Semiconductor light-emitting element

Abstract

To provide a semiconductor light emitting element capable of dynamically changing an output optical image.SOLUTION: A semiconductor light emitting element 1 includes a semiconductor lamination 20, an electrode 16, and an electrode 17. The semiconductor lamination 20 includes an active layer 12 and a phase modulation layer 15. The phase modulation layer 15 has a plurality of phase modulation regions 151. Each of the phase modulation regions 151 includes a basic region 15a that has a first refractive index, and a plurality of different refractive index regions 15b that have a second refractive index different from the first refractive index and are distributed two-dimensionally. The electrode 16 includes a plurality of electrode portions 161 that respectively overlap the plurality of phase modulation regions 151 when viewed from a lamination direction of the semiconductor lamination 20. The plurality of electrode portions 161 are electrically separated from each other. Laser light L that has resonated in each of the plurality of phase modulation regions 151 is emitted onto a common irradiation region as optical images corresponding to the arrangement of the plurality of different refractive index regions 15b. The optical images respectively output from the plurality of phase modulation regions 151 are phase-locked with each other.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This disclosure relates to a semiconductor light-emitting element. [Background technology]

[0002] Patent Document 1 discloses technology relating to a light-emitting device. This light-emitting device is an S-iPM (Static-integrable Phase Modulating) laser that outputs light that forms an optical image in at least one of the directions normal to the main surface and the direction of inclination tilted with respect to the normal surface. This light-emitting device comprises a substrate having a main surface, a light-emitting unit provided on the substrate, and a phase modulation layer. The phase modulation layer is provided on the substrate in an optically coupled state with the light-emitting unit and includes a base layer having a predetermined refractive index and a plurality of regions with different refractive indices having refractive indices different from those of the base layer. On the design surface of the phase modulation layer perpendicular to the normal direction, each of the plurality of regions with different refractive indices is arranged to correspond one-to-one with any grid point of a virtual square grid. In a hypothetical square lattice, among the lattice points, where multiple regions of different refractive indices are associated, the line segment connecting any specific lattice point to the centroid of the specific region of different refractive indices associated with that lattice point is parallel to the line segments connecting the multiple peripheral lattice points adjacent to the specific lattice point by the shortest distance and the centroids of the multiple peripheral regions of different refractive indices associated with each of those peripheral lattice points. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] International Publication No. 2019 / 111787 [Non-patent literature]

[0004] [Non-Patent Document 1] Y. Kurosaka et al., "Effects of non-lasing band in two-dimensional photonic-crystal lasers clarified using omnidirectional bandstructure," Opt. Express 20, 21773-21783 (2012) [Overview of the project] [Problems that the invention aims to solve]

[0005] Semiconductor light-emitting devices that output an arbitrary optical image by controlling the phase spectrum and intensity spectrum of light emitted from multiple light-emitting points arranged in a two-dimensional manner are being studied. One such structure of a semiconductor light-emitting device includes a phase modulation layer provided on a substrate. The phase modulation layer includes a basic layer and multiple regions with different refractive indices, each having a refractive index different from that of the basic layer. When a virtual square grid is set on a plane perpendicular to the thickness direction of this phase modulation layer, each of the regions with different refractive indices is positioned such that the position of each centroid is shifted from the position of the corresponding grid point of the virtual square grid according to the optical image to be output. Such a semiconductor light-emitting device is called an S-iPM laser and outputs light that forms an optical image of an arbitrary shape in a direction inclined with respect to the normal direction of the main surface of the substrate. Conventionally, such semiconductor light-emitting devices are known in which multiple regions with different refractive indices are pre-arranged in a phase modulation layer according to a predetermined optical image, as described in Patent Document 1. Since the multiple regions with different refractive indices are pre-fabricated inside the phase modulation layer, the position of each region with different refractive indices is fixed. Therefore, the optical image output from this semiconductor light-emitting device is static and cannot be moved. However, if the output optical image can be dynamically changed, the range of applications for semiconductor light-emitting devices that can output any optical image may be further expanded. The object of this disclosure is to provide a semiconductor light-emitting device that can dynamically change the output optical image. [Means for solving the problem]

[0006] The semiconductor light-emitting element according to this disclosure comprises a semiconductor stack, a first electrode, and a second electrode. The semiconductor stack has a stacked structure including an active layer and a phase modulation layer between a first surface and a second surface. The phase modulation layer has a plurality of phase modulation regions arranged along a virtual plane perpendicular to the thickness direction of the phase modulation layer and optically coupled to one another. Each of the plurality of phase modulation regions includes a basic region having a first refractive index and a plurality of regions with different refractive indices. The plurality of regions with different refractive indices are provided within the basic region, have a second refractive index different from the first refractive index, and are distributed two-dimensionally along the virtual plane. The first electrode faces the first surface of the semiconductor stack. The second electrode faces the second surface of the semiconductor stack. One or both of the first electrode and the second electrode include a plurality of electrode portions that overlap with the plurality of phase modulation regions when viewed from the stacking direction of the semiconductor stack. The plurality of electrode portions are electrically isolated from each other. Light emitted from the active layer resonates in each of the multiple phase modulation regions of the phase modulation layer, and from each of these multiple phase modulation regions, it is projected onto a common irradiation area located in a direction intersecting both the first and second surfaces of the semiconductor stack, as an optical image corresponding to the arrangement of multiple regions with different refractive indices. The optical images emitted from each of the multiple phase modulation regions are phase-synchronous with each other.

[0007] In this semiconductor light-emitting element, one or both of the first and second electrodes include multiple electrode portions that overlap with multiple phase modulation regions, respectively. The multiple electrode portions are electrically isolated from each other. Therefore, independent currents can be supplied to each of the multiple electrode portions. As a result, the light emission intensity of each of the multiple regions of the active layer that supply light to each of the multiple phase modulation regions is controlled independently, and the light intensity of the multiple light images output from the multiple phase modulation regions is also controlled independently from each other. The multiple light images are irradiated onto a common illumination region. At this time, since the light images output from each of the multiple phase modulation regions are phase-synchronized with each other, the multiple light images can interfere with each other in the common illumination region. Thus, with this semiconductor light-emitting element, the light intensity of the multiple light images output from the multiple phase modulation regions can be individually adjusted, and the multiple light images can be made to interfere with each other to form a single light image, thereby dynamically changing the light image.

[0008] In the semiconductor light-emitting device described above, the light intensity distribution of the light image output from each of the multiple phase modulation regions may include a sinusoidal distribution in which the period or phase in at least one direction is different from that of the at least two phase modulation regions. Alternatively, in the semiconductor light-emitting device described above, the light intensity distribution of the light image output from each of the multiple phase modulation regions may include a sinusoidal distribution in which the period or phase in two mutually orthogonal directions is different from that of the at least two phase modulation regions. In these cases, any light image can be obtained by superimposing multiple light images output from multiple phase modulation regions while individually adjusting the light intensity of each of the multiple light images. In particular, when the periods are different, the multiple light images output from multiple phase modulation regions can become multiple basis images in a discrete cosine transform (DCT).

[0009] In the semiconductor light-emitting element described above, a virtual square lattice is set along a virtual plane, and for each of the multiple lattice points constituting the square lattice, a straight line passing through the corresponding lattice point and inclined at the same angle to the square lattice is set for each lattice point. In each of the multiple phase modulation regions, the centroids of each of the multiple different refractive index regions are positioned on the corresponding straight line, and the distance between the centroid of each different refractive index region and the lattice point corresponding to each different refractive index region may be set individually according to a predetermined optical image. For example, with such a configuration, each of the multiple parts of the semiconductor light-emitting element containing a phase modulation region constitutes an S-iPM laser, and each can output a predetermined optical image that is different from the others. Furthermore, the polarization direction can be aligned between the multiple phase modulation regions.

[0010] In the semiconductor light-emitting element described above, the phase modulation layer may further have a connecting region located between adjacent phase modulation regions. The connecting region includes a basic region having a first refractive index and a plurality of regions with different refractive indices having a second refractive index, and the centroid of the plurality of regions with different refractive indices in the connecting region may be located at a lattice point of a square lattice. In this case, since a gap is provided between adjacent phase modulation regions, it becomes possible to widen the gap between multiple electrode portions, and so-called inter-region crosstalk, in which a portion of the current that should be supplied to each region of the active layer supplying light to these phase modulation regions leaks to adjacent regions, can be reduced. Furthermore, by having the centroid of the plurality of regions with different refractive indices in the connecting region located at a lattice point of a square lattice, the phases of the light images output from each of the plurality of phase modulation regions can be synchronized with each other.

[0011] In the semiconductor light-emitting element described above, the planar shape of the connection region as viewed from the stacking direction of the semiconductor stack may be grid-like. In this case, since a gap can be provided between all phase modulation regions, inter-region crosstalk can be reduced more effectively.

[0012] In the semiconductor light-emitting element described above, the areas of multiple regions with different refractive indices in a cross-section perpendicular to the thickness direction of the phase modulation layer may be set individually according to a predetermined optical image. In this case, not only the phase but also the light intensity can be adjusted for each region with different refractive indices, thereby increasing the degree of freedom in designing the optical image.

[0013] In the semiconductor light-emitting device described above, the square grids of adjacent phase modulation regions may be offset from each other.

[0014] The above semiconductor light-emitting element further comprises a λ / 4 plate provided opposite the light-emitting surface of the semiconductor light-emitting element, and the square grids of adjacent phase-modulation regions may be shifted from each other by n·a + a / 2 (where a is the grid spacing and n is an integer greater than or equal to 0). In this case, the phases of the light images output from each adjacent phase-modulation region are shifted from each other by π (rad). Therefore, circularly polarized light with opposite directions can be output from each adjacent phase-modulation region.

[0015] In the semiconductor light-emitting element described above, the first electrode includes a plurality of electrode portions, and the stacked structure further includes a cladding layer provided between the phase modulation layer and the active layer and the first surface. The cladding layer may include high-resistance regions located between adjacent phase modulation regions when viewed from the stacking direction of the semiconductor stack. In this case, inter-region crosstalk can be reduced.

[0016] In the semiconductor light-emitting device described above, the phase modulation layer is provided between the cladding layer and the active layer, and the high-resistance region may extend to the phase modulation layer. In this case, inter-region crosstalk can be reduced more effectively.

[0017] In the semiconductor light-emitting element described above, the planar shape of the high-resistance region as viewed from the stacking direction of the semiconductor stacking may be lattice-shaped. In this case, since high-resistance regions can be provided between all phase modulation regions as viewed from the stacking direction, inter-region crosstalk can be reduced more effectively.

[0018] The above-described semiconductor light-emitting device further comprises a semiconductor substrate having a main surface and a back surface, the semiconductor stack is provided on the main surface of the semiconductor substrate, the second surface of the semiconductor stack faces the main surface of the semiconductor substrate, the first electrode is provided on the first surface and includes the plurality of electrode portions, and the second electrode may be provided on the back surface of the semiconductor substrate. In this way, by providing the plurality of electrode portions on the surface opposite to the semiconductor substrate with respect to the semiconductor stack, the distance between the plurality of electrode portions and the active layer can be shortened. Therefore, inter-region crosstalk can be reduced. [Effects of the Invention]

[0019] According to this disclosure, it is possible to provide a semiconductor light-emitting element that can dynamically change the output light image. [Brief explanation of the drawing]

[0020] [Figure 1] Figure 1 is a cross-sectional view showing a stacked structure of a semiconductor light-emitting element to which the phase distribution design method of this embodiment is applied. [Figure 2] Figure 2 is a plan view of the phase modulation layer (viewed from the thickness direction). [Figure 3] Figure 3 is a plan view showing an enlarged portion of the phase modulation region. [Figure 4] Figure 4 is a magnified view of a single unit constituent region. [Figure 5] Figure 5 is a diagram illustrating the coordinate transformation from spherical coordinates to coordinates in the XYZ Cartesian coordinate system. [Figure 6] Figure 6 is a plan view showing an enlarged portion of the connection area. [Figure 7] Figure 7 schematically shows the planar shapes of the first and second electrodes, as well as the configuration for supplying current to the first and second electrodes. [Figure 8] Figure 8 shows the electromagnetic field distribution in the phase modulation region. Part 8(a) of Figure 8 shows the electromagnetic field distribution in the resonant mode with symmetry A1 at point M1. Part 8(b) of Figure 8 shows the electromagnetic field distribution in the resonant mode with symmetry B2 at point M1. [Figure 9]Figure 9 shows the electromagnetic field distribution for a comparative example. Part 9(a) shows the electromagnetic field distribution in the resonant mode with symmetry A1 at point M1. Part 9(b) shows the electromagnetic field distribution in the resonant mode with symmetry B2 at point M1. [Figure 10] Figure 10 is a conceptual diagram illustrating examples of multiple optical images output from multiple phase modulation regions. [Figure 11] Figure 11 is a conceptual diagram illustrating another example of multiple optical images output from multiple phase modulation regions. [Figure 12] Figure 12 is a conceptual diagram illustrating yet another example of multiple optical images output from multiple phase modulation regions. [Figure 13] Figure 13 is a conceptual diagram illustrating the first design method. [Figure 14] Figure 14 shows a phase modulation layer having a total of four phase modulation regions, with two columns in the X direction and two rows in the Y direction. [Figure 15] Figure 15 shows a phase modulation layer in which the two phase modulation regions in the first row have phase distribution pattern B, and the two phase modulation regions in the second row have phase distribution pattern A. [Figure 16] Figure 16 is a conceptual diagram illustrating the design methods for phase distribution patterns A and B. [Figure 17] Figure 17 shows a phase modulation layer having a total of m × n phase modulation regions, with m columns in the X direction and n rows in the Y direction. [Figure 18] Figure 18 is a conceptual diagram illustrating a method for designing m × n phase distribution patterns. [Figure 19] Figure 19 is a conceptual diagram illustrating the second design method. [Figure 20] Figure 20 is a conceptual diagram illustrating the design methods for phase distribution patterns A and B. [Figure 21] Figure 21 is a conceptual diagram illustrating a method for designing m × n phase distribution patterns. [Figure 22] Figure 22 is a cross-sectional view showing a stacked structure of a semiconductor light-emitting element as a first modified example. [Figure 23] Figure 23 is a plan view of the cladding layer. [Figure 24] Figure 24 is a cross-sectional view showing the configuration of a semiconductor light-emitting element as a second modified example. [Figure 25] Figure 25 is a plan view showing the phase modulation layer. [Figure 26] Figure 26 is a plan view showing a partially enlarged view of the phase shift region and the surrounding connection region. [Figure 27] Figure 27 is a magnified view of one unit constituent region. [Figure 28] Part (a) of Figure 28 shows the desired optical image in the irradiation region (far field) set when designing the phase distribution pattern A. Part (b) of Figure 28 shows the optical image shown in part (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 28 shows the phase distribution pattern A calculated based on the target amplitude distribution shown in part (b). [Figure 29] Part (a) of Figure 29 shows the desired optical image in the irradiation region (far field) set when designing the phase distribution pattern B. Part (b) of Figure 29 shows the optical image shown in part (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 29 shows the phase distribution pattern B calculated based on the target amplitude distribution shown in part (b). [Figure 30] Part (a) of Figure 30 shows the result of applying phase distribution pattern A to each of the two phase modulation regions located on one diagonal and phase distribution pattern B to each of the two phase modulation regions located on the other diagonal. Part (b) of Figure 30 conceptually shows the difference between the light intensity of the two phase modulation regions located on one diagonal and the light intensity of the two phase modulation regions located on the other diagonal, which is achieved by individually controlling the current of each electrode portion. [Figure 31] Figure 31 shows the final optical image that is expected when optical images emitted from two phase modulation regions having phase distribution pattern A and optical images emitted from two phase modulation regions having phase distribution pattern B are interfered with each other. [Figure 32]Part (a) of Figure 32 shows the final optical image obtained by the first design method. Part (b) of Figure 32 shows the final optical image obtained by the second design method. [Figure 33] Part (a) of Figure 33 shows the desired optical image in the irradiation region (far field) set when designing the phase distribution pattern A. Part (b) of Figure 33 shows the optical image shown in part (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 33 shows the phase distribution pattern A calculated based on the target amplitude distribution shown in part (b). [Figure 34] Part (a) of Figure 34 shows the desired optical image in the irradiation region (far field) set when designing the phase distribution pattern B. Part (b) of Figure 34 shows the optical image shown in part (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 34 shows the phase distribution pattern B calculated based on the target amplitude distribution shown in part (b). [Figure 35] Part (a) of Figure 35 shows the result of applying phase distribution pattern A to each of the two phase modulation regions located on one diagonal and phase distribution pattern B to each of the two phase modulation regions located on the other diagonal. Part (b) of Figure 35 conceptually shows the difference between the light intensity of the two phase modulation regions located on one diagonal and the light intensity of the two phase modulation regions located on the other diagonal, which is achieved by individually controlling the current of each electrode portion. [Figure 36] Figure 36 shows the final optical image expected when an optical image emitted from a phase-modulated region having phase distribution pattern A and an optical image emitted from a phase-modulated region having phase distribution pattern B are interfered with each other. [Figure 37] Figure 37 shows the final optical image obtained from the simulation. [Figure 38] Figure 38 shows the final optical image obtained from the simulation. [Modes for carrying out the invention]

[0021] Specific examples of the semiconductor light-emitting devices of this disclosure will be described below with reference to the drawings. However, the present invention is not limited to these examples, and is intended to include all modifications within the meaning and scope of the claims, as defined by the claims. In the following description, the same elements in the drawings are denoted by the same reference numerals, and redundant descriptions are omitted.

[0022] Figure 1 is a cross-sectional view showing the stacked structure of the semiconductor light-emitting element 1 of this embodiment. In Figure 1, an XYZ Cartesian coordinate system is defined with the axis extending in the thickness direction of the semiconductor light-emitting element 1 as the Z-axis. The semiconductor light-emitting element 1 is a laser light source that forms a standing wave in the XY plane direction and outputs a phase-controlled plane wave in a direction intersecting its thickness direction. The semiconductor light-emitting element 1 is an S-iPM laser and can output an optical image of any shape in a direction perpendicular to the main surface 10a of the semiconductor substrate 10, i.e., the Z direction, or a direction inclined with respect to the Z direction, or a direction including both.

[0023] The semiconductor light-emitting element 1 comprises a semiconductor substrate 10. The semiconductor substrate 10 has a main surface 10a and a back surface 10b. The normal direction of the main surface 10a and the back surface 10b, and the thickness direction of the semiconductor substrate 10 are aligned along the Z direction. The semiconductor substrate 10 is composed of a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor.

[0024] The semiconductor light-emitting element 1 further comprises a semiconductor stack 20. The semiconductor stack 20 is provided on the main surface 10a of the semiconductor substrate 10. The stacking direction of the semiconductor stack 20 is along the Z direction. The semiconductor stack 20 has a stacked structure between the first surface 20a and the second surface 20b, including a cladding layer 11, an active layer 12, a cladding layer 13, a contact layer 14, and a phase modulation layer 15. The second surface 20b of the semiconductor stack 20 faces the main surface 10a of the semiconductor substrate 10. In the illustrated example, the cladding layer 11 is provided on the main surface 10a of the semiconductor substrate 10, the active layer 12 is provided on the cladding layer 11, the phase modulation layer 15 is provided on the active layer 12, the cladding layer 13 is provided on the phase modulation layer 15, and the contact layer 14 is provided on the cladding layer 13. Specifically, the cladding layer 11 is provided between the active layer 12 and the second surface 20b, and the cladding layer 13 is provided between the active layer 12 and the first surface 20a, with the cladding layers 11 and 13 sandwiching the active layer 12 and the phase modulation layer 15. In the illustrated example, the phase modulation layer 15 is provided between the active layer 12 and the cladding layer 13, but the phase modulation layer 15 may also be provided between the cladding layer 11 and the active layer 12. Optical guide layers may be provided between the active layer 12 and the cladding layer 13, and between the active layer 12 and the cladding layer 11, or both, as needed. The optical guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

[0025] The cladding layer 11, active layer 12, cladding layer 13, and contact layer 14 are composed of compound semiconductors such as GaAs-based semiconductors, InP-based semiconductors, or nitride-based semiconductors. The active layer 12 has, for example, a multiple quantum well structure. The energy band gaps of cladding layer 11 and cladding layer 13 are larger than the energy band gap of active layer 12. The thickness directions of cladding layer 11, active layer 12, cladding layer 13, and contact layer 14 coincide with the Z-axis direction.

[0026] 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. Figure 2 is a plan view (viewed from the thickness direction) of the phase modulation layer 15. As shown in Figures 1 and 2, the phase modulation layer 15 has a plurality of phase modulation regions 151 and connection regions 152. The planar shape of the connection regions 152 viewed from the stacking direction of the semiconductor stack 20 is, for example, a grid. Each of the plurality of phase modulation regions 151 is provided in each of the plurality of openings 152a of the grid-shaped connection regions 152.

[0027] The planar shape of each of the multiple phase modulation regions 151 is, for example, a square or a rectangle. The multiple phase modulation regions 151 are arranged two-dimensionally along a virtual plane P perpendicular to the thickness direction of the phase modulation layer 15 (in other words, parallel to the XY plane) and are optically coupled to one another. In the illustrated example, the multiple phase modulation regions 151 are arranged along the X and Y directions. Although the multiple phase modulation regions 151 are arranged two-dimensionally in the illustrated example, they may also be arranged one-dimensionally. In the illustrated example, the multiple phase modulation regions 151 are spaced apart from each other. The connecting region 152 includes a portion 152b provided between adjacent phase modulation regions 151 and an outer frame-shaped portion 152c that encloses the multiple phase modulation regions 151 together.

[0028] As shown in Figure 1, each of the multiple phase modulation regions 151 is composed of a basic region 15a and multiple regions with different refractive indices 15b. Similarly, the connecting region 152 is also composed of a basic region 15a and multiple regions with different refractive indices 15b. The basic region 15a consists of a first refractive index medium. The basic region 15a is composed of a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor. The multiple regions with different refractive indices 15b consist of a second refractive index medium with a different refractive index from the first refractive index medium and exist within the basic region 15a. The regions with different refractive indices 15b are, for example, voids. The regions with different refractive indices 15b are covered by a cap region 15c provided on the basic region 15a. The cap region 15c constitutes part of the phase modulation layer 15 and is made of, for example, the same material as the basic region 15a.

[0029] Multiple regions with different refractive indices 15b are distributed two-dimensionally along a virtual plane P. In each phase modulation region 151, the multiple regions with different refractive indices 15b contain a lattice-like, approximately periodic structure. If the equivalent refractive index of the mode is n and the lattice spacing is a, the wavelength λ0 selected by each phase modulation region 151 is expressed as λ0 = (√2)a × n, for example, in the case of M1 point oscillation. This wavelength λ0 is included within the emission wavelength range of the active layer 12. Each phase modulation region 151 can select a band edge wavelength near wavelength λ0 from the emission wavelength of the active layer 12 and output it to the outside. Light incident from the active layer 12 into each phase modulation region 151 forms a predetermined mode within each phase modulation region 151 according to the arrangement of the regions with different refractive indices 15b, and is output as laser light L from the back surface 10b of the semiconductor substrate 10 to the outside of the semiconductor light-emitting element 1.

[0030] Figure 3 is a plan view showing an enlarged portion of the phase modulation region 151. Although Figure 3 shows only one phase modulation region 151, the configuration of other phase modulation regions 151 is similar. As mentioned above, the phase modulation region 151 includes a basic region 15a and multiple regions with different refractive indices 15b. In Figure 3, a virtual square grid is set up along a virtual plane P for the phase modulation region 151. One side of the square grid is parallel to the X axis, and the other side is parallel to the Y axis. The square-shaped unit constituent regions R, centered on the grid points O of the square grid, are arranged two-dimensionally across multiple columns along the X axis and multiple rows along the Y axis. The XY coordinates of each unit constituent region R are defined by the centroid position of each unit constituent region R. These centroid positions coincide with the grid points O of the virtual square grid. For example, one region with different refractive indices 15b is provided within each unit constituent region R. The planar shape of the region with different refractive indices 15b is, for example, circular. The lattice point O may be located outside the region of different refractive indices 15b, or it may be located inside the region of different refractive indices 15b.

[0031] Figure 4 is a magnified view of one unit constituent region R. As shown in the figure, each of the different refractive index regions 15b has a centroid G. The centroid G of the different refractive index regions 15b is located on a line D set for each lattice point O. Line D is a line that passes through the lattice point O corresponding to each unit constituent region R and is inclined with respect to each side of the square lattice. In other words, line D is a line that is inclined with respect to both the X axis and the Y axis. The inclination angle of line D with respect to one side of the square lattice, in other words, the X axis, is β.

[0032] The inclination angle β is the same for all lines D within the phase modulation region 151. Furthermore, the inclination angle β is the same across multiple phase modulation regions 151. The inclination angle β satisfies 0° < β < 90°, in one example β = 45°. Alternatively, the inclination angle β satisfies 180° < β < 270°, in one example β = 225°. When the inclination angle β satisfies 0° < β < 90° or 180° < β < 270°, the line D extends from the first to the third quadrant of the coordinate plane defined by the X and Y axes. The inclination angle β satisfies 90° < β < 180°, in one example β = 135°. Alternatively, the inclination angle β satisfies 270° < β < 360°, in one example β = 315°. If the inclination angle β satisfies 90° < β < 180° or 270° < β < 360°, the line D extends from the second to the fourth quadrant of the coordinate plane defined by the X and Y axes. Thus, the inclination angle β is an angle other than 0°, 90°, 180°, and 270°.

[0033] Here, let r(x,y) be the distance between the grid point O and the centroid G. x is the position of the x-th grid point on the X-axis, and y is the position of the y-th grid point on the Y-axis. When the distance r(x,y) is a positive value, the centroid G is located in the first or second quadrant. When the distance r(x,y) is a negative value, the centroid G is located in the third or fourth quadrant. When the distance r(x,y) is 0, the grid point O and the centroid G coincide with each other. Preferred inclination angles are 45°, 135°, 225°, and 275°. In the case of these inclination angles, only two of the four wave vectors forming the standing wave at point M, for example, the in-plane wave vectors (±π / a, ±π / a), are phase-modulated, while the other two are not phase-modulated. Therefore, a stable standing wave can be formed.

[0034] The distance r(x,y) is set individually for each different refractive index region 15b according to the phase distribution φ(x,y) corresponding to the optical image to be output from each phase modulation region 151. That is, if the phase φ(x,y) at a certain coordinate (x,y) is φ0, the distance r(x,y) is set to 0. If the phase φ(x,y) is π+φ0, the distance r(x,y) is set to the maximum value R0. If the phase φ(x,y) is -π+φ0, the distance r(x,y) is set to the minimum value -R0. For intermediate phases φ(x,y), the distance r(x,y) is set such that r(x,y)={φ(x,y)-φ0}×R0 / π. If the grid spacing of a virtual square grid is a, the maximum value R0 of r(x,y) will be within the range of, for example, the following equation (1).

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[0035] By determining the distribution of the distance r(x, y) of each of the plurality of phase modulation regions 151 in the anisotropic refractive index region 15b, a desired optical image can be output from each of the plurality of phase modulation regions 151. Each phase modulation region 151 is configured to satisfy the following conditions.

[0036] As a first prerequisite, a virtual square lattice composed of M1×N1 unit constituent regions R having a square shape is set on the XY plane. M1 and N1 are integers of 1 or more.

[0037] As shown in FIG. 5, the radial length r, the inclination angle θ from the Z axis tilt and the rotation angle θ from the X axis specified on the XY plane rot define spherical coordinates (r, θ rot , θ tilt ). As a second prerequisite, the coordinates (ξ, η, ζ) in the XYZ orthogonal coordinate system are assumed to satisfy the relationships shown in the following equations (2) to (4) with respect to the spherical coordinates (r, θ rot , θ tilt ). FIG. 5 is a diagram for explaining the coordinate transformation from the spherical coordinates (r, θ rot , θ tilt ) to the coordinates (ξ, η, ζ) in the XYZ orthogonal coordinate system. The coordinates (ξ, η, ζ) represent a designed optical image on a predetermined plane set in the XYZ orthogonal coordinate system, which is the real space.

Equation

Equation

Equation

[0038] The light emitted from each phase modulation region 151 is set as a set of bright spots directed in the directions defined by the angles θ tilt and θ rot . At this time, the angles θ tilt and θ rotThese shall be converted to coordinate values ​​kx and ky. The coordinate value kx is the normalized wavenumber defined by the following equation (5), and corresponds to K on the X axis. x These are coordinate values ​​on the axis. The coordinate value ky is a normalized wavenumber defined by the following equation (6), and corresponds to the Y axis and K x K perpendicular to the axis y These are coordinate values ​​on the axis. The normalized wavenumber refers to the wavenumber normalized by setting the wavenumber 2π / a, which corresponds to the grid spacing of a hypothetical square grid, to 1.0. In this case, K x Axis and K y In the wavenumber space defined by the axis, a specific wavenumber range containing a beam pattern corresponding to an optical image is composed of M2 × N2 image regions FR, each of which is square in shape. M2 and N2 are integers greater than or equal to 1. The integer M2 does not need to be the same as the integer M1. The integer N2 does not need to be the same as the integer N1. Equations (5) and (6) are disclosed, for example, in Non-Patent Document 1.

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[0039] In wavenumber space, the image region FR(kx,ky) is K x Axial coordinate components kx and K yThe coordinate components kx and y are specified by the coordinate components ky in the axial direction. The coordinate component kx is an integer between 0 and M2-1, and the coordinate component ky is an integer between 0 and N2-1, and the unit constituent region R(x,y) on the XY plane is specified by the coordinate component x in the X direction and the coordinate component y in the Y direction. The coordinate component x is an integer between 0 and M1-1, and the coordinate component y is an integer between 0 and N N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1-1, and the coordinate component y is an integer between N1- The s-axis and t-axis are parallel to the x-axis and y-axis, respectively, and are orthogonal to each other at the lattice point O(x,y) which is the center of the unit constituent region R(x,y).

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[0040] Under the first to fourth preconditions described above, each phase modulation region 151 is configured to satisfy the following conditions. That is, the distance r(x,y) from the lattice point O(x,y) to the centroid G of the corresponding differential refractive index region 15b satisfies the following relationship, and the corresponding differential refractive index region 15b is arranged within the unit configuration region R(x,y). r(x,y) = C × (φ(x,y) - φ0) C: Proportionality constant, for example, R0 / π φ0: Any constant, for example, 0 To obtain a desired optical image, it is advisable to perform an inverse Fourier transform on the optical image and assign a distribution of distances r(x,y) corresponding to the phase φ(x,y) of its complex amplitude to multiple regions 15b with different refractive indices. The phase φ(x,y) and the distance r(x,y) may be proportional to each other.

[0041] Figure 6 is a plan view showing an enlarged portion of the connection region 152. Although only a portion of the connection region 152 is shown in Figure 6, the configuration of the other parts of the connection region 152 is similar. As mentioned above, the connection region 152 also includes the basic region 15a and multiple regions with different refractive indices 15b. In the connection region 152, a virtual square lattice is set up similarly to that in Figure 3. One side of the square lattice is parallel to the X axis, and the other side is parallel to the Y axis. The lattice constant a of the square lattice is equal to the lattice constant a of the phase modulation region 151 and the square lattice. In the connection region 152, the centroid G of the multiple regions with different refractive indices 15b is located at the lattice points of the square lattice. In other words, the positions of the centroid G of the multiple regions with different refractive indices 15b coincide with the positions of the lattice points of the square lattice. Therefore, in the connection region 152, the multiple regions with different refractive indices 15b are arranged periodically along the X and Y axes.

[0042] Refer to Figure 1 again. The semiconductor light-emitting element 1 further comprises an electrode 16 (first electrode) and an electrode 17 (second electrode). Electrode 16 is provided facing the first surface 20a of the semiconductor stack 20, and in the illustrated example, electrode 16 is provided on the first surface 20a, i.e., on the contact layer 14. Electrode 16 makes ohmic contact with the contact layer 14. Electrode 17 is provided facing the second surface 20b of the semiconductor stack 20, and in the illustrated example, electrode 17 is provided on the back surface 10b of the semiconductor substrate 10. Electrode 17 makes ohmic contact with the semiconductor substrate 10.

[0043] Figure 7 schematically shows the planar shapes of electrodes 16 and 17, and the configuration for supplying current to electrodes 16 and 17. As shown in Figure 7, electrode 17 has a plurality of openings 17a. Each opening 17a corresponds one-to-one with each phase modulation region 151. Viewed from the thickness direction of the semiconductor stack 20, the openings 17a overlap with the corresponding phase modulation region 151. The planar shape of each opening 17a is, for example, a square or rectangle. Electrode 16 includes a plurality of electrode portions 161. The plurality of electrode portions 161 are arranged with gaps between them and are electrically isolated from each other. Note that the fact that the electrode portions are electrically isolated from each other means that there are no other paths to electrically connect them except through the semiconductor stack 20. Each electrode portion 161 corresponds one-to-one with each phase modulation region 151. Viewed from the thickness direction of the semiconductor stack 20, the electrode portions 161 overlap with the corresponding phase modulation region 151. The planar shape of each electrode portion 161 is, for example, a square or a rectangle.

[0044] Each of the multiple electrode sections 161 is individually electrically connected to the drive circuit 31 via each of the multiple wirings 33. Electrode 17 is also electrically connected to the drive circuit 31 via wiring 34. The drive circuit 31 is electrically connected to the power supply circuit 32 via wiring 35. The drive circuit 31 receives power from the power supply circuit 32 and supplies drive current between the multiple electrode sections 161 and electrode 17. The drive circuit 31 can freely change the magnitude of the drive current for each electrode section 161. The magnitude of the drive current to each electrode section 161 is set independently for each electrode section 161.

[0045] Refer to Figure 1 again. The parts of the contact layer 14 other than those overlapping with each electrode portion 161 are removed by etching in order to limit the current range. Thus, the contact layer 14 is divided into multiple parts corresponding to the multiple electrode portions 161. The gaps between the multiple parts of the contact layer 14 are filled with a protective film 18. This protects the surface of the semiconductor laminate 20 exposed from the electrodes 16. The protective film 18 is made of an inorganic insulator such as silicon nitride (e.g., SiN) or silicon oxide (e.g., SiO2). Note that the parts of the contact layer 14 other than those overlapping with each electrode portion 161 do not necessarily have to be removed. In that case, the protective film 18 is provided on the contact layer 14 in the gaps between the multiple electrode portions 161.

[0046] On the back surface 10b of the semiconductor substrate 10, areas other than the area where the electrodes 17 are provided, including within the opening 17a, are covered with an anti-reflective film 19. The anti-reflective film 19 in areas other than the opening 17a may be removed. The anti-reflective film 19 consists of a single-layer or multilayer film of a dielectric material, such as silicon nitride (e.g., SiN) or silicon oxide (e.g., SiO2). As the dielectric multilayer film, for example, a film can be used in which two or more dielectric layers selected from the group of dielectric layers consisting of titanium dioxide (TiO2), silicon dioxide (SiO2), silicon monoxide (SiO), niobium oxide (Nb2O5), tantalum pentoxide (Ta2O5), magnesium fluoride (MgF2), titanium dioxide (TiO2), aluminum oxide (Al2O3), cerium oxide (CeO2), indium oxide (In2O3), and zirconium oxide (ZrO2) are laminated. Dielectric multilayer films are formed, for example, by stacking multiple films, each having an optical film thickness of λ / 4 for light of wavelength λ.

[0047] In this embodiment, the electrode 16 facing the first surface 20a includes multiple electrode portions 161. However, instead of this configuration, or in conjunction with this configuration, the electrode 17 facing the second surface 20b may also include multiple electrode portions. In this case, similar to the multiple electrode portions 161, the multiple electrode portions of the electrode 17 are also arranged with gaps between them and are electrically isolated from each other. Each electrode portion of the electrode 17 corresponds one-to-one with each phase modulation region 151. Viewed from the thickness direction of the semiconductor stack 20, each electrode portion of the electrode 17 overlaps with the corresponding phase modulation region 151. The planar shape of each electrode portion of the electrode 17 is, for example, a rectangular frame shape including an opening 17a. Each of the multiple electrode portions of the electrode 17 is individually electrically connected to the drive circuit 31 via each of the multiple wirings. The drive circuit 31 freely changes the magnitude of the drive current for each electrode portion of the electrode 17.

[0048] In the semiconductor light-emitting element 1, when a drive current is supplied between the electrode portion 161 and the electrode 17, recombination of electrons and holes occurs in the portion of the active layer 12 located directly beneath the electrode portion 161, and light is emitted from that portion of the active layer 12. At this time, the electrons and holes contributing to the light emission, as well as the light emitted from the active layer 12, are efficiently confined between the cladding layer 11 and the cladding layer 13.

[0049] Light emitted from the portion of the active layer 12 enters the phase modulation region 151 opposite to that portion, resonates along the virtual plane P in the phase modulation region 151, and forms a predetermined mode corresponding to the arrangement of the multiple regions with different refractive indices 15b. A portion of the laser light L emitted from the phase modulation region 151 is directly output to the outside of the semiconductor light-emitting element 1 through the aperture 17a from the back surface 10b. The remainder of the laser light L emitted from the phase modulation region 151 is reflected by the electrode 16 and then output to the outside of the semiconductor light-emitting element 1 through the aperture 17a from the back surface 10b. At this time, the signal light contained in the laser light L is emitted in a direction that intersects both the first surface 20a and the second surface 20b of the semiconductor stack 20. In other words, the signal light contained in the laser light L is emitted in any direction including a direction perpendicular to the back surface 10b and a direction inclined with respect to the direction perpendicular to the back surface 10b. The light emitted from the semiconductor light-emitting element 1 is composed of signal light. The signal light is primarily the first-order diffracted light or the -1st-order diffracted light of the laser, or both. Hereafter, the first-order diffracted light will be referred to as the first-order light, and the -1st-order diffracted light will be referred to as the -1st-order light.

[0050] The laser light L emitted from each of the multiple phase modulation regions 151 is projected onto a common irradiation area (far field) located in a direction intersecting both the first surface 20a and the second surface 20b of the semiconductor stack 20, forming an optical image corresponding to the arrangement of the multiple different refractive index regions 15b. The multiple different refractive index regions 15b included in at least two of the multiple phase modulation regions 151 have a different arrangement for each phase modulation region 151. Therefore, the optical images emitted from each of the multiple phase modulation regions 151 interfere with each other to form the final optical image.

[0051] In order to obtain a final optical image by interfering with the optical images output from each of the multiple phase modulation regions 151, these optical images are phase-synchronized with one another. In this embodiment, a connection region 152 is provided between adjacent phase modulation regions 151 so that these optical images are phase-synchronized with one another. Since the resonance modes of adjacent phase modulation regions 151 are shared via the connection region 152, the phases of the laser light L resonating in each phase modulation region 151 can be synchronized with one another. Alternatively, the connection region 152 may be eliminated, and adjacent phase modulation regions 151 may be placed next to each other. Even in such a case, the phases of the laser light L resonating in each phase modulation region 151 can be synchronized with one another. In order to phase-synchronize multiple optical images with one another, this must be considered when designing the phase distribution φ(x,y) of each phase modulation region 151, but the design of the phase distribution φ(x,y) considering phase synchronization will be described later.

[0052] Furthermore, in order to obtain a desired optical image by interfering the optical images output from each of the multiple phase modulation regions 151 with each other, it is desirable that the polarization directions of these optical images be aligned. In this embodiment, the centroid G of the different refractive index regions 15b is located on a straight line D set for each grid point O. The inclination angle β of the straight line D is the same for all grid points O within the phase modulation region 151, and is also the same for multiple phase modulation regions 151.

[0053] Here, Figure 8 shows the electromagnetic field distribution in the phase modulation region 151. Part 8(a) of Figure 8 shows the electromagnetic field distribution in the resonant mode with symmetry A1 at point M1. Part 8(b) of Figure 8 shows the electromagnetic field distribution in the resonant mode with symmetry B2 at point M1. In Figure 8, the arrows represent the magnitude and direction of the electric field, and the intensity of the color represents the magnitude of the magnetic field. When the centroid G of the different refractive index regions 15b are arranged on a straight line D, as in this embodiment (the figure schematically shows the change in the arrangement of the central different refractive index regions 15b), it is expected that the polarization directions will be aligned in any electromagnetic field distribution, regardless of the distance between the centroid G of the different refractive index regions 15b and the lattice point O (in other words, regardless of the phase value realized by each different refractive index region 15b).

[0054] On the other hand, Figure 9 shows the electromagnetic field distribution in a comparative example where the centroid G of the different refractive index region 15b is located at a constant distance from the grid point O, and the rotation angle of the vector connecting the grid point O to the centroid G around the grid point O is set for each different refractive index region 15b according to the phase distribution φ(x,y). Part 9(a) of Figure 9 shows the electromagnetic field distribution in the resonant mode of symmetry A1 at point M1. Part 9(b) of Figure 9 shows the electromagnetic field distribution in the resonant mode of symmetry B2 at point M1. In Figure 9 as well, the arrows represent the magnitude and direction of the electric field, and the intensity of the color represents the magnitude of the magnetic field. In this comparative example, in both electromagnetic field distributions, the polarization direction changes according to the rotation angle of the different refractive index region 15b around the grid point O. Therefore, it is almost impossible to expect the polarization directions to be aligned. For these reasons, it is desirable to have a configuration like that of this embodiment, where the centroid G of the different refractive index region 15b is located on a straight line D, and the distance between the centroid G and the grid point O changes according to the phase.

[0055] As described above, the semiconductor light-emitting element 1 of this embodiment forms a final optical image (hologram) by irradiating a common illumination area with multiple optical images output from multiple phase modulation regions 151, and superimposing and interfering the multiple optical images. Figure 10 is a conceptual diagram showing an example of multiple optical images output from multiple phase modulation regions 151. In Figure 10, a total of 64 optical images LA are shown in 8 columns in the X direction and 8 rows in the Y direction, with the darker the optical intensity and the fainter the optical intensity. These are optical images output from a total of 64 phase modulation regions 151, in 8 columns in the X direction and 8 rows in the Y direction. In this example, the optical intensity distribution of the optical images LA output from each of the multiple phase modulation regions 151 includes a sinusoidal distribution in which the period in two mutually orthogonal directions (X direction and Y direction) differs for each phase modulation region 151. Such optical images LA can be used, for example, as a basis image for a discrete cosine transform (DCT). In other words, the final optical image can be realized by performing a discrete cosine transform on the light intensity distribution of the final optical image and outputting the resulting multiple base images from each of the multiple phase modulation regions 151. Furthermore, by changing the magnitude of the driving current of the multiple electrode portions 161 corresponding to each of the multiple phase modulation regions 151, the contribution of each base image to the final optical image can be individually adjusted, thereby presenting a time-varying dynamic optical image.

[0056] Figure 11 is a conceptual diagram showing another example of multiple optical images output from multiple phase modulation regions 151. This example shows multiple optical images LA used as basis images for a discrete wavelet transform (DWT). As in this example, the final optical image can also be realized by performing a discrete wavelet transform on the optical intensity distribution of the final optical image and outputting the resulting basis images from multiple phase modulation regions 151. Furthermore, by changing the magnitude of the drive current of multiple electrode portions 161 corresponding to each of the multiple phase modulation regions 151, the contribution of each basis image to the final optical image can be individually adjusted to present a time-varying dynamic optical image.

[0057] Furthermore, the method is not limited to discrete cosine transforms and discrete wavelet transforms; for example, a collection of multiple optical images to be displayed in the far field may be used to learn their basis images through machine learning (principal nature analysis or dictionary learning, etc.). Also, in the example shown in Figure 10, the periods in two mutually orthogonal directions (X and Y directions) differ for each phase modulation region 151, but the period in one direction (X or Y direction) may also differ for each phase modulation region 151.

[0058] Figure 12 conceptually illustrates yet another example of multiple optical images output from multiple phase modulation regions 151. Figure 12 shows a total of four optical images LA arranged in two columns in the X direction and two rows in the Y direction. These are optical images output from a total of four phase modulation regions 151, arranged in two columns in the X direction and two rows in the Y direction. In this example, the optical intensity distribution of the optical image LA output from each phase modulation region 151 includes a sinusoidal distribution that changes periodically along the Y direction. Furthermore, the phase in the Y direction of the sinusoidal optical intensity distribution of the optical image LA output from each of the two phase modulation regions 151 located on one diagonal is different from the phase in the Y direction of the sinusoidal optical intensity distribution of the optical image LA output from each of the two phase modulation regions 151 located on the other diagonal. In this example, the phase of the sinusoidal light intensity distribution presented in the final optical image can be freely changed by changing the ratio of the magnitude of the drive current of the two electrode portions 161 corresponding to the two phase modulation regions 151 located on one diagonal to the magnitude of the drive current of the two electrode portions 161 corresponding to the two phase modulation regions 151 located on the other diagonal. As shown in the example in Figure 12, the phases in one direction (Y direction) of the sinusoidal light intensity distribution of the optical image LA output from at least two phase modulation regions 151 may be different from each other. The light intensity distribution of the optical image LA output from each phase modulation region 151 may include a sinusoidal distribution that changes periodically along two directions (X direction and Y direction). In that case, the phases in two directions (X direction and Y direction) of the sinusoidal light intensity distribution of the optical image LA output from at least two phase modulation regions 151 may be different from each other.

[0059] Next, we will explain in detail a phase distribution design method that takes into account the phase synchronization of the optical images output from each of the multiple phase modulation regions 151. In the following explanation, the multiple regions with different refractive indices 15b may be referred to as "multiple points". In other words, the method described below is a method for designing the phase distribution φ(x,y) of two or more phase modulation regions 151 that individually modulate the phase of light at multiple points distributed in two dimensions. Also, in the following explanation, "real space" refers to the space of the phase modulation region 151, and "wavenumber space" refers to the space of the optical image (also called the beam pattern) in the irradiation region. [First design method]

[0060] Figure 13 is a diagram conceptually illustrating the first design method. First, as the first step, initial conditions are set (arrow B1 in the figure). For each phase modulation region 151, a first function 203 is set, which is a complex amplitude distribution function that includes the initial value 201 of the amplitude distribution in wavenumber space and the initial value 202 of the phase distribution in wavenumber space. If the initial value 201 of the amplitude distribution in wavenumber space is F0(kx,ky) and the initial value 202 of the phase distribution in wavenumber space is θ0(kx,ky), then the first function 203 is F0(kx,ky)·e iθ0(kx,ky) This is expressed as follows. In this case, the initial value 201 of the amplitude distribution in wavenumber space may be set to a predetermined target amplitude distribution 204 in wavenumber space. If the target amplitude distribution 204 in wavenumber space is F0(kx,ky), then its light intensity distribution (i.e., the desired light image) is F0 2 It is given as (kx, ky). Also, the initial value 202 of the phase distribution in wavespace may be set to a random phase distribution 205.

[0061] Furthermore, in the first step, for each phase modulation region 151, the first function 203 is transformed into a second function 213, which is a complex amplitude distribution function that includes the real-space amplitude distribution 211 and the real-space phase distribution 212, by an inverse Fourier transform such as the Inverse Fast Fourier Transform (IFFT) (arrow B2 in the figure). If the real-space amplitude distribution 211 is A(x,y) and the real-space phase distribution 212 is φ(x,y), then the second function 213 is A(x,y)·e iφ(kx,ky) It is expressed as follows.

[0062] Next, as the second step, the amplitude distribution 211 of the second function 213 in each phase modulation region 151 is replaced with a target amplitude distribution 214 based on a predetermined target intensity distribution in real space (arrows B3 and B4 in the figure). For example, if the predetermined target intensity distribution is A0 2 If (x,y) is given, the target amplitude distribution is given as A0(x,y). In one example, the given target intensity distribution A0 2 (x,y) is constant regardless of x and y, and the target amplitude distribution A0(x,y) is also constant regardless of x and y. In this case, the phase distribution 212 of the second function 213 in each phase modulation region 151 is maintained as is (arrow B5 in the figure). Then, for each phase modulation region 151, the replaced second function 213 is transformed into a third function 223, which is a complex amplitude distribution function that includes the amplitude distribution 221 and the phase distribution 222 in wavespace, by a Fourier transform such as the Fast Fourier Transform (FFT) (arrow B6 in the figure). If the amplitude distribution 221 in wavespace is F(kx,ky) and the phase distribution 222 in wavespace is θ(kx,ky), then the third function 223 is F(kx,ky)·e iθ(kx,ky) It is expressed as follows.

[0063] Next, as the third step, the phase distribution 222 of the third function 223 in each phase modulation region 151 is aligned with the phase distribution 222 of the third function 223 in one of the multiple phase modulation regions 151 (arrow B7 in the figure). At this time, the one phase modulation region 151 that serves as the reference for aligning the phase distributions 222 is arbitrarily determined. Also in this third step, the amplitude distribution 221 of the third function 223 in each phase modulation region 151 is replaced with the target amplitude distribution 204 (arrows B8, B9 in the figure). Then, for each phase modulation region 151, the replaced third function 223 is transformed into a fourth function 233, which is a complex amplitude distribution function that includes the real-space amplitude distribution 231 and the real-space phase distribution 232, by an inverse Fourier transform such as IFFT (arrow B2 in the figure). If the amplitude distribution 231 in real space is A(x,y) and the phase distribution 232 in real space is φ(x,y), then the fourth function 233 is A(x,y)·e iφ(kx,ky) It is expressed as follows.

[0064] Subsequently, the second and third steps are repeated, replacing the second function 213 in the second step with the fourth function 233. Note that, each time the third step is repeated, the position of one phase modulation region 151, which serves as the reference for aligning the phase distributions 222, may be fixed without changing its position. Finally, the phase distribution 232 of the fourth function 233 transformed by the third step is taken as the phase distribution φ(x,y) of each phase modulation region 151 (arrow B10 in the figure).

[0065] As an example, consider a phase modulation layer 15 having a total of four phase modulation regions 151, arranged in two columns in the X direction and two rows in the Y direction, as shown in Figure 14. Of these, two phase modulation regions 151 located on opposite diagonals have phase distribution pattern A, and two phase modulation regions 151 located on the opposite diagonal have phase distribution pattern B. Alternatively, as shown in Figure 15, two phase modulation regions 151 in the first row may have phase distribution pattern B, and two phase modulation regions 151 in the second row may have phase distribution pattern A. Figure 16 is a conceptual diagram showing the design method for phase distribution patterns A and B.

[0066] First, as the first step, we set the initial values ​​(arrow B11 in the figure). That is, for phase distribution pattern A, we set the first function F1(kx,ky)·e, which is a complex amplitude distribution function that includes the initial values ​​of the amplitude distribution F1(kx,ky) in wavespace and the initial values ​​of the phase distribution θ1(kx,ky) in wavespace. iθ1(kx,ky) Set (F1e iθ1 (Abbreviated as ). Furthermore, for phase distribution pattern B, the first function F2(kx,ky)·e is a complex amplitude distribution function that includes the initial values ​​of the amplitude distribution F2(kx,ky) in wavespace and the initial values ​​of the phase distribution θ2(kx,ky) in wavespace. iθ2(kx,ky) Set (hereinafter, F2e iθ2 (This is abbreviated as follows). And the first function F1·e of the phase distribution pattern A. iθ1 This is obtained by an inverse Fourier transform such as IFFT, resulting in a second function A1(x,y)·e, which is a complex amplitude distribution function containing the real-space amplitude distribution A1(x,y) and the real-space phase distribution φ1(x,y). iφ1(x,y) Convert to (arrow B12 in the diagram. Below, A1·e iφ1 (This is abbreviated as follows). Similarly, the first function F2(x,y)·e of phase distribution pattern B iθ2(x,y) This can be transformed using an inverse Fourier transform such as IFFT to obtain the second function A2(x,y)·e, which is a complex amplitude distribution function containing the real-space amplitude distribution A2(x,y) and the real-space phase distribution φ2(x,y). iφ2(x,y) Convert to (arrow B13 in the diagram. Below, A2·e iφ2 (This is abbreviated as ).

[0067] Next, as the second step, the second function A1·e iφ1 The amplitude distribution A1 is a target amplitude distribution A1 based on a predetermined target intensity distribution in real space. ’ Replace it with the second function A2·e iφ2 The amplitude distribution A2 is a target amplitude distribution A2 based on a predetermined target intensity distribution in real space. ’ Replace with (arrow B14 in the figure). At this time, the phase distributions φ1 and φ2 are maintained as they are. Then, the second function A1 after the replacement ’ ·e iφ1This can be transformed, for example, by a Fourier transform such as FFT, into a third function F1·e, which is a complex amplitude distribution function containing the amplitude distribution F1 in wavespace and the phase distribution θ1 in wavespace. iθ1 Convert to (arrow B15 in the diagram). Similarly, the second function A2 after substitution. ’ ·e iφ2 This can be transformed, for example, by a Fourier transform such as FFT, into a third function F2·e, which is a complex amplitude distribution function containing the amplitude distribution F2 in wavespace and the phase distribution θ2 in wavespace. iθ2 Convert to (arrow B16 in the diagram).

[0068] Next, as the third step, the third function F2·e iθ2 The phase distribution θ2 is given by the third function F1·e iθ1 Align the phase distribution θ1. Also, the third function F1·e iθ1 The amplitude distribution F1, and the third function F2·e iθ2 The amplitude distribution F2 is the target amplitude distribution F1 ’ and F2 ’ Replace them with the following (arrow B17 in the diagram). Then, the third function F1 ’ ·e iθ1 This is then transformed by an inverse Fourier transform such as IFFT into a fourth function A1·e, which is a complex amplitude distribution function containing the real-space amplitude distribution A1 and the real-space phase distribution φ1. iφ1 Convert to (arrow B18 in the diagram). Similarly, the third function F2 ’ ·e iθ1 This is then transformed using an inverse Fourier transform such as IFFT into a fourth function A2·e, which is a complex amplitude distribution function containing the real-space amplitude distribution A2 and the real-space phase distribution φ2. iφ2 Convert to (arrow B19 in the diagram).

[0069] From here on, the second function A1·e in the second step iφ1 And the second function A2·e iφ2 The fourth function A1·e iφ1 And the fourth function A2·e iφ2 Repeat steps 2 and 3, replacing each of them accordingly (arrow B20 in the diagram). Then, the fourth function A1·e transformed by the final step 3 is obtained. iφ1Let the phase distribution φ1 be the phase distribution φ(x,y) of phase distribution pattern A. Also, the fourth function A2·e transformed by the final third step. iφ2 Let the phase distribution φ2 be the phase distribution φ(x,y) of phase distribution pattern B.

[0070] As another example, consider the phase modulation layer 15 shown in Figure 17, which has a total of m × n phase modulation regions 151, with m columns in the X direction and n rows in the Y direction. The m × n phase modulation regions 151 have different phase distribution patterns. Figure 18 is a diagram that conceptually shows a method for designing the m × n phase distribution patterns.

[0071] First, as the first step, we set the initial values ​​(arrow B41 in the figure). That is, for m × n phase modulation regions 151, we set the amplitude distribution F in wavenumber space. 1,1 (kx,ky)~F m,n The first function F is a complex amplitude distribution function that includes the initial values ​​of (kx,ky) and the initial values ​​of the phase distributions θ1,1(kx,ky)~θm,n(kx,ky) in wavespace, respectively. 1,1 (kx,ky)·e iθ1,1(kx,ky) ~F m,n (kx,ky)·e iθm,n(kx,ky) Set (F below) 1,1 e iθ1,1 ~F m,n e iθm,n (This is abbreviated as follows). Then, for every 151 phase modulation regions, the first function F 1,1 e iθ1,1 ~F m,n e iθm,n The amplitude distribution A in real space can be obtained by an inverse Fourier transform such as IFFT. 1,1 (x,y)~A m,n The second function A is a complex amplitude distribution function that includes (x,y) and the real-space phase distributions φ1, 1(x,y) ~ φm, n(x,y), respectively. 1,1 (x,y)·e iφ1,1(x,y) ~A m,n (x,y)·e iφm,n(x,y) Convert to (Arrow group B42 in the figure. Hereafter, A 1,1 e iφ1,1 ~A m,n e iφm,n (This is abbreviated as ).

[0072] Next, as the second step, for each phase modulation region 151, the second function A 1,1 e iφ1,1 ~A m,n e iφm,n 's amplitude distribution A 1,1 ~A m,n is replaced with a target amplitude distribution A ’ 1,1 ~A ’ m,n ~A ’ 1,1 e iφ1,1 ~A ’ m,n e iφm,n is converted, for each phase modulation region 151, into a complex amplitude distribution function including the amplitude distribution F 1,1 ~F m,n in the wavenumber space and the phase distribution θ1,1~θm,n in the wavenumber space, which is the third function F 1,1 e iθ1,1 ~F m,n e iθm,n ~F

[0073] Next, as the third step, all the phase distributions θ1,1~θm,n of the third function F 1,1 e iθ1,1 ~F m,n e iθm,n are made to align with the phase distribution θ1,1 of the third function F 1,1 e iθ1,1 ~F 1,1 e iθ1,1 ~F m,n e iθm,n 's amplitude distribution F 1,1 ~F m,n is replaced with the target amplitude distribution F ’ 1,1 ~F ’ m,n ~F ’ 1,1 e iθ1,1 ~F ’ m,n eiθ1,1 The amplitude distribution A in real space can be obtained by an inverse Fourier transform such as IFFT. 1,1 ~A m,n And the fourth function A is a complex amplitude distribution function that includes the real-space phase distributions φ1, 1~φm, and n, respectively. 1,1 e iφ1,1 ~A m,n e iφm,n Convert to (arrow group B46 in the diagram).

[0074] From here on, the second function A of the second step 1,1 e iφ1,1 ~A m,n e iφm,n The fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n Repeat steps 2 and 3, substituting each of the following (arrow B47 in the diagram). Then, the fourth function A transformed by the final step 3 is obtained. 1,1 e iφ1,1 ~A m,n e iφm,n Let the phase distributions φ1,1 to φm, and n be the phase distributions φ(x,y) of each phase modulation region 151. [Second design method]

[0075] Figure 19 is a conceptual diagram illustrating the second design method. Note that the first and second steps are the same as those described in the first design method, so their explanation is omitted.

[0076] In the first third step, the phase distribution 222 of the third function 223 in each phase modulation region 151 is replaced with a predetermined phase distribution that is the same in multiple phase modulation regions 151 (arrow B21 in the figure). The phase values ​​of multiple points (kx, ky) in the predetermined phase distribution may be equal to each other. In this case, the phase values ​​of multiple points (kx, ky) in the predetermined phase distribution may be zero (0 rad). At this time, the amplitude distribution 221 is maintained as is (arrow B22 in the figure). Then, the third function 223 is transformed into the fourth function 233 by an inverse Fourier transform such as IFFT (arrow B2 in the figure).

[0077] The second step is repeated by replacing the second function 213 with the fourth function 233. In the subsequent (second) third step, the amplitude distribution 221 of the third function 223 is replaced with the target amplitude distribution 204 (arrows B23 and B24 in the figure). At this time, the phase distribution 222 remains unchanged (arrow B25 in the figure). Then, the replaced third function 223 is transformed into the fourth function 233 by an inverse Fourier transform such as IFFT (arrow B2 in the figure).

[0078] Subsequently, the second and third steps are repeated, with the second function 213 in the second step being replaced by the fourth function 233. In the third step, the phase distribution 222 is replaced with a predetermined phase distribution, and the amplitude distribution 221 is replaced with the target amplitude distribution 204, alternately. The predetermined phase distribution may be fixed without changing it after each repetition of the third step. The phase distribution 232 of the fourth function 233 transformed in the final third step is taken as the phase distribution φ(x,y) of each phase modulation region 151 (arrow B10 in the figure).

[0079] As an example, consider a phase modulation layer 15 having a total of four phase modulation regions 151, arranged in two columns in the X direction and two rows in the Y direction, as shown in Figure 14 or Figure 15. Two of these phase modulation regions 151 have phase distribution pattern A, and the other two phase modulation regions 151 have phase distribution pattern B. Figure 20 is a conceptual diagram showing the design method for phase distribution patterns A and B. Note that the first and second steps are the same as the first design method described above, so their explanation is omitted.

[0080] In the first step 3, the third function F1·e iθ1 The phase distribution θ1 and the third function F2·e iθ2 The phase distribution θ2 is replaced with a predetermined phase distribution θ' common to both phase distribution pattern A and phase distribution pattern B (arrow B31 in the figure). At this time, the amplitude distributions F1 and F2 are maintained as they are. Then, the third function F1·e iθ’ and the third function F2·e iθ’ The fourth function A1·e is obtained by inverse Fourier transform such as IFFT. iφ1 And the fourth function A2·e iφ2Convert them to the following (arrows B32 and B33 in the diagram).

[0081] Second function A1·e iφ1 And the second function A2·e iφ2 The fourth function A1·e iφ1 And the fourth function A2·e iφ2 Replace each of these and repeat the second step (arrows B34~B36 in the diagram), and in the subsequent (second) third step, the third function F1·e iθ1 The amplitude distribution F1, and the third function F2·e iθ2 The amplitude distribution F2 is the target amplitude distribution F1 ’ and F2 ’ Replace them with the following (arrow B37 in the diagram). Then, the third function F1 ’ ·e iθ1 and the third function F2 ’ ·e iθ2 The fourth function A1·e is obtained by inverse Fourier transform such as IFFT. iφ1 And the fourth function A2·e iφ2 Convert them to the respective values ​​(arrows B38 and B39 in the diagram).

[0082] From here on, the second function A1·e in the second step iφ1 And the second function A2·e iφ2 The fourth function A1·e iφ1 And the fourth function A2·e iφ2 The second and third steps are repeated, replacing each of the following (arrow B20 in the figure). In the third step, the phase distributions θ1 and θ2 are replaced alternately (arrow B31 in the figure), and the amplitude distributions F1 and F2 are replaced (arrow B37 in the figure). Finally, the fourth function A1·e is transformed by the third step. iφ1 Let the phase distribution φ1 be the phase distribution φ(x,y) of phase distribution pattern A. Also, the fourth function A2·e transformed by the final third step. iφ2 Let the phase distribution φ2 be the phase distribution φ(x,y) of phase distribution pattern B.

[0083] As another example, consider the phase modulation layer 15 shown in Figure 17, which has a total of m × n phase modulation regions 151, with m columns in the X direction and n rows in the Y direction. The m × n phase modulation regions 151 have different phase distribution patterns. Figure 21 is a diagram that conceptually shows a method for designing the m × n phase distribution patterns. Note that the first and second steps are the same as the first design method described above, so their explanation will be omitted.

[0084] In the first step 3, the third function F 1,1 e iθ1,1 ~F m,n e iθm,n All phase distributions θ1,1 to θm,n are replaced with a common and predetermined phase distribution θ' (arrow B51 in the figure). At this time, the amplitude distribution F 1,1 ~F m,n This remains unchanged. And the third function F 1,1 e iθ’ ~F m,n e iθ’ Then, by inverse Fourier transform such as IFFT, the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n Convert each to the respective (arrow group B52 in the diagram).

[0085] Second function A 1,1 e iφ1,1 ~A m,n e iφm,n The fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n Replace them respectively and repeat the second step (arrows B53 and group of arrows B54 in the figure), and in the subsequent (second) third step, the third function F 1,1 e iθ1,1 ~F m,n e iθm,n Amplitude distribution F 1,1 ~F m,n The target amplitude distribution F ’ 1,1 ~F ’ m,n Replace them with the following (arrow B55 in the diagram). Then, the third function F ’ 1,1 e iθ1,1~F ’ m,n e iθm,n Then, by inverse Fourier transform such as IFFT, the fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n Convert each to the respective (arrow group B56 in the diagram).

[0086] From here on, the second function A of the second step 1,1 e iφ1,1 ~A m,n e iφm,n The fourth function A 1,1 e iφ1,1 ~A m,n e iφm,n The second and third steps are repeated, replacing each of them (arrow B47 in the figure). In the third step, the phase distribution θ1,1 to θm,n is replaced (arrow B51 in the figure), and the amplitude distribution F 1,1 ~F m,n The substitution (arrow B55 in the diagram) is performed alternately. Then, the fourth function A is transformed by the final third step. 1,1 e iφ1,1 ~A m,n e iφm,n Let the phase distributions θ1,1 to θm,n be the phase distributions φ(x,y) of each phase modulation region 151.

[0087] The effects obtained by the semiconductor light-emitting element 1 of this embodiment, as described above, will now be explained. In the semiconductor light-emitting element 1, one or both of the electrodes 16 and 17 include multiple electrode portions (for example, multiple electrode portions 161) that overlap with multiple phase modulation regions 151, respectively. The multiple electrode portions are electrically isolated from each other. Therefore, an independent current can be supplied to each of the multiple electrode portions. As a result, the light emission intensity of each of the multiple regions of the active layer 12 that supplies light to each of the multiple phase modulation regions 151 is controlled independently, and the light intensity of the multiple optical images LA output from the multiple phase modulation regions 151 is also controlled independently from each other. The multiple optical images LA are irradiated into a common irradiation area. At this time, since the optical images LA output from each of the multiple phase modulation regions 151 are phase-synchronized with each other, the multiple optical images LA can interfere with each other in the common irradiation area. Thus, according to the semiconductor light-emitting element 1 of this embodiment, the light intensity of the multiple optical images LA output from the multiple phase modulation regions 151 can be individually adjusted, and the multiple optical images LA can be made to interfere with each other to form a single final optical image, so that the final optical image can be dynamically changed.

[0088] As described above, the light intensity distribution of the optical image LA output from each of the multiple phase modulation regions 151 may include a sinusoidal distribution in which the period or phase in at least one direction is different from that of at least two phase modulation regions 151. Alternatively, the light intensity distribution of the optical image LA output from each of the multiple phase modulation regions 151 may include a sinusoidal distribution in which the period or phase in two mutually orthogonal directions is different from that of at least two phase modulation regions 151. In these cases, an arbitrary final optical image can be obtained by superimposing the multiple optical images LA output from the multiple phase modulation regions 151 while individually adjusting the light intensity of the multiple optical images LA. In particular, when the periods are different, the multiple optical images LA output from the multiple phase modulation regions 151 can become multiple basis images in the discrete cosine transform.

[0089] As in this embodiment, a virtual square lattice is set along a virtual plane P, and for each of the multiple lattice points O constituting the square lattice, a straight line D is set that passes through the corresponding lattice point O and is inclined with respect to the square lattice at the same angle β. In this case, in each of the multiple phase modulation regions 151, the centroid G of each of the multiple different refractive index regions 15b is placed on the corresponding straight line D, and the distance r(x,y) between the centroid G of each different refractive index region 15b and the lattice point O corresponding to each different refractive index region 15b may be set individually according to a predetermined optical image LA. For example, with such a configuration, each of the multiple parts of the semiconductor light-emitting element 1 containing each phase modulation region 151 constitutes an S-iPM laser and can output different predetermined optical images LA from each other. In addition, the polarization direction can be aligned among the multiple phase modulation regions 151.

[0090] As in this embodiment, the phase modulation layer 15 may have a connection region 152 located between adjacent phase modulation regions 151. The connection region 152 includes a basic region 15a having a first refractive index and a plurality of regions with different refractive indices 15b having a second refractive index, and the centroid of the plurality of regions with different refractive indices 15b of the connection region 152 may be located at a grid point O of a square lattice. In this case, since a gap is provided between adjacent phase modulation regions 151, it becomes possible to widen the gap between the plurality of electrode portions 161, and so-called inter-region crosstalk, in which a portion of the current that should be supplied to each region of the active layer 12 that supplies light to these phase modulation regions 151 leaks to adjacent regions, can be reduced. Furthermore, by having the centroid G of the plurality of regions with different refractive indices 15b of the connection region 152 located at a grid point O of a square lattice, the phases of the optical images LA output from each of the plurality of phase modulation regions 151 can be synchronized with each other.

[0091] As in this embodiment, the planar shape of the connection region 152 as viewed from the stacking direction of the semiconductor stack 20 may be grid-like. In this case, since a gap can be provided between all the phase modulation regions 151, inter-region crosstalk can be reduced more effectively.

[0092] As in this embodiment, the semiconductor stack 20 is provided on the main surface 10a of the semiconductor substrate 10, the second surface 20b of the semiconductor stack 20 faces the main surface 10a of the semiconductor substrate 10, the electrode 16 is provided on the first surface 20a and includes a plurality of electrode portions 161, and the electrode 17 may be provided on the back surface 10b of the semiconductor substrate 10. In this way, by providing a plurality of electrode portions 161 on the surface of the semiconductor stack 20 opposite to the semiconductor substrate 10, the distance between the plurality of electrode portions 161 and the active layer 12 can be shortened. Therefore, inter-region crosstalk can be reduced. [First variation]

[0093] Figure 22 is a cross-sectional view showing the stacked structure of the semiconductor light-emitting element 1A as a first modified example of the above embodiment. The difference between the semiconductor light-emitting element 1A and the above embodiment is that the semiconductor stack 20 has a cladding layer 13A instead of the cladding layer 13. The arrangement of the cladding layer 13A is the same as that of the cladding layer 13 in the above embodiment. The other configurations of the semiconductor light-emitting element 1A are the same as in the above embodiment, so a detailed explanation is omitted. In this modified example, the electrode 16 always includes a plurality of electrode portions 161.

[0094] The cladding layer 13A includes a high-resistance region 21 and a basic region 22. The configuration of the basic region 22 is the same as that of the cladding layer 13 in the above embodiment. The high-resistance region 21 has a higher resistivity than the basic region 22. The high-resistance region 21 may be made of an insulator.

[0095] The high-resistance region 21 is located between adjacent phase-modulation regions 151 when viewed from the stacking direction of the semiconductor stack 20. Furthermore, the high-resistance region 21 is provided on the connection region 152 of the phase-modulation layer 15. The region formed by projecting the high-resistance region 21 onto a virtual plane P is included in the region formed by projecting the connection region 152 onto the virtual plane P. In the illustrated example, when the phase-modulation layer 15 is provided between the cladding layer 13A and the active layer 12, the high-resistance region 21 extends from the interface on the first surface 20a side of the cladding layer 13A to the cap region 15c of the phase-modulation layer 15. However, the high-resistance region 21 does not contact the basic region 15a or the different refractive index regions 15b. In other words, in the stacking direction (Z direction) of the semiconductor stack 20, a gap is provided between the high-resistance region 21 and the basic region 15a and the different refractive index regions 15b.

[0096] Figure 23 is a plan view (viewed from the thickness direction) of the cladding layer 13A. As described above, the cladding layer 13A includes a high-resistance region 21 and a basic region 22. The planar shape of the high-resistance region 21, as viewed from the stacking direction of the semiconductor stack 20, is, for example, a grid. The basic region 22 is provided in each of the multiple openings 21a of the grid-shaped high-resistance region 21.

[0097] The planar shape of each of the multiple openings 21a is, for example, a square or a rectangle. Viewed from the stacking direction of the semiconductor stack 20, each of the multiple openings 21a overlaps with the corresponding phase modulation region 151. The high-resistance region 21 includes a portion 21b provided between adjacent phase modulation regions 151 when viewed from the stacking direction of the semiconductor stack 20, and an outer frame-shaped portion 21c that encloses the multiple phase modulation regions 151 together.

[0098] In Figure 23, the high-resistance region 21 penetrates the basic region 22 and reaches the phase modulation layer 15, but the high-resistance region 21 does not necessarily have to reach the phase modulation layer 15. In that case, the lowest end of the high-resistance region 21 is located within the basic region 22.

[0099] As shown in this modified example, the cladding layer of the semiconductor stack may include high-resistance regions 21 located between adjacent phase-modulated regions 151 when viewed from the stacking direction of the semiconductor stack. In this case, the leakage of current flowing between each electrode portion 161 and the region of the active layer 12 located directly beneath each electrode portion 161 into the region of the active layer 12 located directly beneath the adjacent electrode portion 161 (i.e., inter-region crosstalk) can be reduced.

[0100] As shown in this modified example, the high-resistance region 21 may extend from the interface on the first surface 20a side of the cladding layer 13A to the phase modulation layer 15. In this case, current leakage can be prevented over the entire thickness of the cladding layer 13A, thus more effectively reducing inter-region crosstalk.

[0101] As shown in this modified example, the planar shape of the high-resistance region 21 as viewed from the stacking direction of the semiconductor stack 20 may be grid-like. In this case, since the high-resistance region 21 can be provided between all the phase modulation regions 151 as viewed from the stacking direction, inter-region crosstalk can be reduced more effectively. [Second variation]

[0102] Figure 24 is a cross-sectional view showing the configuration of a semiconductor light-emitting element 1B as a second modified example of the above embodiment. The semiconductor light-emitting element 1B differs from the above embodiment in that it includes a phase modulation layer 15A instead of the phase modulation layer 15, and includes a λ / 4 plate 24. The λ / 4 plate 24 extends along a virtual plane P and is positioned opposite the back surface 10b of the semiconductor substrate 10 (i.e., the light-emitting surface of the semiconductor light-emitting element 1B). The axis of the λ / 4 plate 24 is perpendicular to the straight line D shown in Figures 3 and 4.

[0103] Figure 25 is a plan view showing the phase modulation layer 15A. In addition to the configuration of the phase modulation layer 15 of the above embodiment, the phase modulation layer 15A further has a phase shift region 153. The phase shift region 153 is provided between adjacent phase modulation regions 151. In the illustrated example, the phase shift region 153 is provided inside a portion 152b of the connection region 152, and consists of a plurality of portions extending along the X direction and a plurality of portions extending along the Y direction that intersect each other. The planar shape of the phase shift region 153 as viewed from the stacking direction of the semiconductor stack 20 is, for example, a grid.

[0104] Figure 26 is a plan view showing a partially enlarged view of the phase shift region 153 and the surrounding connection region 152. As shown in Figure 26, the phase shift region 153 is provided between a square grid set in the connection region 152 located on one side of the phase shift region 153 and a square grid set in the connection region 152 located on the other side. The phase shift region 153 has an arbitrary width. Depending on the width of the phase shift region 153, the square grids of the connection region 152 located on one side of the phase shift region 153 and the square grids of the connection region 152 located on the other side are shifted relative to each other. These square grids are common to the square grids set in the phase modulation region 151 adjacent to the connection region 152. Therefore, the square grids of adjacent phase modulation regions 151 are shifted relative to each other.

[0105] In one example, when the lattice constant of a square lattice is a, the phase-shift region 153 has a width of n·a+a / 2 (where n is a non-negative integer). As a result, the square lattice of the connection region 152 located on one side of the phase-shift region 153 and the square lattice of the connection region 152 located on the other side are shifted by n·a+a / 2. Consequently, the square lattices of adjacent phase-modulation regions 151 are also shifted by n·a+a / 2. In this case, the phases of the optical images LA output from each of the adjacent phase-modulation regions 151 are shifted by π (rad). Therefore, by these optical images LA passing through the λ / 4 plate 24, it is possible to output circularly polarized light with opposite rotations from each of the adjacent phase-modulation regions 151. This makes it possible to electrically change the intensity ratio of left-handed and right-handed circularly polarized light. Such a semiconductor light-emitting device can be used, for example, as a light source for optical quantum communication or a quantum computer. [Third variation]

[0106] The areas of multiple different refractive index regions 15b in a cross-section perpendicular to the thickness direction of the phase modulation layer 15 may be set individually according to a predetermined optical image LA. In this case, not only the phase but also the light intensity can be adjusted for each different refractive index region 15b, thereby increasing the design flexibility of the optical image LA. Figure 27 is a magnified view of one unit constituent region R. In the example shown in this figure, the area of ​​the different refractive index region 15b is largest when the centroid G of the different refractive index region 15b coincides with the grid point O, and the area of ​​the different refractive index region 15b decreases as the centroid G of the different refractive index region 15b moves away from the grid point O (i.e., as the distance r(x,y) increases). In this way, the area of ​​the different refractive index region 15b may be changed according to the relative position of the centroid G of the different refractive index region 15b with respect to the grid point O. This makes it possible to keep the light intensity constant regardless of the phase distribution φ(x,y). [First Embodiment]

[0107] The inventors applied the phase distribution design method of the above embodiment to a phase modulation layer 15 having four phase modulation regions 151 shown in Figure 14 and performed a phase distribution design simulation. Part (a) of Figure 28 shows the desired optical image in the irradiation region (far field) set when designing the phase distribution pattern A. In Part (a) of Figure 28, the lighter the color, the greater the optical intensity, and the darker the color, the smaller the optical intensity. As shown in Part (a) of Figure 28, the target optical image for the phase distribution pattern A was an optical image having a sinusoidal optical intensity distribution in which the optical intensity changes periodically along one direction. Part (b) of Figure 28 shows the optical image shown in Part (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 28 is a figure showing the phase distribution pattern A calculated based on the target amplitude distribution shown in Part (b). In Part (c) of Figure 28, the lighter the color, the closer to 2π (rad), and the darker the color, the closer to 0 (rad).

[0108] Part (a) of Figure 29 shows the desired optical image in the irradiation region (far field) set when designing phase distribution pattern B. In part (a) of Figure 29, the lighter the color, the greater the light intensity, and the darker the color, the smaller the light intensity. As shown in part (a) of Figure 29, the target optical image for phase distribution pattern B was an optical image having a sinusoidal optical intensity distribution in which the optical intensity changes periodically along a direction perpendicular to the direction of change of optical intensity in part (a) of Figure 28. However, the period of the sine wave was the same as in part (a) of Figure 28. Part (b) of Figure 29 shows the optical image shown in part (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 29 shows the phase distribution pattern B calculated based on the target amplitude distribution shown in part (b). In part (c) of Figure 29, the lighter the color, the closer to 2π (rad), and the darker the color, the closer to 0 (rad).

[0109] Part (a) of Figure 30 shows the result of applying a phase distribution pattern A to each of the two phase modulation regions 151 located on one diagonal and a phase distribution pattern B to each of the two phase modulation regions 151 located on the other diagonal. Part (b) of Figure 30 conceptually shows the difference in light intensity between the two phase modulation regions 151 located on one diagonal and the two phase modulation regions 151 located on the other diagonal, which is achieved by individually controlling the current of each electrode portion 161. In Part (b) of Figure 30, the lighter the color, the greater the light intensity, and the darker the color, the smaller the light intensity.

[0110] Figure 31 shows the final optical image expected when optical images emitted from two phase modulation regions 151 having phase distribution pattern A (see part (a) in Figure 28) and optical images emitted from two phase modulation regions 151 having phase distribution pattern B (see part (a) in Figure 29) are interfered with each other. When these optical images are interfered with, it is expected that the peaks of the optical intensity will reinforce each other and the bottoms of the optical intensity will weaken each other, resulting in an optical intensity distribution resembling a checkerboard pattern.

[0111] Figure 32 shows the final optical image obtained by this simulation. Part (a) of Figure 32 shows the optical image obtained by the first design method of the above embodiment. Part (b) of Figure 32 shows the optical image obtained by the second design method of the above embodiment. Comparing these figures, it can be seen that the checkerboard pattern is clearer with the second design method. Furthermore, it can be seen that the checkerboard pattern is even clearer with the first design method compared to the second design method. In this simulation, the clearer the checkerboard pattern, the better the phase synchronization is performed and the more accurately the optical images interfere with each other. Therefore, it has become clear that the phases of multiple optical images output from multiple phase modulation regions 151 can be synchronized with each other by either the first or second design method, and a predetermined interference effect can be produced in a hologram formed by superimposing multiple optical images in one region. Furthermore, it has become clear that this effect is more pronounced with the first design method than with the second design method. [Second Example]

[0112] Next, the inventors applied the first design method of the above embodiment to a phase modulation layer 15 having four phase modulation regions 151 shown in Figure 14 and performed another phase distribution design simulation. Part (a) of Figure 33 shows the desired optical image in the irradiation region (far field) set when designing the phase distribution pattern A. In Part (a) of Figure 33, the lighter the color, the greater the optical intensity, and the darker the color, the smaller the optical intensity. As shown in Part (a) of Figure 33, the target optical image for the phase distribution pattern A was an optical image having a sinusoidal optical intensity distribution in which the optical intensity changes periodically along one direction. Part (b) of Figure 33 shows the optical image shown in Part (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Part (c) of Figure 33 is a figure showing the phase distribution pattern A calculated based on the target amplitude distribution shown in Part (b). In Part (c) of Figure 33, the lighter the color, the closer to 2π (rad), and the darker the color, the closer to 0 (rad).

[0113] Section (a) of Figure 34 shows the desired optical image in the irradiation region (far field) set when designing phase distribution pattern B. In section (a) of Figure 34, lighter colors indicate higher light intensity, and darker colors indicate lower light intensity. As shown in section (a) of Figure 34, the target optical image for phase distribution pattern B, similar to phase distribution pattern A, was an optical image having a sinusoidal optical intensity distribution in which the optical intensity changes periodically along one direction. However, the period of the sine wave was set to be the same as the desired optical image when designing phase distribution pattern A, and the phase of the sine wave was shifted relative to the desired optical image when designing phase distribution pattern A. Section (b) of Figure 34 shows the optical image shown in section (a) converted to wavenumber space, i.e., the target amplitude distribution in wavenumber space. Section (c) of Figure 34 shows phase distribution pattern B calculated based on the target amplitude distribution shown in section (b). In section (c) of Figure 34, lighter colors are closer to 2π (rad), and darker colors are closer to 0 (rad).

[0114] Part (a) of Figure 35 shows the result of applying phase distribution pattern A to each of the two phase modulation regions 151 located on one diagonal and phase distribution pattern B to each of the two phase modulation regions 151 located on the other diagonal. Part (b) of Figure 35 conceptually shows the difference in light intensity between the two phase modulation regions 151 located on one diagonal and the two phase modulation regions 151 located on the other diagonal, which is achieved by individually controlling the current of each electrode portion 161. In Part (b) of Figure 35, the lighter the color, the greater the light intensity, and the darker the color, the smaller the light intensity.

[0115] Figure 36 shows the final optical image expected when optical images emitted from two phase modulation regions 151 having phase distribution pattern A (see part (a) in Figure 27) and optical images emitted from two phase modulation regions 151 having phase distribution pattern B (see part (a) in Figure 34) are interfered with each other. When these optical images are interfered, it is expected that a sinusoidal optical intensity distribution with a phase corresponding to the ratio of the optical intensity of the optical images emitted from the two phase modulation regions 151 having phase distribution pattern A to the optical intensity of the optical images emitted from the two phase modulation regions 151 having phase distribution pattern B will be obtained.

[0116] Figures 37 and 38 show the final optical images obtained by this simulation. Figure 37 shows the case where the phase difference between the optical image emitted from the phase modulation region 151 having phase distribution pattern A (see part (a) in Figure 27) and the optical image emitted from the phase modulation region 151 having phase distribution pattern B (see part (a) in Figure 34) is 45°. Figure 38 shows the case where the phase difference between these optical images is 135°. When the optical intensity of the optical image emitted from the phase modulation region 151 having phase distribution pattern A is PA, and the optical intensity of the optical image emitted from the phase modulation region 151 having phase distribution pattern B is PB, the optical intensity ratio is expressed as (PA / PB). To facilitate understanding the phase change in response to the change in light intensity ratio, Figures 37 and 38 show the final optical images for light intensity ratios (PA / PB) of 0 / 1.00, 0.25 / 0.75, 0.50 / 0.50, 0.75 / 0.25, and 1.00 / 0, arranged in a direction intersecting the direction of change in light intensity.

[0117] As shown in these figures, the semiconductor light-emitting element of the above embodiment makes it possible to realize a sinusoidal light intensity distribution in which the phase can be dynamically changed by dynamically changing the ratio of the light intensity of the light image emitted from a plurality of phase modulation regions 151 having different phase distribution patterns.

[0118] The semiconductor light-emitting element according to this disclosure is not limited to the embodiments described above, and various other modifications are possible. For example, in the above embodiments, as an example of optical image LA, a sinusoidal optical image with different periods or phases in at least two optical image LAs was shown, but the optical image LAs are not limited to this. According to the semiconductor light-emitting element according to this disclosure, a final optical image can be obtained by interfering any optical image LAs. [Explanation of Symbols]

[0119] 1,1A,1B...Semiconductor light-emitting element, 10...Semiconductor substrate, 10a...Main surface, 10b...Back surface, 11...Cladding layer, 12...Active layer, 13...Cladding layer, 14...Contact layer, 15,15A...Phase modulation layer, 15a...Basic region, 15b...Different refractive index region, 15c...Cap region, 16...Electrode (first electrode), 17...Electrode (second electrode), 17a...Aperture, 18...Protective film, 19...Anti-reflective film, 20...Semiconductor stacking, 20a...First surface, 20b...Second surface, 21...High resistance region, 22...Basic region, 24...λ / 4 plate, 31...Drive circuit, 32...Power supply circuit, 33~35...Wiring, 151...Phase modulation region, 152...Connection region, 152a...Aperture Part, 152b, 152c...part, 153...phase shift region, 161...electrode part, 201...initial value of amplitude distribution in wavenumber space, 202...initial value of phase distribution in wavenumber space, 203...first function, 204...target amplitude distribution, 205...random phase distribution, 211...amplitude distribution in real space, 212...phase distribution in real space, 213...second function, 214...target amplitude distribution, 221...amplitude distribution in wavenumber space, 222...phase distribution in wavenumber space, 223...third function, 231...amplitude distribution in real space, 232...phase distribution in real space, 233...fourth function, D...straight line, G...centroid, L...laser light, LA...optical image, O...lattice point, P...virtual plane, R...unit constituent region.

Claims

1. A semiconductor laminate having a laminated structure including an active layer and a phase modulation layer between a first surface and a second surface, wherein the phase modulation layer has a plurality of phase modulation regions, and the plurality of phase modulation regions are arranged along a virtual plane perpendicular to the thickness direction of the phase modulation layer and optically coupled to one another in such a manner that the resonance modes of adjacent phase modulation regions are shared, and each of the plurality of phase modulation regions includes a basic region having a first refractive index and a plurality of different refractive index regions provided within the basic region and having a second refractive index different from the first refractive index, and distributed two-dimensionally along the virtual plane, A first electrode facing the first surface of the semiconductor stack, A second electrode facing the second surface of the semiconductor stack, Equipped with, One or both of the first electrode and the second electrode include a plurality of electrode portions that overlap with the plurality of phase modulation regions when viewed from the stacking direction of the semiconductor stack, and the plurality of electrode portions are electrically isolated from each other. When a virtual square grid is set along the virtual plane for each phase modulation region, the relative positions of the centroids of each of the multiple different refractive index regions with respect to each of the multiple grid points constituting the square grid are individually set according to a predetermined optical image. The phase modulation layer further has connection regions located between adjacent phase modulation regions, The connection region includes a basic region having the first refractive index and a plurality of regions with different refractive indices having the second refractive index. The centroid of the plurality of different refractive index regions in the connection region is located at a lattice point of a square lattice, the lattice constant of the square lattice in the connection region is equal to the lattice constant of the square lattice in each of the plurality of phase modulation regions, and each side of the square lattice in the connection region is aligned in the same direction as each side of the square lattice in each of the plurality of phase modulation regions. Light emitted from the active layer resonates along the virtual plane in each of the multiple phase modulation regions of the phase modulation layer, and is irradiated from each of the multiple phase modulation regions into a common irradiation region located in a direction intersecting both the first and second surfaces of the semiconductor stack, forming a predetermined light image corresponding to the arrangement of the multiple different refractive index regions. A semiconductor light-emitting element wherein the light intensity distribution of the light image output from each of the plurality of phase modulation regions includes a sinusoidal distribution in which the period or phase in at least one direction is different from that of the other in at least two of the phase modulation regions.

2. A semiconductor laminate having a laminated structure including an active layer and a phase modulation layer between a first surface and a second surface, wherein the phase modulation layer has a plurality of phase modulation regions, and the plurality of phase modulation regions are arranged along a virtual plane perpendicular to the thickness direction of the phase modulation layer and optically coupled to one another in such a manner that the resonance modes of adjacent phase modulation regions are shared, and each of the plurality of phase modulation regions includes a basic region having a first refractive index and a plurality of different refractive index regions provided within the basic region and having a second refractive index different from the first refractive index, and distributed two-dimensionally along the virtual plane, A first electrode facing the first surface of the semiconductor stack, A second electrode facing the second surface of the semiconductor stack, Equipped with, One or both of the first electrode and the second electrode include a plurality of electrode portions that overlap with the plurality of phase modulation regions when viewed from the stacking direction of the semiconductor stack, and the plurality of electrode portions are electrically isolated from each other. When a virtual square grid is set along the virtual plane for each phase modulation region, the relative positions of the centroids of each of the multiple different refractive index regions with respect to each of the multiple grid points constituting the square grid are individually set according to a predetermined optical image. The phase modulation layer further has connection regions located between adjacent phase modulation regions, The connection region includes a basic region having the first refractive index and a plurality of regions with different refractive indices having the second refractive index. The centroid of the plurality of different refractive index regions in the connection region is located at a lattice point of a square lattice, the lattice constant of the square lattice in the connection region is equal to the lattice constant of the square lattice in each of the plurality of phase modulation regions, and each side of the square lattice in the connection region is aligned in the same direction as each side of the square lattice in each of the plurality of phase modulation regions. Light emitted from the active layer resonates along the virtual plane in each of the multiple phase modulation regions of the phase modulation layer, and is irradiated from each of the multiple phase modulation regions into a common irradiation region located in a direction intersecting both the first and second surfaces of the semiconductor stack, forming a predetermined light image corresponding to the arrangement of the multiple different refractive index regions. A semiconductor light-emitting element, wherein the light intensity distribution of the light image output from each of the plurality of phase modulation regions includes a sinusoidal distribution in which the period or phase in two mutually orthogonal directions is different from that of the two phase modulation regions.

3. The semiconductor light-emitting element according to claim 1 or 2, wherein, for each of the plurality of grid points constituting the square grid, a straight line passing through the corresponding grid point and inclined at the same angle with respect to the square grid is set for each grid point, and in each of the plurality of phase modulation regions, the centroids of each of the plurality of different refractive index regions are arranged on the corresponding straight line, and the distance between the centroid of each different refractive index region and the grid point corresponding to each different refractive index region is individually set according to a predetermined optical image.

4. The semiconductor light-emitting element according to claim 3, wherein the planar shape of the connection region as viewed from the stacking direction of the semiconductor stack is grid-like.

5. The semiconductor light-emitting element according to claim 3 or 4, wherein the areas of the plurality of different refractive index regions in a cross section perpendicular to the thickness direction of the phase modulation layer are individually set according to a predetermined optical image.

6. The semiconductor light-emitting element according to any one of claims 3 to 5, wherein the square grids of adjacent phase modulation regions are offset from each other.

7. The semiconductor light-emitting element further comprises a λ / 4 plate provided opposite to the light-emitting surface, The square grids of the phase modulation regions adjacent to each other are, n・a + a / 2 (where a is the grid spacing and n is a non-negative integer) A semiconductor light-emitting element according to any one of claims 3 to 5, wherein they are offset from each other by only a small amount.

8. The first electrode includes the plurality of electrode portions, The laminated structure further includes a cladding layer provided between the phase modulation layer and the active layer and the first surface, The semiconductor light-emitting element according to any one of claims 1 to 7, wherein the cladding layer includes a high-resistance region located between adjacent phase-modulation regions when viewed from the stacking direction of the semiconductor stack.

9. The phase modulation layer is provided between the cladding layer and the active layer. The semiconductor light-emitting element according to claim 8, wherein the high-resistance region extends from the interface on the first surface side of the cladding layer to the phase modulation layer.

10. The semiconductor light-emitting element according to claim 8 or 9, wherein the planar shape of the high-resistance region as viewed from the stacking direction of the semiconductor stack is lattice-shaped.

11. The semiconductor substrate further comprises a main surface and a back surface, The semiconductor stack is provided on the main surface of the semiconductor substrate, and the second surface of the semiconductor stack faces the main surface of the semiconductor substrate. The first electrode is provided on the first surface and includes the plurality of electrode portions, The semiconductor light-emitting element according to any one of claims 1 to 10, wherein the second electrode is provided on the back surface of the semiconductor substrate.

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