG. 30, a goal of the phase distribution pattern A is to form a light image having a light intensity distribution with a sinusoidal wave shape in which a light intensity changes periodically in only one direction. Part (b) of FIG. 30 illustrates a distribution obtained by converting the light image illustrated in part (a) to the wave number space, that is, a target amplitude distribution in the wave number space. Part (c) of FIG. 30 is a diagram illustrating the phase distribution pattern A which was calculated on the basis of the target amplitude distribution illustrated in part (b). In part (c) of FIG. 30, the phase becomes closer to 2 (rad) as the color becomes lighter, and the phase becomes closer to 0 (rad) as the color becomes darker.

[0161] Part (a) of FIG. 31 illustrates a desired light image in an irradiation area (a far field) which was set when the phase distribution pattern B was designed. In part (a) of FIG. 31, the light intensity becomes larger as the color becomes lighter, and the light intensity becomes smaller as the color becomes darker. As illustrated in part (a) of FIG. 31, similarly to the phase distribution pattern A, a goal of the phase distribution pattern B was to form a light image having a light intensity distribution with a sinusoidal wave shape in which a light intensity changes periodically in only one direction. Here, the period of the sinusoidal wave was set to the same as the desired image when the phase distribution pattern A was designed, and the phase of the sinusoidal wave was shifted with respect to the desired light image when the phase distribution pattern A was designed. Part (b) of FIG. 31 illustrates a distribution obtained by converting the light image illustrated in part (a) to the wave number space, that is, a target amplitude distribution in the wave number space. Part (c) of FIG. 31 is a diagram illustrating a phase distribution pattern B which was calculated on the basis of the target amplitude distribution illustrated in part (b). In part (c) of FIG. 31, the phase becomes closer to 2 (rad) as the color becomes lighter, and the phase becomes closer to 0 (rad) as the color becomes darker.

[0162] Part (a) of FIG. 32 is a diagram illustrating an example in which the phase distribution pattern A was applied to two phase modulation areas 151 located on one diagonal and the phase distribution pattern B was applied to two phase modulation areas 151 located on the other diagonal. Part (b) of FIG. 32 is a diagram conceptually illustrating a difference between a light intensity in the two phase modulation areas 151 located on one diagonal and a light intensity in the two phase modulation areas 151 located on the other diagonal which is realized by individually controlling currents of the electrode parts 161. In part (b) of FIG. 32, the light intensity becomes larger as the color become lighter, and the light intensity becomes smaller as the color becomes darker.

[0163] FIG. 33 is a diagram illustrating a final light image which is supposed when a light image emitted from two phase modulation areas 151 having the phase distribution pattern A (see part (a) of FIG. 30) and a light image emitted from two phase modulation areas 151 having the phase distribution pattern B (see part (a) of FIG. 31) are caused to interfere with each other. When these light images are caused to interfere with each other, it is expected to obtain a light intensity distribution with a sinusoidal wave shape having a phase corresponding to a ratio of the light intensity of the light image emitted from the two phase modulation areas 151 having the phase distribution pattern B to the light intensity of the light image emitted from the two phase modulation areas 151 having the phase distribution pattern A.

[0164] FIGS. 34 and 35 are diagrams illustrating a final light image acquired through the simulation. FIG. 34 illustrates an example in which a phase difference between a light image emitted from a phase modulation area 151 having the phase distribution pattern A (see part (a) of FIG. 30) and a light image emitted from a phase modulation area 151 having the phase distribution pattern B (see part (a) of FIG. 31) is 45. FIG. 35 illustrates an example in which the phase difference between the light images is 135. When the light image emitted from the phase modulation areas 151 having the phase distribution pattern A is PA and the light image emitted from the phase modulation area 151 having the phase distribution pattern B is PB, the light intensity ratio is expressed as (PA/PB). In order to facilitate understanding of a change in phase with a change in the light intensity ratio, in FIGS. 34 and 35, final light images when the light intensity ratio (PA/PB) is 0/1.00, 0.25/0.75, 0.50/0.50, 0.75/0.25, and 1.00/0 are arranged in a direction crossing the changing direction of the light intensity.

[0165] As illustrated in the drawings, with the phase distribution design method according to the embodiment, it is possible to realize a light intensity distribution with a sinusoidal wave shape of which the phase can change dynamically by dynamically changing the light intensity ratio of light images emitted from a plurality of phase modulation areas 151 having different phase distribution patterns.

[0166] The phase distribution design method, the phase distribution design device, the phase distribution design program, and the recording medium according to the present disclosure are not limited to the aforementioned embodiment and can be modified in various forms. For example, in the first design method according to the embodiment, the position of one phase modulation area 151 serving as a reference for making the phase distribution 222 the same is fixed without being changed while the third step is repeated, but the position of the one phase modulation area 151 may be changed while the third step is repeated. In the second design method according to the embodiment, the phase values of a plurality of points in a predetermined phase distribution are set to the same when the phase distribution 222 of the third function 223 is replaced with the predetermined phase distribution in the third step, but the phase values of at least two points may be different. When the phase values of a plurality of points are the same, the phase values are not limited to zero.

REFERENCE SIGNS LIST

[0167] 1 . . . Semiconductor light-emitting device, 10 . . . Semiconductor substrate, 10a . . . Main surface, 10b . . . Rear surface, 11 . . . Clad layer, 12 . . . Active layer, 13 . . . Clad layer, 14 . . . Contact layer, 15 . . . Phase modulation layer, 15a . . . Basic region, 15b . . . Different-refractive-index region, 15c . . . Cap region, 16 . . . Electrode (first electrode), 17 . . . Electrode (second electrode), 17a . . . Opening, 18 . . . Protection film, 19 . . . Antireflection film, 20 . . . Semiconductor stacked layer, 20a . . . First face, 20b . . . Second face, 31 . . . Drive circuit, 32 . . . Power supply circuit, 33 to 35 . . . Line, 151 . . . Phase modulation area, 152 . . . Connection area, 152a . . . Opening, 152b, 152c . . . Part, 161 . . . Electrode part, 201 . . . Initial value of amplitude distribution in wave number space, 202 . . . Initial value of phase distribution in wave number 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 wave number space, 222 . . . Phase distribution in wave number 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. . . Centroid, L. . . Laser light, LA. . . Light image, O. . . Lattice point, P. . . Virtual plane, R. . . Unit constituent area