Light-emitting device

Abstract

Provided is a light-emitting device comprising: a light-emitting unit; and a phase modulation layer optically coupled to the light-emitting unit. The phase modulation layer has a basic layer, and a plurality of different refractive index regions having a refractive index different from that of the basic layer and being distributed in a first surface intersecting the thickness direction of the phase modulation layer. In the phase modulation layer, a light extraction region is formed including, in accordance with the arrangement of the plurality of different refractive index regions, a first region and a second region separated from the first region with an intermediate region therebetween along the first surface. In the light extraction region, the plurality of different refractive index regions are arranged such that light emitted from the light-emitting unit and resonating in an in-plane direction of the first surface in the phase modulation layer is diffracted in an out-of-plane direction of the first surface in the first region and the second region.

Description

Light-emitting devices

[0001] The present disclosure relates to light emitting devices.

[0002] Research has been conducted on semiconductor light-emitting devices that output arbitrary optical images by controlling the phase and intensity distributions of light emitted from multiple light-emitting points arranged two-dimensionally. One such semiconductor light-emitting device structure has a phase modulation layer optically coupled to an active layer. The phase modulation layer has a base layer and multiple modified refractive index regions with refractive indices different from that of the base layer. When a virtual square lattice is defined in a plane perpendicular to the thickness direction of the phase modulation layer, the center of gravity of each modified refractive index region is shifted from the lattice point of the virtual square lattice according to the optical image. Such a semiconductor light-emitting device is called an S-iPM (Static-Integrate Phase Modulating) laser, and outputs an optical image of any two-dimensional shape, including a direction perpendicular to the main surface of the substrate on which the phase modulation layer is provided and a direction inclined relative to this. Non-Patent Document 1 describes technology related to S-iPM lasers.

[0003] Yoshitaka Kurosaka et al., “Phase-modulating lasers toward on-chip integration”, Scientific Reports, 6:30138 (2016)

[0004] The semiconductor light-emitting devices described above are required to emit an optical image having a stripe pattern. In particular, in applications such as fine endoscopes, flow channel devices, and microscope measurements, a fine stripe pattern is required at a short distance of, for example, several millimeters.

[0005] An object of the present disclosure is to provide a light-emitting device that can form a fine striped pattern at a short distance.

[0006] a light-emitting device according to the present disclosure, the light-emitting device being [1] "a light-emitting unit; and a phase modulation layer optically coupled to the light-emitting unit, wherein the phase modulation layer has a base layer and a plurality of modified refractive index regions having a refractive index different from that of the base layer and distributed in a first plane intersecting a thickness direction of the phase modulation layer, wherein the phase modulation layer has a light extraction region including a first region and a second region spaced apart from the first region along the first plane with an intermediate region sandwiched therebetween according to an arrangement of the plurality of modified refractive index regions, wherein the light extraction region includes a first region and a second region spaced apart from the first region across an intermediate region along the first plane, wherein the plurality of modified refractive index regions are arranged in the light-extraction region such that light emitted from the light-emitting unit and resonating in an in-plane direction of the first surface in the phase modulation layer is diffracted in an out-of-plane direction of the first surface in the first region and the second region, wherein the light emitted from the light-emitting unit and resonating in the in-plane direction in the phase modulation layer is not diffracted in the out-of-plane direction in the intermediate region, and wherein the outgoing light diffracted in the out-of-plane direction in each of the first region and the second region interfere with each other to form interference fringes in a Fresnel region."

[0007] In this light-emitting device, the phase modulation layer optically coupled to the light-emitting section includes a base layer and a plurality of modified refractive index regions having a refractive index different from that of the base layer and distributed within a first plane intersecting the thickness direction of the phase modulation layer. In this case, light emitted from the light-emitting section and resonating in the in-plane direction of the first surface in the phase modulation layer can be diffracted out-of-plane toward the first surface and emitted to the outside, or can be prevented from being diffracted out-of-plane toward the first surface and emitted to the outside, depending on the arrangement of the modified refractive index regions. In contrast, the phase modulation layer has a light extraction region including a first region and a second region separated from the first region by an intermediate region. In the first region and the second region, the plurality of modified refractive index regions are arranged so that the light is diffracted (emitted) in the out-of-plane direction of the first surface, and in the intermediate region, the light is prevented from being diffracted (emitted) in the out-of-plane direction of the first surface. This makes it possible for this light-emitting device to form interference fringes in the Fresnel region due to interference of light emitted from each of the first and second regions. Therefore, this light-emitting device can form a fine stripe pattern at close range.

[0008] The Fresnel region in the present disclosure may be defined as follows, for example. That is, in diffraction theory, the Fresnel region is a region near an aperture where the following Fresnel approximation holds for the distance r from the aperture plane (x aperture, y aperture) to the observation position (x observation, y observation). In such a near field, the electromagnetic field can be handled by Fresnel diffraction, which Fresnel approximates the distance. Note that z indicates the position in the direction perpendicular to the xy plane. Distance r = {z ２ + (x opening - x observation) ２ + (y opening - y observation) ２} １／２ ~z[1+(1 / 2){(x opening-x observation) / z} ２ +(1 / 2){(y opening - y observation) / z} ２ ]

[0009] On the other hand, when k is the wave number (1 / λ) and λ is the wavelength, in the far field where the observation position is far from the aperture, the position z on the optical axis is z>>k(x aperture ２ +y opening ２ ) max / 2, the square terms of the x aperture and y aperture can be ignored, and the distance R is approximated as follows. Such a far field can be handled by Fraunhofer diffraction (Fourier transform) and is called the Fraunhofer region. Note that "max" means the maximum value of the XY coordinates of the aperture plane. Distance R ~ z [1 + (1 / 2) {(x observation) / z} ２ +(1 / 2){(y observation) / z} ２ −(x observation)(x aperture) / z ２ −(y observation)(y aperture) / z ２ ]

[0010] The Fraunhofer region (far field) is defined as z>>k (x aperture) in the above formula. ２ +y opening ２ ) max / 2, but this is not strict and serves as a rough guide. In the present disclosure, the aperture plane is a plane along the first plane, and is an exit plane for diffracted light on which the first and second regions in the phase modulation layer are arranged, and the first and second directions correspond to the x and y directions, respectively. Furthermore, a third direction intersecting the first and second directions corresponds to the z direction.

[0011] As an example, if the width of the first region in the first direction and the length of the first region in the second direction are 5 μm and 200 μm, respectively, and the wavelength is 1 μm, the above formula becomes z>>2.0 cm, so as a guideline, up to about 2 cm can be considered as a Fresnel region. In other words, in the present disclosure, up to the extent shown in the following formula can be considered as a Fresnel region. z~k(x aperture ２ +y opening ２ ) max / 2

[0012] The light-emitting device according to the present disclosure may be [2] "the light-emitting device according to the above [1], in which the phase modulation layer has an M-point photonic crystal structure or a J-point photonic crystal structure."

[0013] The light-emitting device according to the present disclosure may be [3] "the light-emitting device according to the above [1] or [2], in which the plurality of modified refractive index areas are two-dimensionally distributed within the first surface."

[0014] The light-emitting device according to the present disclosure may be [4] "the light-emitting device according to any one of the above [1] to [3], in which a plurality of the modified refractive index areas are arranged in the intermediate region." In this case, by arranging the modified refractive index areas in the intermediate region, it is possible to prevent light from being diffracted in an out-of-plane direction of the first surface and from being emitted to the outside.

[0015] The light-emitting device according to the present disclosure may be [5] "the light-emitting device according to any one of the above [1] to [4], wherein the first region and the second region are linear regions extending longer in a second direction along the first surface and intersecting the first direction than in a first direction along the first surface." In this case, a pseudo-double slit is realized in which the first region and the second region each serve as a slit, and it is possible to preferably form interference fringes due to interference of the emitted light in the Fresnel region.

[0016] The light-emitting device according to the present disclosure may be [6] "the light-emitting device according to the above [5], wherein the width of the first region and the second region in the first direction is 20 times or less the wavelength of the light." In this case, it is possible to preferably form a large number of fine stripes over a wider region.

[0017] The light-emitting device according to the present disclosure may be [7] "the light-emitting device according to the above [5] or [6], wherein the width of the intermediate region in the first direction is 20 to 200 times the wavelength of the light." In this way, by setting the width of the intermediate region, i.e., the pseudo-slit spacing between the first region and the second region, it is possible to more suitably generate interference in the Fresnel region.

[0018] The light-emitting device according to the present disclosure may be [8] "the light-emitting device according to any one of [5] to [7] above, wherein the length in the second direction of the first region and the second region is 20 to 1000 times the wavelength of the light." In this way, by making the lengths of the first region and the second region, i.e., the length of the pseudo slit formed by the first region and the second region, relatively short, it is possible to ensure uniformity of the irradiation intensity regardless of deviation in distance of the irradiation target of the emitted light.

[0019] The light-emitting device according to the present disclosure may be [9] "the light-emitting device according to any one of [1] to [4] above, wherein the first region and the second region are dot-like regions." In this way, even if the first region and the second region are dot-like regions, interference fringes can be formed in the Fresnel region due to interference of light emitted from each of the first region and the second region. In this case, the fringe pattern can be controlled by adjusting the arrangement of the dot-like first region and the dot-like second region.

[0020] The light-emitting device according to the present disclosure may be the light-emitting device described in any one of [1] to [9] above, wherein the light extraction region includes one or more third regions configured by arranging a plurality of the modified refractive index regions so that light emitted from the light-emitting portion and resonating in the in-plane direction of the first surface in the phase modulation layer is diffracted in the out-of-plane direction of the first surface. When there is one third region, the one third region is arranged along the first surface while being separated from the first region and the second region with the intermediate region sandwiched therebetween. When there are multiple third regions, one third region is arranged along the first surface while being separated from the first region, the second region, and another third region with the intermediate region sandwiched therebetween. The out-of-plane light diffracted in the third region, the first region, and the second region interfere with each other to form interference fringes in the Fresnel region. In this way, the light emitted from one or more third regions may be used to form a striped pattern. In this case, by forming a two-dimensional striped pattern, it becomes possible to perform measurements in two axial directions simultaneously.

[0021] The light-emitting device according to the present disclosure may be

[11] "the light-emitting device according to any one of the above [1] to

[10] , including a substrate, the light-emitting portion and the phase modulation layer being formed on the substrate, a ridge waveguide including at least the phase modulation layer being formed on the substrate, and the first region and the second region being connected to each other by the ridge waveguide." In this case, the light extraction efficiency can be improved by current confinement by the ridge waveguide.

[0022] The light-emitting device according to the present disclosure may be

[12] "the light-emitting device according to the above

[11] , further comprising a control unit for individually controlling the amount of current injected into each of the first region and the second region." In this case, it is possible to control the stripe pattern by controlling the amount of current injected into the first region and the second region.

[0023] The light-emitting device according to the present disclosure may be

[13] "the light-emitting device according to any one of [1] to

[12] above, in which a lens phase distribution for focusing the emitted light is superimposed on a phase distribution relating to the arrangement of the modified refractive index areas in the light extraction area." In this case, it is possible to irradiate the emitted light over a wider range in the length direction of the stripes.

[0024] The light-emitting device according to the present disclosure may be

[14] "the light-emitting device according to any one of [1] to

[13] above, in which an inclined phase distribution for inclining the emitted light is superimposed on a phase distribution relating to the arrangement of the modified refractive index areas in the light extraction area." In this case, it is possible to irradiate an irradiation target with the emitted light at an angle.

[0025] The light-emitting device according to the present disclosure may be

[15] "the light-emitting device according to any one of [1] to

[14] above, in which the first region and the second region are separated from each other." By separating the first region and the second region in this manner, for example, a pseudo double slit may be formed, and interference fringes may be formed due to interference of the emitted light.

[0026] The light-emitting device according to the present disclosure may be

[16] "the light-emitting device according to any one of [1] to

[10] above, wherein the light extraction region is formed in a ring shape including the first region and the second region and surrounding the intermediate region." In this way, the first region and the second region, which are part of the light extraction region formed in a ring shape surrounding the intermediate region, may form, for example, a pseudo double slit, and interference fringes may be formed due to interference of the emitted light.

[0027] According to the present disclosure, it is possible to provide a light-emitting device capable of forming a fine striped pattern at a short distance.

[0028] FIG. 1 is a partially cutaway perspective view showing a light-emitting device according to this embodiment. FIG. 2 is a cross-sectional view showing the layered structure of the light-emitting device shown in FIG. 1. FIG. 3 is a perspective view of the phase modulation layer shown in FIGS. 1 and 2. FIG. 4 is a plan view of the phase modulation layer shown in FIGS. 1 and 2. FIG. 5 is an enlarged view of a unit constituent region. FIG. 6 is a plan view showing an example in which a substantially periodic refractive index structure is applied to a specific region of the phase modulation layer. FIG. 7 is a diagram showing a phase modulation layer in spherical coordinates (r, θ ｒｏｔ ,θ ｔｉｌｔ 8 is a diagram for explaining coordinate conversion from (ξ, η, ζ) to coordinates (ξ, η, ζ) in an XYZ orthogonal coordinate system. FIG. 8 is a plan view showing a reciprocal lattice space related to a phase modulation layer of a light emitting device that performs M-point oscillation. FIG. 9 is a diagram conceptually showing an example of a phase distribution. FIG. 10 is a diagram for schematically explaining the structure around the light line LL. FIG. 11 is a diagram for explaining a phase distribution φ ２FIG. 12 is a conceptual diagram illustrating a state in which a diffraction vector is added to the in-plane wave vector in four directions minus the wave number spread. FIG. 13 is a plan view illustrating another form of the phase modulation layer (first region and second region). FIG. 14 is a diagram illustrating the arrangement of modified refractive index areas in the phase modulation layer (first region and second region) illustrated in FIG. 13. FIG. 15 is a diagram illustrating a specific design of the first region and second region (double slit) used in the propagation calculation of the emitted light. FIG. 16 is a diagram illustrating calculation results (calculation results of aperture width dependency) when the slit width is changed. FIG. 17 is a diagram illustrating calculation results (calculation results of aperture spacing dependency) when the slit spacing is changed. FIG. 18 is a diagram illustrating calculation results (calculation results of aperture height dependency) when the slit length is changed. FIG. 19 is a diagram illustrating analysis results of the propagation characteristics of the element. FIG. 20 is a diagram illustrating analysis results of the propagation characteristics of the element. FIG. 21 is a diagram illustrating the propagation characteristics of another element as another example of the light-emitting device 1 according to this embodiment. FIG. 22 is a diagram showing the propagation characteristics of an element when ±1st-order light is superimposed. FIG. 23 is a diagram showing the propagation characteristics of an element when ±1st-order light is superimposed. FIG. 24 is a diagram showing the propagation characteristics of an element when ±1st-order light is superimposed. FIG. 25 is a diagram showing the propagation characteristics of an element when only +1st-order light is present. FIG. 26 is a diagram showing the propagation characteristics of an element when only +1st-order light is present. FIG. 27 is a diagram showing the propagation characteristics of an element when only +1st-order light is present. FIG. 28 is a diagram for explaining specific designs of the first region and the second region (double slit) used in the propagation calculation of the output light. FIG. 29 is a diagram showing the propagation characteristics of an element when ±1st-order light is superimposed. FIG. 30 is a diagram showing the propagation characteristics of an element when ±1st-order light is superimposed. FIG. 31 is a diagram showing the propagation characteristics of an element when ±1st-order light is superimposed. FIG. 32 is a diagram showing the propagation characteristics of an element when only +1st-order light is present. Fig. 33 is a diagram showing the propagation characteristics of the element in the case of only +1st order light. Fig. 34 is a diagram showing the propagation characteristics of the element in the case of only +1st order light. Fig. 35 is a diagram showing slits in the case of forming multi-slits. Fig. 36 is a diagram showing the calculation results (propagation characteristics). Fig. 37 is a diagram showing the calculation results (propagation characteristics). Fig. 38 is a diagram showing slits in another case of forming multi-slits.FIG. 39 is a diagram showing calculation results (propagation characteristics). FIG. 40 is a diagram showing calculation results (propagation characteristics). FIG. 41 is a diagram showing a cross-shaped slit. FIG. 42 is a diagram showing calculation results (propagation characteristics). FIG. 43 is a diagram showing calculation results (propagation characteristics). FIG. 44 is a diagram showing an example where the light extraction region is formed in an annular shape. FIG. 45 is a diagram showing calculation results (propagation characteristics). FIG. 46 is a diagram showing calculation results (propagation characteristics). FIG. 47 is a diagram showing an example where the light extraction region is formed in another annular shape. FIG. 48 is a diagram showing calculation results (propagation characteristics). FIG. 49 is a diagram showing calculation results (propagation characteristics). FIG. 50 is a diagram showing an example where the light extraction region is formed in an elliptical annular shape. FIG. 51 is a diagram showing calculation results (propagation characteristics). FIG. 52 is a diagram showing calculation results (propagation characteristics). FIG. 53 is a diagram showing a case where the light extraction region is formed in another elliptical annular shape. FIG. 54 is a diagram showing calculation results (propagation characteristics). FIG. 55 is a diagram showing calculation results (propagation characteristics). FIG. 56 shows the propagation characteristics (|E|) when the amplitude intensity is changed. ２ ) when the amplitude intensity is changed. ２ ) is a diagram showing the propagation characteristics (E.real) when the amplitude intensity is made different. FIG. 59 is a diagram for explaining two-aperture diffraction according to a modified example. FIG. 60 is a diagram for explaining a rectangular aperture and the divergence angle related to one rectangular aperture. FIG. 61 is a diagram for explaining two rectangular apertures and the divergence angle and interference distance related to two rectangular apertures. FIG. 62 is a diagram showing the aperture shape when the interval between the first region and the second region (aperture interval) is changed to various values. FIG. 63 is a diagram showing the Fourier spectrum (absolute value (far field solution)) corresponding to each part of FIG. 62. FIG. 64 is a diagram showing the light intensity (|E| ２) corresponding to each part of FIG. 62. FIG. 65 is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 62. FIG. 66 is a diagram for explaining an example in which a plurality of rectangular apertures are arranged on the circumference. FIG. 67 is a diagram showing the aperture shape when the number of rectangular apertures (number of N) is changed sequentially. FIG. 68 is a diagram showing the Fourier spectrum (absolute value (far field solution)) corresponding to each part of FIG. 67. FIG. 69 is a diagram showing the light intensity (|E| ２ ) in the case of FIG. 68. FIG. 70 is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 68. FIG. 71 is a diagram showing the case where three rectangular apertures are arranged on the circumference (N=3). FIG. 72 is a diagram showing the light intensity (|E| ２ ) and how a striped pattern is formed. FIG. 73 is a diagram showing the case where there are four rectangular openings on the circumference (N=4). FIG. 74 is a diagram showing the light intensity (|E| ２ ) and how a striped pattern is formed. FIG. 75 is a diagram showing the case where there are six rectangular openings on the circumference (N=6). FIG. 76 is a diagram showing the light intensity (|E| ２ ) and how a striped pattern is formed. FIG. 77 is a diagram showing a case where a plurality of rectangular apertures are arranged on a straight line along the X direction (ξ direction). FIG. 78 is a graph showing a function f(x) expressed by the following equation (50). FIG. 79 is a diagram showing a case where a plurality of rectangular apertures are arranged on the intersections of a plurality of straight lines along the X direction (ξ direction) and a plurality of straight lines along the Y direction (η direction). FIG. 80 is a diagram showing aperture shapes when the number of rectangular apertures (number N) is changed in arrayed multipoint rectangular aperture diffraction (two-dimensional). FIG. 81 is a diagram showing Fourier spectra (absolute values ​​(far-field solution)) corresponding to each part of FIG. 80. FIG. 82 is a diagram showing the light intensity (|E| ２) is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 81. FIG. 84 is a diagram showing the aperture shape when the aperture spacing is sequentially changed for each number of rectangular apertures in arrayed multipoint rectangular aperture diffraction (two-dimensional). FIG. 85 is a diagram showing the Fourier spectrum (absolute value (far-field solution)) corresponding to each part of FIG. 84. FIG. 86 is a diagram showing the light intensity (|E| ２ 87 is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each portion of FIG. 84 . FIG. 88 is a cross-sectional view showing the stacked structure of a light-emitting device according to this modification. FIG. 89 is a plan view of the light-emitting device shown in FIG. 88 . FIG. 90 is a schematic plan view showing, on an enlarged scale, the ridge waveguide shown in FIG. 89 . FIG. 91 is a schematic plan view showing, on an enlarged scale, a modification of the ridge waveguide shown in FIG. 89 . FIG. 92 is a schematic plan view showing, on an enlarged scale, another modification of the ridge waveguide shown in FIG. 89 . FIG. 92 is a schematic plan view showing, on an enlarged scale, yet another modification of the ridge waveguide shown in FIG. 89 . FIG. 94 is a cross-sectional view showing a modification of the ridge waveguide shown in FIG. 88 . FIG. 95 is a cross-sectional view showing another modification of the ridge waveguide shown in FIG. 88 . FIG. 96 is a plan view showing a modification of the ridge waveguide shown in FIG. 89 . FIG. 97 is a plan view showing another modification of the ridge waveguide shown in FIG. 89 . Fig. 98 is a plan view showing yet another modified example of the ridge waveguide shown in Fig. 89. Fig. 99 is a schematic plan view showing an example of the arrangement of modified refractive index areas when the ridge waveguide has an inclined portion. Fig. 100 is a plan view showing a modified example of the ridge waveguide shown in Fig. 96. Fig. 101 is a diagram showing a modified example of the aperture shape. Fig. 102 is a diagram showing the aperture shape when a plurality of circular apertures are arranged on the circumference when the first region etc. are circular. Fig. 103 is a diagram showing the Fourier spectrum (absolute value (far field solution)) corresponding to each part of Fig. 102. Fig. 104 is a diagram showing the light intensity (|E| ２) is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 102. FIG. 106 is a diagram showing the aperture shapes when the shapes of three apertures arranged on the circumference are changed. FIG. 107 is a diagram showing the Fourier spectrum (absolute value (far field solution)) corresponding to each part of FIG. 106. FIG. 108 is a diagram showing the light intensity (|E| ２ ) corresponding to each part of FIG. 106. FIG. 109 is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 106. FIG. 110 is a diagram showing the aperture shapes when elliptical rectangular apertures are arranged and when rectangular apertures are arranged at unequal intervals on the circumference. FIG. 111 is a diagram showing the aperture shapes when the number of rectangular apertures is changed in the example shown in FIG. 110(a). FIG. 112 is a diagram showing the Fourier spectrum (absolute value (far field solution)) corresponding to each part of FIG. 111. FIG. 113 is a diagram showing the light intensity (|E| ２ ) is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 111. FIG. 115 is a diagram showing the aperture shape in the example shown in (b) and (c) of FIG. 110. FIG. 116 is a diagram showing the Fourier spectrum (absolute value (far field solution)) corresponding to each part of FIG. 115. FIG. 117 is a diagram showing the light intensity (|E| ２ 118 is a diagram showing the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 115. FIG. 119 is a cross-sectional view showing the stacked structure of the light-emitting device having the ridge waveguide shown in FIG.

[0029] Hereinafter, a light-emitting device according to an embodiment will be described in detail with reference to the drawings. In the description of each drawing, duplicated descriptions of the same or corresponding elements may be omitted.

[0030] Fig. 1 is a partially cutaway perspective view showing the configuration of a light-emitting device according to this embodiment. Fig. 2 is a cross-sectional view showing the layered structure of the light-emitting device shown in Fig. 1. Fig. 3 is a perspective view of the phase modulation layer shown in Figs. 1 and 2. Figs. 1 to 3 show an orthogonal coordinate system in which the axis extending in the thickness direction of the light-emitting device 1 at the center thereof is the Z-axis, and two axes intersecting each other in a plane intersecting the Z-axis are the X-axis and the Y-axis.

[0031] The light-emitting device 1 is a laser light source that forms a standing wave in the XY plane and outputs a phase-controlled plane wave in a direction intersecting its thickness direction. The light-emitting device 1 is a Si-iPM laser, and can output an optical image of any shape in a direction perpendicular to the main surface 10a of the semiconductor substrate 10 (i.e., the Z direction), a direction inclined relative to the Z direction, or both.

[0032] 1 and 2 , the light-emitting device 1 includes an active layer 12 as a light-emitting portion provided on a semiconductor substrate 10, a pair of cladding layers 11 and 13 sandwiching the active layer 12, and a contact layer 14 provided on the cladding layer 13. The semiconductor substrate 10, the cladding layers 11 and 13, and the contact layer 14 are made of compound semiconductors such as GaAs-based semiconductors, InP-based semiconductors, or nitride-based semiconductors. The energy bandgaps of the cladding layers 11 and 13 are larger than the energy bandgaps of the active layer 12. The thickness directions of the semiconductor substrate 10, the cladding layer 11, the active layer 12, the cladding layer 13, and the contact layer 14 coincide with the Z-axis direction.

[0033] The light-emitting device 1 further includes a phase modulation layer 15 optically coupled to the active layer 12. In this embodiment, the phase modulation layer 15 is provided between the active layer 12 and the cladding layer 13. The thickness direction of the phase modulation layer 15 coincides with the Z-axis direction. The phase modulation layer 15 may be provided between the cladding layer 11 and the active layer 12. An optical guide layer may be provided, if necessary, between at least one of the active layer 12 and the cladding layer 13 and the active layer 12 and the cladding layer 11. The optical guide layer may include a carrier barrier layer for efficiently confining carriers in the active layer 12.

[0034] The phase modulation layer 15 is composed of a basic layer 15a made of a first refractive index medium and a plurality of modified refractive index areas 15b made of a second refractive index medium having a refractive index different from that of the first refractive index medium and present within the basic layer 15a.

[0035] The multiple modified refractive index regions 15b are two-dimensionally distributed within a first plane (here, the XY plane) intersecting the thickness direction of the phase modulation layer 15 (here, the Z direction). In the phase modulation layer 15, a light extraction region 15P is formed according to the arrangement (described later) of the multiple modified refractive index regions 15b. The light extraction region 15P includes a first region 151 and a second region 152 that is spaced apart from the first region 151 along a first direction (here, the X direction) along the XY plane, with an intermediate region 155 sandwiched between them. The first region 151 and the second region 152 are each linear regions that extend longer in the Y direction (second direction) that is along the XY plane and intersects the X direction than in the X direction. The first region 151 and the second region 152 are separated from each other.

[0036] The plurality of modified refractive index areas 15b includes a lattice-like, approximately periodic structure. When the equivalent refractive index of the mode is n and the lattice spacing is a, the wavelength λ selected by the phase modulation layer 15 is ０ is the wavelength λ ０ = (√2) a × n, which is the wavelength corresponding to the M-point band edge. ０ is a wavelength included in the emission wavelength range of the active layer 12. The phase modulation layer 15 is configured to modulate the wavelength λ ０The light incident on the phase modulation layer 15 forms a predetermined mode in accordance with the arrangement of the modified refractive index regions 15 b within the phase modulation layer 15, and is emitted as laser light from the surface of the light-emitting device 1 to the outside.

[0037] The light-emitting device 1 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 forms ohmic contact with the contact layer 14. The electrode 17 forms ohmic contact with the semiconductor substrate 10. The electrode 17 has an opening 17a in a central region of the back surface 10b. The electrode 16 is provided in a central region of the surface of the contact layer 14. The portion of the contact layer 14 other than the electrode 16 is covered with a protective film 18 (see FIG. 2). The contact layer 14 not in contact with the electrode 16 may be removed to limit the current range. The back surface 10b of the semiconductor substrate 10, except for the region where the electrode 17 is provided, is covered with an anti-reflection film 19, including the inside of the opening 17a. The anti-reflection film 19 in the region other than the opening 17a may be removed.

[0038] In the light-emitting device 1, when a driving current is supplied between the electrodes 16 and 17, recombination of electrons and holes occurs in the active layer 12, causing the active layer 12 to emit light. The electrons and holes that contribute to this light emission, as well as the light generated in the active layer 12, are efficiently confined between the cladding layers 11 and 13.

[0039] Light emitted from the active layer 12 enters the phase modulation layer 15 and forms a predetermined mode corresponding to the lattice structure inside the phase modulation layer 15 (resonating in the XY plane). The laser light emitted from the phase modulation layer 15 passes through the opening 17a from the rear surface 10b and is directly output to the outside of the light-emitting device 1. Alternatively, the laser light emitted from the phase modulation layer 15 is reflected by the electrode 16 and then passed through the opening 17a from the rear surface 10b and is output to the outside of the light-emitting device 1. At this time, the signal light contained in the laser light is output in any direction, including a direction perpendicular to the main surface 10a and directions inclined relative to that direction.

[0040] It is this signal light that constitutes the light emitted from the light-emitting device 1. The signal light is mainly the first-order diffracted light or the -1st-order diffracted light of the laser light (hereinafter referred to as the first-order light and the -1st-order light, respectively), or both. As will be described later, the output of the zeroth-order light of the laser light is suppressed from the phase modulation layer 15 of this embodiment.

[0041] Here, in the light extraction region 15P, multiple modified refractive index regions 15b are arranged so that light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15 is diffracted in the out-of-plane direction of the XY plane (direction intersecting the XY plane) in the first region 151 and the second region 152. Furthermore, in the intermediate region 155, multiple modified refractive index regions 15b are arranged so that light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15 is not diffracted in the out-of-plane direction of the XY plane. As a result, in the phase modulation layer 15, light is extracted from the first region 151 and the second region 152, while the intermediate region 155 and the other regions 160 are regions 15Q where light is not extracted (total reflection occurs). Next, the arrangement of the modified refractive index regions 15b in the first region 151 and the second region 152 will be described.

[0042] The phase modulation layer 15 includes a base layer 15a made of a first refractive index medium and multiple modified refractive index areas 15b made of a second refractive index medium having a refractive index different from that of the first refractive index medium. In FIG. 4 , a virtual square lattice is defined in the XY plane for 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. Square unit constituent regions R, each centered on a lattice point O of the square lattice, are two-dimensionally arranged in multiple columns along the X axis and multiple rows along the Y axis. The XY coordinates of each unit constituent region R are defined by the center of gravity of the respective unit constituent region R. These center of gravity positions coincide with the lattice point O of the virtual square lattice. For example, one modified refractive index area 15b is provided in each unit constituent region R. The planar shape of the modified refractive index area 15b is, for example, circular. The lattice point O may be located outside the modified refractive index area 15b or may be included inside the modified refractive index area 15b.

[0043] FIG. 5 is an enlarged view of the unit constituent region R. As shown in the figure, each modified refractive index area 15b has a center of gravity G. Here, the angle between the vector from lattice point O toward the center of gravity G and the X-axis is defined as α(x, y). x indicates the position of the xth lattice point on the X-axis, and y indicates the position of the yth lattice point on the Y-axis. When the rotation angle α is 0°, the direction of the vector connecting lattice point O and the center of gravity G coincides with the positive direction of the X-axis. Furthermore, the length of the vector connecting lattice point O and the center of gravity G is defined as r(x, y). In one example, r(x, y) is constant throughout the first area 151 and the second area 152, regardless of x and y.

[0044] As shown in FIG. 4 , the direction of the vector connecting the lattice point O and the center of gravity G, i.e., the rotation angle α of the center of gravity G of the modified refractive index area 15b around the lattice point O, is individually set for each lattice point O according to the phase distribution φ(x, y) corresponding to the desired shape of the emitted light. In the present disclosure, this arrangement of the center of gravity G is referred to as the first arrangement. The phase distribution φ(x, y) has a specific value for each position determined by the values ​​of x and y, but is not necessarily expressed by a specific function. The rotation angle distribution α(x, y) is determined by extracting the phase distribution φ(x, y) from the complex amplitude distribution obtained by Fourier transforming the desired shape of the emitted light. When determining the complex amplitude distribution from the desired shape of the emitted light, it is recommended to apply an iterative algorithm such as the Gerchberg-Saxton (GS) method, which is commonly used in calculations for hologram generation. In this case, it is possible to improve the reproducibility of the beam pattern.

[0045] FIG. 6 is a plan view showing an example in which a substantially periodic refractive index structure is applied to a specific region of the phase modulation layer 15. In the example shown in FIG. 6, a substantially periodic structure (e.g., the structure shown in FIG. 4) for emitting a desired optical image is formed within a square inner region RIN. Meanwhile, a circular modified refractive index region 15b is disposed in the outer region ROUT surrounding the inner region RIN, with the lattice points of the square lattice and the center of gravity of the square lattice coinciding. The lattice spacing a of the virtually set square lattice is identical within the inner region RIN and the outer region ROUT. In the structure shown in FIG. 9, light is distributed within the outer region ROUT as well, thereby suppressing the generation of high-frequency noise (so-called window function noise) caused by abrupt changes in light intensity around the periphery of the inner region RIN. Furthermore, light leakage in a direction perpendicular to the thickness direction can be suppressed, thereby reducing the threshold current. This example is not limited to this; the substantially periodic structure (e.g., the structure shown in FIG. 4) for emitting a desired optical image may be formed throughout the entire first region 151 and the second region 152.

[0046] In order to obtain a desired distribution of the light-converging points U, the rotation angle distribution α(x, y) of the modified refractive index area 15b in the phase modulation layer 15 (first area 151 and second area 152) is determined by the following procedure.

[0047] As a first prerequisite, in an XYZ orthogonal coordinate system defined by a Z axis coinciding with the normal direction and an XY plane coinciding with one surface of the phase modulation layer 15 including the multiple modified refractive index areas 15b, a square M １ ×N １ pieces (M １ , N １ A virtual square lattice composed of unit constituent regions R (where R is an integer of 1 or more) is set on the XY plane.

[0048] As a second prerequisite, the coordinates (ξ, η, ζ) in the XYZ orthogonal coordinate system are determined by the length r of the moving radius and the tilt angle θ from the Z axis, as shown in FIG. ｔｉｌｔ and the rotation angle θ from the X-axis specified on the XY plane ｒｏｔ and the spherical coordinates (r, θ ｒｏｔ ,θ ｔｉｌｔ) satisfy the relationships shown in the following formulas (1) to (3). ｒｏｔ ,θ ｔｉｌｔ ) to coordinates (ξ, η, ζ) in the XYZ Cartesian coordinate system, and the coordinates (ξ, η, ζ) represent a designed light image on a predetermined plane set in the XYZ Cartesian coordinate system, which is real space.

[0049]

[0050]

[0051]

[0052] The light emitted from the light-emitting device 1 is reflected at an angle θ ｔｉｌｔ and θ ｒｏｔ When the set of bright spots is directed in the direction specified by the angle θ ｔｉｌｔ and θ ｒｏｔ is the normalized wave number defined by the following equation (4) and corresponds to the X axis. ｘ The coordinate value kx on the axis and the normalized wave number defined by the following equation (5) which corresponds to the Y axis and is K ｘ K perpendicular to the axis ｙ The normalized wave number is a wave number normalized by setting the wave number 2π / a, which corresponds to the lattice spacing of a virtual square lattice, to 1.0. ｘ axis and K ｙ In the wavenumber space defined by the axes, specific wavenumber ranges including the beam pattern corresponding to the optical image are each a square-shaped M ２ ×N ２ pieces (M ２ , N ２ is an integer of 1 or more). ２ is an integer M １ Similarly, the integer N ２ is an integer N １Equations (4) and (5) are disclosed, for example, in Y. Kurosaka et al., "Effects of non-lasing band intwo-dimensional photonic-crystal lasers clarified using omnidirectional bandstructure," Opt. Express 20, 21773-21783 (2012).

[0053]

[0054] a: lattice constant of a virtual square lattice λ: oscillation wavelength of the light-emitting device 1

[0055] The third prerequisite is that in wave number space, K ｘ Axial coordinate component kx (0 or more M ２ -1 or less integer) and K ｙ Axial coordinate component ky (0 or more N ２ The image region FR(kx, ky) specified by the coordinate component x (0 to M) in the X-axis direction is １ -1 or less) and the coordinate component y (0 or more N １ The complex amplitude F(x, y) obtained by performing a two-dimensional inverse discrete Fourier transform on a unit constituent region R(x, y) on the X-Y plane specified by x and y (an integer equal to or less than -1) is given by the following equation (6), where j is the imaginary unit. The complex amplitude F(x, y) is defined by the following equation (7), where the amplitude term is A(x, y) and the phase term is φ(x, y). As a fourth prerequisite, the unit constituent region R(x, y) is defined by the s-axis and t-axis, which are parallel to the X-axis and Y-axis, respectively, and are orthogonal to each other at the lattice point O(x, y) that is the center of the unit constituent region R(x, y).

[0056]

[0057]

[0058] Under the above first to fourth preconditions, the first region 151 and the second region 152 are configured to satisfy the following fifth and sixth conditions. That is, the fifth condition is satisfied when the center of gravity G is located away from the lattice point O(x, y) within the unit constituent region R(x, y). The sixth condition is satisfied when the line segment length r from the lattice point O(x, y) to the corresponding center of gravity G is ２ (x, y) is M １ pieces x N １ With the angle α(x, y) between the s-axis and the line segment connecting the lattice point O(x, y) and the corresponding center of gravity G, set to a common value in each of the unit constituent regions R, the angle α(x, y) is satisfied by arranging the corresponding modified refractive index area 15b within the unit constituent region R(x, y) so that the following relationship is satisfied: α(x, y) = C × φ(x, y) + B, where C is a proportionality constant, e.g., 180° / π, and B is an arbitrary constant, e.g., 0.

[0059] Next, we will explain the M-point oscillation of the light-emitting device 1. For the light-emitting device 1 to oscillate at the M-point band edge, the lattice spacing a of a virtual square lattice, the emission wavelength λ of the active layer 12, and the equivalent refractive index n of the mode should satisfy the condition λ = (√2)n × a. FIG. 8 is a plan view showing the reciprocal lattice space related to the phase modulation layer of a light-emitting device that performs M-point oscillation. Point P in the figure represents a reciprocal lattice point. Arrow B1 in the figure represents the fundamental reciprocal lattice vector, and arrows K1, K2, K3, and K4 represent four in-plane wave vectors. Each of the in-plane wave vectors K1 to K4 has a wave number spread SP due to the rotation angle distribution α(x, y).

[0060] The magnitude of the in-plane wave vectors K1 to K4 (i.e., the magnitude of the standing wave in the in-plane direction) is smaller than the magnitude of the primitive reciprocal lattice vector B1. Therefore, the vector sum of the in-plane wave vectors K1 to K4 and the primitive reciprocal lattice vector B1 does not become 0, and the wave number in the in-plane direction cannot become 0 due to diffraction, so diffraction does not occur in the direction perpendicular to the plane (Z-axis direction). If this continues, the M-point oscillation light-emitting device 1 will not output not only the zeroth-order light in the direction perpendicular to the plane (Z-axis direction), but also +1st-order light and -1st-order light in directions inclined with respect to the Z-axis direction.

[0061] In this embodiment, the M-point oscillation light-emitting device 1 is configured as follows to the phase modulation layer 15 (first region 151 and second region 152), so that zeroth-order light is not output, but a portion of +1st-order light and -1st-order light is output. That is, as shown in FIG. 9 , a diffraction vector V1 having a certain magnitude and direction is added to the in-plane wave vectors K1 to K4, so that the magnitude of at least one of the in-plane wave vectors K1 to K4 (in the figure, the in-plane wave vector K3) is made smaller than 2π / λ (λ: wavelength of light output from the active layer 12). In other words, at least one of the in-plane wave vectors K1 to K4 after the diffraction vector V1 is added is contained within a light line LL, which is a circular region with a radius of 2π / λ.

[0062] In Fig. 9, the in-plane wave vectors K1 to K4 indicated by dashed lines represent the wave vectors before the addition of the diffraction vector V1, while the in-plane wave vectors K1 to K4 indicated by solid lines represent the wave vectors after the addition of the diffraction vector V1. The light line LL corresponds to the total reflection condition, and a wave vector whose magnitude falls within the light line LL has a component in the direction perpendicular to the surface (Z-axis direction). In one example, the direction of the diffraction vector V1 is along the Γ-M1 axis or the Γ-M2 axis. The magnitude of the diffraction vector V1 is in the range of 2π / (√2)a-2π / λ to 2π / (√2)a+2π / λ, and in one example, is 2π / (√2)a.

[0063] Next, we consider the magnitude and direction of the diffraction vector V1 for placing at least one of the in-plane wave vectors K1 to K4 within the light line LL. The following formulas (8) to (11) show the in-plane wave vectors K1 to K4 before the diffraction vector V1 is added.

[0064]

[0065]

[0066]

[0067]

[0068] The spreads Δkx and Δky of the wave vectors satisfy the following formulas (12) and (13), respectively. ｍａｘ and the maximum value of the spread in the y-axis direction Δky ｍａｘ is defined by the angular spread of the optical image of the design.

[0069]

[0070]

[0071] When the diffraction vector V1 is expressed as in the following formula (14), the in-plane wave vectors K1 to K4 after the diffraction vector V1 is added are expressed as the following formulas (15) to (18).

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] In the formulas (15) to (18), if it is considered that any of the in-plane wave vectors K1 to K4 falls within the light line LL, the relationship of the following formula (19) holds.

[0078]

[0079] That is, by adding a diffraction vector V1 that satisfies the formula (19), any of the in-plane wave vectors K1 to K4 falls within the light line LL, and a part of the +1st order light and the -1st order light is output.

[0080] The size (radius) of the light line LL is set to 2π / λ for the following reason. FIG. 10 is a diagram for schematically explaining the structure surrounding the light line LL. The diagram shows the boundary between the device and air in the Z direction. The magnitude of the wave vector of light in a vacuum is 2π / λ, but when light propagates through a device medium as shown in FIG. 10, the magnitude of the wave vector Ka in the medium with a refractive index n is 2πn / λ. In this case, in order for light to propagate through the boundary between the device and air, the wave number components parallel to the boundary must be continuous (law of conservation of wave numbers).

[0081] 10, when the wave vector Ka and the Z axis form an angle θ, the length of the wave vector Kb projected onto the plane (i.e., the in-plane wave vector) is (2πn / λ) sin θ. On the other hand, since the refractive index n of a medium is generally greater than 1, the law of conservation of wave numbers no longer holds when the angle at which the in-plane wave vector Kb in the medium is greater than 2π / λ. In this case, the light is totally reflected and cannot be extracted to the air side. The magnitude of the wave vector corresponding to this total reflection condition is the magnitude of the light line LL, i.e., 2π / λ.

[0082] As an example of a specific method of adding a diffraction vector V1 to the in-plane wave vectors K1 to K4, a phase distribution φ according to a desired output light shape is １ (x, y), the phase distribution φ ２ In this case, the phase distribution φ(x, y) of the phase modulation layer 15 (first region 151 and second region 152) is expressed as φ(x, y)=φ １ (x, y) + φ ２ It is expressed as (x, y). １ As mentioned above, (x, y) corresponds to the phase of the complex amplitude when the desired shape of the emitted light is Fourier transformed. ２ (x, y) is the phase distribution for adding the diffraction vector V1 that satisfies the above equation (19).

[0083] FIG. 11 shows the phase distribution φ ２ 1 is a diagram conceptually illustrating an example of (x, y) in which a first phase value φ Ａ and a first phase value φ Ａ a second phase value φ different from Ｂ In one example, the phase values ​​φ Ａ is 0 (rad), and the phase value φ Ｂ is π (rad), where the first phase value φ Ａ and a second phase value φ Ｂ and change in increments of π. Such an arrangement of phase values ​​makes it possible to suitably realize a diffraction vector V1 along the Γ-M1 axis or the Γ-M2 axis. In the case of a checkerboard arrangement, V1 = (±π / a, ±π / a), and the diffraction vector V1 exactly cancels out one of the in-plane wave vectors K1 to K4 in FIG. 9. Therefore, the axis of symmetry between the +1st-order light and the -1st-order light coincides with the Z direction, i.e., the direction perpendicular to the in-plane direction of the phase modulation layer 15. In general, the angular distribution θ2(x, y) of the diffraction vector V is expressed as the dot product of the diffraction vector V(Vx, Vy) and the position vector r(x, y), and is given by the following equation: θ2(x, y) = V r = Vx x + Vy y

[0084] Therefore, when V = V1, the phase values ​​are 0 and π for a position vector r(xa, ya) (x and y are both integers). On the other hand, as described above, the diffraction vector V1 may be shifted from (±π / a, ±π / a) as long as at least one of the in-plane wave vectors K1 to K4 falls within the range in which the light line LL is included.

[0085] In this embodiment, when the wavenumber spread based on the angular spread of the output light is contained in a circle of radius Δk centered at a certain point in wavenumber space, it can also be simply considered as follows: By adding a diffraction vector V1 to the four-directional in-plane wavenumber vectors K1 to K4, the magnitude of at least one of the four-directional in-plane wavenumber vectors K1 to K4 is made smaller than 2π / λ (light line LL). This can be considered as meaning that by adding the diffraction vector V1 to the four-directional in-plane wavenumber vectors K1 to K4 minus the wavenumber spread Δk, the magnitude of at least one of the four-directional in-plane wavenumber vectors K1 to K4 is made smaller than the value {(2π / λ) - Δk} obtained by subtracting the wavenumber spread Δk from 2π / λ.

[0086] FIG. 12 is a diagram conceptually illustrating the above-mentioned idea. As shown in the figure, when a diffraction vector V1 is added to in-plane wave vectors K1 to K4 excluding the wave number spread Δk, the magnitude of at least one of the in-plane wave vectors K1 to K4 becomes smaller than {(2π / λ)-Δk}. In FIG. 12, region LL2 is a circular region with a radius of {(2π / λ)-Δk}. In FIG. 12, the in-plane wave vectors K1 to K4 indicated by dashed lines represent the wave vectors before the addition of the diffraction vector V1, and the in-plane wave vectors K1 to K4 indicated by solid lines represent the wave vectors after the addition of the diffraction vector V1. Region LL2 corresponds to the total reflection condition taking into account the wave number spread Δk, and wave vectors whose magnitude falls within region LL2 also propagate in the direction perpendicular to the plane (the Z-axis direction).

[0087] In this embodiment, the magnitude and direction of the diffraction vector V1 for placing at least one of the in-plane wave vectors K1 to K4 within the region LL2 will be described. The following formulas (20) to (23) show the in-plane wave vectors K1 to K4 before the diffraction vector V1 is added.

[0088]

[0089]

[0090]

[0091]

[0092] Here, when the diffraction vector V1 is expressed as in the above-mentioned formula (14), the in-plane wave vectors K1 to K4 after the diffraction vector V1 is added are expressed by the following formulas (24) to (27).

[0093]

[0094]

[0095]

[0096]

[0097] In formulas (24) to (27), if it is considered that any of the in-plane wave vectors K1 to K4 falls within region LL2, the relationship of the following formula (28) holds. That is, by adding a diffraction vector V1 that satisfies formula (28), any of the in-plane wave vectors K1 to K4 excluding the wave number spread Δk falls within region LL2. Even in such a case, it is possible to output a part of the +1st-order light and the -1st-order light without outputting the 0th-order light.

[0098]

[0099] FIG. 13 is a plan view showing another form of the phase modulation layer 15 (first region 151 and second region 152). FIG. 14 is a diagram showing the arrangement of the modified refractive index areas 15b in the phase modulation layer 15 (first region 151 and second region 152) shown in FIG. 12. As shown in FIGS. 13 and 14, the center of gravity G of each modified refractive index area 15b of the phase modulation layer 15 may be arranged on a straight line D. The straight line D passes through a lattice point O corresponding to each unit constituent region R and is inclined with respect to each side of the square lattice. In other words, the straight line D is inclined with respect to both the X-axis and the Y-axis. The inclination angle of the straight line D with respect to one side (X-axis) of the square lattice is β.

[0100] In this case, the tilt angle β is constant within the phase modulation layer 15 (the first region 151 and the second region 152). The tilt angle β satisfies 0°<β<90°, and in one example, β=45°. Alternatively, the tilt angle β satisfies 180°<β<270°, and in one example, β=225°. When the tilt angle β satisfies 0°<β<90° or 180°<β<270°, the straight line D extends from the first quadrant to the third quadrant of the coordinate plane defined by the X-axis and the Y-axis. The tilt angle β satisfies 90°<β<180°, and in one example, β=135°. Alternatively, the tilt angle β satisfies 270°<β<360°, and in one example, β=315°. When the tilt angle β satisfies 90°<β<180° or 270°<β<360°, the straight line D extends from the second quadrant to the fourth quadrant of the coordinate plane defined by the X-axis and the Y-axis. Thus, the tilt angle β is an angle excluding 0°, 90°, 180°, and 270°.

[0101] Here, the distance between the lattice point O and the center of gravity G is r(x, y). x is the position of the xth lattice point on the X axis, and y is the position of the yth lattice point on the Y axis. When the distance r(x, y) is a positive value, 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 0, the lattice point O and the center of gravity G coincide with each other. The tilt angles are preferably 45°, 135°, 225°, or 275°. At these tilt angles, only two of the four wave vectors (e.g., in-plane wave vectors (±π / a, ±π / a)) forming the standing wave at point M are phase-modulated, and the other two are not, thereby forming a stable standing wave.

[0102] The distance r(x, y) between the center of gravity G of each modified refractive index area and the lattice point O corresponding to each unit constituent area R is set individually for each modified refractive index area 15b according to the phase distribution φ(x, y) corresponding to the desired output light shape. In the present disclosure, this arrangement of the center of gravity G is referred to as the second arrangement. The phase distribution φ(x, y) and the distance distribution r(x, y) have specific values ​​for each position determined by the values ​​of x and y, but are not necessarily expressed by a specific function. The distribution of distance r(x, y) is determined from the phase distribution φ(x, y) extracted from the complex amplitude distribution obtained by performing an inverse Fourier transform on the desired output light shape.

[0103] That is, when the phase φ(x, y) at a certain coordinate (x, y) is φ0, the distance r(x, y) is set to 0, when the phase φ(x, y) is π+φ0, the distance r(x, y) is set to the maximum value R0, and when the phase φ(x, y) is -π+φ0, the distance r(x, y) is set to the minimum value -R0. For phases φ(x, y) in between, the distance r(x, y) is set so that r(x, y) = {φ(x, y) - φ0} × R0 / π. The initial phase φ0 can be set arbitrarily.

[0104] If the lattice spacing of a virtual square lattice is a, then the maximum value R of r(x, y) falls within the range of the following equation (29), for example: When determining the complex amplitude distribution from a desired optical image, it is possible to improve the reproducibility of the beam pattern by applying an iterative algorithm such as the GS method, which is commonly used in calculations for generating holograms.

[0105]

[0106] In this second embodiment, a desired light emission shape (number and positions of light-collecting points, etc.) can be obtained by determining the distribution of the distance r(x, y) of the modified refractive index areas 15b of the phase modulation layer 15 (first area 151 and second area 152). Under the same first to fourth preconditions as those of the first embodiment, the phase modulation layer 15 (first area 151 and second area 152) is configured to satisfy the following condition. That is, the distance r(x, y) from the lattice point O(x, y) to the center of gravity G of the corresponding modified refractive index area 15b is: r(x, y) = C × (φ(x, y) - φ0), where C is a proportionality constant, for example, R0 / π, and φ0 is an arbitrary constant, for example, 0.

[0107] The corresponding modified refractive index areas 15b are arranged in the unit constituent area R(x, y) so as to satisfy the following relationship. To obtain a desired light output shape, the light output shape can be subjected to an inverse Fourier transform, and a distribution of distances r(x, y) corresponding to the phase φ(x, y) of the complex amplitude can be provided to the multiple modified refractive index areas 15b. The phase φ(x, y) and the distances r(x, y) may be proportional to each other.

[0108] In this second embodiment, too, in a light-emitting device that oscillates at point M, the following device is applied to the phase modulation layer 15 (first region 151 and second region 152), so that the zeroth-order light is not output into the light line LL, and a portion of the +1st-order light and the −1st-order light is output. Specifically, as shown in FIG. 9 , a diffraction vector V1 having a certain magnitude and direction is added to the in-plane wave vectors K1 to K4, so that the magnitude of at least one of the in-plane wave vectors K1 to K4 is made smaller than 2π / λ. That is, at least one of the in-plane wave vectors K1 to K4 after the diffraction vector V1 is added is contained within the light line LL, which is a circular region with a radius of 2π / λ. By adding the diffraction vector V1 that satisfies the above-mentioned formula (19), one of the in-plane wave vectors K1 to K4 is contained within the light line LL, and a portion of the +1st-order light and the −1st-order light is output.

[0109] 12 , by adding a diffraction vector V1 to the four-directional in-plane wave vectors K1 to K4 minus the wave number spread Δk (i.e., the four-directional in-plane wave vectors in an M-point oscillation square lattice PCSEL), the magnitude of at least one of the four directional in-plane wave vectors K1 to K4 may be made smaller than the value obtained by subtracting the wave number spread Δk from 2π / λ, i.e., {(2π / λ)−Δk}. That is, by adding a diffraction vector V1 that satisfies the above-described formula (28), any of the in-plane wave vectors K1 to K4 falls within the region LL2, and a portion of the +1st-order light and a portion of the −1st-order light are output.

[0110] As a result, in the light extraction region 15P, light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15 is diffracted in the out-of-plane direction of the XY plane (direction intersecting the XY plane) in the first region 151 and the second region 152, and a portion of the +1st order light and the -1st order light are output only from the first region 151 and the second region 152. As a result, as shown in Figure 15, a pseudo double slit is formed in the phase modulation layer 15, with the first region 151 and the second region 152 each serving as a slit, and interference fringes due to interference of the emitted light can be formed in the Fresnel region. Next, more specific features will be described.

[0111] 15 is a diagram illustrating a specific design of the first and second regions (double slits) used in the propagation calculation (angular spectrum method) of the emitted light. Here, the width W15 of the first region 151 and the second region 152 in the X direction is set to 1 to 20 wavelengths (20 times or less the wavelength λ), the distance D15 between the first region 151 and the second region 152 in the X direction (i.e., the width D15 of the intermediate region 155 in the X direction) is set to 20 μm to 100 μm (for example, 20 to 200 times the wavelength λ), and the length L15 of the first region 151 and the second region 152 in the Y direction is set to 200 μm (for example, 20 to 1000 times the wavelength λ). The calculation was performed with a wavelength λ of 0.94 μm, a calculation area of ​​500 μm square, a calculation interval dx=dy of 0.47 μm (½ of the wavelength λ), and a propagation distance dZ of up to 2000 μm at a pitch of 50 μm.

[0112] FIG. 16 shows the calculation results (calculation results of aperture width dependency) when the width W15 is changed. In the calculation results of FIG. 16, the spacing D15 is set to 40 μm (43 times the wavelength λ). The width W15 is set to 0.94 μm (1 time the wavelength λ) in (a), 2.35 μm (2.5 times the wavelength λ) in (b), 4.7 μm (5 times the wavelength λ) in (c), and 9.4 μm (10 times the wavelength λ) in (d). In each of (a) to (d), the left column shows the slit shape in the XY plane, the middle column shows the Fourier spectrum, and the right column shows the propagation results in the XZ plane. It can be seen that, regardless of the width W15, fine interference fringes are formed at close distances due to interference of the emitted light. In particular, with regard to aperture width dependency, it was confirmed that the smaller the aperture width (width W15), the more fine fringes are formed.

[0113] FIG. 17 shows the calculation results (aperture spacing dependency calculation results) when the spacing D15 is changed. In the calculation results of FIG. 17, the width W15 is set to 4.7 μm (5 times the wavelength λ). The spacing D15 is set to 20 μm (21 times the wavelength λ) in (a), 40 μm (43 times the wavelength λ) in (b), 60 μm (64 times the wavelength λ) in (c), and 100 μm (106 times the wavelength λ) in (d). In each of (a) to (d), the left column shows the slit shape in the XY plane, the middle column shows the Fourier spectrum, and the right column shows the propagation results in the XZ plane. It can be seen that, for all spacings D15, fine interference fringes are formed at close distances due to interference of the emitted light. In particular, with regard to the aperture spacing dependency, it was confirmed that the larger the aperture spacing (spacing D15), the more fine fringes are formed.

[0114] FIG. 18 shows the calculation results (calculation results of aperture height dependence) when the length L15 is changed. In the calculation results of FIG. 18, the spacing D15 is 60 μm (64 times the wavelength λ) and the width W15 is 4.7 μm (5 times the wavelength λ). The length L15 is set to 20 μm (21 times the wavelength λ) in (a), 50 μm (53 times the wavelength λ) in (b), 100 μm (106 times the wavelength λ) in (c), and 200 μm (213 times the wavelength λ) in (d). In each of (a) to (d), the left column shows the slit shape in the XY plane, the middle column shows the Fourier spectrum, and the right column shows the propagation results in the XZ plane. It can be seen that, regardless of the length L15, minute interference fringes are formed at close range due to interference of the emitted light. In particular, it was confirmed that, with regard to the aperture height dependency, the smaller the aperture height (length L15), the larger the intensity modulation period in the propagation direction (here, the Z direction).

[0115] The explanation continues. As an example of the light-emitting device 1 according to this embodiment, an element using a partially diffracting M-point photonic crystal (a photonic crystal that realizes M-point oscillation) will be described. In this element structure, the spacing D15 is 60 μm (64 times the wavelength λ), the width W15 is 2.0 μm (twice the wavelength λ), and the length L15 is 200 μm (213 times the wavelength λ). Next, the results of the diffraction calculation (angular spectrum method) of this element will be described. Here, the wavelength λ is 0.94 μm, the calculation area is 500 μm square, the calculation interval dx = dy is 0.5 μm, and the propagation distance dZ is up to 2000 μm at a pitch of 50 μm.

[0116] 19 and 20 are diagrams showing the analysis results of the propagation characteristics of the element. (a) to (d) of FIG. 19 respectively show the XY cross section of the propagation characteristics at Z = 0 μm, the XY cross section at Z = 500 μm, the XY cross section at Z = 1000 μm, and the Fourier spectrum. FIG. 20 also shows the XZ cross section of the propagation characteristics. As shown in FIGS. 19 and 20, it was confirmed that this element also produces fine interference fringes at close range due to interference of the emitted light.

[0117] 21 is a diagram showing the propagation characteristics of another element as another example of the light-emitting device 1 according to this embodiment. (a) to (k) of FIG. 21 show, respectively, the XY cross section of the propagation characteristics at Z = 0 μm, Z = 100 μm, Z = 200 μm, Z = 300 μm, Z = 400 μm, Z = 500 μm, Z = 600 μm, Z = 700 μm, Z = 800 μm, Z = 900 μm, and Z = 1000 μm. In this element structure, the spacing D15 is 60 μm (64 times the wavelength λ), the width W15 is 2.0 μm (twice the wavelength λ), and the length L15 is 200 μm (213 times the wavelength λ). However, in this element, the spacing D15 and width W15 are values ​​along the Y direction, and the length L15 is a value along the X direction. That is, in this element, the first region 151 and the second region 152 are arranged along the Y direction and are linear regions that extend longer along the X direction than along the Y direction. It was confirmed that this element also produces fine, low-noise interference fringes at close range due to interference of the emitted light.

[0118] Here, in the light-emitting device 1 according to this embodiment, a lens phase distribution for concentrating emitted light can be superimposed on the phase distribution φ(x, y) relating to the arrangement of the modified refractive index areas 15b in the light extraction area 15P (first area 151 and second area 152). The lens phase distribution is expressed by, for example, the following equation (30). This lens phase distribution φ Ｌ (x, y) can act as a convex lens element for the emitted light. λ is the wavelength in the medium of the phase modulation layer 15, (x, y) is the lattice point position in the plane, and f is the focal length. The sign of the focal length f may be either positive or negative. When the sign of the focal length f is positive, it becomes a concave lens, and when the sign is negative, it becomes a convex lens.

[0119]

[0120] The lens phase distribution superimposed on the phase distribution φ(x, y) is, for example, a lens phase distribution φ for focusing light in only one direction, as shown in the following equation (31): ＬIt may be (x, y). When the sign on the right side is positive, it becomes a one-dimensional concave lens element, and −1st-order light is condensed in the region where z > 0. When the sign on the right side is negative, it becomes a one-dimensional convex lens element.

[0121]

[0122] As described above, in the light-emitting device 1 according to this embodiment, an arbitrary lens phase distribution for concentrating the emitted light can be superimposed on the phase distribution φ(x, y) relating to the arrangement of the modified refractive index areas 15b in the light extraction area 15P (first area 151 and second area 152).

[0123] As an example of the light-emitting device 1 according to this embodiment, there is an element using a partially diffracting M-point photonic crystal, and the phase distribution φ(x, y) is expressed by the lens phase distribution φ Ｌ The following describes an element in which the area where stripes are formed is expanded in one direction by superimposing a component (diverging light) with a positive sign in (x, y). However, since −1st-order light also exists at the same time, in an actual device, the lens phase distribution φ Ｌ The result is a superposition of both components (divergent light and convergent light) of ± signs in (x, y). In this element structure, the spacing D15 is 60 μm, the width W15 is 4.7 μm, and the length L15 is 200 μm. Next, the results of the diffraction calculation (angular spectrum method) of this element will be explained. Here, the wavelength λ is 0.94 μm, the calculation area is 500 μm square, the calculation interval dx = dy is 0.47 μm (1 / 2 of the wavelength λ), and the propagation distance dZ is up to 2000 μm with a pitch of 50 μm.

[0124] Figures 22, 23, and 24 show the propagation characteristics of the prototype element when ±1st-order light corresponding to an actual device is superimposed. (a) to (c) of Figures 22 to 24 correspond to the cases where the focal length fx in the X direction is 0.1 mm, the focal length fy in the Y direction is 0.1 mm, and the focal length fy in the Y direction is 1.0 mm, respectively. In each figure in Figure 22, from left to right, the aperture phase, Fourier spectrum, and propagation characteristics are shown in the XY cross section at Z = 0.5 mm, the XY cross section at Z = 1.0 mm, the XY cross section at Z = 1.5 mm, and the XY cross section at Z = 2.0 mm. Figure 23 shows the YZ cross section, and Figure 24 shows the XZ cross section. It was confirmed that the element could achieve the propagation characteristics shown in Figures 22 to 24.

[0125] Figures 25, 26, and 27 show the propagation characteristics of the element for +1st-order light only. (a) to (c) of Figures 25 to 27 correspond to the cases where the X-direction focal length fx is 0.1 mm, the Y-direction focal length fy is 0.1 mm, and the Y-direction focal length fy is 1.0 mm, respectively. In each figure in Figure 25, from left to right, the aperture phase, Fourier spectrum, and propagation characteristics are shown in the XY cross section at Z = 0.5 mm, the XY cross section at Z = 1.0 mm, the XY cross section at Z = 1.5 mm, and the XY cross section at Z = 2.0 mm. Furthermore, Figure 26 shows the YZ cross section, and Figure 27 shows the XZ cross section. It was confirmed that the element could achieve the propagation characteristics shown in Figures 25 to 27. In particular, (b) and (c) of Figures 25 to 27 show that there is no focusing of the -1st-order light, and it simply diverges.

[0126] As described above, in the light-emitting device 1 according to this embodiment, the phase modulation layer 15 optically coupled to the active layer 12 (light-emitting portion) includes a basic layer 15a and a plurality of modified refractive index regions 15b that have a refractive index different from that of the basic layer 15a and are two-dimensionally distributed within a first plane (XY plane) that intersects with the thickness direction (Z direction) of the phase modulation layer 15. In this case, depending on the arrangement of the modified refractive index regions 15b, light that is emitted from the active layer 12 and resonates in the in-plane direction of the XY plane in the phase modulation layer 15 can be diffracted in the out-of-plane direction of the XY plane and emitted to the outside, or can be prevented from being diffracted in the out-of-plane direction of the XY plane and emitted to the outside.

[0127] In contrast, the phase modulation layer 15 has a light extraction region 15P including a first region 151 and a second region 152 separated from the first region 151 with an intermediate region 155 sandwiched therebetween, and in the first region 151 and the second region 152, a plurality of modified refractive index regions 15b are arranged so that the light is diffracted (emitted) in an out-of-plane direction of the XY plane, and in the intermediate region 155, a plurality of modified refractive index regions 15b are arranged so that the light is not diffracted (not emitted) in an out-of-plane direction of the XY plane. The first region 151 and the second region 152 are linear regions that are elongated in the Y direction.

[0128] As a result, in the light-emitting device 1, a pseudo double slit is realized in which the first region 151 and the second region 152 each serve as a slit, and interference fringes due to interference of the emitted light can be formed in the Fresnel region. Thus, the light-emitting device 1 can form a fine stripe pattern at close range.

[0129] In the light-emitting device 1 according to this embodiment, the width W15 in the X direction of the first region 151 and the second region 152 may be 20 times the wavelength λ or less, which makes it possible to preferably form a large number of fine stripes over a wider region.

[0130] In the light-emitting device 1 according to this embodiment, the width of the intermediate region 155 in the X direction (i.e., the distance D15 between the first region 151 and the second region 152) may be 20 to 200 times the wavelength λ of the light. By setting the slit distance in this manner, it is possible to more suitably generate interference in the Fresnel region.

[0131] Furthermore, in the light-emitting device 1 according to this embodiment, the length L15 in the Y direction of the first region 151 and the second region 152 may be 20 to 1000 times the wavelength λ of the light. By making the length of the slit relatively short in this manner, it is possible to ensure uniformity in the irradiation intensity of the emitted light despite deviations in the distance to the target to be irradiated.

[0132] Furthermore, in the light-emitting device 1 according to this embodiment, the lens phase distribution φ for converging the emitted light is set to a phase distribution φ(x, y) related to the arrangement of the modified refractive index areas 15b in the light extraction area 15P. Ｌ (x, y) may be superimposed, in which case the emitted light can be irradiated over a wider range in the longitudinal direction of the stripes.

[0133] The above embodiment has described one aspect of the present invention. Therefore, the light-emitting device according to the present invention is not limited to the light-emitting device 1 according to the above embodiment, and may be modified as desired. For example, in the above embodiment, the lens phase distribution φ Ｌ An example of the case where (x, y) is superimposed has been described.

[0134] In contrast, in the light-emitting device 1, the lens phase distribution φ Ｌ Alternatively, instead of (x, y), the lens phase distribution φ Ｌ In addition to (x, y), a tilt phase distribution for tilting the emitted light may be superimposed. ＴｉｌｔＸ (x, y) is expressed by the following equation (32). According to this, a phase that is inclined in the X direction by a linear function is given. k ｘ is set to 0.1(2π / λ) or 0.2(2π / λ).

[0135]

[0136] The light-emitting device 1 according to this modification is an element using a partially diffracting M-point photonic crystal, and has a phase distribution φ(x, y) that is inclined relative to the phase distribution φ(x, y) as shown in Equation (32). ＴｉｌｔＸ An element was prototyped when (x, y) was superimposed. In this element structure, the spacing D15 was 60 μm, the width W15 was 2.0 μm, and the length L15 was 200 μm. Next, the results of the diffraction calculation (angular spectrum method) of this element will be explained. Here, as shown in FIG. 28, the wavelength λ was 0.94 μm, the calculation area was 1000 μm square, the calculation interval dx = dy was 0.47 μm (1 / 2 of the wavelength λ), and the propagation distance dZ was up to 2000 μm with a pitch of 50 μm.

[0137] 29, 30, and 31 are diagrams showing the propagation characteristics of an element when ±1st-order light corresponding to an actual device is superimposed. ｘ When is set to 0.1 (2π / λ), and k ｘ This corresponds to the case where the angle is set to 0.2 (2π / λ). In each diagram in FIG. 29, from the left column, the aperture phase, Fourier spectrum, and propagation characteristics are shown in the XY cross section at Z = 0.5 mm, the XY cross section at Z = 1.0 mm, the XY cross section at Z = 1.5 mm, and the XY cross section at Z = 2.0 mm. FIG. 30 shows the YZ cross section, and FIG. 31 shows the XZ cross section. It was confirmed that the element obtained the propagation characteristics shown in FIGS. 29 to 31, and that the emitted light could be tilted arbitrarily with respect to the Z direction.

[0138] 32, 33, and 34 are diagrams showing the propagation characteristics of the element in the case of only +1st-order light. ｘ When is set to 0.1 (2π / λ), and k ｘ This corresponds to the case where the angle is set to 0.2 (2π / λ). In each diagram in Figure 32, from the left column, the aperture phase, Fourier spectrum, and propagation characteristics are shown in the XY cross section at Z = 0.5 mm, the XY cross section at Z = 1.0 mm, the XY cross section at Z = 1.5 mm, and the XY cross section at Z = 2.0 mm. Also, Figure 33 shows the YZ cross section, and Figure 34 shows the XZ cross section. It was confirmed that the element obtained the propagation characteristics shown in Figures 32 to 34, and that the emitted light could be tilted arbitrarily with respect to the Z direction.

[0139] As described above, in the light-emitting device 1, the phase distribution φ(x, y) related to the arrangement of the modified refractive index areas 15b in the light extraction area 15P is compared with the tilted phase distribution φ ＴｉｌｔＸ (x, y) may be superimposed. In this case, it is possible to irradiate the emitted light obliquely onto the irradiation target. As a result, for example, in a module in which the light-receiving surface of the detector facing the irradiation target and the light-emitting surface of the light-emitting device 1 are arranged side by side, it is possible to irradiate light obliquely onto the area facing the light-receiving surface.

[0140] Meanwhile, in the above embodiment, the light-emitting device 1 realizing a pseudo double slit has been described. However, a multi-slit having three or more slits may be formed in the light-emitting device 1. Next, an example of forming a multi-slit will be described.

[0141] FIG. 35 is a diagram showing slits when a multi-slit is formed. (a) of FIG. 35 shows an example in which a double slit is formed by a first region 151 and a second region 152, as in the above embodiment. In this case, the distance D15 is 100 μm. (b) of FIG. 35 shows the light extraction region 15P, which includes a third region 153 spaced apart from the first region 151 on the opposite side of the second region 152 along the X direction, with an intermediate region 156 sandwiched therebetween. In the light extraction region 15P, multiple modified refractive index regions 15b are arranged so that light emitted from the active layer 12 and resonating in the XY in-plane direction in the phase modulation layer 15 is diffracted in the out-of-plane direction in the third region 153.

[0142] The arrangement of the modified refractive index areas 15b in the third region 153 is similar to that of the first region 151 and the second region 152. In the intermediate region 156, a plurality of modified refractive index areas 15b are arranged so that light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15 is not diffracted in the out-of-plane direction. That is, in (b) of Figure 35, a pseudo multi-slit (three slits) is formed in which the first region 151, the second region 152, and the third region 153 each serve as a slit. The spacing D15 in this case is 50 µm.

[0143] Figures 35(c) to 35(e) show the cases of five slits (spacing D15 = 25 μm), six slits (spacing D15 = 20 μm), and twelve slits (spacing D15 = 10 μm), respectively. Diffraction calculations (angular spectrum method) were performed for each of these cases. Here, the wavelength λ was set to 0.94 μm, the calculation area was set to 500 μm square, the aperture width (Y) (length L15) was set to 200 μm, the aperture width (X) (width W15) was set to 0.94 μm × 10 (10 times the wavelength λ), the calculation interval dx = dy was set to 0.47 μm (1 / 2 the wavelength λ), and the propagation distance dZ was set to 2000 μm at a pitch of 50 μm.

[0144] Figures 36 and 37 show the calculation results (propagation characteristics). Figures 36(a) and 36(b) respectively show the double-slit case shown in Figure 35(a) and the three-slit case shown in Figure 35(b). Figures 37(a) to 37(c) respectively show the three-slit case shown in Figure 35(c), the six-slit case shown in Figure 35(d), and the twelve-slit case shown in Figure 35(e). In each figure, the left column shows the XY cross section at Z = 2 mm, and the right column shows the XZ cross section. As shown in Figures 36 and 37, it was confirmed that a fine stripe pattern can also be formed at close range using multiple slits.

[0145] Figure 38 shows another example of a multi-slit configuration. Similar to Figures 35(a) to 35(e), Figures 38(a) to 38(e) show the cases of double slits, three slits, five slits, six slits, and 12 slits, respectively. Figure 38(f) shows the case of 21 slits. However, in Figure 38, the opening width (X) (width W15) is set to 0.94 μm × 1 (1x wavelength λ). Diffraction calculations (angular spectrum method) were performed for each of the above cases. Here, the wavelength λ was set to 0.94 μm, the calculation area was set to 500 μm square, the aperture width (Y) (length L15) was set to 200 μm, the aperture width (X) (width W15) was set to 0.94 μm × 1 (1 time the wavelength λ), the calculation interval dx = dy was set to 0.47 μm (1 / 2 the wavelength λ), and the propagation distance dZ was set to up to 2000 μm at a pitch of 50 μm.

[0146] Figures 39 and 40 show the calculation results (propagation characteristics). (a) to (c) of Figure 39 show, respectively, the double-slit case shown in Figure 38(a), the three-slit case shown in Figure 38(b), and the five-slit case shown in Figure 38(c). (a) to (c) of Figure 40 show, respectively, the six-slit case shown in Figure 38(d), the six-slit case shown in Figure 38(d), the twelve-slit case shown in Figure 38(e), and the twenty-one-slit case shown in Figure 38(f). In each figure, the left column shows the XY cross section at Z = 2 mm, and the right column shows the XZ cross section. As shown in Figures 39 and 40, it was confirmed that even with such a multi-slit configuration, a fine stripe pattern can be formed at close range.

[0147] In the light-emitting device 1, instead of the first region 151 and the second region 152, a first region 151A and a second region 152B may be used as shown in Fig. 41. The first region 151A and the second region 152A have the same properties as the first region 151 and the second region 152, but differ in that they extend in the X direction and the Y direction so as to intersect with each other to form a cross-shaped light extraction region 15P. Note that (b) in Fig. 41 shows the Fourier spectrum.

[0148] Diffraction calculations (angular spectrum method) were performed for the case shown in Fig. 41. Here, the wavelength λ was set to 0.94 µm, the calculation area was set to 500 µm square, the aperture width (Y) (the length of each slit in the long direction) was set to 200 µm, the aperture width (X) (the width W15 of each slit) was set to 0.94 µm x 1 (1x the wavelength λ), the calculation interval dx = dy was set to 0.47 µm (1 / 2 the wavelength λ), and the propagation distance dZ was set to up to 2000 µm at a pitch of 50 µm.

[0149] Figures 42 and 43 are diagrams showing the calculation results (propagation characteristics). Figure 42 (a) to (d) show, respectively, the XY cross section of the propagation characteristics at Z = 500 μm, the XY cross section at Z = 1000 μm, the XY cross section at Z = 1500 μm, and the XY cross section at Z = 2000 μm. Figure 43 also shows the YZ cross section of the propagation characteristics. As shown in Figures 42 and 43, it was confirmed that a fine stripe pattern can be formed even with such cross-shaped slits.

[0150] In the above embodiment, the first region 151 and the second region 152 are separated from each other. However, in the light-emitting device 1, the light extraction region 15P may be formed in a ring shape that includes the first region 151 and the second region 152 and surrounds the intermediate region 155. Fig. 44 is a diagram showing an example of the light extraction region 15P formed in a ring shape.

[0151] As shown in Fig. 44, the light extraction region 15P is formed in a circular ring shape. The first region 151 and the second region 152 can be included in the light extraction region 15P as portions of the circular light extraction region 15P that face each other in the X direction. Note that (b) of Fig. 44 shows a Fourier spectrum.

[0152] Diffraction calculations (angular spectrum method) were performed for the case shown in Figure 44. Here, the wavelength λ was 0.94 μm, the calculation area was 500 μm square, the calculation interval dx = dy was 0.47 μm (1 / 2 of the wavelength λ), and the propagation distance dZ was up to 2000 μm at a pitch of 50 μm. In addition, here, the outer diameter of the light extraction area 15P was 47 μm, and the inner diameter of the light extraction area 15P was 41 μm.

[0153] 45 and 46 are diagrams showing the calculation results (propagation characteristics). (a) to (d) in FIG. 45 are, respectively, the XY cross section of the propagation characteristics at Z=500 μm, the XY cross section at Z=1000 μm, the XY cross section at Z=1500 μm, and the XY cross section at Z=2000 μm. FIG. 46 also shows the YZ cross section of the propagation characteristics. As shown in FIGS. 45 and 46, it was confirmed that a fine stripe pattern can be formed even with such annular slit.

[0154] Figure 47 is a diagram showing an example in which the light extraction region 15P is formed in another ring shape. As shown in Figure 47, the light extraction region 15P is formed in a ring shape, as in the case of Figure 44. In addition, here, the inner diameter of the light extraction region 15P is 8.5 μm and the outer diameter is 28 μm. Note that (b) of Figure 47 shows the Fourier spectrum.

[0155] Diffraction calculations (angular spectrum method) were performed for the case shown in Figure 47. Here, the wavelength λ was 0.94 μm, the calculation area was 500 μm square, the calculation interval dx = dy was 0.47 μm (1 / 2 of the wavelength λ), and the propagation distance dZ was up to 2000 μm at a pitch of 50 μm. In addition, here, the outer diameter of the light extraction area 15P was 47 μm, and the inner diameter of the light extraction area 15P was 41 μm.

[0156] Figures 48 and 49 are diagrams showing the calculation results (propagation characteristics). Figure 48 (a) to (d) show, respectively, the XY cross section of the propagation characteristics at Z = 500 μm, the XY cross section at Z = 1000 μm, the XY cross section at Z = 1500 μm, and the XY cross section at Z = 2000 μm. Figure 49 also shows the YZ cross section of the propagation characteristics. It was confirmed that such an annular slit can obtain the propagation characteristics shown in Figures 48 and 49.

[0157] Here, the light extraction region 15P is not limited to a perfect circular ring shape, but may be formed in an elliptical ring shape as shown in Fig. 50. In the example of Fig. 50, the light extraction region 15P has a width of (2x ２ +y ２ ) is formed in an elliptical shape defined by (b) of FIG. 50. Note that (b) of FIG. 50 shows the Fourier spectrum.

[0158] Diffraction calculations (angular spectrum method) were performed for the case shown in Figure 50. Here, the wavelength λ was set to 0.94 μm, the calculation area was set to 500 μm square, the calculation interval dx = dy was set to 0.47 μm (1 / 2 of the wavelength λ), and the propagation distance dZ was set to 2000 μm with a pitch of 50 μm. Figures 51 and 52 show the calculation results (propagation characteristics). Figures 51 (a) to 51 (d) respectively show the XY cross section of the propagation characteristics at Z = 500 μm, the XY cross section at Z = 1000 μm, the XY cross section at Z = 1500 μm, and the XY cross section at Z = 2000 μm. Figure 52 also shows the YZ cross section of the propagation characteristics. As shown in Figures 51 and 52, it was confirmed that a fine stripe pattern can be formed even with such an elliptical annular slit.

[0159] 53 is a diagram showing another case where the light extraction region 15P is formed in an elliptical ring shape. In the example of FIG. 53, the light extraction region 15P has a width of (4× ２ +y ２ ) is formed in an elliptical shape defined by (b) of FIG. 53. Note that (b) of FIG. 53 shows the Fourier spectrum.

[0160] Diffraction calculations (angular spectrum method) were performed for the case shown in Figure 53. Here, the wavelength λ was set to 0.94 μm, the calculation area was set to 500 μm square, the calculation interval dx = dy was set to 0.47 μm (1 / 2 of the wavelength λ), and the propagation distance dZ was set to 2000 μm with a 50 μm pitch. Figures 54 and 55 show the calculation results (propagation characteristics). Figures 54 (a) to (d) show the XY cross sections of the propagation characteristics at Z = 500 μm, Z = 1000 μm, Z = 1500 μm, and Z = 2000 μm, respectively. Figure 55 also shows the YZ cross section of the propagation characteristics. As shown in Figures 54 and 55, it was confirmed that a fine stripe pattern can be formed even with such an elliptical annular slit.

[0161] As described above, in the light-emitting device 1, a pseudo double slit may be formed by the first region 151 and the second region 152, which are part of the light extraction region 15P formed in an annular shape surrounding the intermediate region 155.

[0162] In the light-emitting device 1, the first region 151 and the second region 152, which provide the respective openings of the pseudo-slits, may have different amplitude intensity ratios. The amplitude intensity ratio in the first region 151 and the second region 152 can be adjusted, for example, by changing the shift amount of the modified refractive index region 15b in each of the first region 151 and the second region 152 (e.g., the shift amount of the center of gravity G of the modified refractive index region 15b from the lattice point O(x, y)). For example, the amplitude intensity can be weakened by reducing the shift amount of the modified refractive index region 15b, and diffraction can be prevented by setting the shift amount to zero.

[0163] In this way, the propagation characteristics were calculated for the case where the amplitude intensity was made different between the first region 151 and the second region 152. Here, the aperture interval (distance D15) was set to 60 μm, the aperture height (width W15) was set to 4.7 μm, and the aperture height (length L15) was set to 200 μm.

[0164] 56 and 57 show the propagation characteristics (|E| ２ ) are diagrams showing the results. (a) to (e) of Figures 56 and 57 show, respectively, the cases where the ratio of the amplitude intensity of the first region 151 to the amplitude intensity of the second region 152 is 1:1, 1:2, 1:4, 1:10, and 1:∞ (single slit). Also, for each of (a) to (e) of Figure 56, from the left column, the aperture plane (XY plane) at Z = 0, the Fourier spectrum, the XXY cross section at Z = 0.5 mm, the XY cross section at Z = 1.0 mm, the XY cross section at Z = 1.5 mm, the XY cross section at Z = 2, and the XZ cross section are shown. Also, for each of (a) to (e) of Figure 57, from the left column, the aperture plane (XY plane) at Z = 0 and the YZ cross section are shown.

[0165] Fig. 58 is a diagram showing propagation characteristics (E.real) when the amplitude intensity is varied. (a) to (e) of Fig. 58 show, respectively, the cases where the ratio of the amplitude intensity of the first region 151 to the amplitude intensity of the second region 152 is 1:1, 1:2, 1:4, 1:10, and 1:∞. Furthermore, for each of (a) to (e) of Fig. 58, from the left column, the aperture plane (XY plane), YZ cross section, and XZ cross section at Z=0 are shown.

[0166] As shown in Figures 56 to 58, when the amplitude intensity ratio was 1:1 to 1:10, a fine stripe pattern was formed, although the contrast decreased as the intensity ratio increased. On the other hand, when the amplitude intensity ratio was 1:∞ (single hole), no stripe pattern was obtained. Furthermore, when the amplitude intensity ratio was 1:1 to 1:4, the center position of the stripe in the XY plane changed. As described above, in the light-emitting device 1, it is possible to shift the stripe by changing the amplitude intensity ratio in the first region 151 and the second region 152, and it is believed that this can be applied to high-precision shape measurement as required.

[0167] Although various modifications have been described above, the present invention is not limited to the above-described examples and can be further modified in any manner.

[0168] For example, in the above-described embodiment and modified example, the phase modulation layer 15 has an M-point photonic crystal structure, which is a square lattice photonic crystal structure. However, the phase modulation layer 15 may have a J-point photonic crystal structure with a triangular lattice.

[0169] In addition, in other embodiments and modifications, the modified refractive index structure in the phase modulation layer 15 is shown as modulating the position from the lattice point position as in Figures 5 and 14, but it is also possible to modulate the size instead of the position, or to change the position and size simultaneously.

[0170] Next, further modified examples will be described. In the light-emitting device 1 according to the above embodiment, the phase modulation layer 15 (light extraction region 15P) has a first region 151 and a second region 152 spaced apart along the X direction, and the first region 151 and the second region 152 are linear regions extending elongatedly in the Y direction. However, as shown in (a) of FIG. 59, the first region 151 and the second region 152 may be spaced apart along the X direction with an intermediate region 155 interposed therebetween and may be dot-like regions. Here, dot-like means a shape whose size in the X direction and the size in the Y direction are equal.

[0171] 60A, here, the first region 151 and the second region 152 are each formed as a rectangular opening. In this example, the opening width of the rectangular opening in the X direction (ξ direction) is 2ω ｘ and the opening width in the Y direction (η direction) is 2ω ｙ In this case, aperture diffraction (Fraunhofer diffraction) is expressed by the following formula (33).

[0172]

[0173] where sinc(x) = sin(x) / x and A = 4ω ｘ ω ｙ As shown in FIG. 60(b), the diffraction spread Δ and spread angle θ due to a rectangular aperture are expressed by the following formula (34) (for example, the spread in the X direction Δ ｘ and the divergence angle θ ｘ and similarly for the Y direction).

[0174]

[0175] When the opening width becomes smaller, the expansion angle θ ｘ becomes larger, and the divergence angle θ ｘ For example, when the wavelength λ is 0.94 μm and 2ω ｘ = 2ω ｙ = 5 μm, the divergence angle θ ｘ is about 10.65 deg, and the spread Δ ｘ is about 752 μm.

[0176] In contrast to this, when two rectangular apertures are provided, such as the first region 151 and the second region 152 shown in (a) of FIG. 59, the aperture diffraction is such that the aperture widths are both 2ω as shown in (a) of FIG. ｘ , 2ω ｙ When the opening interval (the interval between the first region 151 and the second region 152) is L, it is expressed by the following formula (35).

[0177]

[0178] The sinc function part of I(x, y) in the above equation (35) represents the rectangular aperture diffraction, and the cos function part represents the stripes with a period (λz / L). At this time, as shown in FIG. 61(b), the spread Δ (Δ = (λz ｓ The distance in the Z direction at which the distance (ω) / ω) is equal to the aperture interval L is the interference distance Z, which is the distance at which interference of the light emitted from each aperture begins. ｓ and Z ｓ = (Lω) / λ. When the aperture interval L becomes smaller, the interference distance Zs also becomes smaller, and when the aperture interval L becomes larger, the interference distance Zs also becomes smaller. As an example, when the wavelength λ is 0.94 μm and 2ω ｘ = 2ω ｙ = 5 μm, Z = 2 mm, the interference distance Z ｓ = 266 μm.

[0179] Figure 59(b) shows the propagation characteristics (E.real) in the case of the above-described two-aperture diffraction. In the example of Figure 59(b), the aperture spacing L = 100 μm, and the range shown is 2000 μm in the Z direction and 800 μm in the X direction. As shown in Figure 59(b), it can be seen that the light emitted from each rectangular aperture (first region 151 and second region 152) overlaps as it propagates in the Z direction, causing interference with each other and forming a fine stripe pattern.

[0180] Fig. 62 is a diagram showing the aperture shape when the distance (aperture interval) between the first and second regions is changed to various values. The aperture intervals L of the respective parts in Fig. 62 are 20 μm, 50 μm, 100 μm, and 150 μm from the top left, and 200 μm, 300 μm, and 400 μm from the bottom left.

[0181] FIG. 63 shows the Fourier spectrum (absolute value (far solution)) corresponding to each part of FIG. 62, and FIG. 64 shows the light intensity (|E| ２) and Fig. 65 shows the electric field amplitude (E.real) at Z = 2 mm corresponding to each part of Fig. 62. Each part of Fig. 64 and Fig. 65 is an area of ​​800 μm square in the X and Y directions. As shown in Figs. 62 to 65, it can be seen that a fine stripe pattern is formed even when the opening interval L is changed to each value. The stripe interval s in the stripe pattern is expressed as s = (λz) / L, and the interference distance Z ｓ As mentioned above, ｓ When the aperture interval L becomes smaller, the fringe interval s becomes larger, the number of fringes decreases, and the interference distance Z ｓ Furthermore, when the aperture interval L increases, the fringe interval s decreases, the number of fringes increases, and the interference distance Zs increases.

[0182] Specifically, when the aperture spacing L is set to 20 μm, 50 μm, 100 μm, 150 μm, 200 μm, 300 μm, and 400 μm as described above, the calculated results of the fringe spacing s using the above formula (values ​​at wavelength λ = 0.94 μm and Z = 2000 μm) are 94 μm, 37.6 μm, 18.8 μm, 12.5 μm, 9.4 μm, 6.3 μm, and 4.7 μm, respectively. Furthermore, when the central fringe spacing is measured from the propagation calculation results shown in Figures 64 and 65 under similar conditions, the results are 93 μm, 38 μm, 18.8 μm, 12.2 μm, 9.4 μm, and 6.1 μm (unknown when the aperture spacing L is 400 μm), and it can be seen that the interference at the position Z = 2 mm of the two-aperture diffraction can be explained by Fraunhofer diffraction.

[0183] From the above, the following findings were obtained regarding interference due to two-aperture diffraction (two-aperture interference). (1) Two-aperture interference is the product of rectangular aperture diffraction and the interference effect (the above formula (35)). (2) When the aperture width of the rectangular aperture is narrow, the divergence angle θ of rectangular aperture diffraction increases. (3) Two-aperture interference depends on the aperture width ω of the divergence angle θ of rectangular aperture diffraction, and interference occurs within this. (4) Due to the interference effect, two-aperture interference has the following tendency, independent of the aperture width ω. (4-1) Fringe spacing s = (λz) / L (λ: wavelength, z: distance in the propagation direction, L: aperture spacing). (4-2) When the aperture spacing L becomes smaller, the fringe spacing s becomes larger, the number of fringes decreases, and the interference distance Z ｓ(4-2) When the aperture interval L increases, the fringe interval s decreases, the number of fringes increases, and the interference distance Zs increases.

[0184] The above-described modified examples are examples in which the phase modulation layer 15 (light extraction region 15p) includes two rectangular openings (i.e., the first region 151 and the second region 152). On the other hand, in the light-emitting device 1, the phase modulation layer 15 (light extraction region 15p) may have three or more rectangular openings.

[0185] 66A is a diagram showing a case where three or more rectangular openings are provided on the circumference. In this example, the phase modulation layer 15 (light extraction region 15p) has a plurality of rectangular openings P Ｎ (N is an integer of 3 or more). In this case, for example, a rectangular opening P １ is the first region 151, and the rectangular opening P ２ is defined as the second region 152, the phase modulation layer 15 (light extraction region 15p) has one or more third regions 153 (rectangular openings P ３ ~P Ｎ The third region 153 is a region in which a plurality of modified refractive index regions 15 b are arranged so that light emitted from the active layer 12 and resonating in the in-plane direction of the first surface in the phase modulation layer 15 is diffracted in the out-of-plane direction of the first surface.

[0186] In this case, when there is one third region 153 (when N = 3), the one third region 153 is arranged within the first surface (here, circumferentially) while being spaced apart from the first region 151 and the second region 152 with an intermediate region 155 sandwiched therebetween. Also, when there are multiple third regions 153 (when N ≧ 4), one third region 153 is arranged within the first surface (here, circumferentially) while being spaced apart from the first region 151, the second region 152, and another third region 153 with an intermediate region 155 sandwiched therebetween. Then, the outgoing light beams diffracted in the out-of-plane direction in each of the third region 153, the first region 151, and the second region 152 interfere with each other, thereby forming interference fringes in the Fresnel region.

[0187] In the example of FIG. 66(a), as shown in FIG. 66(b), the opening width of each rectangular opening in the X direction (ξ direction) is 2ω ｘ and the opening width in the Y direction (η direction) is 2ω ｙ As an example, 2ω ｘ and 2ω ｙ are 5 μm, and the radius r of the circumference on which the rectangular apertures are arranged is 100 μm. In this case, aperture diffraction (multiple points on the circumference of a rectangular aperture) is expressed by the following formula (36): ｍ is expressed by the following equation (37).

[0188]

[0189]

[0190] The sinc function part in I(x, y) of the above equation (36) represents the rectangular aperture diffraction, and the exponential function part represents the interference fringes.

[0191] Fig. 67 is a diagram showing the aperture shapes when the number of rectangular apertures (the number N) is changed in sequence. The numbers of rectangular apertures in Fig. 67 are 1, 2, 3, and 4 from the top left, 5, 6, 7, and 8 from the middle left, and 12 and 20 from the bottom left.

[0192] FIG. 68 shows the Fourier spectrum (absolute value (far solution)) corresponding to each part of FIG. 67, and FIG. 69 shows the light intensity (|E| ２ ) and Fig. 70 shows the electric field amplitude (E.real) at Z = 2 mm corresponding to each part of Fig. 68. Each part of Figs. 69 and 70 has an area of ​​800 μm square in the X and Y directions. As shown in Figs. 67 to 70, the phase modulation layer 15 (light extraction region 15p) has a plurality of rectangular openings P Ｎ (N is an integer of 3 or more) in the case where the stripe pattern is formed. ＮThe pattern includes a pattern in which an interference fringe formed by the interference of light emitted from each of any two rectangular apertures among the rectangular apertures interacts with (for example, forms an intersection with) an interference fringe formed by the interference of light emitted from each of any two rectangular apertures, at least one of which is different.

[0193] 71(a) is a diagram showing a case where there are three rectangular openings on the circumference (when N=3). In the example of FIG. 71(a), as shown in FIG. 71(b), each rectangular opening P １ ~P ３ The opening width in the X direction (ξ direction) is 2ω ｘ and the opening width in the Y direction (η direction) is 2ω ｙ As an example, 2ω ｘ and 2ω ｙ are 5 μm, and the radius r of the circumference on which the rectangular openings are arranged is 100 μm.

[0194] In this case, the aperture diffraction (multiple points on a circumference of a rectangular aperture) is expressed by the above formula (36), but Θ in the above formula (36) ｍ corresponds to the case where m=1, 2, 3, and is expressed by the following formula (38).

[0195]

[0196] Therefore, I(x, y) in the above equation (36) is expressed as Θ in the above equation (38). １ ~Θ ３ Using the above equation, it is expressed as in the following equation (39). However, the cos function part of the following equation (39) is obtained by expressing the exponential function part of I(x, y) in the above equation (36) as the sum of complex exponential functions using each element of the matrix of the following equation (40). Furthermore, each element of the matrix of the following equation (40) is as shown in the following equation (41). The following equation (40) is obtained by expressing the ΣΣexp(j(Θ ｍ１ -Θ ｍ２)) for the sake of convenience in calculation. For this reason, in the following formula (40), the lower left part of the matrix is ​​omitted, but the (j,i) component M(j,i) has an element with the opposite sign, such as M(j,i) = -M(i,j), for the (i,j) component M(i,j). This point is also true for formulas (44) and (48) described later. ΣΣexp(j(Θ ｍ１ -Θ ｍ２ )) terms determine the interference pattern.

[0197]

[0198]

[0199]

[0200] From the above, the period L per term of the interference fringes shown in I(x, y) in the above equation (39) is １ When the radius of the circumference is r = 100 μm, the wavelength λ = 0.94 μm, and z = 2000 μm, L １ = (λz) / (r√3) = 10.85 μm, and the period of the third term (period of intersections) L ２ (See FIG. 72(b)), L ２ = {(λz) / (r√3)}·(2 / √3) = (2λz) / (3r) = 12.53 μm. This is the light intensity (|E| ２ ) is in good agreement with the dot spacing of 12.5 μm measured in

[0201] 73 is a diagram showing a case where there are four rectangular openings on the circumference (when N=4). In the example of FIG. 73(a), as shown in FIG. 73(b), each rectangular opening P １ ~P ４ The opening width in the X direction (ξ direction) is 2ω ｘ and the opening width in the Y direction (η direction) is 2ω ｙ As an example, 2ω ｘ and 2ω ｙ are 5 μm, and the radius r of the circumference on which the rectangular openings are arranged is 100 μm.

[0202] In this case, the aperture diffraction (multiple points on a circumference of a rectangular aperture) is expressed by the above formula (36), but Θ in the above formula (36) ｍ corresponds to the case where m=1, 2, 3, 4, and is expressed by the following formula (42).

[0203]

[0204] Therefore, I(x, y) in the above equation (36) is Θ in the above equation (42) １ ~Θ ４ is expressed as in the following equation (43): where the cos function part of the following equation (43) is obtained by expressing the exponential function part of I(x, y) in the above equation (36) as a sum of complex exponential functions using each element of the matrix of the following equation (44). Furthermore, each element of the matrix of the following equation (44) is as shown in the following equation (45).

[0205]

[0206]

[0207]

[0208] From the above, the period L of the intersections of the interference fringes shown in I(x, y) in the above equation (43) ２ (See FIG. 74(b)), when the radius of the circumference is r=100 μm, the wavelength λ=0.94 μm, and z=2000 μm, L ２ = (λz) / (r√2) = 13.29 μm. This is the light intensity (|E| ２ ) is in good agreement with the dot spacing of 13.3 μm measured in

[0209] 75 is a diagram showing a case where six rectangular openings are arranged on the circumference (N=6). In the example of FIG. 75(a), as shown in FIG. 75(b), each rectangular opening P １ The opening width of P in the X direction (ξ direction) is 2ω ｘ and the opening width in the Y direction (η direction) is 2ω ｙ As an example, 2ω ｘ and 2ω ｙ are 5 μm, and the radius r of the circumference on which the rectangular openings are arranged is 100 μm.

[0210] In this case, the aperture diffraction (multiple points on a circumference of a rectangular aperture) is expressed by the above formula (36), but Θ in the above formula (36) ｍ corresponds to the case where m=1, 2, 3, 4, 5, 6, and is expressed by the following formula (46).

[0211]

[0212] Therefore, I(x, y) in the above equation (36) is Θ in the above equation (46) １ Using Θ6, it is expressed as in the following equation (47). However, the cos function part of the following equation (47) is obtained by expressing the exponential function part of I(x, y) in the above equation (36) as the sum of complex exponential functions using each element of the matrix in the following equation (48). Also, α in the following equation (47) is α=(πr) / (λz).

[0213]

[0214]

[0215] From the above, the period L of the intersections of the interference fringes shown in I(x, y) in the above equation (47) ２ (See FIG. 76(b)). When the radius of the circumference is r=100 μm, the wavelength λ=0.94 μm, and z=2000 μm, L ２ = (2λz) / (√3r) = 21.71 μm. This is the light intensity (|E| ２ ) is in good agreement with the dot spacing of 21.8 μm measured in

[0216] From the above, the following findings were obtained regarding interference due to circumferential multi-point aperture diffraction (circumferential multi-point aperture interference). (1) Circumferential multi-point aperture interference is also the product of rectangular aperture diffraction and the interference effect (formula (36) above). (2) Circumferential multi-point aperture interference has the following tendencies due to the interference effect. (2-1) 2 points: The stripe pattern is a one-dimensional stripe (same as 2-aperture interference). (2-2) 3 points: The stripe pattern is a two-dimensional triangular lattice (a periodic, close-packed two-dimensional multi-point array). (2-3) 4 points: The stripe pattern is a two-dimensional square lattice (a periodic two-dimensional multi-point array). (2-4) 6 points: The stripe pattern is a two-dimensional triangular lattice (a wider pitch than 3 points). (2-5) Others: A mandala-patterned array of bright points.

[0217] The above-described modified examples are examples in which the phase modulation layer 15 (light extraction region 15p) includes a plurality of rectangular openings (i.e., the first region 151, the second region 152, and one or more third regions 153) on the circumference. On the other hand, in the light-emitting device 1, the rectangular openings in the phase modulation layer 15 (light extraction region 15p) may be arranged on a one-dimensional or two-dimensional straight line.

[0218] FIG. 77 shows a plurality of rectangular openings P ｍ 66A is a diagram showing an arrangement of rectangular openings P ｍ One of the rectangular openings P ｍ When another one of the second regions 152 is used as the second region 152, the phase modulation layer 15 (light extraction region 15p) has one or more third regions 153 (rectangular openings P ｍ The remainder of the

[0219] In the example of FIG. 77(a), as shown in FIG. 77(b), each rectangular opening P ｍ The opening width in the X direction (ξ direction) is 2ω ｘ and the opening width in the Y direction (η direction) is 2ω ｙ As an example, 2ω ｘ and 2ω ｙ and are 5 μm. In this case, aperture diffraction (array-arranged multi-point rectangular aperture diffraction (one-dimensional)) is expressed by the following formula (49).

[0220]

[0221] The rectangular aperture diffraction is represented by the sinc function part in I(x, y) of the above formula (49), and the interference fringes are represented by the sin function part. The function form of the interference fringes represented by this sin function part is represented by the following formula (50) using the coefficient a.

[0222]

[0223] 78 is a graph showing the function f(x) expressed by the above formula (50). The main properties of the function f(x) are as shown in the following formula (51).

[0224]

[0225] The fringe spacing s is s = (λz) / L = 18.8 μm (where the aperture spacing L = 100 μm, wavelength λ = 0.94, z = 2000 μm), which is the same as the fringe spacing s in two-aperture diffraction.

[0226] FIG. 79 shows a plurality of rectangular openings P at the intersections of a plurality of straight lines along the X direction (ξ direction) and a plurality of straight lines along the Y direction (η direction). ｍ 79(a) shows the case where rectangular apertures P (m=1 to N) are arranged (i.e., the case where rectangular apertures are arranged in a two-dimensional array). In the example of FIG. 79(a), as shown in FIG. 79(b), each rectangular aperture P ｍ The opening width in the X direction (ξ direction) is 2ω ｘ and the opening width in the Y direction (η direction) is 2ω ｙ As an example, 2ω ｘ and 2ω ｙ In this case, the aperture diffraction (array-arranged multi-point rectangular aperture diffraction (two-dimensional)) is expressed by the following formula (52): ｘ is the aperture spacing in the X direction, and L ｙ is the aperture spacing in the Y direction.

[0227]

[0228] Stripe spacing s in the X direction ｘ and the stripe spacing s in the Y direction ｙ are respectively, s ｘ = (λz) / L ｘ , and s ｙ = (λz) / L ｙ which is the same as the fringe spacing s in two-aperture diffraction.

[0229] 80 is a diagram showing the aperture shape when the number of rectangular apertures (number N) is changed in arrayed multi-point rectangular aperture diffraction (two-dimensional). From the top left of FIG. 80, N=4 (2×2) and the aperture spacing L ｘ , L ｙ = 200 μm, N = 9 (3 × 3), and the opening interval L ｘ , L ｙ= 100 μm, N = 16 (4 × 4), and the opening interval L ｘ , L ｙ = 66.7 μm, and in order from the bottom left, N = 25 (5 × 5) and the opening interval L ｘ , L ｙ = 50 μm, N = 400 (20 × 20), and the opening interval L ｘ , L ｙ In both cases, rectangular openings are arranged in an area of ​​200 μm square in the X and Y directions.

[0230] FIG. 81 shows the Fourier spectrum (absolute value (far solution)) corresponding to each part of FIG. 80, and FIG. 82 shows the light intensity (|E| ２ ) and Figure 83 shows the electric field amplitude (E.real) at Z = 2 mm corresponding to each part of Figure 81. Each part of Figures 82 and 83 is an 800 μm square area in the X and Y directions. As shown in Figures 80 to 83, it can be seen that in array-arranged multipoint rectangular aperture diffraction (two-dimensional), even when the number of rectangular apertures is changed to various values, a fine stripe pattern is formed. The theoretical stripe spacing at Z = 2 mm is 9.4 μm, 18.8 μm, 28.2 μm, 37.6 μm, and 178.6 μm, respectively.

[0231] From the above, the following findings were obtained regarding interference due to arrayed multipoint rectangular aperture diffraction (two-dimensional): (1) At 2x2, the stripe pattern becomes a two-dimensional square lattice (a periodic two-dimensional array of multipoints), similar to the four-point case of circumferential multipoint aperture interference. (2) At 3x3 or larger, the stripe pattern changes due to the appearance of bright spots associated with the main bright spot due to the influence of the tail of the interference function. (3) At 20x20, the stripe pattern approaches that of a 1x1 rectangular aperture.

[0232] Next, we will consider the case where the number of rectangular apertures and the aperture interval are changed in the arrayed multi-point rectangular aperture diffraction (two-dimensional). Figure 84 is a diagram showing the aperture shape when the aperture interval is sequentially changed for each number of rectangular apertures in the arrayed multi-point rectangular aperture diffraction (two-dimensional). Here, the aperture interval is the aperture interval Lｘ and opening interval L ｙ The upper part of Fig. 84 shows the case where the number of rectangular openings is 4 (2 × 2 case), the middle part of Fig. 84 shows the case where the number of rectangular openings is 9 (3 × 3 case), and the lower part of Fig. 84 shows the case where the number of rectangular openings is 16 (4 × 4 case). In the upper, middle, and lower parts of Fig. 84, the opening intervals are 50 μm, 100 μm, and 200 μm, respectively, from the left.

[0233] FIG. 85 shows the Fourier spectrum (absolute value (far solution)) corresponding to each part of FIG. 84, and FIG. 86 shows the light intensity (|E| ２ ), and FIG. 87 shows the electric field amplitude (E.real) at Z=2 mm corresponding to each part of FIG. 84. Each part of FIGS. 86 and 87 is an area of ​​800 μm square in the X and Y directions. As shown in FIGS. 84 to 87, it can be seen that in arrayed multipoint rectangular aperture diffraction (two-dimensional), a stripe pattern is formed even when the aperture spacing of the rectangular apertures is changed. Furthermore, the theoretical stripe spacing s at Z=2 mm is 37.6 μm, 18.8 μm, and 9.4 μm when the aperture spacing is 50 μm, 100 μm, and 200 μm, respectively. For example, the light intensity (|E| ２ ) which is in good agreement with the dot spacing measured in

[0234] From the above, the following further findings were obtained regarding interference due to arrayed multipoint rectangular aperture diffraction (two-dimensional): (1) The spacing between each bright spot (stripe spacing s) closely matches the theoretical value. (2) For a 2x2 array, the stripe pattern forms a two-dimensional square lattice (a periodic two-dimensional array of multipoints), similar to the four-point case of circular multipoint aperture interference. (3) For an aperture spacing of 3x3 or greater, the stripe pattern changes due to the influence of the tail of the interference function, with bright spots appearing adjacent to the main bright spot when the aperture spacing is 100 μm or less (bright spot spacing of 18.8 μm or greater). (4) For an aperture spacing of 200 μm (bright spot spacing of 9.4 μm), clear bright spot arrays were obtained even with 3x3 and 4x4 arrays. In other words, it is believed that the influence of the tail of the interference function can be suppressed by increasing the aperture spacing sufficiently. However, to maintain an aperture spacing of 200 μm, the area increases as the number of rectangular apertures increases.

[0235] Next, another modified example will be described. Fig. 88 is a cross-sectional view showing the layered structure of a light-emitting device according to this modified example. As shown in Fig. 88, a light-emitting device 1A according to this modified example differs from the light-emitting device 1 according to the above embodiment in that it includes a ridge waveguide 52.

[0236] That is, the light-emitting device 1A includes a base 51 and a ridge waveguide 52. The base 51 includes a semiconductor substrate 10, a cladding layer 11, a waveguide layer (guiding layer) 21A, and an active layer 12. The cladding layer 11, the waveguide layer 21A, and the active layer 12 are stacked in this order on the major surface 10a of the semiconductor substrate 10. The waveguide layer 21A is made of a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor. As an example, the waveguide layer 21A is made of AlGaAs.

[0237] The ridge waveguide 52 includes a phase modulation layer 15, a waveguide layer (guiding layer) 22A, a cladding layer 13, and a contact layer 14. The phase modulation layer 15, the waveguide layer 22A, the cladding layer 13, and the contact layer 14 are stacked in this order on the base 51 (i.e., the active layer 12). The waveguide layer 22A is made of a compound semiconductor such as a GaAs-based semiconductor, an InP-based semiconductor, or a nitride-based semiconductor. As an example, the waveguide layer 22A is made of AlGaAs.

[0238] As described above, in the light-emitting device 1A, the active layer 12 and the phase modulation layer 15 are formed on the semiconductor substrate 10, and a ridge waveguide 52 including at least the phase modulation layer 15 is formed on the semiconductor substrate 10. By setting the width of the ridge waveguide 52 (the size in a direction intersecting the extending direction of the ridge waveguide 52) to, for example, a sub-wavelength to several times the wavelength of the light emitted from the active layer 12, it is possible to suppress the proliferation of modes.

[0239] Fig. 89 is a plan view of the light-emitting device shown in Fig. 88. As shown in Fig. 89, in the light-emitting device 1A, the ridge waveguide 52 (i.e., the phase modulation layer 15) extends linearly along the X direction when viewed from the Z direction. The first region 151 and the second region 152 are arranged along the X direction within the ridge waveguide 52, spaced apart from each other with an intermediate region 155 sandwiched therebetween. Therefore, the first region 151 and the second region 152 are connected to each other by the ridge waveguide 52.

[0240] 90 is a schematic plan view showing an enlarged view of the ridge waveguide shown in FIG. 89 . As shown in FIG. 90 , in the light-emitting device 1A, the modified refractive index areas 15b are formed in a rectangular shape extending in the Y direction (the width direction of the ridge waveguide 52), and in the phase modulation layer 15, a plurality of such modified refractive index areas 15b are arranged along the X direction. As a result, in the light-emitting device 1A, a diffraction grating is formed according to the arrangement of the modified refractive index areas 15b. In the intermediate region 155, the modified refractive index areas 15b are arranged to form a first-order diffraction grating that prevents perpendicular diffraction of light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15. The first-order diffraction grating in the intermediate region 155 has a grating spacing a1 = wavelength λ / 2 / refractive index n. As a result, in the intermediate region 155, light from the active layer 12 is prevented from being diffracted in an out-of-plane direction of the XY plane (in-plane diffraction in the direction Dds shown in the figure).

[0241] On the other hand, in this example, the modified refractive index area 15b is arranged in the first area 151 and the second area 152 so as to form a second-order diffraction grating that perpendicularly diffracts light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15. The second-order diffraction gratings in the first area 151 and the second area 152 have a grating spacing a2 = wavelength λ / refractive index n. This causes the light from the active layer 12 to be diffracted in the out-of-plane direction of the XY plane in the first area 151 and the second area 152.

[0242] Thus, here, the phase modulation layer 15 has a plurality of modified refractive index areas 15b distributed one-dimensionally in the XY plane, and a light extraction area 15p including a first area 151 and a second area 152 is formed according to the arrangement of the plurality of modified refractive index areas 15b (for example, according to the grating spacing of the diffraction grating formed by the modified refractive index areas 15b as described above). Furthermore, a plurality of modified refractive index areas 15b is also arranged in the intermediate area 155.

[0243] The modified refractive index area 15b does not have to be formed in the intermediate area 155. That is, in the intermediate area 155, the transverse mode in the ridge width direction may be controlled by the ridge structure of the ridge waveguide 52, without forming a diffraction grating.

[0244] 91 , in the first region 151 and the second region 152, modified refractive index regions 15b may be arranged so as to form a first-order diffraction grating, similar to the intermediate region 155. In this case, in the first region 151 and the second region 152, by controlling the amount of diffraction by the amount of shift of the shift vector, it is possible to make light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15 diffracted in the out-of-plane direction of the XY plane.

[0245] 92 , in the light-emitting device 1A, the phase modulation layer 15 may be configured with a first region 151, a second region 152, and an intermediate region 155 according to the arrangement of the two-dimensionally distributed multiple modified refractive index regions 15b, as in the light-emitting device 1 according to the above embodiment. In this case, the intermediate region 155 is configured as a waveguide having an M-point photonic crystal structure that prevents vertical diffraction of light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15, according to the arrangement of the modified refractive index regions 15b. As a result, in the intermediate region 155, the light from the active layer 12 is prevented from being diffracted in an out-of-plane direction of the XY plane (in-plane diffraction in the direction Dds shown in the figure).

[0246] On the other hand, in this example, the first region 151 and the second region 152 have a Γ-point photonic crystal structure that vertically diffracts light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in accordance with the arrangement of the modified refractive index region 15b. As a result, in the first region 151 and the second region 152, the light from the active layer 12 is diffracted in the out-of-plane direction of the XY plane. According to this example, the transverse mode can be controlled by the ridge structure and photonic crystal structure of the ridge waveguide 52.

[0247] 93, modified refractive index areas 15b may be arranged in the first area 151 and the second area 152 so as to form an M-point photonic crystal structure, similar to the intermediate area 155. In this case, in the first area 151 and the second area 152, by controlling the amount of diffraction depending on the amount of shift of the shift vector, it is possible to make light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15 diffracted in the out-of-plane direction of the XY plane.

[0248] Here, in the light-emitting device 1A described above, an example has been described in which the ridge waveguide 52 is formed up to the upper part of the active layer 12 (the side opposite to the semiconductor substrate 10). However, as shown in Fig. 94, in the light-emitting device 1A, the ridge waveguide 52 may be formed to include the active layer 12. More specifically, in the example of Fig. 94, the base 51 includes the semiconductor substrate 10 and a part 11a of the cladding layer 11 facing the semiconductor substrate 10, and the ridge waveguide 52 includes a remaining part 11b of the cladding layer 11 facing the semiconductor substrate 10, the waveguide layer 21A, the active layer 12, the phase modulation layer 15, the waveguide layer 22A, the cladding layer 13, and the contact layer 14. In this way, by forming the ridge waveguide 52 up to the lower part of the active layer 12 (toward the semiconductor substrate 10), stronger light confinement is possible at the interface between air and the semiconductor, and light absorption loss by the active layer 12 around the ridge waveguide 52 can be suppressed when the active layer 12 is formed over an area wider than the ridge waveguide 52.

[0249] Furthermore, as shown in FIG. 95, in the light-emitting device 1A, the ridge waveguide 52 may be formed asymmetrically in a cross section intersecting the extension direction of the ridge waveguide 52 (here, the X direction).

[0250] In the above, an example has been described in which the ridge waveguide 52 extends linearly in one direction (here, the X direction). However, the ridge waveguide 52 may extend in a curved line within the XY plane.

[0251] For example, as shown in FIG. 96 , in the light-emitting device 1A, the ridge waveguide 52 may extend in an annular shape in the XY plane. In the example of FIG. 96 , the phase modulation layer 15 (light extraction region 15P) includes a first region 151, a second region 152, and one third region 153. That is, the example of FIG. 96 is an example of circumferential multi-point rectangular aperture diffraction (when N = 3). The first region 151, the second region 152, and the third region 153 are spaced apart from each other on the circumference, sandwiching an intermediate region 155 between them. The first region 151, the second region 152, and the third region 153 are connected to each other by the ridge waveguide 52.

[0252] Similarly, as shown in Fig. 97, the ridge waveguide 52 may be formed to extend in a polygonal ring shape in the XY plane. Fig. 97(a) shows an example in which the ridge waveguide 52 is in a hexagonal ring shape, and Fig. 97(b) shows an example in which the ridge waveguide 52 is in a triangular ring shape.

[0253] Furthermore, as shown in Figure 98, in the light-emitting device 1A, the phase modulation layer 15 (light extraction region 15P) may have multiple third regions 153. That is, the light-emitting device 1A may have N = 4 or more circumferential multi-point rectangular aperture diffraction. The example in Figure 98 (a) is an example of an example with two third regions 153, i.e., an example of N = 4 circumferential multi-point rectangular aperture diffraction, and Figure 98 (b) is an example of an example with four third regions 153, i.e., an example of N = 6 array-arranged multi-point rectangular aperture diffraction.

[0254] As described above, when the ridge waveguide 52 has a structure inclined with respect to the X and Y directions, as shown in FIG. 99 , in the first region 151 (and the second region 152 and third region 153), for example, by arranging the modified refractive index region 15b to form a triangular lattice Γ-point photonic crystal structure that vertically diffracts light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15, it is possible to diffract light from the active layer 12 in an out-of-plane direction of the XY plane. In this case, in-plane diffraction occurs in the direction Dds1. In addition, in this case, the lattice spacing a5 = wavelength λ / (√3 / 2) / refractive index n.

[0255] Furthermore, in the first region 151 (and the second and third regions 152 and 153), for example, the modified refractive index region 15b may be arranged to form a triangular lattice J-point photonic crystal structure that does not diffract light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15 perpendicularly, and the amount of diffraction may be controlled by the shift amount of the shift vector, so that the light from the active layer 12 is diffracted in the out-of-plane direction of the XY plane. In this case, in-plane diffraction occurs in the direction Dds2, diffracting the light in six directions, which may facilitate propagation of the light (diffraction at the triangular lattice J-point is a combination of diffractions in three directions, but symmetrical diffraction also occurs, resulting in diffraction in six directions). In this case, the lattice spacing a6 = wavelength λ / (3 / 2) / refractive index n. For ease of explanation, Figure 99 shows the two types of first regions 151 described above in one ridge waveguide 52.

[0256] 100 , in the light-emitting device 1A, a plurality of modified refractive index regions 15 b (a plurality of linear modified refractive index regions 15 b extending in the width direction of the ridge waveguide 52) are formed radially around the center point of the annular ring in the ridge waveguide 52, thereby forming a second-order diffraction grating in the first region 151, the second region 152, and the third region 153, which vertically diffracts light emitted from the active layer 12 and resonating in the in-plane direction of the XY plane in the phase modulation layer 15. Alternatively, a first-order diffraction grating may be formed while controlling the amount of diffraction by the shift amount of the shift vector, thereby causing vertical diffraction so that the light from the active layer 12 is diffracted in the out-of-plane direction of the XY plane. In this case, as shown in the figure, a modified refractive index region 15 b may also be arranged in the intermediate region 155 to form a first-order diffraction grating, or a modified refractive index region 15 b need not be arranged in the intermediate region 155.

[0257] According to the light-emitting device 1A of the above-described modified example, even when the light extraction regions 15P, such as the first region 151, the second region 152, and the third region 153, are configured in a dotted pattern, the light extraction efficiency can be improved by current confinement by the ridge waveguide 52. In this case, as shown in FIG. 88 , the light-emitting device 1A may further include a control unit 60 for individually controlling the amount of current injected into each of the first region 151 and the second region 152 (and the third region 153). In this case, controlling the amount of current injected into the first region 151 and the second region 152 (and the third region 153) makes it possible to control the stripe pattern. Furthermore, in the light-emitting device 1A, the ridge side surfaces of the ridge waveguide 52 may be covered with a reflective film, such as a highly reflective metal, to suppress radiation from the ridge side surfaces.

[0258] 101 , the above-described modified example has been described in which the first region 151, the second region 152, and the third region 153 (hereinafter sometimes referred to as the first region 151, etc.) are dot-shaped and each is a square F1 (an example of a rectangular opening). However, the shape of the first region 151, etc. is not limited to a rectangle and may be, for example, a circle F2, a horizontally elongated ellipse F3, a vertically elongated ellipse F4, a horizontally elongated rectangle F5, or a vertically elongated rectangle F6. Here, "horizontally elongated" means that the size in the X direction is relatively larger than the size in the Y direction, and "vertically elongated" means that the size in the Y direction is relatively larger than the size in the X direction. Therefore, in the horizontally elongated ellipse F3, the vertically elongated ellipse F4, the horizontally elongated rectangle F5, and the vertically elongated rectangle F6, the sizes in the X direction and the Y direction of the first region 151, etc. are not equal. Therefore, as described above, the first region 151, etc. being point-like can be considered to have a size in the X direction and a size in the Y direction of about several wavelengths (for example, 1 wavelength or more and 20 wavelengths or less), and the ratio between them being within a certain range (for example, about 1 to 3).

[0259] Next, consider the case where the first region 151, etc., has a shape other than a square F1. FIG. 102 is a diagram showing aperture shapes when the first region, etc., has a circular shape (i.e., when the first region, etc., is a circular aperture) and multiple circular apertures are arranged on the circumference. Starting from the left in the upper row of FIG. 102, the diagrams show cases where the number of circular apertures is 1, 2, 3, and 4. Starting from the left in the middle row of FIG. 102, the diagrams show cases where the number of circular apertures is 5, 6, 7, and 8. Starting from the left in the lower row of FIG. 102, the diagrams show cases where the number of circular apertures is 12, 20, and annular apertures formed continuously on the circumference. The diameter of each circular aperture is 5 μm. Each portion of FIG. 102 is an 800 μm square area in the X and Y directions.

[0260] FIG. 103 shows the Fourier spectrum (absolute value (far-field solution)) corresponding to each part of FIG. 102, and FIG. 104 shows the light intensity (|E| ２), and Figure 105 shows the electric field amplitude (E.real) at Z = 2 mm corresponding to each part of Figure 102. Each part of Figures 104 and 105 is an 800 μm square area in the X and Y directions. As shown in Figures 102 to 105, it can be seen that a striped pattern is formed. The tendency of the striped pattern is similar to that of the circular multi-point rectangular aperture diffraction described above, but because the aperture shape has changed to a circular shape F2, the window function of the aperture changes from a sinc function to a Bessel function.

[0261] Next, we will consider the case where the number of apertures arranged on the circumference is set to three and the aperture shape is changed. FIG. 106 is a diagram showing the aperture shapes when the shapes of three apertures arranged on the circumference are changed. Starting from the left in the upper row of FIG. 106 , the following cases are shown: an aperture shape of square F1, an aperture shape of circle F2, and an aperture shape of horizontally elongated ellipse F3; and starting from the left in the lower row of FIG. 106 , the following cases are shown: an aperture shape of vertically elongated ellipse F4, an aperture shape of horizontally elongated rectangle F5, and an aperture shape of vertically elongated rectangle F6. Each part of FIG. 106 is an 800 μm square area in the X and Y directions.

[0262] FIG. 107 shows the Fourier spectrum (absolute value (far solution)) corresponding to each part of FIG. 106, and FIG. 108 shows the light intensity (|E| ２ ), and Figure 109 shows the electric field amplitude (E.real) at Z = 2 mm corresponding to each part of Figure 106. Each part of Figures 108 and 109 is an 800 μm square area in the X and Y directions. As shown in Figures 106 to 109, it can be seen that a stripe pattern is formed regardless of the aperture shape. Furthermore, although the aperture window function changes depending on the aperture shape, changing the area in which the beam spreads, the tendency of the stripe pattern is the same.

[0263] Next, further modified examples will be described. In the above-described modified example, as shown in FIG. 66, we considered circumferential multipoint rectangular aperture diffraction in which rectangular apertures such as the first region 151 are arranged at equal intervals on the circumference. However, in the light-emitting device 1A, as shown in FIG. 110(a), rectangular apertures such as the first region 151 may be arranged at equal intervals on an ellipse, or as shown in FIG. 110(b) and FIG. 110(c), rectangular apertures such as the first region 151 may be arranged at unequal intervals on the circumference. In the example of FIG. 110(a), rectangular apertures are arranged on an ellipse whose minor axis is 100 μm long and whose major axis is 150 μm long. In addition, in the example of FIG. 110(b), rectangular apertures are arranged at 0°, 90°, and 240° positions on the circumference, and in the example of FIG. 110(c), rectangular apertures are arranged at 0°, 150°, and 210° positions on the circumference.

[0264] Fig. 111 is a diagram showing the aperture shapes when the number of rectangular apertures is changed in the example shown in Fig. 110(a). Starting from the left in the top row of Fig. 111, the cases where the number of rectangular apertures is 3, 4, 5, and 6 are shown. Starting from the left in the middle row of Fig. 111, the cases where the number of rectangular apertures is 7, 8, 12, and 20 are shown. Starting from the left in the bottom row of Fig. 111, the cases where an elliptical ring aperture formed continuously on an ellipse, an annular aperture formed continuously on a circumference with a radius of 100 µm, and an annular aperture formed continuously on a circumference with a radius of 150 µm are shown. Each part of Fig. 111 is an area of ​​800 µm square in the X and Y directions.

[0265] FIG. 112 shows the Fourier spectrum (absolute value (far solution)) corresponding to each part of FIG. 111, and FIG. 113 shows the light intensity (|E| ２), and Fig. 114 shows the electric field amplitude (E.real) at Z = 2 mm corresponding to each part of Fig. 111. Each part of Figs. 113 and 114 is an area of ​​800 μm square in the X and Y directions. As shown in Figs. 111 to 114, when rectangular apertures are arranged on an ellipse, distortion occurs compared to circumferential multipoint rectangular aperture diffraction, but it can be seen that a striped pattern is formed.

[0266] Fig. 115 is a diagram showing the aperture shapes in the examples shown in (b) and (c) of Fig. 110. From the left side of Fig. 115, the cases of rectangular aperture arrangements (0°, 90°, 240°) corresponding to (b) of Fig. 110 and rectangular aperture arrangements (0°, 150°, 240°) corresponding to (c) of Fig. 110 are shown. Each part of Fig. 115 is an 800 μm square area in the X and Y directions.

[0267] FIG. 116 shows the Fourier spectrum (absolute value (far solution)) corresponding to each part of FIG. 115, and FIG. 117 shows the light intensity (|E| ２ ), and Fig. 118 shows the electric field amplitude (E.real) at Z = 2 mm corresponding to each part of Fig. 115. Each part of Figs. 117 and 118 is an area of ​​800 μm square in the X and Y directions. As shown in Figs. 115 to 118, even when rectangular apertures are arranged at unequal intervals on the circumference, it can be seen that a striped pattern is formed, although distortion occurs compared to circumferential (equally spaced) multi-point rectangular aperture diffraction.

[0268] The above-described modifications are merely a partial list of the light-emitting device 1 according to the embodiment. Therefore, the light-emitting device 1 is not limited to the modifications described above and may be further modified. For example, the openings, such as the first region 151 arranged on a circumference or ellipse, are not limited to rectangular openings and may have any other shape, such as a circle. Furthermore, such openings of any shape may be arranged at equal or unequal intervals along any shape, not limited to a circumference or ellipse. The opening shapes, number of openings, and opening arrangements according to the above-described modifications may be applied to a device having a ridge waveguide 52, such as the light-emitting device 1A, or to a device not having a ridge waveguide 52, such as the light-emitting device 1. Furthermore, the ridge waveguide 52 may also be applied to a device having a linear opening (such as the first region 151), such as the light-emitting device 1.

[0269] 119 , in the light-emitting device 1A, the formation (etching) of the ridge waveguide 52 may be stopped at the top of the phase modulation layer 15 (the side opposite the semiconductor substrate 10). In this case, the ridge waveguide 52 does not include the phase modulation layer 15, but includes the waveguide layer 22A, cladding layer 13, and contact layer 14. The base 51 includes the semiconductor substrate 10, cladding layer 11, waveguide layer 21A, active layer 12, and phase modulation layer 15. In this case, the refractive index difference between the ridge portion and the etched portion can be finely adjusted, making it easier to control the transverse mode in the ridge width direction to a single mode.

[0270] 1...light-emitting device, 12...active layer (light-emitting portion), 15...phase modulation layer, 15a...base layer, 15b...modified refractive index region, 15P...light extraction region, 52...ridge waveguide, 151...first region, 152...second region, 153...third region, 155...intermediate region, 156...intermediate region.

Claims

1. A light-emitting device comprising: a light-emitting section; and a phase modulation layer optically coupled to the light-emitting section, wherein the phase modulation layer has a base layer and a plurality of modified refractive index areas having a refractive index different from that of the base layer and distributed in a first plane intersecting a thickness direction of the phase modulation layer, wherein the phase modulation layer has a light extraction region including a first region and a second region separated from the first region along the first surface with an intermediate region therebetween according to an arrangement of the plurality of modified refractive index areas, wherein in the light extraction region, the plurality of modified refractive index areas are arranged such that light emitted from the light-emitting section and resonating in an in-plane direction of the first surface in the phase modulation layer is diffracted in an out-of-plane direction of the first surface in the first region and the second region, wherein the intermediate region prevents light emitted from the light-emitting section and resonating in the in-plane direction in the phase modulation layer from being diffracted in the out-of-plane direction, and wherein the outgoing light diffracted in the out-of-plane direction in each of the first region and the second region interfere with each other to form interference fringes in a Fresnel region.

2. The light-emitting device according to claim 1, wherein the phase modulation layer has an M-point photonic crystal structure or a J-point photonic crystal structure.

3. The light-emitting device according to claim 1 or 2, wherein the multiple modified refractive index areas are distributed two-dimensionally within the first surface.

4. A light-emitting device according to any one of claims 1 to 3, wherein a plurality of modified refractive index areas are arranged in the intermediate area.

5. A light-emitting device as described in any one of claims 1 to 4, wherein the first region and the second region are linear regions extending longer in a second direction that runs along the first surface and intersects with the first direction than in a first direction that runs along the first surface.

6. The light-emitting device according to claim 5, wherein the width of the first region and the second region in the first direction is 20 times or less than the wavelength of the light.

7. The light-emitting device according to claim 5 or 6, wherein the width of the intermediate region in the first direction is 20 times or more and 200 times or less the wavelength of the light.

8. A light-emitting device according to any one of claims 5 to 7, wherein the length of the first region and the second region in the second direction is not less than 20 times and not more than 1000 times the wavelength of the light.

9. The light-emitting device according to any one of claims 1 to 4, wherein the first region and the second region are dot-like regions.

10. The light extraction region includes one or more third regions configured by arranging a plurality of the modified refractive index regions such that light emitted from the light emitting section and resonating in the in-plane direction of the first surface in the phase modulation layer is diffracted in the out-of-plane direction of the first surface, and when there is one third region, the one third region is arranged along the first surface while being spaced apart from the first region and the second region with the intermediate region therebetween, and when there are multiple third regions, one of the third regions is arranged along the first surface while being spaced apart from the first region, the second region, and another of the third regions with the intermediate region therebetween, and the emitted light diffracted in the out-of-plane direction in each of the third region, the first region, and the second region interfere with each other to form interference fringes in the Fresnel region. A light emitting device according to any one of claims 1 to 9.

11. A light-emitting device as described in any one of claims 1 to 10, comprising a substrate, the light-emitting portion and the phase modulation layer being formed on the substrate, a ridge waveguide including at least the phase modulation layer being formed on the substrate, and the first region and the second region being connected to each other by the ridge waveguide.

12. The light emitting device according to claim 11, further comprising a control unit for individually controlling the amount of current injected into each of the first region and the second region.

13. A light-emitting device according to any one of claims 1 to 12, wherein a lens phase distribution for focusing the emitted light is superimposed on a phase distribution relating to the arrangement of the modified refractive index areas in the light extraction area.

14. A light-emitting device according to any one of claims 1 to 13, wherein an inclined phase distribution for inclining the emitted light is superimposed on a phase distribution relating to the arrangement of the modified refractive index areas in the light extraction area.

15. The light emitting device according to any one of claims 1 to 14, wherein the first region and the second region are separated from each other.

16. The light-emitting device according to any one of claims 1 to 10, wherein the light extraction region is formed in an annular shape that includes the first region and the second region and surrounds the intermediate region.

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