JP2019106396A - Phase modulation layer layout method - Google Patents

Abstract

To reduce one light of primary light and minus primary light in response to the other light.SOLUTION: A method includes: a first step S1 of preparing a plurality of complex amplitude distributions in regard to each of progressive waves AR, AL, AU, and AD; a second step S2 of modifying each complex amplitude distribution in regard to each progressive wave; a third step S3 of obtaining a comprehensive complex amplitude distribution by overlapping each complex amplitude distribution modulated in regard to each progressive wave; and a fourth step S4 of extracting a phase distribution from the comprehensive complex amplitude distribution, and determining a center of gravity of each modified refractive index area. In the second step S2, a positive and a negative between one of the progressive waves AR and AL and a phase item of each complex amplitude distribution of one of the progressive waves AU and AD is inverted. In the fourth step S4, the center of gravity of each modified refractive index area is arranged onto a straight line inclined to a square lattice by passing through a lattice point of a virtual square lattice, and the center of gravity of each modified refractive index area and a distance from the corresponded lattice point are determined on the basis of a phase distribution.SELECTED DRAWING: Figure 18

Description

  The present invention relates to a phase modulation layer design method.

  Patent Document 1 describes a technique related to a semiconductor light emitting device. The semiconductor light emitting device includes an active layer, a pair of cladding layers sandwiching the active layer, and a phase modulation layer optically coupled to the active layer. The phase modulation layer includes a base layer and a plurality of different refractive index regions different in refractive index from the base layer. If an XYZ orthogonal coordinate system is set with the thickness direction of the phase modulation layer as the Z-axis direction, and a virtual square lattice with a lattice spacing a is set in the XY plane, each different refractive index area is its barycentric position Are arranged so as to be deviated by a distance r from the grid point position in the virtual square lattice. The distance r satisfies 0 <r ≦ 0.3a.

International Publication No. 2016/148075

  A light emitting device has been studied which outputs an arbitrary light image by controlling the phase spectrum and intensity spectrum of light emitted from a plurality of light emitting points arranged in a two-dimensional manner. One of the structures of such a light emitting device is a structure provided with a phase modulation layer provided on a substrate. The phase modulation layer has a base layer and a plurality of different refractive index regions different in refractive index from the base layer, and a virtual square lattice is set in a plane perpendicular to the thickness direction of the phase modulation layer. In addition, the barycentric position of each modified refractive index area is shifted from the lattice point position of the virtual square lattice according to the light image. Such a light emitting device is called an S-iPM (Static-integrable Phase Modulating) laser and outputs an optical image of an arbitrary shape in a direction inclined with respect to the direction perpendicular to the main surface of the substrate.

  From such a light emitting device, primary light and -1 order light modulated in the opposite direction to the primary light are output. The primary light forms a desired output light image in a first direction inclined with respect to the direction perpendicular to the main surface of the substrate. The -1st-order light forms a light image that is rotationally symmetric to the output light image in a second direction that is symmetrical to the first direction with respect to an axis that intersects the main surface of the substrate and extends in a direction perpendicular to the main surface Do. However, depending on the application, either primary light or primary light may not be required. In such a case, it is desirable to reduce unnecessary light of the primary light and the -1 order light with respect to the necessary light.

  The present invention has been made in view of such problems, and a phase modulation layer designing method capable of reducing one of primary light and -1 order light with respect to the other light. Intended to provide.

  In order to solve the problems described above, a phase modulation layer design method according to the present invention includes a base layer and a plurality of different refractive index regions different in refractive index from the base layer, and provided on a substrate A method of designing a phase modulation layer of a light emitting device comprising an optically coupled phase modulation layer and outputting an optical image in a direction perpendicular to the main surface of the substrate and / or inclined with respect to the direction When a virtual square lattice is set in a plane perpendicular to the thickness direction of the phase modulation layer, a first region and a second region aligned in one lattice point arranging direction across the center point of the phase modulation layer. A first traveling wave traveling in the direction from the second region to the first region when defining a region and a third region and a fourth region arranged in the other lattice point arranging direction across the center point of the phase modulation layer; Second traveling wave traveling from the first area to the second area, from the fourth area First step of preparing a plurality of complex amplitude distributions corresponding to light images for the third traveling wave traveling in the direction to the three regions and the fourth traveling wave traveling in the direction from the third region to the fourth region A second step of correcting the complex amplitude distribution of each traveling wave, a third step of superposing the corrected complex amplitude distribution of each traveling wave to obtain an overall complex amplitude distribution, and an overall complex amplitude distribution And 4. a fourth step of extracting a phase distribution from and determining a barycentric position of each modified refractive index region based on the phase distribution. In the second step, the phase term of the complex amplitude distribution of one of the first traveling wave and the second traveling wave is reversed, and the phase term of the complex amplitude distribution of one of the third traveling wave and the fourth traveling wave is reversed. Invert. In the fourth step, the center of gravity of each modified refractive index area is disposed on a straight line that is inclined relative to the square lattice through the lattice points of the virtual square lattice, and the center of gravity of each modified refractive index area and the corresponding grid The distance to the point is determined based on the phase distribution.

  According to the findings of the present inventor, from the traveling waves traveling in opposite directions, beam patterns in the opposite direction can be obtained. For example, when a beam pattern of first-order light is mainly obtained from the first traveling wave, a beam pattern of -1st-order light is mainly obtained from the second traveling wave. Similarly, when the beam pattern of the first traveling light is mainly obtained from the third traveling wave, the beam pattern of the −1st order light is mainly acquired from the fourth traveling wave. In view of such facts, in the above-described design method, in the second step, the positive and negative of the phase term of the complex amplitude distribution relating to one of the first traveling wave and the second traveling wave are reversed, and the third traveling wave and the fourth traveling wave are Invert the positive and negative of the phase term of the complex amplitude distribution with respect to one of the traveling waves. If the beam pattern of -1st order light is mainly obtained before inverting the sign of the phase term, the beam pattern of 1st order light is mainly obtained after inverting the sign of the phase term. Conversely, when the beam pattern of primary light is mainly obtained before inverting the sign of the phase term, the beam pattern of −1st order light is mainly obtained after inverting the sign of the phase term. Therefore, according to the above-mentioned design method, it is possible to mainly obtain a beam pattern of primary light (or -1 order light) from all traveling waves, and one of primary light and -1 order light is used. The other light can be dimmed.

  In the above-described phase modulation layer designing method, weighting may be performed on the complex amplitude distribution of each traveling wave in the second step. Thereby, when superposing the complex amplitude distribution on each traveling wave to obtain a comprehensive complex amplitude distribution, the contribution ratio of the complex amplitude distribution of each traveling wave to the overall complex amplitude distribution is set to the intensity ratio of each traveling wave. Accordingly, the desired light image can be expressed more accurately by adjusting it arbitrarily. Also, when the intensities of the first and second traveling waves and the intensities of the third and fourth traveling waves are different from each other, they are added to the complex amplitude distributions of the first and second traveling waves. The weights to be added may be different from the weights to be added to the complex amplitude distributions of the third and fourth traveling waves. Further, the ratio of the intensity of the first traveling wave and the second traveling wave to the intensity of the third traveling wave and the intensity of the fourth traveling wave changes according to the inclination angle of the straight line with respect to the square lattice. Therefore, the ratio of the weight added to each complex amplitude distribution related to the first traveling wave and the second traveling wave and the weight added to each complex amplitude distribution related to the third traveling wave and the fourth traveling wave is a straight line and a square lattice. It may be determined based on the angle formed by

  In the above-described phase modulation layer design method, the inclination angle of the straight line with respect to the square grating may be constant. This makes it possible to easily design the center of gravity of the different refractive index area. Also, in this case, the inclination angles may be angles other than 0 °, 90 °, 180 ° and 270 °. Furthermore, the tilt angle may be 45 °, 135 °, 225 ° or 315 °. As a result, four fundamental waves traveling along a square lattice (when X axis and Y axis along a square lattice are set, light traveling in the X axis positive direction, light traveling in the X axis negative direction, Y axis positive direction The traveling light and the light traveling in the negative Y-axis direction can equally contribute to the light image. Note that when the inclination angle is 0 °, 90 °, 180 °, or 270 °, the straight line corresponds to the X axis or Y axis of the square lattice, but at this time, for example, the inclination angle is 0 ° or 180 °. When the straight line is along the X-axis, two traveling waves facing each other in the Y-axis direction among the four fundamental waves do not receive phase modulation, and thus do not contribute to the signal light. Further, when the inclination angle is 90 ° or 270 ° and the straight line is along the Y axis, two traveling waves opposed in the X axis direction do not contribute to the signal light. Therefore, when the tilt angle is 0 °, 90 °, 180 °, or 270 °, signal light can not be obtained with high efficiency.

  In the above phase modulation layer design method, the light emitting unit may be an active layer provided on a substrate. Thus, the light emitting portion and the phase modulation layer can be easily optically coupled.

  According to the phase modulation layer designing method of the present invention, it is possible to reduce one of the primary light and the −1st light with respect to the other light.

It is a perspective view which shows the structure of a semiconductor light-emitting device as a light-emitting device based on one Embodiment of this invention. It is sectional drawing which shows the laminated structure of a semiconductor light-emitting device. It is a figure which shows the laminated structure of a semiconductor light-emitting device in case a phase modulation layer is provided between a lower cladding layer and an active layer. It is a top view of a phase modulation layer. It is a figure which shows the positional relationship of the different refractive index area | region in a phase modulation layer. It is a top view which shows the example which applied the refractive index substantially periodic structure only in the specific area | region of a phase modulation layer. It is a figure for demonstrating the relationship between the optical image obtained by imaging the output beam pattern of a semiconductor light-emitting device, and distribution of the distance in a phase modulation layer. It is a figure for demonstrating the coordinate transformation from a spherical surface coordinate to the coordinate in a XYZ rectangular coordinate system. (A), (b) It is a figure explaining the point taken care of when phase angle distribution is calculated | required from the Fourier-transform result of a light image, and arrangement | positioning of a different refractive index area | region is determined. (A) The example of the beam pattern (optical image) output from a semiconductor light-emitting device is shown. (B) It is a graph which shows the light intensity distribution in the cross section containing the light emitting surface of a semiconductor light emitting element, and including the axis line perpendicular | vertical to a light emitting surface. (A) It is a figure which shows the phase distribution corresponding to the beam pattern shown by FIG. 10 (a). (B) It is the elements on larger scale of Fig.11 (a). It is a top view which shows notionally the phase modulation layer of square lattice type S-iPM laser. It is a figure which shows notionally the example of the beam pattern of the traveling wave of each direction. In this example, the inclination angle of the straight line D with respect to the X axis and the Y axis is 45 °. It is a graph which shows intensity distribution of a traveling wave in the field of a phase modulation layer. It is a graph which shows intensity distribution of a traveling wave in the field of a phase modulation layer. It is a graph which shows intensity distribution of a traveling wave in the field of a phase modulation layer. It is a graph which shows intensity distribution of a traveling wave in the field of a phase modulation layer. 5 is a flowchart illustrating a method of designing a phase modulation layer according to one embodiment. (A) It is a figure which shows the conventional system which rotates a different refractive index area | region around a lattice point. (B) It is a figure which shows a traveling wave. (A) It is a figure which shows the system which a different refractive index area | region moves on the axis line which inclined with respect to a square lattice through a lattice point. (B) It is a figure which shows a traveling wave. It is a top view which shows the example of the shape in XY plane of a different refractive index area | region. It is a top view which shows the example of the shape in XY plane of a different refractive index area | region. It is a top view of the phase modulation layer concerning the 2nd modification. It is a figure which shows the positional relationship of the different refractive index area | region in the phase modulation layer of a 2nd modification. It is a top view which shows another example of the shape of the modified refractive index area | region in XY plane. It is a top view which shows another example of the shape of the modified refractive index area | region in XY plane. It is a figure which shows the structure of the light-emitting device by a 3rd modification. It is a figure which shows the cross-section of the semiconductor light-emitting device concerning 2nd Embodiment. It is a figure which shows the laminated structure of a semiconductor light-emitting device in case a phase modulation layer is provided between a lower cladding layer and an active layer. It is the top view which looked at the semiconductor light emitting element from the surface side. It is a table | surface which shows the layer structure in case a laser element consists of a GaAs type compound semiconductor (emission wavelength 940 nm band). It is refractive index distribution and mode distribution of a laser element provided with the layer structure shown by FIG. It is a table | surface which shows the layer structure in case a laser element consists of an InP type compound semiconductor (emission wavelength 1300 nm band). It is a refractive index distribution and mode distribution of a laser element provided with the layer structure shown by FIG. It is a table | surface which shows the layer structure in case a laser element consists of a nitride type compound semiconductor (emission wavelength 405 nm band). It is a refractive index distribution and mode distribution of a laser element provided with the layer structure shown by FIG. It is sectional drawing and refractive index distribution for demonstrating the case where waveguide structure is approximated by six layers of slab type | mold waveguides. It is sectional drawing and refractive index distribution for demonstrating the case where a waveguide structure is approximated by five layers of slab type | mold waveguides. It is sectional drawing and refractive index distribution which show three-layer slab structure regarding an optical waveguide layer in six-layer slab type | mold waveguide. It is sectional drawing and refractive index distribution which show three-layer slab structure regarding a contact layer in six-layer slab type | mold waveguide. It is sectional drawing and refractive index distribution which show three-layer slab structure regarding an optical waveguide layer in five-layer slab type | mold waveguide. It is sectional drawing and refractive index distribution which show three-layer slab structure regarding a contact layer in five-layer slab type | mold waveguide. It is sectional drawing and its refractive index distribution which show the 3 layer slab structure which consists of a lower clad layer, an optical waveguide layer, and an upper clad layer. It is a table | surface which shows the example of 5 layer slab structure in case a laser element consists of a GaAs type compound semiconductor. It is a table showing the refractive index n ₁ , n ₂ and n ₃ used in the calculation, the asymmetry parameter a ′ and the refractive index n _clad of the lower cladding layer, and the calculation results of the lower limit value and the upper limit value. Equation (1) and standards influencing for good waveguide width V ₁ of the optical waveguide layer represented by formula (2) is a graph showing the relationship between the normalized propagation factor b. Calculating a refractive index n ₄ used in, n _5, and n _6, a table showing the refractive index n _clad of the asymmetry parameter a 'and the lower cladding layer is a table showing the calculation results of the upper limit. Equation (5) and standards influencing for good waveguide width V ₂ of the contact layer represented by the formula (6) is a graph showing the relationship between the normalized propagation factor b. It is a refractive index distribution and mode distribution of a laser element provided with the layer structure shown by FIG. It is a table | surface which shows the example of a 6 layer slab structure in case a laser element consists of an InP type compound semiconductor. It is a table showing the refractive index n ₁ , n ₂ and n ₃ used in the calculation, the asymmetry parameter a ′ and the refractive index n _clad of the lower cladding layer, and the calculation results of the lower limit value and the upper limit value. Equation (1) and standards influencing for good waveguide width V ₁ of the optical waveguide layer represented by formula (2) is a graph showing the relationship between the normalized propagation factor b. Calculating a refractive index n ₄ used in, n _5, and n _6, a table showing the refractive index n _clad of the asymmetry parameter a 'and the lower cladding layer is a table showing the calculation results of the upper limit. Equation (5) and standards influencing for good waveguide width V ₂ of the contact layer represented by the formula (6) is a graph showing the relationship between the normalized propagation factor b. It is a refractive index distribution and mode distribution of a laser element provided with the layer structure shown by FIG. It is a table | surface which shows the example of the 6 layer slab structure in case a laser element consists of a nitride type compound semiconductor. It is a table showing the refractive index n ₁ , n ₂ and n ₃ used in the calculation, the asymmetry parameter a ′ and the refractive index n _clad of the lower cladding layer, and the calculation results of the lower limit value and the upper limit value. Equation (1) and standards influencing for good waveguide width V ₁ of the optical waveguide layer represented by formula (2) is a graph showing the relationship between the normalized propagation factor b. Calculating a refractive index n ₄ used in, n _5, and n _6, a table showing the refractive index n _clad of the asymmetry parameter a 'and the lower cladding layer is a table showing the calculation results of the upper limit. Equation (5) and standards influencing for good waveguide width V ₂ of the contact layer represented by the formula (6) is a graph showing the relationship between the normalized propagation factor b. It is a refractive index distribution and mode distribution of a laser element provided with the layer structure shown by FIG.

  Hereinafter, an embodiment of a phase modulation layer designing method according to the present invention will be described in detail with reference to the attached drawings. In the description of the drawings, the same elements will be denoted by the same reference symbols, without redundant description.

  FIG. 1 is a perspective view showing a configuration of a semiconductor light emitting element 1A as a light emitting device according to an embodiment of the present invention. An XYZ orthogonal coordinate system is defined in which an axis extending through the center of the semiconductor light emitting element 1A and extending in the thickness direction of the semiconductor light emitting element 1A is the Z axis. The semiconductor light emitting element 1A is an S-iPM laser that forms a standing wave in the XY in-plane direction and outputs a phase controlled plane wave in the Z-axis direction, and as described later, the main surface 10a of the semiconductor substrate 10 Output a two-dimensional light image of an arbitrary shape including a direction perpendicular to (ie, the Z-axis direction) or a direction inclined with respect to this or both.

  FIG. 2 is a view schematically showing a laminated structure of the semiconductor light emitting element 1A. As shown in FIG. 1 and FIG. 2, the semiconductor light emitting element 1A is provided on the main surface 10a of the semiconductor substrate 10 as an active layer 12 as a light emitting portion and on the main surface 10a. A pair of sandwiching cladding layers 11 and 13 and a contact layer 14 provided on the cladding layer 13 are provided. The semiconductor substrate 10 and the layers 11 to 14 are made of, for example, a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor. The energy band gap of the cladding layer 11 and the energy band gap of the cladding layer 13 are larger than the energy band gap of the active layer 12. The thickness direction of the semiconductor substrate 10 and the layers 11 to 14 coincides with the Z-axis direction.

  The semiconductor light emitting device 1A further includes a phase modulation layer 15 optically coupled to the active layer 12. In the present embodiment, the phase modulation layer 15 is provided between the active layer 12 and the cladding layer 13. If necessary, a light guide layer may be provided between at least one of the active layer 12 and the cladding layer 13 and between the active layer 12 and the cladding layer 11. When the light guide layer is provided between the active layer 12 and the cladding layer 13, the phase modulation layer 15 is provided between the cladding layer 13 and the light guide layer. The thickness direction of the phase modulation layer 15 coincides with the Z-axis direction. The light guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

  As shown in FIG. 3, the phase modulation layer 15 may be provided between the cladding layer 11 and the active layer 12. When the light guide layer is provided between the active layer 12 and the cladding layer 11, the phase modulation layer 15 is provided between the cladding layer 11 and the light guide layer.

The phase modulation layer 15 includes a base layer 15a made of a first refractive index medium, and a second refractive index medium having a refractive index different from that of the first refractive index medium, and a plurality of different refractive index areas present in the base layer 15a. And 15b. The plurality of modified refractive index regions 15 b include a substantially periodic structure. Assuming that the effective refractive index of the phase modulation layer 15 is n, the wavelength λ ₀ (= a × n, a is a lattice spacing) selected by the phase modulation layer 15 is included in the emission wavelength range of the active layer 12 . The phase modulation layer 15 can select the wavelength λ ₀ of the emission wavelength of the active layer 12 and output it to the outside. The laser beam incident in the phase modulation layer 15 forms a predetermined mode in the phase modulation layer 15 according to the arrangement of the different refractive index region 15b, and a laser beam having a desired pattern is externally provided from the semiconductor light emitting element 1A. It is emitted to.

  The semiconductor light emitting element 1A further includes an electrode 16 provided on the contact layer 14 and an electrode 17 provided on the back surface 10b of the semiconductor substrate 10. The electrode 16 is in ohmic contact with the contact layer 14, and the electrode 17 is in ohmic contact with the semiconductor substrate 10. Furthermore, the electrode 17 has an opening 17a. The electrode 16 is provided in the central region of the contact layer 14. The portion other than the electrode 16 on the contact layer 14 is covered by a protective film 18. The contact layer 14 not in contact with the electrode 16 may be removed. A portion (including the inside of the opening 17 a) of the back surface 10 b of the semiconductor substrate 10 other than the electrode 17 is covered with the anti-reflection film 19. The antireflective film 19 in the area other than the opening 17a may be removed.

  When a drive current is supplied between the electrode 16 and the electrode 17, recombination of electrons and holes occurs in the active layer 12, and the active layer 12 emits light. The electrons and holes that contribute to the light emission, and the generated light are efficiently confined between the cladding layer 11 and the cladding layer 13.

  The light emitted from the active layer 12 enters the inside of the phase modulation layer 15 and forms a predetermined mode according to the lattice structure inside the phase modulation layer 15. The laser light emitted from the phase modulation layer 15 is directly output from the back surface 10b to the outside of the semiconductor light emitting element 1A through the opening 17a, or after being reflected by the electrode 16, passes from the back surface 10b to the opening 17a. As a result, the light is output to the outside of the semiconductor light emitting element 1A. At this time, the zero-order light contained in the laser light is emitted in the direction perpendicular to the major surface 10a. On the other hand, the signal light (primary light and −1st order light) contained in the laser light is emitted in a two-dimensional arbitrary direction including a direction perpendicular to the major surface 10 a and a direction inclined with respect thereto. It is the signal light that forms the desired light image.

  In one example, the semiconductor substrate 10 is a GaAs substrate, and the cladding layer 11, the active layer 12, the cladding layer 13, the contact layer 14, and the phase modulation layer 15 are compounds composed of group III elements and group V elements, respectively. It is a semiconductor layer. In one embodiment, the cladding layer 11 is an AlGaAs layer, the active layer 12 has a multiple quantum well structure (barrier layer: AlGaAs / well layer: InGaAs), and the base layer 15a of the phase modulation layer 15 is GaAs. The modified refractive index region 15 b is a void, the cladding layer 13 is an AlGaAs layer, and the contact layer 14 is a GaAs layer.

In AlGaAs, the energy band gap and the refractive index can be easily changed by changing the composition ratio of Al. In Al _x Ga _{1 -x} As, when the composition ratio x of relatively small atomic radius is decreased (increased), the energy band gap positively correlated with this decreases (larger), and the atomic radius of GaAs is reduced. The energy band gap is reduced by mixing In with large In of. That is, the Al composition ratio of the cladding layers 11 and 13 is larger than the Al composition ratio of the barrier layer (AlGaAs) of the active layer 12. The Al composition ratio of the cladding layers 11 and 13 is set to, for example, 0.2 to 1.0, and is 0.4 in one embodiment. The Al composition ratio of the barrier layer of the active layer 12 is set to, for example, 0 to 0.3, and is 0.15 in one embodiment.

  Note that noise light having a mesh-like dark part may be superimposed on the beam pattern corresponding to the light image emitted from the semiconductor light emitting element 1A. According to the inventor's research, the noise light having the mesh-like dark part is caused by the higher order mode in the stacking direction inside the semiconductor light emitting element 1A. Here, the fundamental mode in the stacking direction refers to a mode having an intensity distribution in which one peak is present over the region including the active layer 12 and sandwiched between the cladding layer 11 and the cladding layer 13. Is a mode having an intensity distribution in which two or more peaks are present. The peak of the intensity distribution of the fundamental mode is formed in the vicinity of the active layer 12, while the peak of the intensity distribution of the higher mode is also formed in the cladding layer 11, the cladding layer 13, the contact layer 14 and the like. Further, as the mode in the stacking direction, a guided mode and a leaked mode exist, but since the leaked mode does not stably exist, only the guided mode is focused here. Further, although there are TE modes in which the electric field vector exists in the in-plane direction of the layer and TM modes in which the electric field vector exists in the direction perpendicular to the layer surface, the waveguide mode focuses on only the TE mode. When the refractive index of the cladding layer 13 between the active layer 12 and the contact layer is larger than the refractive index of the cladding layer 11 between the active layer 12 and the semiconductor substrate, such a higher order mode occurs notably . Usually, the refractive indices of the active layer 12 and the contact layer 14 are much larger than the refractive indices of the cladding layers 11 and 13. Therefore, when the refractive index of the cladding layer 13 is larger than the refractive index of the cladding layer 11, light is confined also in the cladding layer 13 to form a waveguide mode. This results in higher order modes.

  In the semiconductor light emitting device 1A of the present embodiment, the refractive index of the cladding layer 13 is less than or equal to the refractive index of the cladding layer 11. As a result, the generation of the high-order mode as described above can be suppressed, and noise light having a mesh-like dark portion superimposed on the beam pattern can be reduced.

Further, it is preferable that the three-layer slab waveguide structure configured by the optical waveguide layer and the two layers adjacent to the optical waveguide layer satisfy the following conditions. Specifically, the optical waveguide layer in the three-layer slab waveguide structure is formed of the active layer 12 when the refractive index of the phase modulation layer 15 is smaller than the refractive index of the cladding layer 11. On the other hand, when the refractive index of the phase modulation layer 15 is equal to or higher than the refractive index of the cladding layer 11, the optical waveguide layer is formed of the phase modulation layer 15 and the active layer 12. In any case, the optical waveguide layer does not include the cladding layers 11 and 13. In such a three-layer slab waveguide structure, the normalized waveguide width V ₁ in the TE mode is defined by the following equations (1) and (2), and the asymmetry parameter a ′ and the normalized propagation coefficient b are as follows: when a real number satisfying the equation (3) and (4) respectively, so that the solutions of standards influencing for good waveguide width V ₁ is within the range that exists only one standard influencing for good waveguide width V ₁ and the normalized propagation coefficients b Is set.




Here, the TE mode is a propagation mode in the layer thickness direction, n ₁ is the refractive index of the optical waveguide layer including the active layer 12, n ₂ is the refractive index of the layer having the higher refractive index among the layers adjacent to the optical waveguide layer, N ₁ is the mode order, n _clad is the refractive index of the cladding layer 11, n ₃ is the refractive index of the low refractive index layer among the layers adjacent to the optical waveguide layer, n _eff is the TE mode equivalent in the three-layer slab waveguide structure It is a refractive index.

According to the research of the inventors, it has been found that high-order modes are generated also in the optical waveguide layer (high refractive index layer) including the active layer 12. Then, it has been found that higher order modes can be suppressed by appropriately controlling the thickness and refractive index of the optical waveguide layer. That is, the value of the standard influencing for good waveguide width V ₁ of the optical waveguide layer satisfies the condition described above, generation of higher order modes is further suppressed, and more of the noise light having a net-like dark portion that is superimposed on the beam pattern Further reduction is possible.

Further, another three-layer slab waveguide structure configured by the contact layer and the two layers adjacent to the contact layer preferably satisfies the following conditions. Specifically, in such another three-layer slab waveguide structure, the normalized waveguide width V ₂ of the contact layer 14 is defined by the following equations (5) and (6), and the asymmetry parameter a ′ and the normalization when the propagation coefficients b and real number satisfying the following equation (7) and (8), respectively, so as to fall within the scope of the no standard influencing for good waveguide width V ₂ collapsed, standard influencing for good waveguide width V ₂ and normalized The propagation coefficient b is set.

Here, n ₄ is the refractive index of the contact layer 14, n ₅ is the refractive index of the layer having a high refractive index among the layers adjacent to the contact layer 14, and n ₆ is the low refractive index of the layers adjacent to the contact layer 14. The refractive index of the layer, N ₂ is the mode order, and n _eff is the equivalent refractive index of the TE mode in the other three-layer slab waveguide structure.

  As described above, by appropriately controlling the thickness of the contact layer 14, the generation of the guided mode caused by the contact layer 14 can be suppressed, and the generation of the higher order mode generated in the laser element can be further suppressed.

  In another example, the semiconductor substrate 10 is an InP substrate, and the cladding layer 11, the active layer 12, the phase modulation layer 15, the cladding layer 13, and the contact layer 14 are made of, for example, an InP-based compound semiconductor. In one embodiment, the cladding layer 11 is an InP layer, the active layer 12 has a multiple quantum well structure (barrier layer: GaInAsP / well layer: GaInAsP), and the base layer 15a of the phase modulation layer 15 is GaInAsP The modified refractive index region 15 b is a void, the cladding layer 13 is an InP layer, and the contact layer 14 is a GaInAsP layer.

  In still another example, the semiconductor substrate 10 is a GaN substrate, and the cladding layer 11, the active layer 12, the phase modulation layer 15, the cladding layer 13, and the contact layer 14 are made of, for example, a nitride compound semiconductor. In one embodiment, the cladding layer 11 is an AlGaN layer, the active layer 12 has a multiple quantum well structure (barrier layer: InGaN / well layer: InGaN), and the basic layer 15 a of the phase modulation layer 15 is GaN. The modified refractive index region 15 b is a void, the cladding layer 13 is an AlGaN layer, and the contact layer 14 is a GaN layer.

The same conductivity type as the semiconductor substrate 10 is given to the cladding layer 11, and the opposite conductivity type to the semiconductor substrate 10 is given to the cladding layer 13 and the contact layer 14. In one example, the semiconductor substrate 10 and the cladding layer 11 are n-type, and the cladding layer 13 and the contact layer 14 are p-type. The phase modulation layer 15 has the same conductivity type as the semiconductor substrate 10 when provided between the active layer 12 and the cladding layer 11, and is semiconductor when being provided between the active layer 12 and the cladding layer 13. It has a conductivity type opposite to that of the substrate 10. The impurity concentration is, for example, 1 × 10 ¹⁷ to 1 × 10 ²¹ / cm ³ . The active layer 12 is intrinsic (i-type) to which no impurity is intentionally added, and the impurity concentration is 1 × 10 ¹⁵ / cm ³ or less. The impurity concentration of the phase modulation layer 15 may be intrinsic (i-type) when it is necessary to suppress the influence of loss due to light absorption through the impurity level.

  The thickness of the semiconductor substrate 10 is, for example, 150 μm. The thickness of the cladding layer 11 is, for example, 2000 nm. The thickness of the active layer 12 is, for example, 175 nm. The thickness of the phase modulation layer 15 is, for example, 280 nm. The depth of the modified refractive index area 15b is, for example, 200 nm. The thickness of the cladding layer 13 is, for example, 2000 nm. The thickness of the contact layer 14 is, for example, 150 nm.

  In the above-described structure, the modified refractive index region 15b is a void, but the modified refractive index region 15b may be formed by burying a semiconductor having a refractive index different from that of the base layer 15a. In that case, for example, the pores of the base layer 15a may be formed by etching, and the semiconductor may be embedded in the pores using metal organic chemical vapor deposition, sputtering or epitaxial method. For example, when the base layer 15a is made of GaAs, the modified refractive index region 15b may be made of AlGaAs. Alternatively, after the semiconductor is embedded in the pores of the base layer 15a to form the modified refractive index region 15b, the same semiconductor as the modified refractive index region 15b may be deposited thereon. When the modified refractive index region 15 b is a hole, the hole may be filled with an inert gas such as argon, nitrogen or hydrogen, or air.

The antireflective film 19 is made of, for example, a dielectric single layer film such as silicon nitride (for example, SiN), silicon oxide (for example, SiO ₂ ), or a dielectric multilayer film. Examples of dielectric multilayer films include titanium oxide (TiO ₂ ), silicon dioxide (SiO ₂ ), silicon monoxide (SiO), niobium oxide (Nb ₂ O ₅ ), tantalum pentoxide (Ta ₂ O ₅ ), and fluorine. Dielectric layers such as magnesium fluoride (MgF ₂ ), titanium oxide (TiO ₂ ), aluminum oxide (Al ₂ O ₃ ), cerium oxide (CeO ₂ ), indium oxide (In ₂ O ₃ ), zirconium oxide (ZrO ₂ ) A film in which two or more types of dielectric layers selected from the group are stacked can be used. For example, a film with a thickness of λ / 4 is stacked with an optical film thickness for light of wavelength λ. The protective film 18 is, for example, an insulating film such as silicon nitride (for example, SiN) or silicon oxide (for example, SiO ₂ ). When the semiconductor substrate 10 and the contact layer 14 are made of a GaAs-based semiconductor, the electrode 16 can be made of a material containing at least one of Cr, Ti, and Pt, and Au, for example, a Cr layer and an Au layer Have a laminated structure of The electrode 17 can be made of a material containing at least one of AuGe and Ni, and Au, and has, for example, a laminated structure of an AuGe layer and an Au layer. The materials of the electrodes 16 and 17 are not limited to these ranges as long as ohmic contact can be realized.

  In the above-described structure, as long as the structure includes the active layer 12 and the phase modulation layer 15, the material system, the film thickness, and the layer structure may be variously changed. Here, with respect to a so-called square lattice photonic crystal laser in the case where the perturbation from the virtual square lattice is zero, a scaling law holds. That is, when the wavelength is multiplied by a constant α, a similar standing wave state can be obtained by multiplying the entire square lattice structure by α. Similarly, also in this embodiment, it is possible to determine the structure of the phase modulation layer 15 by the scaling rule according to the wavelength. Therefore, it is also possible to realize the semiconductor light emitting element 1A that outputs visible light by applying the scaling rule according to the wavelength using the active layer 12 that emits light such as blue, green and red.

When the semiconductor light emitting element 1A is manufactured, metal organic chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE) is used to grow each compound semiconductor layer. In the manufacture of the semiconductor light emitting device 1A using AlGaAs, the growth temperature of AlGaAs is 500 ° C. to 850 ° C., and 550 to 700 ° C. is adopted in the experiment, and TMA (trimethylaluminum) as an Al source during growth, TMG (trimethylgallium) and TEG (triethylgallium) as gallium sources, AsH ₃ (arsine) as As sources, Si ₂ H ₆ (disilane) as sources for n-type impurities, DEZn (diethyl) as sources for p-type impurities Use zinc). In the growth of GaAs, TMG and arsine are used but TMA is not used. InGaAs is manufactured using TMG, TMI (trimethylindium) and arsine. The insulating film may be formed by sputtering a target using the constituent material as a raw material or by PCVD (plasma CVD).

  That is, first, the above-described semiconductor light emitting device 1A has an AlGaAs layer as the n-type cladding layer 11, an InGaAs / AlGaAs multiple quantum well structure as the active layer 12, and a phase on the GaAs substrate as the n-type semiconductor substrate 10. A GaAs layer as the base layer 15a of the modulation layer 15 is epitaxially grown sequentially using the MOCVD method or the MBE method.

Next, another resist is applied to the basic layer 15a, and a two-dimensional fine pattern is drawn on the resist by an electron beam drawing apparatus using the alignment mark as a reference, and a two-dimensional fine pattern is formed on the resist by development. . Thereafter, using the resist as a mask, the two-dimensional fine pattern is transferred onto the basic layer 15a by dry etching to form a hole, and then the resist is removed. Before the resist formation, a SiN layer or SiO ₂ layer is formed on the base layer 15a by PCVD, a resist mask is formed thereon, and a SiN layer or SiO ₂ layer is formed using reactive ion etching (RIE). The fine pattern may be transferred, the resist may be removed, and then dry etching may be performed. In this case, the resistance of dry etching can be enhanced. The depth of the holes is, for example, 100 nm. These holes are used as the modified refractive index regions 15 b or, in these holes, a compound semiconductor (AlGaAs) to be converted into the modified refractive index regions 15 b is regrown to the depth of the holes or more. In the case where the hole is a modified refractive index region 15b, a gas such as air, nitrogen or argon may be enclosed in the hole. Thus, the phase modulation layer 15 is formed. When the phase modulation layer 15 is provided between the active layer 12 and the cladding layer 11, the phase modulation layer 15 may be formed on the cladding layer 11 before the formation of the active layer 12.

  Subsequently, an AlGaAs layer as the cladding layer 13 and a GaAs layer as the contact layer 14 are sequentially formed by the MOCVD method or the MBE method, and the electrodes 16 and 17 are formed by the vapor deposition method or the sputtering method. In addition, the protective film 18 and the antireflective film 19 are formed by sputtering, PCVD method or the like as required. The semiconductor light emitting element 1A of the present embodiment is manufactured through the above steps.

  FIG. 4 is a plan view of the phase modulation layer 15. As described above, the phase modulation layer 15 includes the basic layer 15a made of the first refractive index medium, and the modified refractive index area 15b made of the second refractive index medium having a refractive index different from that of the first refractive index medium. Here, a virtual square lattice in the XY plane is set in the phase modulation layer 15. One side of the square lattice is parallel to the X axis, and the other side is parallel to the Y axis. At this time, a square unit constituent region R centered on the lattice point O of the square lattice can be set in a two-dimensional manner over a plurality of columns along the X axis and a plurality of rows along the Y axis. Assuming that the XY coordinates of each unit constituting area R are given by the position of the center of gravity of each unit constituting area R, the position of the center of gravity coincides with the lattice point O of the virtual square lattice. The plurality of different refractive index areas 15 b are provided one by one in each unit configuration area R. The planar shape of the modified refractive index area 15b is, for example, a circular shape. The lattice point O may be located outside the modified refractive index area 15 b or may be included inside the modified refractive index area 15 b.

The ratio of the area S of the differential refractive index area 15b occupied in one unit constituent area R is referred to as a filling factor (FF). Assuming that the lattice spacing of the square lattice is a, the filling factor FF of the modified refractive index area 15 b is given as S / a ² . S is the area of the modified refractive index region 15b in the XY plane, and for example, in the case of a perfect circle, it is given as S = π (d / 2) ² using the diameter d of the true circle. Also, in the case of a square shape, it is given as S = LA ² using the length LA of one side of the square.

  FIG. 5 is a view showing the positional relationship of the modified refractive index area 15 b in the phase modulation layer 15. As shown in FIG. 5, the center of gravity G of each modified refractive index area 15 b is disposed on the straight line D. The straight line D is a straight line which passes through the corresponding grid point O of each unit constituent region R and is inclined with respect to each side of the square lattice. In other words, the straight line D is a straight line inclined with respect to both the X axis and the Y axis. The inclination angle of the straight line D with respect to one side (X axis) of the square lattice is θ. The tilt angle θ is constant in the phase modulation layer 15. The inclination angle θ satisfies 0 ° <θ <90 °, and in one example, θ = 45 °. Alternatively, the inclination angle θ satisfies 180 ° <θ <270 °, and in one example, θ = 225 °. If the inclination angle θ satisfies 0 ° <θ <90 ° or 180 ° <θ <270 °, the straight line D extends from the first quadrant to the third quadrant of the coordinate plane defined by the X and Y axes. Alternatively, the inclination angle θ satisfies 90 ° <θ <180 °, and in one example, θ = 135 °. Alternatively, the inclination angle θ satisfies 270 ° <θ <360 °, and in one example, θ = 315 °. If the inclination angle θ satisfies 90 ° <θ <180 ° or 270 ° <θ <360 °, the straight line D extends from the second quadrant to the fourth quadrant of the coordinate plane defined by the X and Y axes. Thus, the inclination angle θ is an angle excluding 0 °, 90 °, 180 ° and 270 °. Here, the distance between the lattice point O and the center of gravity G is r (x, y). x indicates the position of the x-th grid point on the X axis, and y indicates the position of the y-th grid point on the Y axis. When the distance r (x, y) is a positive value, the center of gravity G is located in the first quadrant (or the second quadrant). When the distance r (x, y) is a negative value, the center of gravity G is located in the third quadrant (or the fourth quadrant). When the distance r (x, y) is zero, the grid point O and the center of gravity G coincide with each other.

The distance r (x, y) between the center of gravity G of each modified refractive index area 15b and the corresponding lattice point O of each unit constituting area R shown in FIG. 4 has each modified refractive index according to the desired light image. It is set individually for each area 15b. The distribution of the distance r (x, y) has a specific value at each position determined by the values of x and y, but is not necessarily represented by a specific function. The distribution of the distance r (x, y) is determined from the complex amplitude distribution obtained by Fourier transforming a desired light image, from which the phase distribution is extracted. That is, when the phase P (x, y) at a certain coordinate (x, y) is P ₀ shown in FIG. 5, the distance r (x, y) is set to 0, and the phase P (x, y) is set. When y) is π + P ₀ , the distance r (x, y) is set to the maximum value R ₀ , and when the phase P (x, y) is −π + P ₀ , the distance r (x, y) is Set to the minimum value -R ₀ . Then, for the intermediate phase P (x, y), the distance r (x, y) is set such that r (x, y) = {P (x, y) -P ₀ } × R ₀ / π Take). Here, the initial phase P ₀ can be set arbitrarily. Assuming that the lattice spacing of a square lattice is a, the maximum value R ₀ of r (x, y) is, for example,

Within the scope of In addition, when obtaining the complex amplitude distribution from the desired light image, the reproducibility of the beam pattern can be obtained by applying an iterative algorithm such as Gerchberg-Saxton (GS) method generally used when calculating the hologram generation. improves.

  FIG. 6 is a plan view showing an example in which the refractive index approximate periodic structure of FIG. 4 is applied only in a specific region of the phase modulation layer. In the example shown in FIG. 6, a substantially periodic structure (for example, the structure of FIG. 4) for emitting a target beam pattern is formed inside a square inner region RIN. On the other hand, in the outer region ROUT surrounding the inner region RIN, a circular circular different refractive index region is arranged in which the lattice point position of the square lattice matches the barycentric position. In the inner region RIN and the outer region ROUT, the lattice spacings of the virtually set square lattices are equal to each other (= a). In the case of this structure, light is also distributed in the outer region ROUT to suppress generation of high frequency noise (so-called window function noise) caused by a sudden change in light intensity in the peripheral portion of the inner region RIN. it can. In addition, light leakage in the in-plane direction can be suppressed, and reduction in threshold current can be expected.

  FIG. 7 is a view for explaining the relationship between an optical image obtained as an output beam pattern of the semiconductor light emitting element 1A and the phase distribution P (x, y) in the phase modulation layer 15. As shown in FIG. The center Q of the output beam pattern is located on an axis perpendicular to the major surface 10 a of the semiconductor substrate 10, and FIG. 7 shows four quadrants having the center Q as an origin. Although FIG. 7 shows the case where light images are obtained in the first quadrant and the third quadrant as an example, it is also possible to obtain images in the second quadrant and the fourth quadrant or all quadrants. In the present embodiment, as shown in FIG. 7, a point-symmetrical light image is obtained with respect to the origin. FIG. 7 shows, as an example, a case where a character "A" is obtained as + 1st diffracted light in the third quadrant, and a pattern obtained by rotating the character "A" 180 degrees in the first quadrant is obtained as the 1st diffracted light. . In the case of a rotationally symmetric light image (for example, a cross, a circle, a double circle, etc.) with the center Q as the origin, the light image is observed as one light image overlapping.

  The light image obtained by imaging the output beam pattern of the semiconductor light emitting element 1A is at least one of a spot, a straight line, a cross, a line drawing, a lattice pattern, a photograph, a stripe pattern, CG (computer graphics), and a character It contains. Here, in order to obtain a desired light image, the distribution of the distance r (x, y) of the modified refractive index area 15 b of the phase modulation layer 15 is determined by the following procedure.

First, as a first precondition, in the XYZ orthogonal coordinate system, each unit is constituted by M1 (integer of 1 or more) × N1 (integer of 1 or more) unit constituent regions R having a square shape on the XY plane Virtual square grid is set. Next, as a second precondition, coordinates (x, y, z) in the XYZ orthogonal coordinate system are, as shown in FIG. 8, the length r of the radius and the tilt angle θ _tilt from the Z axis , With respect to the spherical coordinates (r, θ _tilt , θ _rot ) defined by the rotation angle θ _rot from the X axis specified on the XY plane, expressed by the following equations (10) to (12) Meet the following relationship. FIG. 8 is a diagram for explaining coordinate conversion from spherical coordinates (r, θ _tilt , θ _rot ) to coordinates (x, y, z) in the XYZ orthogonal coordinate system, and the coordinates (x, y, z) represents a designed light image on a predetermined plane set in the XYZ rectangular coordinate system which is a real space. When a set of bright points towards a beam pattern corresponding to a light image emitted by the semiconductor light emitting device in the direction defined by the angle theta _tilt and theta _rot, the angle theta _tilt and theta _rot has the following formula (13) And the coordinate value k _x on the Kx axis corresponding to the X axis, and the normalized wave number defined by the following equation (14) corresponding to the Y axis and along the Kx axis shall be converted into coordinate values k _y on Ky axis orthogonal. The normalized wave number means the wave number normalized with the wave number corresponding to the lattice spacing of a virtual square lattice being 1.0. At this time, in a wave number space defined by the Kx axis and the Ky axis, a specific wave number range including a beam pattern corresponding to an optical image is square M2 (integer of 1 or more) .times.N2 (integer of 1 or more) And the image region FR. The integer M2 does not have to match the integer M1. Similarly, the integer N2 does not have to match the integer N1. Moreover, Formula (13) and Formula (14) are described, for example, in Y. Kurosaka et al., "Effects of non-lasing band in two-dimensional photonic-crystal lasers clarified using omnidirectional band structure," Opt. Express 20, 2177-21783. (2012).

As the third precondition, an image specified by the coordinate component k _x (an integer of 1 or more and M 2 or less) in the wave number space and the coordinate component k _y (an integer of 1 or more and N 2 or less) in the wave direction An XY plane specified by a coordinate component x (an integer of 1 or more and M1 or less) in the X-axis direction and a coordinate component y (an integer of 1 or more and N1 or less) in the Y-axis direction in each of the regions FR (k _x, k _y ) The complex amplitude F (x, y) obtained by performing two-dimensional inverse Fourier transform on the above unit constituent region R (x, y) is given by the following equation (15), where j is an imaginary unit. Further, when the amplitude term is A (x, y) and the phase term is P (x, y), this complex amplitude F (x, y) is defined by the following equation (16). Furthermore, as a fourth precondition, a lattice point O (x, x) where the unit constituent region R (x, y) is parallel to the X axis and the Y axis and is the center of the unit constituent region R (x, y) It is defined by s-axis and t-axis orthogonal in y).


Under the first to fourth conditions, the phase modulation layer 15 is configured to satisfy the following conditions. That is, the distance r (x, y) from the lattice point O (x, y) to the center of gravity G of the corresponding variable refractive index area 15 b is
r (x, y) = C × (P (x, y) -P 0)
C: proportional constant, eg R ₀ / π
P _{0 is an} arbitrary constant, for example 0
The corresponding different refractive index regions 15 b are disposed in the unit constituent region R (x, y) so as to satisfy the following relationship. That is, the distance r (x, y) is set to 0 when the phase P (x, y) at a certain coordinate (x, y) is P ₀ , and the phase P (x, y) is π + P ₀ In this case, the maximum value R ₀ is set, and in the case where the phase P (x, y) is −π + P ₀ , the minimum value −R ₀ is set. When it is desired to obtain a desired light image, the light image is subjected to inverse Fourier transform, and the distribution of the distance r (x, y) according to the phase P (x, y) of its complex amplitude is divided into a plurality of different refractive index regions Give it to 15b. The phase P (x, y) and the distance r (x, y) may be proportional to one another.

  The far-field pattern after Fourier transformation of the laser beam has various shapes such as single or plural spot shapes, annular shapes, linear shapes, character shapes, double annular shapes, or Laguerre-Gaussian beam shapes. It can be taken. Since the beam direction can also be controlled, it is possible to realize, for example, a laser processing machine that electrically performs high-speed scanning by arraying the semiconductor light emitting elements 1A in one or two dimensions. Since the beam pattern is represented by angle information in the far field, if the target beam pattern is a bitmap image or the like represented by two-dimensional position information, it is once converted into angle information. Then, it is preferable to perform inverse Fourier transform after converting to wave number space.

  As a method of obtaining the intensity distribution and the phase distribution from the complex amplitude distribution obtained by the inverse Fourier transform, for example, the intensity distribution I (x, y) is calculated by using the abs function of the numerical analysis software "MATLAB" of The MathWorks. The phase distribution P (x, y) can be calculated by using MATLAB's angle function.

  Here, when the phase distribution P (x, y) is obtained from the result of the inverse Fourier transform of the light image and the distance r (x, y) of each of the different refractive index areas 15 b is determined, Points to be noted in the case of calculation using Fourier transform will be described. An output beam pattern calculated from the complex amplitude distribution obtained by the inverse Fourier transform of FIG. 9A, which is a desired light image, is as shown in FIG. 9B. If the light beam is divided into four quadrants A1, A2, A3 and A4 as shown in FIGS. 9 (a) and 9 (b), the first quadrant of the output beam pattern in FIG. 9 (b) A pattern obtained by rotating the first quadrant of a) by 180 degrees and a pattern in which the third quadrant of FIG. 9A is superimposed appear, and the second quadrant of FIG. 9A is rotated 180 degrees in the second quadrant of the beam pattern. And a pattern in which the fourth quadrant of FIG. 9 (a) is superimposed, and the third quadrant of FIG. 9 (a) is obtained by rotating the third quadrant of FIG. 9 (a) by 180 degrees. A pattern in which one quadrant is overlapped appears, and in the fourth quadrant of the beam pattern, a pattern in which the fourth quadrant in FIG. 9A is rotated 180 degrees and a pattern in which the second quadrant in FIG. At this time, the pattern rotated 180 degrees is due to the -1st order light component.

  Therefore, when using a light image having a value only in the first quadrant as the light image (original light image) before Fourier transform, the first quadrant of the original light image appears in the third quadrant of the obtained beam pattern. A pattern obtained by rotating the first quadrant of the original light image by 180 degrees appears in the first quadrant of the obtained beam pattern.

  Here, FIG. 10A shows an example of a beam pattern (optical image) output from the semiconductor light emitting element 1A. The center of the figure corresponds to an axis perpendicular to the light emitting surface and intersecting the light emitting surface of the semiconductor light emitting element 1A. FIG. 10 (b) is a graph showing the light intensity distribution in a cross section including the axis. FIG. 10 (b) is a far-field image obtained using an FFP optical system (A3267-12 manufactured by Hamamatsu Photonics), a camera (ORCA-05G manufactured by Hamamatsu Photonics), and a beam profiler (Lepas 12 manufactured by Hamamatsu Photonics). The vertical count of image data of dot × 1024 dot is integrated and plotted. The maximum count number in FIG. 10A is normalized at 255, and the central zero-order light B0 is saturated in order to clearly show the intensity ratio of ± 1st-order light. From FIG. 10 (b), the intensity difference between the primary light and the −1st order light can be easily understood. FIG. 11 (a) is a diagram showing a phase distribution corresponding to the beam pattern shown in FIG. 10 (a). FIG.11 (b) is the elements on larger scale of Fig.11 (a). In FIGS. 11A and 11B, the phase at each position in the phase modulation layer 15 is indicated by shading, and the darker part approaches the phase angle 0 °, and the bright part approaches the phase angle 360 °. However, since the center value of the phase angle can be set arbitrarily, the phase angle may not necessarily be set within the range of 0 ° to 360 °. As shown in FIGS. 10 (a) and 10 (b), the semiconductor light emitting device 1A includes primary light including a first light image portion B1 outputted in a first direction inclined with respect to the axis; The first light is output in a second direction that is symmetrical to the first direction with respect to the axis, and the first order light including the second light image portion B2 that is rotationally symmetrical with the first light image portion B1 with respect to the axis. Typically, the first light image portion B1 appears in the first quadrant in the XY plane, and the second light image portion B2 appears in the third quadrant in the XY plane. Depending on the application, only one of the primary light and the −1st light may be used and the other may not be used. In such a case, it is desirable that the light quantity of the other light be kept small as compared to the one light. Therefore, in the present embodiment, as shown in FIG. 10B, an intensity difference is given to the primary light and the −1st light.

  FIG. 12 is a plan view conceptually showing the phase modulation layer 15. Now, the first area T1 and the second area T2 aligned in one lattice point arrangement direction (X-axis direction) sandwiching the center point Q of the phase modulation layer, and the other grating line sandwiching the center point Q of the phase modulation layer A third area T3 and a fourth area T4 aligned in the point arrangement direction (Y-axis direction) are defined. That is, when the origin of the XY orthogonal coordinate system is made to coincide with the central point Q, the first region T1 is a region where the X axis coordinate is positive, and the second region T2 is a region where the X axis coordinate is negative. The area T3 is an area where the Y-axis coordinate is positive, and the fourth area T4 is an area where the Y-axis coordinate is negative. Therefore, the first area T1 and the third area T3 overlap each other in the first quadrant F1 in which both the X-axis coordinate and the Y-axis coordinate are positive. The first area T1 and the fourth area T4 overlap each other in a second quadrant F2 in which the X-axis coordinate is positive and the Y-axis coordinate is negative. The second area T2 and the fourth area T4 overlap each other in a third quadrant F3 in which both the X-axis coordinate and the Y-axis coordinate are negative. The second area T2 and the third area T3 overlap each other in a fourth quadrant F4 in which the X-axis coordinate is negative and the Y-axis coordinate is positive.

  In the phase modulation layer 15 which is a phase modulation layer of the square lattice type S-iPM laser, basic traveling waves AU, AD, AR, and AL along the XY plane are generated as shown in FIG. The traveling wave AR is a first traveling wave traveling in the direction (X-axis positive direction) from the second region T2 to the first region T1. The traveling wave AL is a second traveling wave traveling in the direction (X-axis negative direction) from the first region T1 to the second region T2. The traveling wave AU is a third traveling wave traveling in the direction (the Y-axis positive direction) from the fourth region T4 to the third region T3. The traveling wave AD is a fourth traveling wave that travels in the direction (the Y-axis negative direction) from the third region T3 to the fourth region T4.

  As shown in FIG. 13, from the traveling waves traveling in opposite directions, beam patterns in opposite directions are obtained. For example, a beam pattern BU including only the second light image portion B2 is obtained from the traveling wave AU, and a beam pattern BD including only the first light image portion B1 is obtained from the traveling wave AD. Similarly, a beam pattern BR including only the second light image portion B2 is obtained from the traveling wave AR, and a beam pattern BL including only the first light image portion B1 is obtained from the traveling wave AL. In other words, in the traveling waves traveling in opposite directions to each other, one is primary light and the other is negative. The beam patterns output from the semiconductor light emitting element 1A are those in which the beam patterns BU, BD, BR, and BL overlap.

  Here, FIGS. 14 to 17 are graphs showing intensity distributions of the traveling waves AU, AD, AR, and AL in the plane of the phase modulation layer 15. 14 shows the intensity distribution of the traveling wave AU, FIG. 15 shows the intensity distribution of the traveling wave AD, FIG. 16 shows the intensity distribution of the traveling wave AR, and FIG. 17 shows the intensity distribution of the traveling wave AL. In FIGS. 14 to 17, (a) represents the intensity distribution of the traveling waves AU, AD, AR, and AL by isointensity lines, the horizontal axis represents the position in the X-axis direction, and the vertical axis represents Represents the Y-axis direction position. (B) is a three-dimensional representation of the intensity distribution of the traveling waves AU, AD, AR, and AL, and in addition to the position in the X-axis direction and the position in the Y-axis, an axis representing the intensity of the traveling wave is It is shown. As shown in these figures, the intensities of the traveling waves AU, AD, AR, and AL are unevenly distributed in the plane of the phase modulation layer 15.

  Specifically, the intensity of the traveling wave AU advancing in the Y-axis positive direction becomes stronger as the Y coordinate becomes larger, and becomes weaker as the Y coordinate becomes smaller. Further, the intensity of the traveling wave AD advancing in the negative direction of the Y axis becomes stronger as the Y coordinate becomes smaller, and becomes weaker as the Y coordinate becomes larger. Similarly, the intensity of the traveling wave AR traveling in the positive direction of the X axis becomes stronger as the X coordinate becomes larger, and becomes weaker as the X coordinate becomes smaller. Further, the intensity of the traveling wave AL advancing in the negative direction of the X axis becomes stronger as the X coordinate becomes smaller, and becomes weaker as the X coordinate becomes larger. In other words, in the first quadrant F1, the traveling waves AU and AR are strong, in the second quadrant F2 the traveling waves AD and AR are strong, in the third quadrant F3 the traveling waves AD and AL are strong, and in the fourth quadrant F4 Is strong in traveling waves AU and AL. When the inclination angle θ of the straight line D is 45 °, 135 °, 225 °, or 315 °, the maximum intensities of the traveling waves AU, AD, AR, and AL become equal to one another. When the inclination angle θ of the straight line D is 0 ° <θ <45 °, 135 ° <θ <225 °, or 315 ° <θ <360 °, the maximum strengths of the traveling waves AR and AL are traveling waves. When the inclination angle θ of the straight line D is larger than the maximum intensity of AU and AD, and the inclination angle θ of the straight line D is 45 ° <θ <135 ° or 225 ° <θ <315 °, the maximum intensity of the traveling wave AU or AD is the traveling wave It becomes larger than the maximum strength of AR and AL.

  In this embodiment, the intensity distribution of the traveling waves AU, AD, AR, and AL described above is used to give a difference to the light amounts of the primary light and the −1st light, and one of them is reduced with respect to the other. Do. Therefore, the arrangement of the modified refractive index regions 15b in the phase modulation layer 15 is designed using the following method. FIG. 18 is a flowchart showing a method of designing the phase modulation layer 15 according to the present embodiment.

As shown in FIG. 18, in the first step S1, a plurality of complex amplitude distributions corresponding to light images are prepared for the traveling waves AU, AD, AR, and AL. First, the degree of deviation of the light intensity in the plane of the phase modulation layer 15 is predicted in advance, and the light images obtained by the traveling waves AU, AD, AR, and AL are mutually separated. As a result, four light images corresponding to the traveling waves AU, AD, AR, and AL are obtained. Then, based on these light images, the complex amplitude distribution E _U (x, y) of the traveling wave AU, the complex amplitude distribution E _D (x, y) of the traveling wave AD, and the complex amplitude distribution E of the traveling wave AR _R (x, y) and the complex amplitude distribution E _L (x, y) regarding the traveling wave AL are individually calculated.

E _U (x, y) = A _U (x, y) exp {iP _U (x, y)}
E _D (x, y) = A _D (x, y) exp {i P _D (x, y)}
E _R (x, y) = A _R (x, y) exp {i P _R (x, y)}
E _L (x, y) = A _L (x, y) exp {iP _L (x, y)}
Note that A _U (x, y), A _D (x, y), A _R (x, y), and A _L (x, y) are the intensity distributions of the traveling waves AU, AD, AR, and AL, respectively. P _U (x, y), P _D (x, y), P _R (x, y), and P _L (x, y) are the phases of the traveling waves AU, AD, AR, and AL, respectively. It is a distribution. As described above, these complex amplitude distributions E _U (x, y), E _D (x, y), E _R (x, y), and E _L (x, y) are inverse Fourier images of the respective light images. It is obtained by converting. The method of calculating the complex amplitude distribution is described, for example, in WH Lee, "Sampled fourier transform hologram generated by computer", Appl, Opt, 9, 639-643 (1970).

Next, in a second step S2, complex amplitude distributions E _U (x, y), E _D (x, y), E _R (x, y), and E E for each traveling wave AU, AD, AR, and AL. Modify _L (x, y). In the second step S2, the positive and negative of the phase term of the complex amplitude distribution regarding one of the traveling waves AR and AL are reversed, and the positive and negative of the phase term of the complex amplitude distribution regarding one of the traveling waves AU and AD are reversed. For example, the complex amplitude distributions E _U (x, y), E _D (x, y), E _R (x, y), and E _L (x, y) after correction are respectively as follows.

E _U (x, y) = A _U (x, y) exp {-iP _U (x, y)}
E _D (x, y) = A _D (x, y) exp {i P _D (x, y)}
E _R (x, y) = A _R (x, y) exp {−iP _R (x, y)}
E _L (x, y) = A _L (x, y) exp {iP _L (x, y)}
In this example, although the positive and negative of the phase terms of the complex amplitude distributions E _U (x, y) and E _R (x, y) related to the traveling waves AU and AR are inverted, the complex amplitude distribution E _D related to the traveling waves AD and AL The phase terms of (x, y) and E _L (x, y) may be inverted. In this example, the inclination angle θ of the straight line D is 0 ° <θ <90 ° or 180 ° <θ <270 °, and the inclination angle θ of the straight line D is 90 ° <θ <180 °. Alternatively, if 270 ° <θ <360 °, it is preferable to invert the positive and negative of the phase term of the complex amplitude distribution regarding the traveling wave AU, AL (or the traveling wave AD, AR).

Furthermore, in the second step S2, as shown in the following equation, the complex amplitude distribution E _U (x, y), E _D (x, y), E _R (x, y), and E _L (x , Y) may be weighted arbitrarily. For example, complex amplitude distributions E _U (x, y) and E _D (x, y) are multiplied by the same weight n, and complex amplitude distributions E _R (x, y) and E _L (x, y) are given the same weight m. Multiply. Then, the weight n and the weight m are made different from each other.

E _U (x, y) = nA _U (x, y) exp {-iP _U (x, y)}
E _D (x, y) = n A _D (x, y) exp {i P _D (x, y)}
_{E R (x, y) =} mA R (x, y) exp {-iP R (x, y)}
E _L (x, y) = mA _L (x, y) exp {iP _L (x, y)}
For example, the ratio (m / n) of the weight n to the weight m may be determined based on the inclination angle θ of the straight line D with respect to the square lattice. That is, when the inclination angle θ of the straight line D is 0 ° <θ <45 °, 135 ° <θ <225 °, or 315 ° <θ <360 °, the maximum of the traveling waves AR and AL as described above Since the intensity is larger than the maximum intensity of the traveling waves AU and AD, the ratio (m / n) is increased to increase the contribution of E _R (x, y) and E _L (x, y). When the inclination angle θ of the straight line D is 45 ° <θ <135 ° or 225 ° <θ <315 °, the maximum intensity of the traveling waves AU, AD is the maximum of the traveling waves AR, AL as described above. As it becomes larger than the strength, the ratio (m / n) is reduced to increase the contribution of E _U (x, y) and E _D (x, y). In one embodiment, m = cos θ and n = sin θ.

Subsequently, in the third step S3, as shown in the following equation (17), the complex amplitude distribution E _U (x, y), E _D (x, y), E _R (x, y), and E _An overall (final) complex amplitude distribution E _total (x, y) is obtained by superposing (adding) _L (x, y) on each other.

Finally, in the fourth step S4, comprehensive phase distribution P _total (x, y) is extracted from comprehensive complex amplitude distribution E _total (x, y) as shown in the following equation (18) The position of the center of gravity G of each modified refractive index area 15b is determined based on the overall phase distribution _Ptotal (x, y).

In the fourth step S4, the center of gravity G of each modified refractive index area 15b is disposed on the straight line D, and the distance r (x, y) between the center of gravity G of each modified refractive index area 15b and the corresponding lattice point O _Is determined based on the overall phase distribution P _total (x, y).

In a square lattice of lattice spacing a, assuming that unit vectors of orthogonal coordinates are x and y, basic translation vectors a ₁ = ax and a ₂ = ay, and basic reciprocal lattice vectors b for translation vectors a ₁ and a _{2 1} = (2π / a) x, b ₂ = (2π / a) y. When the wave number vector of the waves present in the lattice is k = nb ₁ + mb ₂ (n, m is an arbitrary integer), the wave number k exists at the saddle point, but the size of the wave number vector is basically inverse If it is equal to the magnitude of the grating vector, a resonant mode (a standing wave in the XY plane) with a grating spacing a equal to the wavelength λ is obtained. In the present embodiment, oscillation in such a resonance mode (standing wave state) is obtained. At this time, in consideration of a TE mode in which an electric field is present in a plane parallel to the square lattice, there are four modes of the standing wave state having the same wavelength and the lattice spacing in this way due to the symmetry of the square lattice. In the present embodiment, a desired beam pattern can be obtained similarly in the case of oscillation in any of these four standing wave states.

  In the semiconductor light emitting element 1A, the standing wave in the phase modulation layer 15 is scattered by the different refractive index area 15b, and the wavefront obtained in the direction perpendicular to the plane is phase-modulated to obtain a desired beam pattern. For this reason, a desired beam pattern can be obtained without the polarizing plate. This beam pattern is not only a pair of single-peak beams (spots), but also, as described above, a character shape, two or more identically shaped spot groups, or a vector whose phase and intensity distribution are spatially nonuniform. It is also possible to use a beam or the like.

  The refractive index of the basic layer 15a is preferably 3.0 to 3.5, and the refractive index of the modified refractive index region 15b is preferably 1.0 to 3.4. Moreover, the average radius of each modified refractive index area | region 15b is 20 nm-120 nm, for example in the case of a 940 nm band. As the size of each modified refractive index area 15 b changes, the diffraction intensity in the Z-axis direction changes. The diffraction efficiency is proportional to the light coupling coefficient κ1 represented by a first-order coefficient when Fourier transforming the shape of the modified refractive index area 15b. The light coupling coefficient is described, for example, in K. Sakai et al., “Coupled-Wave Theory for Square-Lattice Photonic Crystal Lasers with TE Polarization, IEEE J. Q. E. 46, 788-795 (2010)”.

  The effects obtained by the design method of the phase modulation layer 15 according to the present embodiment described above will be described. In the present embodiment, the phase modulation layer 15 optically coupled to the active layer 12 includes the base layer 15a and a plurality of different refractive index areas 15b different in refractive index from the base layer 15a, and is virtually square. The center of gravity G of each of the modified refractive index areas 15b is disposed on a straight line D which passes through the grid point O of the grid and is inclined with respect to the X axis and the Y axis of the square grid. The distance r (x, y) between the center of gravity G of each modified refractive index area 15 b and the corresponding lattice point O is individually set according to the light image. In such a case, the phase of the beam changes according to the distance between the lattice point O and the center of gravity G. Therefore, only by changing the position of the center of gravity G, the phases of the beams emitted from the different refractive index areas 15b can be controlled, and the beam pattern formed as a whole can be made into a desired shape. That is, this semiconductor light emitting element 1A is an S-iPM laser, and according to such a structure, the conventional art in which the center of gravity G of each modified refractive index region 15b has a rotation angle around each lattice point O according to the light image. Similar to the structure, an optical image of an arbitrary shape can be output in a direction inclined with respect to the direction perpendicular to the major surface 10 a of the semiconductor substrate 10.

  Further, according to the study of the present inventor, in the conventional semiconductor light emitting device in which the modified refractive index region is rotated around the lattice point, both traveling waves traveling in opposite directions from each other due to the nature of the arrangement of the modified refractive index region. Is always included. That is, in the conventional method, in any of the four traveling waves AU, AD, AR, and AL that form the standing wave, the primary light and the −1st light appear in the same amount, and further the radius of the rotating circle ( Depending on the distance between the center of gravity of the modified refractive index region and the lattice point), zero-order light is generated. Therefore, it is difficult in principle to give a difference to each light quantity of the primary light and the -1 order light, and it is difficult to selectively reduce one of them. Therefore, it is difficult to reduce the light amount of the −1st order light relative to the light amount of the 1st order light.

Here, in the conventional method shown in FIG. 19 (a) in which the modified refractive index area 15b is rotated around the lattice point O, either the primary light or the −1st light can be selectively reduced. Explain the difficult reason. For a design phase φ (x, y) at a certain position, consider a traveling wave AU in the positive direction of the Y axis shown in FIG. 19B as an example of four traveling waves. At this time, from the geometrical relationship, for the traveling wave AU, the shift from the lattice point O is r · sinφ (x, y), so the phase difference is (2π / a) r · sinφ (x , Y). As a result, if the influence of the phase distribution Φ (x, y) on the traveling wave AU can be ignored because the influence of the size of the modified refractive index area 15 b is small, then Φ (x, y) = exp {j ( 2π / a) r · sin φ (x, y)} The contribution of the phase distribution Φ (x, y) to the 0th-order light and the ± 1st-order light is n = 0 and n = ± when expanded by exp {jnΦ (x, y)} (n: integer) It is given by 1 ingredient. By the way, the mathematical formula concerning the first kind Bessel function Jn (z) of order n

Can be used for series expansion of the phase distribution ((x, y), and each light quantity of zero-order light and ± first-order light can be described. At this time, the zero-order light component of the phase distribution ((x, y) is J ₀ (2πr / a), the first-order light component is J ₁ (2πr / a), and the _−1st- order light component is J ₋₁ (2πr / It is expressed as a). By the way, regarding the ± 1st-order Bessel function, since there is a relationship of J ₁ (x) = − J ₋₁ (x), the sizes of ± 1st-order light components become equal. Here, the traveling wave AU in the positive Y-axis direction is considered as an example of the four traveling waves, but the same relationship holds true for the other three waves (traveling waves AD, AR, AL), and ± 1st-order light The component sizes are equal. From the above discussion, in the conventional method in which the modified refractive index area 15b is rotated around the lattice point O, it is basically difficult to give a difference to the light quantity of ± 1st-order light components.

On the other hand, according to the phase modulation layer 15 of the present embodiment, for a single traveling wave, a difference occurs in the light amount of each of the first-order light and the -1st-order light. In the case of 135 °, 225 °, or 315 °, the ideal phase distribution is obtained as the shift amount _R0 approaches the upper limit value of the above-described equation (9). As a result, 0th-order light is reduced, and in each of the traveling waves AU, AD, AR, and AL, one of the 1st-order light and the -1st-order light is selectively reduced. Therefore, it is possible in principle to give a difference to the light quantity of the primary light and the -1 order light by selectively reducing any one of the traveling waves traveling in opposite directions to each other.

Here, in the method of the present embodiment shown in FIG. 20A in which the differential refractive index area 15b moves on the straight line D inclined with respect to the square lattice through the lattice point O, the first order light and the −1 order The reason why it is possible to selectively reduce any of the light will be explained. For a design phase φ (x, y) at a certain position, consider a Y-axis positive-going traveling wave AU shown in FIG. 20B as an example of four traveling waves. At this time, from the geometrical relationship, for the traveling wave AU, the shift from the lattice point O is r · sin θ · {φ (x, y) −φ ₀ } / π, so the phase difference is The relationship is 2π / a) r · sin θ · {φ (x, y) −φ ₀ } / π. Here, for the sake of simplicity, the inclination angle θ = 45 ° and the phase angle φ ₀ = 0 °. At this time, in the case where the phase distribution 異 (x, y) of the traveling wave AU can be ignored because the influence of the size of the modified refractive index region 15 b is small,

Given by The contribution of the phase distribution ((x, y) to the 0th-order light and the ± 1st-order light is n = 0 and n = ± when expanded by exp {n ((x, y)} (n: integer) It is given by 1 ingredient. By the way, a function f (z) represented by the following equation (21)

However,

Expand the Laurent series,

The following mathematical formula holds. Here, sinc (x) = x / sin (x). Using this mathematical formula, the phase distribution ((x, y) can be subjected to series expansion, and the respective light quantities of the zeroth order light and the ± first order lights can be described. At this time, it is noted that the magnitude of the zero-order light component of the phase distribution ((x, y) is noted that the absolute value of the exponent term exp {jπ (c−n)} of the mathematical formula (21) is 1.

The magnitude of the primary light component is

The magnitude of the -1st order light component is

It is expressed as And, in the equations (24) to (26),

In addition to the first-order light component, the zero-order light component and the -1st-order light component appear except in the case of However, the magnitudes of the ± 1st-order light components are not equal to one another.

  In the above description, the traveling wave AU in the Y-axis positive direction is considered as an example of the four traveling waves, but the same relationship holds true for the other three waves (traveling waves AD, AR, AL), A difference occurs in the size of the light component. From the above discussion, according to the method of the present embodiment in which the modified refractive index area 15b moves on the straight line D inclined from the square lattice through the lattice point O, the principle of giving a difference to the light quantity of ± 1st order light component It becomes possible. Therefore, it becomes possible in principle to reduce −1st-order light or 1st-order light and selectively extract only a desired light image (the first light image portion B1 or the second light image portion B2).

Therefore, in the design method of the present embodiment, the phase of the complex amplitude distribution E _R (x, y) or E _L (x, y) related to one of the traveling waves AR and AL in the second step S2 shown in FIG. As well as inverting the positive and negative of the term, it also inverts the positive and negative of the phase term of the complex amplitude distribution E _U (x, y) or E _D (x, y) related to one of the traveling waves AU, AD. If the beam pattern of -1st order light is mainly obtained before inverting the sign of the phase term, the beam pattern of 1st order light is mainly obtained after inverting the sign of the phase term. Conversely, when the beam pattern of primary light is mainly obtained before inverting the sign of the phase term, the beam pattern of −1st order light is mainly obtained after inverting the sign of the phase term. Therefore, according to the design method of the present embodiment, it is possible to mainly obtain beam patterns of primary light (or −1st order light) from all traveling waves AU, AD, AR, and AL. One of the -1st order light can be dimmed with respect to the other light.

In addition, as described above, in the second step S2, the complex amplitude distribution E _U (x, y), E _D (x, y), E _R (x, y) related to each traveling wave AU, AD, AR, and AL. And E _L (x, y) may be weighted. Thus, the complex amplitude distribution _{E U (x, y),} E D (x, y), E R (x, y), and E _L (x, y) overall complex amplitude by superimposing a distribution E _total When obtaining (x, y), the complex amplitude distribution E _U (x, y), E _D (x, y), E _R (x, y) with respect to the comprehensive complex amplitude distribution E _total (x, y) And E _L (x, y) can be arbitrarily adjusted according to the intensity ratio of each traveling wave AU, AD, AR, and AL, and a desired light image can be expressed more accurately. Also, when the intensity of the traveling waves AR, AL and the intensity of the traveling waves AU, AD are different from each other, as described above, the complex amplitude distributions E _R (x, y) and E _L (related to the traveling waves AR, AL) The weight m to be added to x, y) and the weight n to be added to complex amplitude distributions E _U (x, y) and E _D (x, y) related to the traveling waves AU and AD may be different from each other. Since the ratio of the intensity of the traveling waves AR and AL to the intensity of the traveling waves AU and AD changes according to the inclination angle θ of the straight line D with respect to the square lattice, as described above, the ratio of the weight m to the weight n is an inclination angle It may be determined based on θ.

  Further, as in the present embodiment, the inclination angle θ of the straight line D with respect to the square lattice may be constant in the phase modulation layer 15. This makes it possible to easily design the arrangement of the center of gravity G of the modified refractive index area 15b. Also, in this case, the inclination angle may be 45 °, 135 °, 225 ° or 315 °. Thereby, four fundamental waves (traveling waves AD, AR, AL) traveling along the square lattice can equally contribute to the light image. Further, when the inclination angle θ is 45 °, 135 °, 225 ° or 315 °, the direction of the electromagnetic field on the straight line D is aligned in one direction by selecting an appropriate band edge mode, You can get it. As an example of such a mode, C. Peng, et al., “Coupled-wave analysis for photonic-crystal surface-emitting laserson air holes with arbitrary sidewalls,” Optics Express Vol. 19, No. 24, pp. 24672-24686 (2011). There are modes A and B shown in FIG. In the case where the inclination angle θ is 0 °, 90 °, 180 ° or 270 °, a pair of the progressions in the Y-axis direction or the X-axis direction out of the four traveling waves AU, AD, AR, and AL. Since the wave does not contribute to the primary light (signal light), it is difficult to improve the efficiency of the signal light.

  Also, as in the present embodiment, the light emitting unit may be the active layer 12 provided on the semiconductor substrate 10. Thereby, the light emitting portion and the phase modulation layer 15 can be easily optically coupled.

(First modification)
21 and 22 are plan views showing examples of the shape of the modified refractive index area 15b in the XY plane. In the above embodiment, an example in which the shape of the modified refractive index area 15 b in the XY plane is circular is shown. However, the modified refractive index area 15b may have a shape other than a circular shape. For example, the shape of the modified refractive index area 15b in the XY plane may have mirror symmetry (linear symmetry). Here, mirror symmetry (linear symmetry) refers to the plane shape of the modified refractive index region 15b located on one side of a straight line along the XY plane and the other side of the straight line. It means that the plane shapes of the different refractive index regions 15b located can be mirror-symmetrical (axisymmetric) with each other. As a shape having mirror symmetry (line symmetry), for example, a perfect circle shown in FIG. 21 (a), a square shown in FIG. 21 (b), a regular hexagon shown in FIG. 21 (c), The regular octagon shown in FIG. 21 (d), the regular hexagon shown in FIG. 21 (e), the rectangle shown in FIG. 21 (f), and the ellipse shown in FIG. 21 (g), etc. It can be mentioned. Thus, the shape of the modified refractive index area 15b in the XY plane has mirror symmetry (linear symmetry). In this case, since each unit formation region R of the virtual square lattice of the phase modulation layer 15 has a simple shape, the direction and position of the gravity center G of the corresponding different refractive index region 15b from the lattice point O are made highly accurate. Because it can be determined, patterning with high accuracy is possible.

  Further, the shape of the modified refractive index area 15 b in the XY plane may be a shape that does not have rotational symmetry of 180 °. As such a shape, for example, an equilateral triangle shown in FIG. 22 (a), a right isosceles triangle shown in FIG. 22 (b), a part of two circles or an ellipse shown in FIG. 22 (c) Shape in which the dimension in the short axis direction near one end along the major axis of the ellipse shown in FIG. 22 (d) is smaller than the dimension in the short axis direction near the other end 22 (e), the one end along the long axis of the ellipse shown in FIG. 22 (e) is deformed to a pointed end projecting along the long axis (tears), 22 (h), the one side of the rectangle shown in FIG. 22 (g) is indented in the form of a triangle, and the opposite side is pointed in the form of a triangle (arrow shape) in FIG. 22 (h). The trapezoidal shape shown, the pentagonal shape shown in FIG. 22 (i), and the form in which portions of two rectangles shown in FIG. 22 (j) overlap with each other And Figure 22 (k) at the indicated two shapes with no rectangular portion to each other overlap and mirror symmetry was, and the like. Thus, higher light output can be obtained because the shape of the modified refractive index area 15 b in the XY plane does not have the rotational symmetry of 180 °.

(2nd modification)
FIG. 23 is a plan view of a phase modulation layer 15A according to a second modification of the embodiment. In addition to the configuration (FIG. 4) of the phase modulation layer 15 of the above-described embodiment, the phase modulation layer 15A of this modification further includes a plurality of different refractive index areas 15c different from the plurality of different refractive index areas 15b. Each modified refractive index region 15c is formed of a second refractive index medium having a refractive index different from that of the first refractive index medium of the base layer 15a. The modified refractive index region 15c may be a hole as in the modified refractive index region 15b, and the compound semiconductor may be embedded in the hole. Here, as shown in FIG. 24, in the present modification, a center of gravity G obtained by combining the center of gravity of each modified refractive index area 15 b and the center of gravity of each modified refractive index area 15 c is disposed on a straight line D. . Note that any of the different refractive index regions 15b and 15c is included in the range of the unit configuration region R that constitutes a virtual square lattice. The unit configuration region R is a region surrounded by straight lines bisecting between lattice points of a virtual square lattice. The distance r (x, y) between the center of gravity G and the corresponding lattice point O of each unit constituent region R is individually set for each of the different refractive index regions 15b according to the desired light image. The distribution of the distance r (x, y) is determined from the complex amplitude distribution obtained by Fourier transforming a desired light image, from which the phase distribution is extracted. That is, when the phase P (x, y) at a certain coordinate (x, y) is P ₀ , the distance r (x, y) is set to 0, and the phase P (x, y) is π + P ₀ In some cases, the distance r (x, y) is set to the maximum value R ₀ , and when the phase P (x, y) is −π + P ₀ , the distance r (x, y) is made the minimum value −R ₀ Set Then, for the intermediate phase P (x, y), the distance r (x, y) is set such that r (x, y) = {P (x, y) -P ₀ } × R ₀ / π Take). The initial phase P ₀ can be set arbitrarily.

  The modified refractive index regions 15 c are provided in one-to-one correspondence with the modified refractive index regions 15 b respectively. The planar shape of the modified refractive index area 15c is, for example, circular, but may have various shapes as in the modified refractive index area 15b. FIGS. 25 (a) to 25 (k) show examples of the shapes and relative relationships in the XY plane of the modified refractive index regions 15b and 15c. 25 (a) and 25 (b) show an embodiment in which the modified refractive index regions 15b and 15c have figures of the same shape. FIGS. 25 (c) and 25 (d) show a form in which the modified refractive index regions 15b and 15c have figures of the same shape, and parts of each other overlap. FIG. 25E shows a form in which the modified refractive index regions 15b and 15c have the same shape and the distance between the centers of gravity of the modified refractive index regions 15b and 15c is arbitrarily set for each lattice point. FIG. 25F shows a form in which the modified refractive index regions 15b and 15c have figures of different shapes. FIG. 25 (g) shows a form in which the modified refractive index areas 15b and 15c have figures of different shapes, and the distance between the centers of gravity of the modified refractive index areas 15b and 15c is arbitrarily set for each lattice point.

  Further, as shown in FIG. 25H to FIG. 25K, the modified refractive index region 15b may be configured to include two regions 15b1 and 15b2 which are separated from each other. The distance between the center of gravity of the regions 15b1 and 15b2 (corresponding to the center of gravity of the single modified refractive index region 15b) and the center of gravity of the modified refractive index region 15c may be set arbitrarily for each lattice point. Further, in this case, as shown in FIG. 25H, the regions 15b1 and 15b2 and the modified refractive index region 15c may have figures of the same shape. Alternatively, as shown in FIG. 25 (i), two figures of the regions 15b1 and 15b2 and the modified refractive index region 15c may be different from each other. Further, as shown in FIG. 25 (j), in addition to the angle of the straight line connecting the regions 15b1 and 15b2 to the X axis, the angle of the modified refractive index region 15c to the X axis is arbitrarily set for each grid point It is also good. Further, as shown in FIG. 25 (k), while the regions 15b1 and 15b2 and the modified refractive index region 15c maintain the same relative angle, the angle between the X axis of the straight line connecting the regions 15b1 and 15b2 is every grid point It may be set arbitrarily.

  The shapes of the modified refractive index regions in the XY plane may be identical to each other between the lattice points. That is, the different refractive index regions may have the same figure at all grid points, and may be able to overlap each other between the grid points by translational operation, or translational operation and rotational operation. In that case, it is possible to suppress the generation of noise light and zero-order light that becomes noise in the beam pattern. Alternatively, the shapes of the modified refractive index regions in the XY plane may not necessarily be the same between the lattice points, and for example, as shown in FIG. 26, the shapes may be different between adjacent lattice points. In any of FIGS. 21 to 26, the center of the straight line D passing through each lattice point may be set to coincide with the lattice point O.

  For example, even with the configuration of the phase modulation layer as in this modification, the effects of the above embodiment can be suitably achieved.

(Third modification)
FIG. 27 is a diagram showing a configuration of a light emitting device 1B according to a third modification. The light emitting device 1B includes a support substrate 6, a plurality of semiconductor light emitting devices 1A arranged in a one-dimensional or two-dimensional manner on the support substrate 6, and a drive circuit 4 for individually driving the plurality of semiconductor light emitting devices 1A. Have. The configuration of each semiconductor light emitting element 1A is the same as that of the above embodiment. However, the plurality of semiconductor light emitting elements 1A include a laser element that outputs an optical image in the red wavelength range, a laser element that outputs an optical image in the blue wavelength range, and a laser element that outputs an optical image in the green wavelength range. It may be included. The laser element that outputs an optical image in the red wavelength range is made of, for example, a GaAs-based semiconductor. The laser element that outputs an optical image in the blue wavelength range and the laser element that outputs an optical image in the green wavelength range are made of, for example, a nitride semiconductor. The drive circuit 4 is provided on the back surface or in the inside of the support substrate 6 and drives each of the semiconductor light emitting elements 1A individually. The drive circuit 4 supplies drive current to each of the semiconductor light emitting elements 1A according to an instruction from the control circuit 7.

  A module in which semiconductor light emitting elements corresponding to a plurality of patterns are arranged in advance by providing a plurality of individually driven semiconductor light emitting elements 1A as in this modification and extracting a desired light image from each semiconductor light emitting element 1A. By suitably driving necessary elements, a head-up display can be suitably realized. In addition, the plurality of semiconductor light emitting elements 1A include a laser element that outputs an optical image in the red wavelength range, a laser element that outputs an optical image in the blue wavelength range, and a laser element that outputs an optical image in the green wavelength range. Thus, a color head-up display or the like can be suitably realized.

Second Embodiment
FIG. 28 is a view showing a cross-sectional structure of a semiconductor light emitting device 1C according to the second embodiment. The semiconductor light emitting element 1C is a laser light source that forms a standing wave in the XY in-plane direction and outputs a phase-controlled plane wave in the Z direction, and is the main surface of the semiconductor substrate 10 as in the first embodiment. A two-dimensional light image of an arbitrary shape including a direction perpendicular to 10 a and a direction inclined with respect to this is output. However, although the semiconductor light emitting element 1A of the first embodiment outputs the light image transmitted through the semiconductor substrate 10 from the back surface, the semiconductor light emitting element 1C of this embodiment is from the surface on the cladding layer 13 side with respect to the active layer 12. Output a light image.

  The semiconductor light emitting element 1 </ b> C includes a cladding layer 11, an active layer 12, a cladding layer 13, a contact layer 14, a phase modulation layer 15, a light reflection layer 20, and a current confinement layer 21. The cladding layer 11 is provided on the semiconductor substrate 10. The active layer 12 is provided on the cladding layer 11. The cladding layer 13 is provided on the active layer 12. The contact layer 14 is provided on the cladding layer 13. The phase modulation layer 15 is provided between the active layer 12 and the cladding layer 13. The light reflecting layer 20 is provided between the active layer 12 and the cladding layer 11. The current confinement layer 21 is provided in the cladding layer 13. The configuration (preferred material, band gap, refractive index, etc.) of each layer 11 to 15 is the same as that of the first embodiment. The light reflection layer 20 may be omitted if light absorption by the semiconductor substrate 10 is not a problem.

  The structure of the phase modulation layer 15 is similar to the structure (see FIGS. 4 and 5) of the phase modulation layer 15 described in the first embodiment. If necessary, a light guide layer may be provided between at least one of the active layer 12 and the cladding layer 13 and between the active layer 12 and the cladding layer 11. As shown in FIG. 29, a phase modulation layer 15 may be provided between the cladding layer 11 and the active layer 12. The light guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

  The semiconductor light emitting element 1 </ b> C further includes an electrode 23 provided on the contact layer 14 and an electrode 22 provided on the back surface 10 b of the semiconductor substrate 10. The electrode 23 is in ohmic contact with the contact layer 14, and the electrode 22 is in ohmic contact with the semiconductor substrate 10. FIG. 30 is a plan view of the semiconductor light emitting element 1C as viewed from the electrode 23 side (surface side). As shown in FIG. 30, the electrode 23 has a planar shape such as a frame shape (annular shape), and has an opening 23a. In addition, although the square frame-shaped electrode 23 is illustrated by FIG. 30, the planar shape of the electrode 23 can be various shapes, such as annular | circular shape, for example. The shape of the electrode 22 indicated by a hidden line in FIG. 30 is similar to the shape of the opening 23a of the electrode 23, and is, for example, square or circular. The inner diameter of the opening 23a of the electrode 23 (length of one side when the shape of the opening 23a is a square) is, for example, 20 μm to 50 μm.

  Refer to FIG. 28 again. The contact layer 14 of the present embodiment has a planar shape similar to that of the electrode 23. That is, the central portion of the contact layer 14 is removed by etching to form an opening 14a, and the contact layer 14 has a planar shape such as a frame shape (annular shape). The light emitted from the semiconductor light emitting element 1 </ b> C passes through the opening 14 a of the contact layer 14 and the opening 23 a of the electrode 23. When light passes through the opening 14 a of the contact layer 14, light absorption in the contact layer 14 can be avoided and light emission efficiency can be enhanced. However, when light absorption in the contact layer 14 is acceptable, the contact layer 14 may cover the entire surface of the cladding layer 13 without the opening 14 a. When light passes through the opening 23 a of the electrode 23, light can be suitably emitted from the surface side of the semiconductor light emitting element 1 C without being blocked by the electrode 23.

  The surface of the cladding layer 13 exposed from the opening 14 a of the contact layer 14 (or the surface of the contact layer 14 when the opening 14 a is not provided) is covered with the anti-reflection film 25. An antireflective film 25 may be provided on the outside of the contact layer 14. Further, a portion other than the electrode 22 on the back surface 10 b of the semiconductor substrate 10 is covered with a protective film 24. The material of the protective film 24 is the same as that of the protective film 18 of the first embodiment. The material of the antireflective film 25 is the same as that of the antireflective film 19 of the first embodiment.

  The light reflection layer 20 reflects the light generated in the active layer 12 toward the surface side of the semiconductor light emitting element 1C. The light reflection layer 20 is formed of, for example, a DBR (Disrtibuted Bragg Reflector) layer in which a plurality of layers having different refractive indexes are alternately stacked. Although the light reflection layer 20 of the present embodiment is provided between the active layer 12 and the cladding layer 11, the light reflection layer 20 may be provided between the cladding layer 11 and the semiconductor substrate 10. Alternatively, the light reflecting layer 20 may be provided inside the cladding layer 11.

The same conductivity type as the semiconductor substrate 10 is given to the cladding layer 11 and the light reflecting layer 20, and the opposite conductivity type to the semiconductor substrate 10 is given to the cladding layer 13 and the contact layer 14. In one example, the semiconductor substrate 10, the cladding layer 11, and the light reflecting layer 20 are n-type, and the cladding layer 13 and the contact layer 14 are p-type. The phase modulation layer 15 has the same conductivity type as the semiconductor substrate 10 when provided between the active layer 12 and the cladding layer 11, and is semiconductor when being provided between the active layer 12 and the cladding layer 13. It has a conductivity type opposite to that of the substrate 10. The impurity concentration is, for example, 1 × 10 ¹⁷ to 1 × 10 ²¹ / cm ³ . The active layer 12 is intrinsic (i-type) to which no impurity is intentionally added, and the impurity concentration is 1 × 10 ¹⁵ / cm ³ or less. The impurity concentration of the phase modulation layer 15 may be intrinsic (i-type) when it is necessary to suppress the influence of loss due to light absorption through the impurity level.

The current confinement layer 21 has a structure in which current does not easily pass (or does not pass), and has an opening 21 a in the center. As shown in FIG. 30, the planar shape of the opening 21a is similar to the shape of the opening 23a of the electrode 23, and is, for example, square or circular. The current confinement layer 21 is, for example, an Al oxide layer formed by oxidizing a layer containing Al at a high concentration. Alternatively, the current confinement layer 21 may be a layer formed by injecting protons (H ⁺ ) into the cladding layer 13. Alternatively, the current confinement layer 21 may have a reverse pn junction structure in which a semiconductor layer of the opposite conductivity type to the semiconductor substrate 10 and a semiconductor layer of the same conductivity type as the semiconductor substrate 10 are sequentially stacked.

  An example of dimensions of the semiconductor light emitting device 1C of the present embodiment will be described. The inner diameter (length of one side when the shape of the opening 23a is square) La of the opening 23a of the electrode 23 is in the range of 5 μm to 100 μm, and is, for example, 50 μm. The thickness ta of the phase modulation layer 15 is, for example, in the range of 100 nm to 400 nm, and is, for example, 200 nm. The distance tb between the current confinement layer 21 and the contact layer 14 is in the range of 2 μm to 50 μm. In other words, the interval tb is in the range of 0.02 La to 10 La (e.g., 0.1 La) and in the range of 5.0 ta to 500 ta (e.g., 25 ta). Further, the thickness tc of the cladding layer 13 is larger than the interval tb and is in the range of 2 μm to 50 μm. In other words, the thickness tc is in the range of 0.02 La to 10 La (e.g., 0.1 La) and in the range of 5.0 ta to 500 ta (e.g., 25 ta). The thickness td of the cladding layer 11 is in the range of 1.0 μm to 3.0 μm (for example, 2.0 μm).

  When a drive current is supplied between the electrodes 22 and 23, the drive current reaches the active layer 12. At this time, the current flowing between the electrode 23 and the active layer 12 is sufficiently diffused in the thick cladding layer 13 and passes through the opening 21 a of the current confinement layer 21 so that the central portion of the active layer 12 is uniform. Can spread. Then, recombination of electrons and holes occurs in the active layer 12, and the active layer 12 emits light. The electrons and holes that contribute to the light emission, and the generated light are efficiently confined between the cladding layer 11 and the cladding layer 13. The laser light emitted from the active layer 12 enters the inside of the phase modulation layer 15 to form a predetermined mode according to the lattice structure inside the phase modulation layer 15. The laser light emitted from the inside of the phase modulation layer 15 is reflected by the light reflection layer 20, and emitted from the cladding layer 13 to the outside through the opening 14a and the opening 23a.

(Specific example of the first embodiment)
The inventors examined the conditions that do not generate high-order modes with respect to the thickness and refractive index of the optical waveguide layer including the active layer, and the thickness and refractive index of the contact layer. The examination process and the result are explained below.

  First, the specific structure of the semiconductor light emitting device 1A to be studied in this specific example will be described. FIG. 31 is a table showing a layer structure when the semiconductor light emitting element 1A is made of a GaAs based compound semiconductor (emission wavelength 940 nm band). The table of FIG. 31 shows the conductivity type, composition, layer thickness, and refractive index of each layer. The layer number 1 indicates the contact layer 14, the layer number 2 indicates the upper cladding layer 13, the layer number 3 indicates the phase modulation layer 15, the layer number 4 indicates the light guide layer and the active layer 12, and the layer number 5 indicates the lower cladding layer 11. . FIG. 32 shows the refractive index distribution G21a and the mode distribution G21b of the semiconductor light emitting device 1A having the layer structure shown in FIG. The horizontal axis represents the position in the stacking direction (range: 2.5 μm). At this time, it can be seen that only the fundamental mode is generated, and the higher order mode is suppressed.

  FIG. 33 is a table showing a layer structure when the semiconductor light emitting element 1A is made of an InP-based compound semiconductor (emission wavelength 1300 nm band). The layer number 1 indicates the contact layer 14, the layer number 2 indicates the upper cladding layer 13, the layer number 3 indicates the phase modulation layer 15, the layer number 4 indicates the light guide layer and the active layer 12, and the layer number 5 indicates the lower cladding layer 11. FIG. 34 shows the refractive index distribution G22a and the mode distribution G22b of the semiconductor light emitting device 1A provided with the layer structure shown in FIG. The horizontal axis represents the position in the stacking direction (range: 2.5 μm). At this time, it can be seen that only the fundamental mode is generated, and the higher order mode is suppressed.

  FIG. 35 is a table showing a layer structure when the semiconductor light emitting element 1A is made of a nitride compound semiconductor (emission wavelength 405 nm band). Layer No. 1 is contact layer 14, layer No. 2 is upper clad layer 13, layer No. 3 is carrier barrier layer, layer No. 4 is active layer 12, layer No. 5 is optical guide layer, layer No. 6 is phase modulation layer 15, Layer number 7 indicates the lower cladding layer 11. FIG. 36 shows the refractive index distribution G23a and the mode distribution G23b of the semiconductor light emitting device 1A having the layer structure shown in FIG. The horizontal axis represents the position in the stacking direction (range: 2.5 μm). At this time, it can be seen that only the fundamental mode is generated, and the higher order mode is suppressed.

  In each of the above structures, the filling factor (FF) of the phase modulation layer 15 is 15%. The filling factor is the ratio of the area of the modified refractive index area 15 b occupied in one unit constituent area R.

  Next, the preconditions for the study will be described. In the following examination, TE mode was assumed. That is, leak mode and TM mode are not considered. In addition, the lower cladding layer 11 is sufficiently thick, and the influence of the semiconductor substrate 10 can be ignored. Further, the refractive index of the upper cladding layer 13 is equal to or less than the refractive index of the lower cladding layer 11. And, the active layer 12 (MQW layer) and the light guide layer are regarded as one optical waveguide layer (core layer) having an average dielectric constant and a total film thickness unless otherwise described. Furthermore, the dielectric constant of the phase modulation layer 15 is an average dielectric constant based on the filling factor.

Formulas for calculating the average refractive index and the film thickness of the optical waveguide layer including the active layer 12 and the light guide layer are as follows. That is, ε _core is the average dielectric constant of the optical waveguide layer, which is defined by the following equation (28). ε _i is the dielectric constant of each layer, d _i is the thickness of each layer, and n _i is the refractive index of each layer. n _core is an average refractive index of the optical waveguide layer, which is defined by the following equation (29). d _core is a film thickness of the optical waveguide layer, which is defined by the following equation (30).

Further, the formula for calculating the average refractive index of the phase modulation layer 15 is as follows. That is, n _PM is an average refractive index of the phase modulation layer 15, and is defined by the following equation (31). ε _PM is the dielectric constant of the phase modulation layer 15, n ₁ is the refractive index of the first refractive index medium, n ₂ is the refractive index of the second refractive index medium, and FF is the filling factor.

  In the following discussion, an approximation of the waveguide structure was made with a five or six layer slab waveguide. FIGS. 37 (a) and 37 (b) are a cross-sectional view and a refractive index profile for describing the case where the waveguide structure is approximated by six slab waveguides. FIG. 38A and FIG. 38B are a cross-sectional view and a refractive index distribution for describing the case where the waveguide structure is approximated by a five-layer slab waveguide. As shown in FIGS. 37 (a) and 37 (b), when the refractive index of the phase modulation layer 15 is smaller than the refractive index of the lower cladding layer 11, the phase modulation layer 15 has no waveguiding function, An approximation was made for a six-layer slab waveguide. That is, the optical waveguide layer has a structure that includes the active layer 12 and the light guide layer, but does not include the lower cladding layer 11, the upper cladding layer 13, and the phase modulation layer 15. Such approximation can be applied to, for example, the structures shown in FIGS. 33 and 35 (in this example, InP-based compound semiconductors or nitride-based compound semiconductors).

  Also, as shown in FIGS. 38A and 38B, when the refractive index of the phase modulation layer 15 is equal to or higher than the refractive index of the lower cladding layer 11, the phase modulation layer 15 has a waveguiding function. So an approximation was made for a five-layer slab waveguide. That is, the optical waveguide layer has a structure that includes the phase modulation layer 15 and the active layer 12 but does not include the lower cladding layer 11 and the upper cladding layer 13. Such an approximation can be applied to, for example, the structure shown in FIG. 19 (in this embodiment, a GaAs based compound semiconductor).

  Furthermore, in order to further simplify the calculation, the calculation range is limited to the peripheral portion of each of the optical waveguide layer and the contact layer whose refractive index is higher than the equivalent refractive index of the semiconductor light emitting element 1A. That is, the optical waveguide layer and upper and lower layers adjacent to the optical waveguide layer define a three-layer slab structure of the optical waveguide layer, and the contact layer 14 and the adjacent upper and lower layers form a three-layer slab structure of the contact layer 14 It is prescribed.

  39 (a) and 39 (b) are cross-sectional views for explaining a three-layer slab structure related to the optical waveguide layer in six slab type waveguides (see FIGS. 37 (a) and 37 (b)) Figure and refractive index distribution. In this case, the waveguide mode of the optical waveguide layer is calculated based on the refractive index distribution indicated by the solid line in the refractive index distribution of FIG. 39 (b). FIGS. 40 (a) and 40 (b) illustrate the three-layer slab structure of the contact layer 14 in a six-layer slab waveguide (see FIGS. 37 (a) and 37 (b)). And a refractive index distribution. In this case, the waveguide mode of the contact layer 14 is calculated based on the refractive index distribution shown by the solid line in FIG. 40 (b).

  41 (a) and 41 (b) are a cross-sectional view and a refractive index distribution for describing a three-layer slab structure related to an optical waveguide layer in a five-layer slab waveguide (see FIG. 38). In this case, the waveguide mode of the optical waveguide layer is calculated based on the refractive index distribution indicated by the solid line in FIG. 41 (b). FIGS. 42A and 42B are a cross-sectional view and a refractive index distribution for describing a three-layer slab structure related to the contact layer 14 in a five-layer slab waveguide (see FIG. 38). . In this case, the waveguide mode of the contact layer 14 is calculated based on the refractive index distribution shown by the solid line in FIG. 42 (b).

  The refractive index of the lower cladding layer 11 is equivalent to the equivalent refraction of the semiconductor light emitting element 1A so that the waveguide mode does not leak to the semiconductor substrate 10 through the lower cladding layer 11 in the approximation by the above-described three-layer slab structure. It needs to be below the rate.

Here, an analysis formula of the three-layer slab structure will be described. 43 (a) and 43 (b) show a three-layer slab structure 30 composed of the lower cladding layer 11, the optical waveguide layer 31, and the upper cladding layer 13 and the refractive index distribution thereof. Here, the refractive index of the lower clad layer 11 and n _2, the refractive index of the optical waveguide layer 31 is n _1, the refractive index of the upper cladding layer 13 and n _3. When the standard influencing for good waveguide width V ₁ of the optical waveguide layer 31 is defined by the above formula (1), as long as it is within the range of solutions of standard influencing for good waveguide width V ₁ is the only one guided mode Is the basic mode only. However, when the waveguide modes of the above-mentioned five-layer slab structure and six-layer slab structure are examined by the analysis formula of the three-layer slab structure, the waveguide mode does not have to leak to the lower cladding layer 11. The conditions shown in) also need to be satisfied at the same time.

As for the contact layer 14, in FIG. 43 (a) and FIG. 43 (b), the lower cladding layer 11 is replaced with the upper cladding layer 13, the optical waveguide layer 31 is replaced with the contact layer 14, and the upper cladding layer 13 is replaced with the air layer. It is good. Then, assuming that the refractive index of the contact layer 14 is n ₄ and the refractive index of the air layer is n ₅ , the above equation (5) regarding the normalized waveguide width V ₂ of the contact layer 14 is obtained. Then, within the range in which there is no solution of the normalized waveguide width V ₂ , no waveguide mode exists in the contact layer 14. However, when the waveguide modes of the above-mentioned five-layer slab structure and six-layer slab structure are examined by the analysis formula of the three-layer slab structure, the waveguide mode does not have to leak to the lower cladding layer 11. The conditions shown in) also need to be satisfied at the same time.

  By analyzing the waveguide mode generated by changing the film thickness of the upper cladding layer 13, it was confirmed that the film thickness of the upper cladding layer 13 does not affect the waveguide mode.

(When the semiconductor light emitting element 1A is made of a GaAs compound semiconductor)
FIG. 44 is a table showing an example of a five-layer slab structure in the case where the semiconductor light emitting element 1A is made of a GaAs based compound semiconductor. The range of the film thickness of the optical waveguide layer (layer No. 4) and the contact layer (layer No. 2) in this five-layer slab structure can be obtained by the following calculation.

FIG. 45 (a) is a table showing the refractive indices n ₁ , n ₂ and n ₃ , the asymmetry parameter a ′, and the refractive index n _clad of the lower cladding layer 11 used in the calculation. In this case, the equation standards influencing for good waveguide width V ₁ of the optical waveguide layer, indicated by (1) and (2), the relationship between the normalized propagation coefficients b, is shown in Figure 46. In FIG. 46, graphs G31a to G31f indicate the cases of mode orders N = 0 to 5, respectively. In this graph, the waveguide mode is only the fundamental mode (i.e. N = 0), the solution of standard influencing for good waveguide width V ₁ is a one becomes a range, which is inside the range H _1. The range H ₁ has a lower limit value of the normalized waveguide width V ₁ corresponding to N = 0 when the normalized propagation coefficient b is 0, and N = 1 when the normalized propagation coefficient b is 0. The upper limit value is a value corresponding to the normalized waveguide width V ₁ corresponding to FIG. 45 (b) is a table showing calculation results of such lower limit value and upper limit value.

FIG. 47 (a) is a table showing the refractive indices n ₄ , n ₅ , and n ₆ , the asymmetry parameter a ′, and the refractive index n _clad of the lower cladding layer 11 used in the calculation. In this case, the above equation (5) and standards influencing for good waveguide width V ₂ of the contact layer 14 as indicated by the equation (6), the relationship between the normalized propagation coefficients b, is shown in Figure 48. In FIG. 48, graphs G32a to G32f indicate the cases of mode orders N = 0 to 5, respectively. In this graph, the guided mode due to the contact layer 14 does not occur, the waveguide mode of the semiconductor light emitting device 1A is only the fundamental mode of the optical waveguide layer is no solution standards influencing for good waveguide width V ₂ range a is a inner range H _2. The range H ₂ has a lower limit value of 0, and a normalized waveguide width V ₂ corresponding to N = 0 when the normalized propagation coefficient b is a value b ₁ corresponding to the refractive index of the lower cladding layer 11 It is a range to be an upper limit value. FIG. 47 (b) is a table showing the calculation results of such upper limit value.

  FIG. 49 shows the refractive index distribution G24a and the mode distribution G24b of the semiconductor light emitting device 1A having the layer structure shown in FIG. It can be seen that only the fundamental mode is prominent and the higher order modes are suppressed.

(When the semiconductor light emitting element 1A is made of an InP-based compound semiconductor)
FIG. 50 is a table showing an example of a six-layer slab structure when the semiconductor light emitting element 1A is made of an InP-based compound semiconductor. The range of the film thickness of the optical waveguide layer (layer No. 5) and the contact layer (layer No. 2) in this six-layer slab structure can be obtained by the following calculation.

FIG. 51 (a) is a table showing the refractive indices n ₁ , n ₂ and n ₃ , the asymmetry parameter a ′, and the refractive index n _clad of the lower cladding layer 11 used in the calculation. In this case, the equation standards influencing for good waveguide width V ₁ of the optical waveguide layer, indicated by (1) and (2), the relationship between the normalized propagation coefficients b, is shown in Figure 52. In FIG. 52, graphs G33a to G33f indicate the cases of mode orders N = 0 to 5, respectively. In this graph, the waveguide mode is only the fundamental mode (i.e. N = 0), the solution of standard influencing for good waveguide width V ₁ is a one becomes a range, which is inside the range H _1. The definition of the range H ₁ is the same as in the case of GaAs-based compound semiconductor described above. FIG. 51 (b) is a table showing calculation results of the lower limit value and the upper limit value.

FIG. 53 (a) is a table showing the refractive indices n ₄ , n ₅ and n ₆ , the asymmetry parameter a ′, and the refractive index n _clad of the lower cladding layer 11 used in the calculation. In this case, the above equation (5) and standards influencing for good waveguide width V ₂ of the contact layer 14 as indicated by the equation (6), the relationship between the normalized propagation factor b, so that the graph shown in FIG. 54. In FIG. 54, graphs G34a to G34f indicate the cases of mode orders N = 0 to 5, respectively. In this graph, the guided mode due to the contact layer 14 does not occur, the waveguide mode of the semiconductor light emitting device 1A is only the fundamental mode of the optical waveguide layer is no solution standards influencing for good waveguide width V ₂ range a is a inner range H _2. Defining the range H ₂ is the same as in the case of GaAs-based compound semiconductor described above. FIG. 53 (b) is a table showing the calculation results of such upper limit value.

  FIG. 55 shows the refractive index distribution G25a and the mode distribution G25b of the semiconductor light emitting device 1A provided with the layer structure shown in FIG. It can be seen that only the fundamental mode is prominent, and higher order modes are suppressed.

(When the semiconductor light emitting element 1A is made of a nitride compound semiconductor)
FIG. 56 is a table showing an example of a six-layer slab structure when the semiconductor light emitting element 1A is made of a nitride compound semiconductor. The range of the film thickness of the optical waveguide layer (layer No. 4) and the contact layer (layer No. 2) in this six-layer slab structure can be obtained by the following calculation.

FIG. 57 (a) is a table showing the refractive indexes n ₁ , n ₂ and n ₃ , the asymmetry parameter a ′, and the refractive index n _clad of the lower cladding layer 11 used in the calculation. In this case, the equation standards influencing for good waveguide width V ₁ of the optical waveguide layer, indicated by (1) and (2), the relationship between the normalized propagation coefficients b, is shown in Figure 58. In FIG. 58, graphs G35a to G35f indicate the cases of mode orders N = 0 to 5, respectively. In this graph, the waveguide mode is only the fundamental mode (i.e. N = 0), the solution of standard influencing for good waveguide width V ₁ is a one becomes a range, which is inside the range H _1. When the normalized propagation coefficient b is the value b ₁ , the range H ₁ has the lower limit value of the normalized waveguide width V ₁ corresponding to N = 0 when the normalized propagation coefficient b is the value b _1. The upper limit value is a value of the normalized waveguide width V ₁ corresponding to N = 1 of FIG. 57 (b) is a table showing calculation results of the lower limit value and the upper limit value.

FIG. 59 (a) is a table showing the refractive indices n ₄ , n ₅ and n ₆ , the asymmetry parameter a ′, and the refractive index n _clad of the lower cladding layer 11 used in the calculation. In this case, the above equation (5) and standards influencing for good waveguide width V ₂ of the contact layer 14 as indicated by the equation (6), the relationship between the normalized propagation coefficients b, is shown in Figure 60. In FIG. 60, graphs G36a to G36f indicate the cases of mode orders N = 0 to 5, respectively. In this graph, the guided mode due to the contact layer 14 does not occur, the waveguide mode of the semiconductor light emitting device 1A is only the fundamental mode of the optical waveguide layer is no solution standards influencing for good waveguide width V ₂ range a is a inner range H _2. Defining the range H ₂ is the same as in the case of GaAs-based compound semiconductor described above. FIG. 59 (b) is a table showing the calculation results of such upper limit value.

  FIG. 61 shows the refractive index distribution G26a and the mode distribution G26b of the semiconductor light emitting device 1A provided with the layer structure shown in FIG. It can be seen that only the fundamental mode is prominent, and higher order modes are suppressed.

  The light emitting device according to the present invention is not limited to the embodiment described above, and various other modifications are possible. For example, in the above embodiment, the laser devices made of GaAs, InP, and nitride (especially GaN) compound semiconductors are exemplified, but the present invention is applied to laser devices made of various other semiconductor materials. it can.

  In the above embodiment, an example in which the active layer 12 provided on the semiconductor substrate 10 common to the phase modulation layer 15 is used as the light emitting portion has been described, but in the present invention, the light emitting portion is separated from the semiconductor substrate 10 It may be provided. As long as the light emitting unit is optically coupled to the phase modulation layer and supplies light to the phase modulation layer, the same effect as that of the above embodiment can be suitably achieved even with such a configuration.

  DESCRIPTION OF SYMBOLS 1A ... Semiconductor light emitting element, 1B ... Light emitting device, 1C ... Semiconductor light emitting element, 4 ... Drive circuit, 6 ... Support substrate, 7 ... Control circuit, 10 ... Semiconductor substrate, 10a ... Principal surface, 10b ... Back surface, 11, 13 ... Cladding layer 12 Active layer 14 Contact layer 14a Opening 14 Phase modulation layer 15a Basic layer 15b, 15c Differential refractive index region 16, 17, 22, 23 Electrode 17a, 23a ... opening 18 protective film 19 antireflective film 20 light reflection layer 21 current constricting layer 21a opening 24 protective film 25 antireflective film a: lattice spacing AD, AL, AR, AU: traveling wave, B1: first light image portion, B2: second light image portion, BD, BL, BR, BU: beam pattern, D: straight line, G: center of gravity, O: lattice point, R: unit Composition area, RIN ... inner area, ROUT ... outer area.

Claims (5)

A base layer and a plurality of different refractive index regions different in refractive index from the base layer, and provided with a phase modulation layer provided on a substrate and optically coupled to a light emitting portion, the main surface of the substrate A method of designing the phase modulation layer of a light emitting device which outputs an optical image in a perpendicular direction or a direction inclined with respect to the direction, or both.
When a virtual tetragonal lattice is set in a plane perpendicular to the thickness direction of the phase modulation layer, the first region and the second region arranged in one lattice point arranging direction across the center point of the phase modulation layer And, when defining a third region and a fourth region arranged in the other lattice point arranging direction across the center point of the phase modulation layer, a first progression from the second region to the first region Wave, a second traveling wave traveling in the direction from the first area to the second area, a third traveling wave traveling in the direction from the fourth area to the third area, and the third area to the fourth area Providing a plurality of complex amplitude distributions corresponding to the light image for each of the fourth traveling wave traveling in the direction to the region;
A second step of correcting the complex amplitude distribution for each traveling wave;
A third step of superposing the corrected complex amplitude distribution on each traveling wave to obtain an overall complex amplitude distribution;
And fourth step of extracting a phase distribution from the comprehensive complex amplitude distribution and determining a barycentric position of each modified refractive index area based on the phase distribution,
In the second step, the positive and negative of the phase term of the complex amplitude distribution relating to one of the first traveling wave and the second traveling wave are reversed, and the complex relating to one of the third traveling wave and the fourth traveling wave Invert the positive and negative of the phase term of the amplitude distribution,
In the fourth step, the centers of gravity of the different refractive index areas are disposed on a straight line which is inclined with respect to the square lattice through the lattice points of the virtual square lattice, and the centers of gravity of the respective different refractive index areas; A phase modulation layer design method, wherein a distance to a corresponding grid point is determined based on the phase distribution.   The phase modulation layer designing method according to claim 1, wherein the complex amplitude distribution related to each traveling wave is weighted in the second step.   The weight added to each complex amplitude distribution related to the first traveling wave and the second traveling wave and the weight added to each complex amplitude distribution related to the third traveling wave and the fourth traveling wave are different from each other. 2. The phase modulation layer design method according to 2.   A ratio of a weight added to each complex amplitude distribution related to the first traveling wave and the second traveling wave, and a weight added to each complex amplitude distribution related to the third traveling wave and the fourth traveling wave is the straight line The phase modulation layer design method according to claim 3, wherein the phase modulation layer is determined based on an angle formed by the square lattice.   The phase modulation layer design method according to any one of claims 1 to 4, wherein the light emitting unit is an active layer provided on the substrate.