JP7477420B2 - Optical waveguide structure and light source device - Google Patents

Description

This disclosure relates to an optical waveguide structure and a light source device.

Patent Document 1 discloses a technology related to a light-emitting device. This light-emitting device is a static-integrable phase modulating (S-iPM) laser, and includes a phase modulation layer optically coupled to a light-emitting section. The phase modulation layer includes a base layer and a plurality of modified refractive index areas. The plurality of modified refractive index areas have a refractive index different from that of the base layer, and are distributed two-dimensionally in a plane perpendicular to the thickness direction of the phase modulation layer. When a virtual square lattice is set in the plane, the center of gravity of each modified refractive index area is disposed away from the corresponding lattice point, and the angle of the vector connecting the corresponding lattice point and the center of gravity is set individually for each modified refractive index area. The lattice spacing a of the virtual square lattice and the emission wavelength λ of the light-emitting section satisfy the condition for M-point oscillation. In the reciprocal lattice space of the phase modulation layer, four in-plane wave vectors are formed, each including a wave number spread corresponding to the angular spread of the light image, and the magnitude of at least one in-plane wave vector is smaller than 2π/λ.

Non-Patent Document 1 discloses technology related to a semiconductor laser. This semiconductor laser has a surface grating distributed Bragg reflector formed in an AlGaAs-GaAs asymmetric epitaxial waveguide.

Non-Patent Document 2 describes a waveguide grating, which is a fine periodic structure smaller than the optical wavelength that is provided in an optical waveguide. Non-Patent Document 2 discloses a high-power semiconductor laser that monolithically integrates a surface-emitting grating coupler. By using gratings with different planar patterns, guided light is directly extracted from the substrate surface as a parallel beam or a focused beam.

Non-Patent Document 3 discloses a photonic crystal laser with a double hole structure that oscillates at the Γ point. The technology described in Non-Patent Document 3 selectively suppresses the coupling coefficients κ (±2,0) and κ (0,±2), which are proportional to the (±2,0)- and (0,±2)-order Fourier coefficients that contribute to one-dimensional oscillation, by adjusting the hole spacing and depth of the double hole structure.

International Publication No. 2020/045453

Hoshin H. Yee et al., “Surface-grating distributed Bragg reflector quantum-well lasers fabricated in AlGaAs-GaAs asymmetric epitaxial waveguides”,Applied optics, Vol. 38, No. 30, pp. 6325-6332 (1999) "Optics", The Optical Society of Japan, Vol. 37, No. 6, pp. 350-351, 2008 Masahiro Yoshida et al., “Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow-divergence beams”, Nature Materials, Vol. 18, pp. 121-128 (2019).

As a method for spatially optically coupling an optical waveguide extending along a plane with an optical waveguide extending in a direction intersecting the plane, there is a method that utilizes the diffraction effect of a diffraction grating. For example, in the structure described in Non-Patent Document 2, the direction of light emitted from an end-emitting semiconductor laser is changed to a direction intersecting the substrate surface using a surface grating distributed Bragg reflector. However, while the structure described in Non-Patent Document 2 is a periodic structure in a single direction, there is no mechanism for limiting the transverse mode in the width direction of the waveguide, and one-dimensional local oscillation occurs in the single direction. One-dimensional local oscillation causes localization of the mode due to one-dimensional diffraction. When the waveguide width is widened, this phenomenon makes the light intensity distribution non-uniform and unstable, and the emitted light becomes unstable. For this reason, in order to obtain stable emitted light, the waveguide width is limited to a range (about several μm) in which the transverse single mode is obtained, and the output is also limited.

This disclosure was made in consideration of these problems, and aims to provide an optical waveguide structure and a light source device that can reduce one-dimensional local oscillation.

In order to solve the above-mentioned problems, the optical waveguide structure according to the present disclosure includes an optical diffraction layer. The optical diffraction layer has a thickness direction perpendicular to a virtual plane, and diffracts light input along the virtual plane in a direction intersecting the virtual plane and outputs it. The optical diffraction layer includes a basic layer and a plurality of modified refractive index areas that have a refractive index different from that of the basic layer and are distributed two-dimensionally in the virtual plane. When a virtual square lattice is set in the virtual plane, the center of gravity of each modified refractive index area is disposed away from the corresponding lattice point, and the angle of the vector connecting the corresponding lattice point and the center of gravity is set individually for each modified refractive index area. The lattice spacing a of the virtual square lattice and the wavelength λ of the light satisfy the condition for M-point oscillation. The distribution of the angle satisfies the condition for light to be output in a direction intersecting the virtual plane. When each modified refractive index area is virtually rotated around the corresponding lattice point as the center of rotation, a ring shape or a circle shape is obtained. The absolute value of the annular or circular (m, n)-order Fourier coefficient (where (m, n) = (±1, ±1)) is 0.01 or less, or 10% or less of the maximum peak value of the circular (m, n)-order Fourier coefficient.

In this optical waveguide structure, the lattice spacing a of the virtual square lattice and the wavelength λ of the light satisfy the conditions for M-point oscillation. Normally, in the standing wave state of M-point oscillation, the light propagating in the optical diffraction layer is totally reflected, so the light output in the direction intersecting the virtual plane is suppressed. However, in this optical waveguide structure, the centers of gravity of the multiple modified refractive index areas are positioned away from the corresponding lattice points of the virtual square lattice, and the angle of the vector connecting the corresponding lattice points and the center of gravity is set individually for each modified refractive index area, and the distribution of the angles satisfies the conditions for light to be output in a direction intersecting the virtual plane. With such a structure, light input along the virtual plane can be diffracted in a direction intersecting the virtual plane.

In addition, in this optical waveguide structure, when each modified refractive index region is virtually rotated around the corresponding lattice point as the center of rotation, a circular ring or circle is obtained, and the absolute value of the (m, n)-th order Fourier coefficient (where (m, n) = (±1, ±1)) of the circular ring or circle is 0.01 or less, or 10% or less of the maximum peak value of the (m, n)-th order Fourier coefficient of the circular ring or circle. In this way, the (m, n)-th order Fourier coefficient of each modified refractive index region has an extremely small value, so that one-dimensional local oscillation can be reduced. Therefore, according to this optical waveguide structure, phenomena such as mode localization due to one-dimensional diffraction and flat band diffraction can be suppressed, the light intensity distribution is made closer to uniform by two-dimensional diffraction, and the area that can be output in a single mode can be increased in area, so that the emitted light image can be made high-resolution and high-quality.

In the above optical waveguide structure, the (m, n)-th order Fourier coefficient of the annular or circular shape may be zero. In this case, the above effect can be more pronounced.

In the above optical waveguide structure, the ratio (F2/F1) between the (m, n)-order Fourier coefficient _F1 of the inner circle defining the annular shape and the (m, n)-order Fourier coefficient _F2 of the outer circle defining the annular shape may be _0.99 or more and _1.01 or less. The Fourier coefficient of the annular shape is calculated as the difference between the Fourier coefficient of the outer circle defining the annular shape and the Fourier coefficient of the inner circle defining the annular shape. Therefore, since the Fourier coefficient of the outer circle and the Fourier coefficient of the inner circle are close to each other in this way, the Fourier coefficient of the annular shape can be brought close to zero, and one-dimensional local oscillation can be more effectively reduced.

In the above optical waveguide structure, the Fourier coefficient _F1 and the Fourier coefficient _F2 may be equal to each other. In this case, the Fourier coefficient of the annular shape becomes sufficiently small, so that the above-mentioned effect can be achieved.

In the above optical waveguide structure, the radius of the inner circle may be smaller than 0.27 times the lattice spacing a, and the radius of the outer circle may be larger than 0.27 times the lattice spacing a. In the M-point oscillation structure, the circular Fourier coefficient takes an extreme value when its radius is 0.27 times the lattice spacing a. Therefore, by making the radius of the inner circle smaller than 0.27 times the lattice spacing a and the radius of the outer circle larger than 0.27 times the lattice spacing a, it is easy to make the Fourier coefficient of the inner circle and the Fourier coefficient of the outer circle closer to each other.

In the above optical waveguide structure, the planar shape of each modified refractive index area may be a C-shape with the corresponding lattice point as the center of the inner and outer arcs. In this case, the angle of the vector connecting the center of gravity of each modified refractive index area and the lattice point can be set arbitrarily by changing the circumferential position of the opening part of the C-shape. Furthermore, if the C-shape is virtually rotated once around the lattice point as the center of rotation, a circular ring shape can be suitably obtained. Since the C-shape is close to a circular ring shape, the Fourier coefficients of the planar shape of each modified refractive index area can be accurately brought close to the Fourier coefficients of the circular ring shape.

In the above optical waveguide structure, the planar shape of each modified refractive index area may be a circle with the corresponding lattice point located outside it. Even in this case, a circular ring shape can be suitably obtained by virtually rotating the circle around the lattice point.

In the above optical waveguide structure, the planar shape of each modified refractive index area may be a polygon with the corresponding lattice point located outside it. Even in this case, a circular ring shape can be suitably obtained by virtually rotating the polygon once around the lattice point as the center of rotation.

In the above optical waveguide structure, the radius of the circle may be 0.43 to 0.44 times the lattice spacing a. In the M-point oscillation structure, the Fourier coefficient of the circle becomes zero when the radius is a certain value within the range of 0.43 to 0.44 times the lattice spacing a. Therefore, in this case, the Fourier coefficient of the planar shape of the modified refractive index area can be brought close to zero, and one-dimensional local oscillation can be more effectively reduced.

In the above optical waveguide structure, the planar shape of each modified refractive index area is a sector with the corresponding lattice point as the center of the arc, and the arc may be a major arc. In this case, the angle of the vector connecting the center of gravity of each modified refractive index area and the lattice point can be set arbitrarily by changing the circumferential position of the cutout portion of the sector. Furthermore, if this sector is virtually rotated once around the lattice point as the center of rotation, a circular shape can be suitably obtained. Since a sector with a major arc is close to a circular shape, the Fourier coefficients of the planar shape of each modified refractive index area can be accurately brought close to the Fourier coefficients of a circular shape.

In the above optical waveguide structure, the planar shape of each modified refractive index area may be a circle with the corresponding lattice point located inside it. Even in this case, a circular shape can be suitably obtained by virtually rotating the circle once around the lattice point as the center of rotation.

In the above optical waveguide structure, the planar shape of each modified refractive index area may be a polygon with a corresponding lattice point located inside it. Even in this case, a circular shape can be suitably obtained by virtually rotating the polygon once around the lattice point as the center of rotation.

In the above optical waveguide structure, the condition for light to be output in a direction intersecting with the virtual plane may be that the magnitude of at least one of the four in-plane wave vectors, each of which includes the wave number spread due to the distribution of angles, is smaller than 2π/λ (light line) in the reciprocal lattice space of the optical diffraction layer. When the magnitude of at least one in-plane wave vector is smaller than 2π/λ (light line), the in-plane wave vector has a component in a direction perpendicular to the virtual plane and does not undergo total reflection at the interface with air, so that a portion of the light input along the virtual plane can be output in a direction intersecting with the virtual plane.

Another optical waveguide structure according to the present disclosure includes an optical diffraction layer. The optical diffraction layer has a thickness direction perpendicular to a virtual plane, and diffracts light input along the virtual plane in a direction intersecting the virtual plane and outputs it. The optical diffraction layer includes a basic layer and a plurality of modified refractive index areas that have a different refractive index from the basic layer and are distributed two-dimensionally in the virtual plane. When a virtual square lattice is set in the virtual plane, the center of gravity of each modified refractive index area coincides with the corresponding lattice point. The lattice spacing a of the virtual square lattice and the wavelength λ of the light satisfy the condition for Γ-point oscillation. Each modified refractive index area has an annular or circular shape centered on the corresponding lattice point. The absolute value of the annular or circular (m, n)-order Fourier coefficient (where (m, n) = (±2, 0) and (0, ±2)) is 0.01 or less, or 20% or less of the maximum peak value of the circular (m, n)-order Fourier coefficient.

In this optical waveguide structure, the lattice spacing a of the virtual square lattice and the wavelength λ of the light satisfy the conditions for Γ-point oscillation. With this type of structure, light input along a virtual plane can be diffracted in a direction that intersects with the virtual plane.

In addition, in this optical waveguide structure, each modified refractive index region has an annular or circular shape centered on the corresponding lattice point. The absolute value of the (m, n)-order Fourier coefficient (where (m, n) = (±2, 0) and (0, ±2)) of the annular or circular shape is 0.01 or less, or 20% or less of the maximum peak value of the (m, n)-order Fourier coefficient of the circular shape. In this way, the (m, n)-order Fourier coefficient of each modified refractive index region has an extremely small value, so that one-dimensional local oscillation can be reduced. Therefore, this optical waveguide structure suppresses phenomena such as mode localization due to one-dimensional diffraction and flat band diffraction, makes the light intensity distribution closer to uniform, and enables the area in which output can be made in a single mode to be large, so that the emitted light image can have high resolution and high image quality.

In the above-mentioned other optical waveguide structure, the (m, n)-th order Fourier coefficient of the annular or circular shape may be zero. In this case, the above-mentioned effect can be more pronounced.

In the above-mentioned another optical waveguide structure, the ratio (F2/F1) between the (m, n)-order Fourier coefficient _F1 of the inner circle defining the annular shape and the (m, n)-order Fourier coefficient _F2 of the outer circle defining the annular shape may be 0.99 or more and _1.01 or less. As described above, the _Fourier coefficient of the annular shape is calculated as the difference between the Fourier coefficient of the outer circle defining the annular shape and the Fourier coefficient of the inner circle defining the annular shape. Therefore, by having the Fourier coefficient of the outer circle and the Fourier coefficient of the inner circle close to each other in this way, the Fourier coefficient of the annular shape can be made close to zero, so that one-dimensional local oscillation can be more effectively reduced.

In the above-mentioned another optical waveguide structure, the Fourier coefficient F ₁ and the Fourier coefficient F ₂ may be equal to each other. In this case, the Fourier coefficient of the annular shape becomes sufficiently small, so that the above-mentioned effect can be obtained.

In the above-mentioned other optical waveguide structure, the radius of the inner circle may be smaller than 0.19 times the lattice interval a, and the radius of the outer circle may be larger than 0.19 times the lattice interval a. Alternatively, in the above-mentioned other optical waveguide structure, the radius of the inner circle may be smaller than 0.44 times the lattice interval a, and the radius of the outer circle may be larger than 0.44 times the lattice interval a. In the Γ-point oscillation structure, the circular Fourier coefficient takes an extreme value when its radius is 0.19 or 0.44 times the lattice interval a. Therefore, by having the radius of the inner circle smaller than 0.19 (or 0.44) times the lattice interval a, and the radius of the outer circle larger than 0.19 (or 0.44) times the lattice interval a, it is easy to bring the Fourier coefficient of the inner circle and the Fourier coefficient of the outer circle closer to each other.

In the above-mentioned alternative optical waveguide structure, the radius of the circle may be 0.30 to 0.31 times the lattice spacing a. In the Γ-point oscillation structure, the Fourier coefficient of the circle becomes zero when its radius is a certain value within the range of 0.30 to 0.31 times the lattice spacing a. Therefore, in this case, the Fourier coefficient of the planar shape of the modified refractive index area can be brought close to zero, and one-dimensional local oscillation can be more effectively reduced.

In each of the above optical waveguide structures, the modified refractive index area is a hole, and the top of the hole may be open. When a semiconductor layer is formed on the optical diffraction layer to block the hole, the semiconductor material may enter the hole, causing a slight deformation of the hole shape. By opening the top of the hole (without regrowing the semiconductor layer), the shape of the hole is maintained, and the shape of the modified refractive index area can be formed with high precision. Alternatively, the inside of the hole may be completely filled using an atomic layer deposition (ALD) device or the like. In this case, the modified refractive index area can be formed while maintaining the shape of the hole, and since the hole is completely filled, a physically robust structure can be obtained.

The light source device according to the present disclosure includes any one of the optical waveguide structures described above and a light emitting unit. The light emitting unit is arranged alongside the optical waveguide structure in a direction along the imaginary plane, and inputs light into the optical diffraction layer along the imaginary plane.

Another light source device according to the present disclosure includes a plurality of optical waveguide structures that are any of the optical waveguide structures described above, and a light emitting unit. The light emitting unit inputs light into the optical diffraction layer of each optical waveguide structure along an imaginary plane. The plurality of optical waveguide structures are arranged side by side in the circumferential direction of the light emitting unit within the imaginary plane.

These light source devices have at least one of the optical waveguide structures described above, so that light input from the light emitting section to the optical diffraction layer along a virtual plane can be diffracted in a direction intersecting the virtual plane and output. In addition, these light source devices have at least one of the optical waveguide structures described above, so one-dimensional local oscillation can be reduced. Therefore, phenomena such as mode localization due to one-dimensional diffraction and flat band diffraction can be suppressed, the light intensity distribution can be made closer to uniform, and the area in which output can be made in a single mode can be increased in area, so that the emitted optical image can have high resolution and high image quality.

In each of the above light source devices, the light may be spatially coherent. In this case, the uniformity of the oscillation in the light diffraction layer can be further improved.

In each of the above light source devices, the light emitting section is a semiconductor laser including an active layer and a photonic crystal layer, and the photonic crystal layer may oscillate at M points. In this case, the laser light from the photonic crystal laser can be efficiently (without vertical diffraction) input to the light diffraction layer along a virtual plane. The photonic crystal laser can be made larger in area than an end-face resonating type laser, and can provide a wide beam of light to the light diffraction layer. Therefore, the light emission diameter can be increased while the intensity of the light output by diffraction from the light diffraction layer is made closer to uniform, and a narrow radiation beam with little diffraction spread can be emitted.

This disclosure provides an optical waveguide structure and a light source device that can reduce one-dimensional local oscillation.

1 is a perspective view illustrating a schematic configuration of a light source device according to a first embodiment of the present disclosure. FIG. 2 is a diagram illustrating a laminated structure of the light source device. FIG. 2 is a plan view of a light diffractive layer. FIG. 2 is an enlarged view of one unit constituent region. 4 is a plan view showing an example in which the approximately periodic refractive index structure of FIG. 3 is applied only within a specific region of the light diffractive layer. FIG. 13 is a diagram for explaining coordinate transformation from spherical coordinates (r, θ _rot , θ _tilt ) to coordinates (ξ, η, ζ). 10 is a diagram for explaining points to note when performing calculations using a general discrete Fourier transform (or fast Fourier transform) when determining the arrangement of each modified refractive index area. FIG. FIG. 2 is a plan view showing a reciprocal lattice space for a photonic crystal layer that oscillates at the Γ point. FIG. 9 is a three-dimensional perspective view of the reciprocal lattice space shown in FIG. 8 . FIG. 2 is a plan view showing a reciprocal lattice space for a photonic crystal layer oscillating at point M. FIG. 2 is a plan view showing a reciprocal lattice space for an optical diffraction layer that oscillates at the Γ point. FIG. 12 is a three-dimensional perspective view of the reciprocal lattice space shown in FIG. 11 . FIG. 2 is a plan view showing a reciprocal lattice space for a light diffractive layer that oscillates at point M. FIG. 13 is a conceptual diagram for explaining an operation of adding a diffraction vector having a certain magnitude and direction to four in-plane wave vectors. FIG. 13 is a diagram for illustrating a schematic structure surrounding a light line. FIG. 2 is a diagram conceptually illustrating an example of an angular distribution θ ₂ (x, y). 1A is a conceptual diagram showing how the oscillation mode becomes localized to form a higher-order mode, and FIG. 1B is a conceptual diagram showing how flat-band oscillation occurs and flat-band competition occurs. 1A is a diagram conceptually illustrating how two-dimensional diffraction is promoted, and FIG. 1B is a diagram conceptually illustrating how modes are widely distributed over the entire area of the light diffractive layer. FIG. 13 is a graph showing the relationship of equation (25). 1 is an enlarged photograph showing a C-shaped modified refractive index area with a lattice spacing of a = 200 nm formed by dry etching a GaAs layer as a base layer as an example, where (a) shows a plurality of modified refractive index areas, and (b) shows a further enlarged view of part of (a). FIG. 13 is a graph showing the relationship of equation (25). FIG. 13 is a perspective view showing an example in which the input direction of light is inclined at 45° with respect to the X direction and the Y direction. 4 is a graph showing a refractive index distribution and a mode distribution of a laser oscillation part having the configuration of Table 1. 13 is a graph showing a refractive index distribution and a mode distribution of an optical waveguide having the configuration of Table 2. 25 is a graph in which the mode distribution shown in FIG. 23 and the mode distribution shown in FIG. 24 are superimposed. FIG. 13 is a conceptual diagram for explaining an operation of adding a diffraction vector to the in-plane wave vectors in four directions after removing the wave number spread. 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. FIG. 11 is a perspective view illustrating a schematic configuration of a light source device according to a second embodiment of the present disclosure. FIG. 11 is a plan view of a light diffractive layer included in the light guide unit according to the second embodiment. FIG. 2 is an enlarged view of one unit constituent region. FIG. 13 is a graph showing the relationship of equation (35). 4A to 4C are diagrams illustrating examples of the planar shape of a modified refractive index area. FIG. 11 is a perspective view illustrating a light source device according to a third embodiment of the present disclosure. FIG. 11 is a perspective view illustrating a light source device according to a fourth embodiment of the present disclosure. FIG. 2 is a diagram illustrating a laminated structure of the light source device. 11 is a graph showing a refractive index distribution and a mode distribution of a laser oscillation part having the configuration of Table 3. 13 is a graph showing a refractive index distribution and a mode distribution of an optical waveguide having the configuration of Table 4. 44 is a graph in which the mode distribution shown in FIG. 42 and the mode distribution shown in FIG. 43 are superimposed. FIG. 13 is a diagram illustrating a laminated structure of a light source device according to a modification of the fourth embodiment. 13 is a graph showing a refractive index distribution and a mode distribution of a laser oscillation part having the configuration of Table 5. 13 is a graph showing a refractive index distribution and a mode distribution of an optical waveguide having the configuration of Table 6. 48 is a graph in which the mode distribution shown in FIG. 46 and the mode distribution shown in FIG. 47 are superimposed. FIG. 13 is a perspective view illustrating a light source device according to a fifth embodiment of the present disclosure.

Specific examples of the optical waveguide structure and light source device disclosed herein are described below with reference to the drawings. Note that the present invention is not limited to these examples, but is intended to include all modifications within the scope of the claims and meaning equivalent to the claims. In the following description, the same elements in the description of the drawings are given the same reference numerals, and duplicate descriptions are omitted.

First Embodiment
Fig. 1 is a perspective view showing a configuration of a light source device 1A according to a first embodiment of the present disclosure. Fig. 2 is a diagram showing a stacked structure of the light source device 1A. In Fig. 1 and Fig. 2, a coordinate system is defined in which the stacking direction of the light source device 1A is the Z direction, and the X direction, the Y direction, and the Z direction are mutually orthogonal.

1 and 2, the light source device 1A includes a substrate 3, a laser oscillator 10A, and an optical waveguide 20A. The laser oscillator 10A corresponds to the light emitting section in this disclosure. The optical waveguide 20A corresponds to the optical waveguide structure in this disclosure. The laser oscillator 10A and the optical waveguide 20A are arranged in a direction along the XY plane (X direction in the illustrated example) and are provided adjacent to each other on a common substrate 3. The laser oscillator 10A is an edge-emitting semiconductor laser and outputs spatially coherent laser light Lin along the XY plane. The laser oscillator 10A inputs this laser light Lin to the optical waveguide 20A. The optical waveguide 20A diffracts the input laser light Lin to output light Lout in a direction intersecting the XY plane. The XY plane corresponds to a virtual plane in this disclosure.

The substrate 3 is made of a material capable of crystal growth of the semiconductor layers constituting the laser oscillator 10A and the optical waveguide 20A. In one example, the substrate 3 is a semiconductor substrate of a first conductivity type (e.g., n-type). The substrate 3 has a flat principal surface 3a, which is a crystal growth surface, and a back surface 3b that is parallel to the principal surface 3a and faces away from the principal surface 3a. The principal surface 3a and the back surface 3b are parallel to the XY plane.

The laser oscillator 10A has a semiconductor laminate 11A provided on the main surface 3a. The semiconductor laminate 11A has a lower cladding layer 12, an active layer 13, an optical confinement layer 14, an upper cladding layer 15, and a contact layer 16, which are laminated in order in the Z direction. The lower cladding layer 12 is provided on the main surface 3a. The active layer 13 is provided on the lower cladding layer 12. The optical confinement layer 14 is provided on the active layer 13. The upper cladding layer 15 is provided on the optical confinement layer 14. That is, the active layer 13 is located between the lower cladding layer 12 and the upper cladding layer 15, and the optical confinement layer 14 is located between the active layer 13 and the upper cladding layer 15. The contact layer 16 is provided on the upper cladding layer 15.

The lower cladding layer 12 has a first conductivity type. The upper cladding layer 15 has a second conductivity type. The thickness and refractive index of the upper cladding layer 15 may be equal to or different from those of the lower cladding layer 12. The active layer 13 is made of a material having a smaller energy band gap and a larger refractive index than the lower cladding layer 12 and the upper cladding layer 15. The width of the active layer 13 in the direction intersecting the light output direction, i.e., the Y direction (i.e., the waveguide width), is set to a size that maintains a single transverse mode. The light confinement layer 14 is provided to control the distribution of light in the stacking direction. The refractive index of the light confinement layer 14 is larger than that of the upper cladding layer 15 and smaller than that of the active layer 13. The contact layer 16 has a second conductivity type.

The laser oscillator 10A further includes electrodes 17 and 18. The electrode 17 is a first conductive type electrode provided on the rear surface 3b of the substrate 3 and makes ohmic contact with the rear surface 3b. The electrode 18 is a second conductive type electrode provided on the contact layer 16 and makes ohmic contact with the contact layer 16. The area of the rear surface 3b that is not covered by the electrode 17 is covered by an insulating protective film 31. The area of the surface of the contact layer 16 that is not covered by the electrode 18 is covered by an insulating protective film 32. The protective films 31 and 32 are, for example, insulating silicon compound films (SiO ₂ , SiN, etc.). The contact layer 16 in the area not covered by the electrode 18 may be removed. In this case, the area into which the current is injected can be limited, so that the laser oscillator 10A can be driven efficiently. The protective film 31 is provided as necessary, and may be omitted if not necessary.

When a driving current is supplied between electrodes 17 and 18, recombination of electrons and holes occurs in active layer 13, causing active layer 13 to emit light. The electrons and holes that contribute to this emission, as well as the generated light, are efficiently confined between lower cladding layer 12 and upper cladding layer 15. This light is output as single-mode laser light from laser oscillation unit 10A along the XY plane to optical waveguide unit 20A.

The optical waveguide 20A is arranged alongside the laser oscillator 10A in a direction along the XY plane (the X direction in the figure). As shown in FIG. 2, the optical waveguide 20A has a semiconductor laminate 21A arranged on the main surface 3a. The semiconductor laminate 21A has a lower cladding layer 22, an active layer 23, an optical confinement layer 24, and an optical diffraction layer 25A, which are laminated in order in the Z direction. The lower cladding layer 22 is arranged on the main surface 3a. The active layer 23 is arranged on the lower cladding layer 22. The optical confinement layer 24 is arranged on the active layer 23. The optical diffraction layer 25A is arranged on the optical confinement layer 24. That is, the active layer 23 is located between the lower cladding layer 22 and the optical diffraction layer 25A, and the optical confinement layer 24 is located between the active layer 23 and the optical diffraction layer 25A. The semiconductor laminate 21A is composed of a compound semiconductor, such as a GaAs-based semiconductor, an InP-based semiconductor, or a Group III nitride-based semiconductor.

The lower cladding layer 22 may be a common layer formed simultaneously with the lower cladding layer 12, or may be a layer formed separately. The active layer 23 may be a common layer formed simultaneously with the active layer 13, or may be a layer formed separately. The optical confinement layer 24 may be a common layer formed simultaneously with the optical confinement layer 14, or may be a layer formed separately. That is, the composition and thickness of the lower cladding layer 22, the active layer 23, and the optical confinement layer 24 may be the same as or different from the lower cladding layer 12, the active layer 13, and the optical confinement layer 14, respectively.

The light diffraction layer 25A is composed of a basic layer 25a made of a first refractive index medium and a second refractive index medium having a refractive index different from that of the first refractive index medium, and is configured to include a plurality of modified refractive index areas 25b present in the basic layer 25a. The plurality of modified refractive index areas 25b include a substantially periodic structure. When the equivalent refractive index of the mode is n, the wavelength λ ₀ selected by the light diffraction layer 25A is included in the emission wavelength range of the active layer 13. The light diffraction layer 25A can select a band edge wavelength near the wavelength λ ₀ among the emission wavelengths of the active layer 13 and output it to the outside. The laser light incident on the light diffraction layer 25A forms a predetermined mode in accordance with the arrangement of the modified refractive index areas 25b in the light diffraction layer 25A, and is emitted from the surface of the light diffraction layer 25A in a direction intersecting the XY plane as laser light Lout having a predetermined pattern. At this time, the laser light Lout is emitted in any two-dimensional direction including a direction perpendicular to the main surface 3a and a direction inclined thereto. The laser light Lout is mainly composed of 1st order light and −1st order light. As will be described later, 0th order light is not output from the light diffracting layer 25A of this embodiment.

In one example, the substrate 3 is a GaAs substrate, and the lower cladding layers 12 and 22, the active layers 13 and 23, the optical confinement layers 14 and 24, the upper cladding layer 15, the contact layer 16, and the optical diffraction layer 25A mainly contain GaAs-based compound semiconductors. In one embodiment, the lower cladding layers 12 and 22 are AlGaAs layers, the active layers 13 and 23 have a multiple quantum well structure (barrier layer: AlGaAs/well layer: InGaAs), the optical confinement layers 14 and 24 are AlGaAs layers, the basic layer 25a of the optical diffraction layer 25A is made of AlGaAs, the modified refractive index region 25b is a hole, the upper cladding layer 15 is an AlGaAs layer, and the contact layer 16 is a GaAs layer.

In the above case, the thickness of the substrate 3 is 50 μm or more and 300 μm or less, and in one embodiment, it is 150 μm. The thickness of the lower cladding layer 12, 22 and the upper cladding layer 15 is 0.5 μm or more and 10 μm or less, and in one embodiment, it is 2.0 μm. The thickness of the active layers 13, 23 is 100 nm or more and 300 nm or less, and in one embodiment, it is 200 nm. The thickness of the optical confinement layers 14 and 24 is 10 nm or more and 500 nm or less, and in one embodiment, it is 300 nm. The thickness of the optical diffraction layer 25A is 100 nm or more and 500 nm or less, and in one embodiment, it is 300 nm. The thickness of the contact layer 16 is 50 nm or more and 500 nm or less, and in one embodiment, it is 100 nm.

In AlGaAs, the energy band gap and the refractive index can be easily changed by changing the composition ratio of Al. In Al _x Ga _1-x As, when the composition ratio x of Al, which has a relatively small atomic radius, is decreased (increased), the energy band gap, which is positively correlated with it, becomes smaller (larger), and when In, which has a large atomic radius, is mixed into GaAs to form InGaAs, the energy band gap becomes smaller. That is, the Al composition ratio of the lower cladding layer 12 and the upper cladding layer 15 is larger than the Al composition ratio of the barrier layer (AlGaAs) of the active layer 13. The Al composition ratio of the lower cladding layer 12, 22 and the upper cladding layer 15 is set to, for example, 0.20 to 1.00, and is 0.56 in one embodiment. The Al composition ratio of the barrier layer of the active layer 13 is set to, for example, a range of 0.00 to 0.30, and is 0.15 in one embodiment. The Al composition ratio of the optical confinement layers 14 and 24 is set within the range of, for example, 0.00 to 0.50, and in one embodiment, is 0.38.

In another example, the substrate 3 is an InP substrate, and the lower cladding layers 12 and 22, the active layers 13 and 23, the optical confinement layers 14 and 24, the upper cladding layer 15, the contact layer 16, and the optical diffraction layer 25A mainly contain, for example, InP-based compound semiconductors. In one embodiment, the lower cladding layers 12 and 22 are InP layers, the active layers 13 and 23 have a multiple quantum well structure (barrier layer: GaInAsP/well layer: GaInAsP), the basic layer 25a of the optical diffraction layer 25A is an InP layer or a GaInAsP layer, the modified refractive index region 25b is an air hole, the optical confinement layers 14 and 24 are GaInAsP layers, the upper cladding layer 15 is an InP layer, and the contact layer 16 is a GaInAsP layer, a GaInAs layer, or an InP layer.

In yet another embodiment, the lower cladding layers 12 and 22 are InP layers, the active layers 13 and 23 have a multiple quantum well structure (barrier layer: AlGaInAs/well layer: AlGaInAs), the basic layer 25a of the optical diffraction layer 25A is an InP layer or an AlGaInAs layer, the modified refractive index region 25b is an air hole, the optical confinement layers 14 and 24 are AlGaInAs layers, the upper cladding layer 15 is an InP layer, and the contact layer 16 is a GaInAs or InP layer. This material system and the material system using GaInAsP/InP described in the previous paragraph can be applied to optical communication wavelengths in the 1.3/1.55 μm band, and can also emit light with eye-safe wavelengths longer than 1.4 μm.

In yet another example, the substrate 3 is a GaN substrate, and the lower cladding layers 12 and 22, the active layers 13 and 23, the optical confinement layers 14 and 24, the upper cladding layer 15, the contact layer 16, and the optical diffraction layer 25A mainly contain, for example, nitride-based compound semiconductors. In one embodiment, the lower cladding layers 12 and 22 are AlGaN layers, the active layers 13 and 23 have a multiple quantum well structure (barrier layer: InGaN/well layer: InGaN), the basic layer 25a of the optical diffraction layer 25A is GaN, the modified refractive index region 25b is a hole, the optical confinement layers 14 and 24 are GaN layers, the upper cladding layer 15 is an AlGaN layer, and the contact layer 16 is a GaN layer.

The lower cladding layers 12 and 22 are given the same conductivity type as the substrate 3, and the upper cladding layer 15 and the contact layer 16 are given the opposite conductivity type to that of the substrate 3. In one example, the substrate 3 and the lower cladding layers 12 and 22 are n-type, and the upper cladding layer 15 and the contact layer 16 are p-type. The light diffraction layer 25A has the opposite conductivity type to that of the substrate 3. The impurity concentration is, for example, 1×10 ¹⁶ cm- ³ to 1×10 ²¹ cm- ³ . The active layer 13 is intrinsic (i-type) to which no impurities are intentionally added, and the impurity concentration is 1×10 ¹⁶ /cm ³ or less. The light confinement layers 14 and 24 may have the opposite conductivity type to that of the substrate 3, or may be i-type.

In the above-mentioned structure, the modified refractive index region 25b is a hole, but the modified refractive index region 25b may be formed by filling the hole with a semiconductor having a refractive index different from that of the basic layer 25a. In that case, for example, the hole in the basic layer 25a may be formed by etching, and the semiconductor may be filled in the hole using metal organic chemical vapor deposition, sputtering, or epitaxial method. For example, when the basic layer 25a is made of GaAs, the modified refractive index region 25b may be made of AlGaAs. In addition, after the modified refractive index region 25b is formed by filling the hole in the basic layer 25a with a semiconductor, the same semiconductor as the modified refractive index region 25b may be deposited thereon. The top of the hole may be open as shown in FIG. 2, or may be covered with a semiconductor layer formed on the light diffraction layer 25A. Alternatively, a dielectric may be filled in the hole in the modified refractive index region 25b using an atomic layer deposition (ALD) apparatus. In this case, a physically robust structure can be obtained.

Figure 3 is a plan view of the light diffraction layer 25A. The light diffraction layer 25A has a configuration as an S-iPM laser that oscillates at point M. The light diffraction layer 25A includes a basic layer 25a made of a first refractive index medium, and multiple modified refractive index areas 25b made of a second refractive index medium that has a refractive index different from that of the first refractive index medium. Here, a virtual square lattice is set in the XY plane in the light diffraction layer 25A. One side of the square lattice is parallel to the X axis, and the other side is parallel to the Y axis.

In this case, square unit constituent regions R centered on lattice point O of the square lattice can be set two-dimensionally across multiple columns along the X axis and multiple rows along the Y axis. If the XY coordinates of each unit constituent region R are given by the position of the center of gravity of each unit constituent region R, this position of the center of gravity coincides with lattice point O of the virtual square lattice. A plurality of modified refractive index areas 25b are provided, for example, one each in each unit constituent region R.

Figure 4 is an enlarged view of one unit constituent region R. As shown in Figure 4, the planar shape of the modified refractive index area 25b is, for example, a C-shape with the lattice point O as the center of the inner and outer arcs. Specifically, the planar shape of the modified refractive index area 25b is defined by an inner circumferential arc 151, an outer circumferential arc 152, a line segment 153 connecting one end of the arc 151 to one end of the arc 152, and a line segment 154 connecting the other end of the arc 151 to the other end of the arc 152. The arcs 151 and 152 are major arcs. In other words, the central angles of the arcs 151 and 152 are greater than 180°. The central angles of the arcs 151 and 152 are equal to each other. The central angles of the arcs 151 and 152 are, for example, greater than or equal to 300° and less than 360°. The line segments 153 and 154 extend along the radial direction of the arcs 151 and 152.

Each of the modified refractive index areas 25b has a center of gravity G. Here, the angle between the vector from the lattice point O toward the center of the C-shaped opening and the X-axis is θ(x, y). x indicates the position of the x-th lattice point on the X-axis, and y indicates the position of the y-th lattice point on the Y-axis. Adding 180° to this angle θ(x, y) equals the angle between the vector from the lattice point O toward the center of gravity G and the X-axis. Therefore, in the following calculations, the angle θ(x, y) is considered to correspond to the angle between the vector from the lattice point O toward the center of gravity G and the X-axis. The distance between the lattice point O and the center of gravity G is constant regardless of x and y (throughout the entire light diffraction layer 25A). Note that the optical image obtained does not change even if a constant is added to the phase angle, so the phase angle may be designed without adding 180°.

As shown in FIG. 4, the angle θ is set individually for each lattice point O according to a phase pattern corresponding to the desired output beam pattern in the light Lout. The phase pattern, i.e., the angular distribution θ(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. In other words, the angular distribution θ(x, y) is determined from the phase distribution extracted from the complex amplitude distribution obtained by performing an inverse Fourier transform on the desired output beam pattern in the light Lout. Note that when determining the complex amplitude distribution from the desired output beam pattern, the reproducibility of the beam pattern is improved by applying an iterative algorithm such as the Gerchberg-Saxton (GS) method, which is commonly used in calculations for hologram generation.

Figure 5 is a plan view showing an example in which the refractive index approximately periodic structure of Figure 3 is applied only in a specific region of the light diffraction layer 25A. In the example shown in Figure 5, an approximately periodic structure (e.g., the structure of Figure 3) for emitting the target beam pattern is formed inside the square inner region RIN. On the other hand, in the outer region ROUT surrounding the inner region RIN, a circular modified refractive index region whose center of gravity coincides with the lattice point position of the square lattice is arranged. The lattice spacing of the virtually set square lattice is the same both inside the inner region RIN and in the outer region ROUT. In this structure, there is an advantage that the occurrence of high-frequency noise (so-called window function noise) caused by a sudden change in light intensity in the periphery of the inner region RIN can be suppressed by distributing light also in the outer region ROUT. In addition, light leakage in the in-plane direction can be suppressed, and a lower threshold and improved light output efficiency can be expected.

To obtain a desired beam pattern, the angular distribution θ(x, y) of the modified refractive index region 25b of the optical diffraction layer 25A is determined by the following procedure. First, as a first prerequisite, in an orthogonal coordinate system defined by a Z axis that coincides with the normal direction of the main surface 3a of the substrate 3 and an XY plane that coincides with one surface of the optical diffraction layer 25A that includes multiple modified refractive index regions 25b and includes mutually orthogonal X and Y axes, a virtual square lattice is set on the XY plane, which is composed of M1×N1 (M1 and N1 are integers of 1 or more) unit constituent regions R, each of which has a square shape.

As a second precondition, the coordinates (ξ, η, ζ) in this orthogonal coordinate system satisfy the relationships shown in the following formulas (1) to (3) with respect to the spherical coordinates (r, θ _rot , θ _tilt ) defined by the length r of the radius, the tilt angle θ _tilt from the Z axis, and the rotation angle θ _rot from the X axis specified on the XY plane, as shown in Fig. 6. Note that Fig. 6 is a diagram for explaining the coordinate conversion from the spherical coordinates (r, θ _rot , θ _tilt ) to the coordinates (ξ, η, ζ), and the coordinates (ξ, η, ζ) express a designed beam pattern on a predetermined plane set in the above orthogonal coordinate system, which is a real space. When the beam pattern output from the optical waveguide 20A is a set of bright spots directed in a direction defined by the angles θ _tilt and θ _rot , the angles θ _tilt and θ _rot are converted into a coordinate value k _x on the Kx axis corresponding to the X axis, which is a normalized wave number defined by the following formula (4), and a coordinate value k _y on the Ky axis corresponding to the Y axis and perpendicular to the Kx axis, which is a normalized wave number defined by the following formula (5). The normalized wave number means a wave number normalized with the wave number 2π/a corresponding to the lattice interval a of a virtual square lattice as 1.0. At this time, in the wave number space defined by the Kx axis and the Ky axis, a specific wave number range including the beam pattern is composed of M2×N2 image regions FR (M2, N2 are integers equal to or greater than 1), each of which is a square. Note that the integer M2 does not need to match the integer M1. Similarly, the integer N2 does not need to match the integer N1. Furthermore, formulas (4) and (5) are disclosed, for example, in Y. Kurosaka et al., “Effects of non-lasing band in two-dimensional photonic-crystal lasers clarified using omnidirectional band structure”, Opt. Express 20, 21773-21783 (2012).





a: lattice spacing (lattice constant) of a virtual square lattice
λ: oscillation wavelength of the laser oscillation unit 10A

As a third precondition, in wavenumber space, an image region FR(k _{x , k y ) specified by a coordinate component k x} (an integer between 0 and M2-1) in the Kx-axis direction and a coordinate component k _y (an integer between 0 and N2-1) in the Ky-axis direction is subjected to a two-dimensional inverse discrete Fourier transform into a unit constituent region R( _x , _y ) on an XY plane specified by a coordinate component x (an integer between 0 and M1-1) in the X-axis direction and a coordinate component y (an integer between 0 and N1-1) in the Y-axis direction, and a complex amplitude F(x, y) is given by the following formula (6) where j is an imaginary unit. Furthermore, when the amplitude term is A(x, y) and the phase term is P(x, y), this complex amplitude F(x, y) is defined by the following formula (7). Furthermore, as a fourth prerequisite, a unit constituent region R(x, y) is defined by s-axis and t-axis which are parallel to the X-axis and Y-axis, respectively, and are orthogonal to each other at a lattice point O(x, y) which is the center of the unit constituent region R(x, y).

Under the above first to fourth prerequisites, the light diffraction layer 25A is configured to satisfy the following first and second conditions. That is, the first condition is that the center of gravity G is disposed in a unitary constituent region R(x, y) away from the lattice point O(x, y). The second condition is that, in a state where the line segment length r(x, y) from the lattice point O(x, y) to the corresponding center of gravity G is set to a common value in each of the M1×N1 unitary constituent regions R, the angle θ(x, y) between the line segment connecting the lattice point O(x, y) and the corresponding center of gravity G and the s-axis is
θ(x,y)=C×P(x,y)+B
C: proportionality constant, e.g. 180°/π
B: An arbitrary constant, e.g., 0
The corresponding modified refractive index area 25b is disposed within the unit constituent area R(x, y) so as to satisfy the following relationship.

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

Here, we will explain the points to note when calculating the angular distribution θ(x, y) from the Fourier transform result of the output beam pattern and determining the arrangement of each modified refractive index area 25b using a general discrete Fourier transform (or fast Fourier transform). If the light image before the Fourier transform is divided into four quadrants, A1, A2, A3, and A4, as shown in Figure 7(a), the resulting beam pattern will be as shown in Figure 7(b). That is, in the first quadrant of the beam pattern, a pattern appears in which the first quadrant of FIG. 7(a) rotated 180 degrees is superimposed on the third quadrant of FIG. 7(a), in the second quadrant of the beam pattern, a pattern appears in which the second quadrant of FIG. 7(a) rotated 180 degrees is superimposed on the fourth quadrant of FIG. 7(a), in the third quadrant of the beam pattern, a pattern appears in which the third quadrant of FIG. 7(a) rotated 180 degrees is superimposed on the first quadrant of FIG. 7(a), and in the fourth quadrant of the beam pattern, a pattern appears in which the fourth quadrant of FIG. 7(a) rotated 180 degrees is superimposed on the second quadrant of FIG. 7(a).

Therefore, if an output beam pattern (original image) before the Fourier transform has values only in the first quadrant, the first quadrant of the original light image will appear in the third quadrant of the resulting beam pattern, and a pattern obtained by rotating the first quadrant of the original light image by 180 degrees will appear in the first quadrant of the resulting beam pattern.

In this way, in the optical diffraction layer 25A, the wavefront is phase-modulated to obtain a desired beam pattern. This beam pattern can be not only a pair of single-peaked beams (spots), but also a character shape, a group of two or more identically shaped spots, or a vector beam whose phase and intensity distribution are spatially non-uniform.

The diffraction intensity changes as the size of each modified refractive index region 25b changes. This diffraction efficiency is proportional to the optical coupling coefficient, which is expressed as a coefficient obtained by Fourier transforming the shape of the modified refractive index region 25b. The optical coupling coefficient is described in, for example, Y. Liang et al., "Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting lasers with transverse-electric polarization: finite-size effect", Optics Express 20, 15945-15961 (2012).

Next, the characteristics of the light diffraction layer 25A of this embodiment will be described in detail. In this embodiment, the lattice spacing a of the virtual square lattice and the emission wavelength λ (i.e., the wavelength of the light Lin) of the active layer 13 satisfy the condition of M-point oscillation. Furthermore, the angular distribution θ(x, y) satisfies the condition for the light Lout to be output in a direction intersecting the XY plane, i.e., in the Z direction or in a direction inclined relative to the Z direction. When considering the reciprocal lattice space in the light diffraction layer 25A, four in-plane wave vectors are formed that are phase modulated by the angular distribution θ(x, y) and form standing waves each including a wave number spread corresponding to the angular spread of the output beam pattern. The condition for the light Lout to be output in a direction intersecting the XY plane is, for example, that the magnitude of at least one of the four in-plane wave vectors is smaller than 2π/λ (light line). These points will be described in detail below.

First, for comparison, a photonic crystal layer of a PCSEL in which circular modified refractive index areas are provided on the lattice points of a virtual square lattice (i.e., the modified refractive index areas are arranged periodically) will be described. The photonic crystal layer of the PCSEL outputs laser light in a direction perpendicular to the main surface of the substrate while forming standing waves with an oscillation wavelength according to the arrangement period of the modified refractive index areas in a plane perpendicular to the thickness direction. The photonic crystal layer of the PCSEL is usually designed to oscillate at the Γ point. For Γ point oscillation, it is preferable that the lattice spacing a of the virtual square lattice, the wavelength λ of the light input to the photonic crystal layer, and the equivalent refractive index n of the mode satisfy the condition λ = na.

FIG. 8 is a plan view showing a reciprocal lattice space related to a photonic crystal layer that oscillates at the Γ point. This figure shows a case where a plurality of modified refractive index areas are located on the lattice points of a square lattice, and the point P in the figure represents a reciprocal lattice point. In addition, the arrow B1 in the figure represents a primitive reciprocal lattice vector, and the arrow B2 represents a reciprocal lattice vector that is twice the primitive reciprocal lattice vector B1. In addition, the arrows K1, K2, K3, and K4 represent four in-plane wave vectors. The four in-plane wave vectors K1, K2, K3, and K4 are coupled to each other through diffractions of 90° and 180° to form a standing wave state. Here, the Γ-X axis and the Γ-Y axis, which are orthogonal to each other in the reciprocal lattice space, are defined. The Γ-X axis is parallel to one side of the square lattice, and the Γ-Y axis is parallel to the other side of the square lattice. The in-plane wave vector is a vector obtained by projecting a wave vector into the Γ-X and Γ-Y plane. That is, the in-plane wave vector K1 faces the positive direction of the Γ-X axis, the in-plane wave vector K2 faces the positive direction of the Γ-Y axis, the in-plane wave vector K3 faces the negative direction of the Γ-X axis, and the in-plane wave vector K4 faces the negative direction of the Γ-Y axis. As is clear from Fig. 8, in the photonic crystal layer oscillating at point Γ, 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 equal to the magnitude of the primitive reciprocal lattice vector B1. If the magnitude of the in-plane wave vectors K1 to K4 is k, the relationship of the following mathematical formula (8) holds.

Figure 9 is a three-dimensional perspective view of the reciprocal lattice space shown in Figure 8. Figure 9 also shows the Z axis, which is perpendicular to the Γ-X axis and Γ-Y axis directions. This Z axis is the same as the Z axis shown in Figure 1. As shown in Figure 9, in the case of a photonic crystal layer that oscillates at the Γ point, the wave number in the in-plane direction becomes 0 due to diffraction, and diffraction occurs in the direction perpendicular to the plane (Z direction) (arrow K5 in the figure). Therefore, the laser light is basically output in the Z direction.

回折は波数ベクトルＫ６～Ｋ９に逆格子ベクトルＧ（＝２ｍπ／ａ、ｍ：整数）のベクトル和の方向に生じるが、Ｍ点で発振する光回折層２５Ａの場合、回折によって面内方向の波数が０となり得ず、面垂直方向（Ｚ方向）への回折は生じない。従って、レーザ光はＺ方向には出力されない。 As described above, the photonic crystal layer of the PCSEL does not usually oscillate at the M point. For the M point oscillation, the lattice interval a of the virtual square lattice, the emission wavelength λ of the active layer 13, and the equivalent refractive index n of the mode satisfy the condition of λ=(√2)n×a. FIG. 10 is a plan view showing a reciprocal lattice space related to the photonic crystal layer oscillating at the M point. This figure also shows a case where a plurality of modified refractive index areas are located on the lattice points of the square lattice, and the point P in the figure represents the reciprocal lattice point. The arrow B1 in the figure represents the fundamental reciprocal lattice vector similar to that in FIG. 8, and the arrows K6, K7, K8, and K9 represent the four in-plane wave number vectors. Here, the Γ-M1 axis and the Γ-M2 axis are defined as being orthogonal to each other in the reciprocal lattice space. The Γ-M1 axis is parallel to one diagonal direction of the square lattice, and the Γ-M2 axis is parallel to the other diagonal direction of the square lattice. The in-plane wave vector is a vector obtained by projecting a wave vector onto the Γ-M1-Γ-M2 plane. That is, the in-plane wave vector K6 faces the positive direction of the Γ-M1 axis, the in-plane wave vector K7 faces the positive direction of the Γ-M2 axis, the in-plane wave vector K8 faces the negative direction of the Γ-M1 axis, and the in-plane wave vector K9 faces the negative direction of the Γ-M2 axis. As is clear from FIG. 10, in the photonic crystal layer oscillating at point M, the magnitude of the in-plane wave vectors K6 to K9 (i.e., the magnitude of the standing wave in the in-plane direction) is smaller than the magnitude of the fundamental reciprocal lattice vector B1. If the magnitude of the in-plane wave vectors K6 to K9 is k, the relationship of the following mathematical formula (9) is established.

Diffraction occurs in the direction of the vector sum of the reciprocal lattice vector G (=2mπ/a, m: integer) of the wave vectors K6 to K9, but in the case of the light diffractive layer 25A that oscillates at point M, the wave number in the in-plane direction cannot become 0 due to diffraction, and diffraction does not occur in the direction perpendicular to the plane (Z direction). Therefore, the laser light is not output in the Z direction.

Next, consider lasing the optical diffraction layer having the approximately periodic structure shown in FIG. 3 at the Γ point. The conditions for Γ point oscillation are the same as those for the PCSEL described above. FIG. 11 is a plan view showing a reciprocal lattice space related to the optical diffraction layer lasing at the Γ point. The fundamental reciprocal lattice vector B1 is the same as that of the PCSEL with Γ point oscillation (see FIG. 8), but the in-plane wave vectors K1 to K4 are phase-modulated by the angular distribution θ(x, y), and each has a wave number spread SP corresponding to the spread angle of the output beam pattern. The wave number spread SP can be expressed as a rectangular region with the ends of the in-plane wave vectors K1 to K4 in the PCSEL with Γ point oscillation as the center, and the lengths of the sides in the X direction and Y direction are 2Δkx _max and 2Δky _max , respectively. Due to such wave number spread SP, each in-plane wave number vector K1 to K4 spreads to a rectangular range of (Kix+Δkx, Kiy+Δky) (i=1 to 4, Kix is the X-direction component of vector Ki, and Kiy is the Y-direction component of vector Ki). Here, -Δkx _max ≦Δkx≦Δkx _max , -Δky _max ≦Δky≦Δky _max . The magnitudes of Δkx _max and Δky _max are determined according to the spread angle of the output beam pattern.

Figure 12 is a three-dimensional perspective view of the reciprocal lattice space shown in Figure 11. Figure 12 also shows the Z axis perpendicular to the Γ-X axis and the Γ-Y axis. This Z axis is the same as the Z axis shown in Figure 1. As shown in Figure 12, in the case of an optical diffraction layer that oscillates at the Γ point, a beam pattern LM is output that has a spatial spread that includes zero-order light in the direction perpendicular to the surface (Z direction) and first-order light and -1st-order light in a direction inclined relative to the Z direction.

Next, consider oscillating the optical diffraction layer having the approximately periodic structure shown in FIG. 3 at point M. The conditions for M-point oscillation are the same as those for the PCSEL described above. FIG. 13 is a plan view showing a reciprocal lattice space for an optical diffraction layer oscillating at point M. The fundamental reciprocal lattice vector B1 is the same as that of the PCSEL for M-point oscillation (see FIG. 10), but the in-plane wave vectors K6 to K9 each have a wave number spread SP due to the angular distribution θ(x, y). The shape and size of the wave number spread SP are the same as those for the Γ-point oscillation described above. Not only in the PCSEL in which the modified refractive index areas are periodically arranged, but also in the optical diffraction layer having the approximately periodic structure shown in FIG. 3, in the case of M-point oscillation, the magnitude of the in-plane wave number vectors K6 to K9 (i.e., the magnitude of the standing wave in the in-plane direction) is smaller than the magnitude of the fundamental reciprocal lattice vector B1. Therefore, the wave number in the in-plane direction cannot become 0 due to diffraction, and diffraction in the direction perpendicular to the plane (Z direction) does not occur. Therefore, zero-order light in the direction perpendicular to the surface (Z direction) and first-order light and -1st-order light in a direction inclined to the Z direction are not output.

Here, in this embodiment, in a substantially periodic structure that oscillates at point M, the following device is applied to the optical diffraction layer 25A, so that the 1st order light and a part of the -1st order light are output without outputting the 0th order light. Specifically, as shown in FIG. 14, a diffraction vector V having a certain magnitude and direction is added to the in-plane wave vectors K6 to K9, so that the magnitude of at least one of the in-plane wave vectors K6 to K9 (in the figure, the in-plane wave vector K8) is made smaller than 2π/λ. In other words, at least one of the in-plane wave vectors K6 to K9 (in-plane wave vector K8) after the diffraction vector V is added falls within a circular region (light line) LL of radius 2π/λ. In FIG. 14, the in-plane wave vectors K6 to K9 shown by dashed lines represent the state before the diffraction vector V is added, and the in-plane wave vectors K6 to K9 shown by solid lines represent the state after the diffraction vector V is added. 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 direction). In one example, the direction of the diffraction vector V is along the Γ-M1 axis or the Γ-M2 axis, and its magnitude is within the range of 2π/(√2)a-2π/λ to 2π/(√2)a+2π/λ, and as an example, is 2π/(√2)a.

なお、波数ベクトルの広がりΔｋｘ及びΔｋｙは、下記の数式（１４）及び（１５）をそれぞれ満たし、面内波数ベクトルのＸ方向の広がりの最大値Δｋｘ_ｍａｘ及びＹ方向の広がりの最大値Δｋｙ_ｍａｘは、設計の出力ビームパターンの角度広がりにより規定される。

ここで、回折ベクトルＶを下記の数式（１６）のように表したとき、回折ベクトルＶが加えられた後の面内波数ベクトルＫ６～Ｋ９は下記の数式（１７）～（２０）となる。

数式（１７）～（２０）において波数ベクトルＫ６～Ｋ９のいずれかがライトラインＬＬ内に収まることを考慮すると、下記の数式（２１）の関係が成り立つ。

すなわち、数式（２１）を満たす回折ベクトルＶを加えることにより、波数ベクトルＫ６～Ｋ９のいずれかがライトラインＬＬ内に収まり、１次光及び－１次光の一部が出力される。 The magnitude and direction of the diffraction vector V for placing at least one of the in-plane wave vectors K6 to K9 within the light line LL will be considered. The following formulas (10) to (13) show the in-plane wave vectors K6 to K9 before the diffraction vector V is added.

The spreads Δkx and Δky of the wave vector satisfy the following formulas (14) and (15), respectively, and the maximum value Δkx _max of the spread of the in-plane wave vector in the X direction and the maximum value Δky _max of the spread in the Y direction are defined by the angular spread of the designed output beam pattern.

Here, when the diffraction vector V is expressed as in the following formula (16), the in-plane wave number vectors K6 to K9 after the diffraction vector V is added become the following formulas (17) to (20).

In the formulas (17) to (20), if it is considered that any of the wave vectors K6 to K9 falls within the light line LL, the relationship of the following formula (21) holds.

That is, by adding a diffraction vector V that satisfies the formula (21), any one of the wave vectors K6 to K9 falls within the light line LL, and a part of the 1st order light and the −1st order light is output.

The size (radius) of the light line LL is set to 2π/λ for the following reason. Figure 15 is a diagram for explaining the peripheral structure of the light line LL, and shows the boundary between the device and air as viewed from a direction perpendicular to the Z direction. The magnitude of the wave vector of light in a vacuum is 2π/λ, but when light propagates through the device medium as shown in Figure 15, the magnitude of the wave vector Ka in the medium with a refractive index of n is 2πn/λ. At this time, in order for light to propagate through the boundary between the device and air, the wave number component parallel to the boundary must be continuous (law of conservation of wave number). In Figure 15, when the wave vector Ka and the Z axis form an angle θ, the length of the wave vector Kb projected in the plane (i.e., the in-plane wave vector) is (2πn/λ) sin θ. On the other hand, generally, due to the relationship of the refractive index of the medium n>1, the law of conservation of wave number does not hold at an angle where the in-plane wave vector Kb in the medium is larger than 2π/λ. At this time, 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, which is 2π/λ.

As an example of a specific method of adding the diffraction vector V to the in-plane wave vectors K6 to K9, a method of superimposing an angular distribution θ ₂ (x, y) that is unrelated to the output beam pattern on an angular distribution θ ₁ (x, y) that is a phase distribution according to the output beam pattern can be considered. In this case, the angular distribution θ (x, y) of the light diffraction layer 25A is expressed as follows:
θ(x,y)= _θ1 (x,y)+ _θ2 (x,y)
θ ₁ (x, y) corresponds to the phase of the complex amplitude when the output beam pattern is Fourier transformed as described above. Also, θ ₂ (x, y) is an angular distribution for adding a diffraction vector V that satisfies the above formula (21). FIG. 16 is a conceptual diagram showing an example of the angular distribution θ ₂ (x, y). As shown in FIG. 16, in this example, a first phase value φ _A and a second phase value φ _B having a value different from the first phase value φ _A are arranged in a checkerboard pattern. In one embodiment, the phase value φ _A is 0 (rad) and the phase value φ _B is π (rad). That is, the first phase value φ _A and the second phase value φ _B change by π. The angular distribution θ ₂ (x, y) corresponding to such phase values can suitably realize a diffraction vector V along the Γ-M1 axis or the Γ-M2 axis. When arranged in a checkerboard pattern as described above, V = (±π/a, ±π/a), which exactly cancels out the wave vectors K6 to K9 in Fig. 13. The angular distribution _θ2 (x, y) of the diffraction vector V is expressed as the inner 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=Vxx+Vyy

The characteristics of each modified refractive index region 25b of the light diffraction layer 25A of this embodiment will be further described. When one-dimensional diffraction (diffraction in the 180° direction) is large in the light diffraction layer 25A, as conceptually shown in part (a) of FIG. 17, localization of the oscillation mode progresses, local oscillation occurs, and local one-dimensional oscillation competition occurs. This contributes to the formation of a higher-order mode. Also, as conceptually shown in part (b) of FIG. 17, flat band oscillation occurs and flat band competition occurs. In addition, in FIG. 17, the arrows indicate the diffraction direction of light. Here, flat band oscillation is a phenomenon in which a standing wave is formed and oscillated in a flat region of the photonic band in the Γ-X direction near the band end in the case of the Γ point, and in the Γ-M direction near the band end in the case of the M point, resulting in a zigzag resonance state as shown in FIG. 17(b). At this time, the output beam becomes elongated, resulting in an optical image that is elongated relative to the design pattern. And, in competition with the band end oscillation at the same time, flat band competition in which flat band oscillation occurs may occur. These phenomena cause the light intensity distribution in the light diffraction layer 25A to become non-uniform, leading to deterioration in the quality of the light image relative to the design pattern. In contrast, when one-dimensional local oscillation is suppressed, two-dimensional diffraction is promoted, as shown in part (a) of FIG. 18. Therefore, localization of the oscillation mode is suppressed and higher-order modes are less likely to be formed, so that the threshold gain difference between the fundamental mode and the higher-order mode can be increased. In addition, flat-band oscillation can be suppressed to suppress flat-band competition. Furthermore, as shown in part (b) of FIG. 18, the modes can be widely distributed over the entire area of the light diffraction layer 25A. Therefore, the light intensity distribution of the output beam pattern can be made uniform, and the area that can be output in a single mode can be increased in area, so that the emitted light image can have high resolution and high quality.

Therefore, the conditions for reducing one-dimensional diffraction in the light diffraction layer 25A are examined. According to the knowledge of the present inventor, in the case of M-point oscillation, the closer the (±1, ±1)-order Fourier coefficient of the fundamental wave is to zero, the more the one-dimensional diffraction in the 180° direction of the light incident on the light diffraction layer 25A is suppressed. That is, the diffraction between light waves is expressed by the coupling coefficient κ of the three-dimensional coupled wave theory shown in the following paper, which is proportional to the Fourier coefficient, so if the above Fourier coefficient is zero, the κ that contributes to the coupling in the 180° direction of the M-point oscillation becomes 0, and direct coupling of light waves in the 180° direction does not occur. However, indirect coupling via higher-order diffraction does exist.
Paper: Yong Liang et al., “Three-dimensional coupled-wave model for square-lattice photonic crystal lasers with transverseelectric polarization: A general approach”, Physical Review,B84, 195119 (2011)
In addition, the (±1, ±1) order Fourier coefficients approaching zero means that the four (+1, +1) order Fourier coefficients, (+1, -1) order, (-1, +1) order, and (-1, -1) order Fourier coefficients approaching zero.

The planar shape of the modified refractive index area 25b of this embodiment is a C-shape with the lattice point O as the center of the inner and outer arcs, as shown in FIG. 4. When the modified refractive index area 25b having such a planar shape is virtually rotated around the corresponding lattice point O as the center of rotation, a circular ring shape is obtained. The inner radius of this circular ring shape is equal to the radius _r1 of the inner circumference circle, and the outer radius is equal to the radius _r2 of the outer circumference circle. In the following description, in considering the diffraction action in the light diffraction layer 25A, each modified refractive index area 25b is approximately regarded as a two-dimensional photonic crystal having this circular ring shape.

The relationship between the Fourier coefficient and the radius of a circle is generally expressed by the following formula (22): where ρ is the absolute value of the Fourier order, _J1 is the first-order Bessel function, R is the radius of the circle, and circ(r) is a function expressed by formula (23). Note that the radius R is a value normalized by the lattice interval a.

The Fourier coefficients of the annular shape are obtained by subtracting the Fourier coefficients of the inner circle from the Fourier coefficients of the outer circle. That is, the Fourier coefficients of the annular shape are expressed by the following formula (24), where _R1 is the radius of the inner circle (= _r1 ) and _R2 is the radius of the outer circle (= _r2 ).

When the optical diffraction layer 25A is oscillated at M points, the lattice interval a is determined so that the wave number of the fundamental wave is k = 2πn/λ = 2π/(√2)a. Therefore, in the case of M point oscillation, the Fourier coefficient of the circle shown in formula (22) is ρ = √2 for the orders (±1, ±1) that contribute to one-dimensional diffraction, so it is expressed by the following formula (25). Here, r is the radius of the circle. Note that the radius r is a value normalized by the lattice interval a.

FIG. 19 is a graph of the relationship of formula (25). In FIG. 19, the vertical axis represents the Fourier coefficient, and the horizontal axis represents the magnification of the radius of the circle to the lattice interval a. As shown in the figure, the Fourier coefficient in M-point oscillation is a maximum value (0.10) when the radius of the circle is 0.27 times the lattice interval a. And the Fourier coefficient increases and decreases with almost the same gradient before and after the maximum value. When the planar shape of the modified refractive index area 25b is approximately a circular ring shape, if the Fourier coefficient of the inner circle and the Fourier coefficient of the outer circle are equal to each other, the Fourier coefficient of the circular ring shape becomes zero. Therefore, in order to make the Fourier coefficient of the circular ring shape zero, as shown in FIG. 19, it is good to set each of the two radii corresponding to a certain Fourier coefficient Fa to the radius _r1 of the inner circle and the radius _r2 of the outer circle. In this case, the radius _r1 of the inner circle is smaller than 0.27 times the lattice spacing a, and the radius _r2 of the outer circle is larger than 0.27 times the lattice spacing a.

In the above description, the one-dimensional local oscillation is suppressed by making the Fourier coefficient zero, but even if the Fourier coefficient is not strictly zero, it is possible to suppress the one-dimensional local oscillation by making its absolute value extremely small.Specifically, if the absolute value of the (±1, ±1) order Fourier coefficient of the annular shape obtained by virtually rotating the modified refractive index area 25b around the lattice point O is 0.01 or less, or is 10% or less of the maximum peak value (0.10 in the example of FIG. 19) of the circular (±1, ±1) order Fourier coefficient, the one-dimensional local oscillation can be effectively suppressed.In addition, if the ratio (F 2 /F 1 ) of the (±1, ±1) order Fourier coefficient F ₁ of the inner circle that defines the annular shape to the (±1, ± ₁ ) order Fourier coefficient F ₂ of the outer circle that defines the _annular shape is 0.99 or more and 1.01 or less, the one-dimensional local oscillation can be effectively suppressed. In one embodiment, radius _r1 is 0.195 times the lattice spacing a, and radius _r2 is 0.34 times the lattice spacing a.

FIG. 20 is an enlarged photograph showing a modified refractive index area 25b in a C-shape with a lattice spacing a=200 nm, formed by dry etching a GaAs layer as a basic layer 25a, as an example. Part (a) of FIG. 20 shows a plurality of modified refractive index areas 25b, and part (b) of FIG. 20 shows a further enlarged view of part (a). The diameter of the inner circle of the modified refractive index area 25b is 42 nm, and the radius _r1 is 0.105 times the lattice spacing a. The diameter of the outer circle is 160 nm, and the radius _r2 is 0.40 times the lattice spacing a. At this time, as shown in FIG. ₂₁ , the (±1, ±1) order Fourier coefficients of the circle with radius r1 and the (±1, ±1) order Fourier coefficients of the circle with radius _r2 are equal to each other, so they cancel each other out, and the (±1, ±1) order Fourier coefficients of the ring obtained by rotating this C-shape are almost zero. Therefore, one-dimensional local oscillation can be effectively suppressed.

In the light source device 1A of this embodiment, as long as the active layer 13 and the optical diffraction layer 25A are provided, the material, thickness, and structure of each layer can be changed in various ways. Here, the scaling law holds for a so-called square lattice photonic crystal laser in which the perturbation from the virtual square lattice is zero. That is, when the wavelength becomes a constant α times, a similar standing wave state can be obtained by multiplying the entire square lattice structure by α. Similarly, in this embodiment, the structure of the optical diffraction layer 25A can be determined by the scaling law according to the wavelength. Therefore, it is also possible to realize a light source device 1A that outputs visible light by using an active layer 13 that emits light such as blue, green, and red, and applying the scaling law according to the wavelength.

When manufacturing the light source device 1A, metal organic chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE) is used for the growth of each compound semiconductor layer. In manufacturing the light source device 1A using AlGaAs, the growth temperature is 500°C to 850°C, and 550°C to 700°C was adopted in the experiment. During growth, TMA (trimethylaluminum) can be used as the Al source, TMG (trimethylgallium) and TEG (triethylgallium) can be used as the gallium source, AsH ₃ (arsine) can be used as the As source, Si ₂ H ₆ (disilane) can be used as the source for n-type impurities, and DEZn (diethylzinc) can be used as the source for p-type impurities. The insulating film can be formed by sputtering a target using its constituent substances as the source, or by PCVD (plasma enhanced chemical vapor deposition).

When manufacturing the light source device 1A, first, the lower cladding layers 12, 22, the active layers 13, 23, the optical confinement layers 14, 24, the upper cladding layer 15, the semiconductor layer that will become the basic layer 25a of the optical diffraction layer 25A, and the contact layer 16 are epitaxially grown in sequence on the main surface 3a of the substrate 3 using the MOCVD (metal organic chemical vapor deposition) method.

Next, the region on the contact layer 16 that will become the laser oscillation section 10A is covered with a silicon compound such as SiN, and a part of the contact layer 16 and the upper cladding layer 15 in the region that will become the optical waveguide section 20A is etched to expose the base layer 25a. A resist is applied to the base layer 25a, and a two-dimensional fine pattern is drawn on the resist by an electron beam drawing device and developed to form a two-dimensional fine pattern on the resist. Thereafter, the two-dimensional fine pattern is transferred onto the base layer 25a by dry etching using the resist as a mask, holes (holes) are formed, and the resist is removed. Note that, before forming the resist, a SiN layer or a SiO ₂ layer may be formed on the base layer 25a by the PCVD method, a resist mask is formed thereon, and a fine pattern is transferred to the SiN layer or the SiO ₂ layer by reactive ion etching (RIE), and the resist is removed before dry etching. In this case, the resistance to dry etching can be improved. These holes are made into the modified refractive index area 25b, or a compound semiconductor (e.g., AlGaAs) that will become the modified refractive index area 25b is regrown in these holes to a depth equal to or greater than the depth of the holes. When the holes are made into the modified refractive index area 25b, a gas such as air, nitrogen, hydrogen, or argon may be filled into the holes. Alternatively, a dielectric may be embedded in the holes of the modified refractive index area 25b using an atomic layer deposition apparatus. In this case, a physically robust structure can be obtained. In addition, if no film is formed on the modified refractive index area 25b after dry etching, the hole shape can be maintained, and changes in characteristics due to changes in the hole shape can be suppressed. Next, the electrodes 17 and 18 are formed by deposition or sputtering. In addition, protective films 31 and 32 are formed by sputtering, PCVD, or the like, as necessary.

The effects obtained by the light source device 1A and the optical waveguide section 20A of the present embodiment described above will be described. In the optical waveguide section 20A, the lattice spacing a of the virtual square lattice and the wavelength λ of the light Lin satisfy the condition of M-point oscillation. Normally, in the standing wave state of M-point oscillation, the light propagating in the optical diffraction layer is totally reflected, so that the light output in the direction intersecting the XY plane is suppressed. However, in the optical waveguide section 20A of the present embodiment, each center of gravity G of the multiple modified refractive index areas 25b is disposed away from the corresponding lattice point O of the virtual square lattice, and the angle θ of the vector connecting the corresponding lattice point O and the center of gravity G is set individually for each modified refractive index area 25b, and the distribution of the angle θ satisfies the condition for the light Lout to be output in a direction intersecting the XY plane. With such a structure, the light Lin input along the XY plane can be diffracted in a direction intersecting the XY plane.

In addition, in this optical waveguide 20A, when each modified refractive index area 25b is virtually rotated around the corresponding lattice point O, a circular shape is obtained, and the absolute value of the (±1, ±1) order Fourier coefficient of the circular shape is 0.01 or less, or 10% or less of the maximum peak value of the (±1, ±1) order Fourier coefficient of the circular shape. In this way, the (±1, ±1) order Fourier coefficient of each modified refractive index area 25b has an extremely small value, so that one-dimensional local oscillation can be reduced. Therefore, according to this optical waveguide 20A, phenomena such as mode localization due to one-dimensional diffraction and flat band diffraction can be suppressed, the light intensity distribution is made closer to uniform by two-dimensional diffraction, and the area that can be output in a single mode can be increased in area, so that the emitted optical image can be made high resolution and high quality. Furthermore, the return light noise from the optical diffraction layer 25A to the laser oscillation section 10A can be reduced, enabling stable element operation.

The light source device 1A of this embodiment can be easily manufactured with high precision using semiconductor processes. Furthermore, since no other optical systems such as collimating lenses or diffractive optical elements are required, no optical axis misalignment occurs. Therefore, the tolerance for installation errors of the light source device 1A can be increased.

In addition, in a conventional distributed Bragg reflector, a coupling waveguide is required between the light source and the distributed Bragg reflector to make the light uniform over the entire area of the diffraction grating. In contrast, according to the optical waveguide section 20A of this embodiment, even if light is incident on a part of the optical diffraction layer 25A or if light Lin with non-uniform light intensity is incident on the optical diffraction layer 25A, the two-dimensional diffraction action in the optical diffraction layer 25A can spread the light over the entire area of the optical diffraction layer 25A, and output a uniform beam pattern with little light bias. Therefore, even if a Fabry-Perot type single mode laser diode is used as the light source, for example, it is possible to omit the coupling waveguide and make the device smaller.

As mentioned above, the (±1, ±1) order Fourier coefficients of the annular shape obtained by virtually rotating each modified refractive index area 25b around the corresponding lattice point O as the center of rotation may be zero. In this case, the above-mentioned effect can be more pronounced.

As described above, the ratio (F2/F1) of the (±1,±1) order Fourier coefficient _F1 of the inner circle defining the above-mentioned annular shape to the (±1,±1) order Fourier coefficient _F2 of the outer circle defining the above-mentioned annular shape may be _0.99 or more and _1.01 or less. Since the Fourier coefficients of the outer circle and the Fourier coefficients of the inner circle are close to each other in this way, the Fourier coefficients of the annular shape can be made close to zero, and one-dimensional local oscillation can be more effectively reduced.

As described above, the (±1, ±1) order Fourier coefficient _F1 of the inner circle defining the above-mentioned annular shape and the (±1, ±1) order Fourier coefficient _F2 of the outer circle defining the above-mentioned annular shape may be equal to each other. In this case, the Fourier coefficient of the above-mentioned annular shape becomes sufficiently small, so that the above-mentioned effect can be achieved.

As described above, the radius _r1 of the inner circle of the above-mentioned annular shape may be smaller than 0.27 times the lattice interval a, and the radius _r2 of the outer circle may be larger than 0.27 times the lattice interval a. As shown in Fig. 19, in the M-point oscillation structure, the circular Fourier coefficient takes an extreme value when its radius is 0.27 times the lattice interval a. Therefore, by making the radius _r1 of the inner circle smaller than 0.27 times the lattice interval a and the radius _r2 of the outer circle larger than 0.27 times the lattice interval a, it is easy to make the Fourier coefficient of the inner circle and the Fourier coefficient of the outer circle closer to each other.

As in this embodiment, the planar shape of each modified refractive index area 25b may be a C-shape with the corresponding lattice point O as the center of the inner and outer arcs. In this case, the angle θ of the vector connecting the center of gravity G of each modified refractive index area 25b and the lattice point O can be arbitrarily set by changing the circumferential position of the opening part of the C-shape. In addition, if the C-shape is virtually rotated once around the lattice point O as the center of rotation, a circular ring shape can be suitably obtained. Since the C-shape is close to a circular ring shape, the Fourier coefficient of the planar shape of each modified refractive index area 25b can be accurately brought close to the Fourier coefficient of the circular ring shape, and one-dimensional diffraction can be suitably suppressed. In addition, by making the planar shape of the modified refractive index area 25b a C-shape, the area of the modified refractive index area 25b can be increased while realizing the above-mentioned circular ring shape. Therefore, it is possible to increase the area of the area that can be output in a single mode, and the emitted light image can be made to have high resolution and high image quality.

As in this embodiment, the condition for light to be output in a direction intersecting with the virtual plane may be that the magnitude of at least one of the four in-plane wave vectors K6 to K9, each of which includes a wave number spread due to the distribution of the angle θ, is smaller than 2π/λ (light line) in the reciprocal lattice space of the light diffraction layer 25A. When the magnitude of at least one in-plane wave vector is smaller than 2π/λ (light line), the in-plane wave vector has a component in the Z direction and does not undergo total reflection at the interface with the air, so that a portion of the light Lin input along the XY plane can be output in a direction intersecting with the XY plane.

In addition, according to the light source device 1A of this embodiment, which is equipped with the optical waveguide section 20A, the light Lin input from the laser oscillation section 10A to the optical diffraction layer 25A along the XY plane can be diffracted in a direction intersecting the XY plane and output. In addition, the above action can reduce one-dimensional local oscillation. Therefore, it is possible to suppress phenomena such as mode localization due to one-dimensional diffraction and flat band diffraction, make the light intensity distribution closer to uniform, and increase the area where output is possible in a single mode, thereby enabling the emitted optical image to have high resolution and high image quality.

As in this embodiment, the light Lin may be spatially coherent. In this case, the uniformity of the oscillation in the light diffraction layer 25A can be further improved, and the output beam pattern can be made closer to the designed pattern.

As mentioned above, the top of the hole in the modified refractive index area 25b may be open. When a semiconductor layer is formed on the light diffraction layer 25A to block the hole, the semiconductor material may enter the hole and the shape of the hole may be slightly deformed. By opening the top of the hole (without re-growing the semiconductor layer), the shape of the hole is maintained and the shape of the modified refractive index area 25b can be formed with high precision.

In addition, in this embodiment, the optical diffraction layer 25A may emit not only 1st order light and -1st order light, but also 2nd order or higher order light. In such a case, by tilting the emission direction of the 1st order light and -1st order light with respect to the surface perpendicular direction (Z direction), the emission direction of the higher order light can be made different from that of the 1st order light and -1st order light, making it easier to separate the 1st order light and -1st order light from the higher order light. In addition, by making the angle between the emission direction of the higher order light and the Z direction equal to or greater than the total reflection angle, it is also possible to prevent the higher order light from being output.

In addition, in this embodiment, the arrangement direction of the laser oscillation section 10A and the optical waveguide section 20A, i.e., the X direction, is parallel to one side of the square lattice, but each side of the square lattice may be inclined with respect to the X direction and the Y direction. Figure 22 is a perspective view showing an example in which each side of the square lattice is inclined at 45° with respect to the input direction of the light Lin. Even in such a configuration, the effects of this embodiment can be achieved.

Here, an example of the light source device 1A of this embodiment is shown. The following Table 1 shows an example of the thickness and refractive index of each layer constituting the laser oscillation section 10A. FIG. 23 is a graph showing the refractive index distribution G11 and mode distribution G12 of the laser oscillation section 10A having the configuration of this Table 1. In the figure, section T11 corresponds to the lower cladding layer 12, section T12 corresponds to the active layer 13, section T13 corresponds to the light confinement layer 14, section T14 corresponds to the upper cladding layer 15, section T15 corresponds to the contact layer 16, and section T16 corresponds to air. Table 2 is a table showing an example of the thickness and refractive index of each layer constituting the optical waveguide section 20A. FIG. 24 is a graph showing the refractive index distribution G21 and mode distribution G22 of the optical waveguide section 20A having the configuration of this Table 2. In the figure, section T21 corresponds to the lower cladding layer 22, section T22 corresponds to the active layer 23, section T23 corresponds to the optical confinement layer 24, section T24 corresponds to the optical diffraction layer 25A, and section T25 corresponds to air.

Figure 25 is a graph in which the mode distribution G12 shown in Figure 23 and the mode distribution G22 shown in Figure 24 are superimposed. As shown in Figure 25, according to this embodiment, the mode distribution G12 of the laser oscillator 10A and the mode distribution G22 of the optical waveguide 20A almost coincide with each other, and it can be seen that high coupling efficiency between the laser oscillator 10A and the optical waveguide 20A can be obtained. In this embodiment, the coupling efficiency is 0.988.

(First Modification)
In the above-described embodiment, when the wave number spread based on the distribution of the angle θ is included in a circle of radius Δk centered on a certain point in the wave number space, it can be simply considered as follows. That is, by adding a diffraction vector V to the four-directional in-plane wave number vectors K6 to K9, the magnitude of at least one of the four-directional in-plane wave number vectors K6 to K9 is made smaller than 2π/λ (light line LL). This can be considered as adding a diffraction vector V to the four-directional in-plane wave number vectors K6 to K9 minus the wave number spread Δk (i.e., the four-directional in-plane wave number vectors in the square lattice PCSEL with M-point oscillation, see FIG. 10), making the magnitude of at least one of the four-directional in-plane wave number vectors K6 to K9 smaller than the value {(2π/λ)-Δk} obtained by subtracting the wave number spread Δk from 2π/λ.

Figure 26 is a diagram conceptually illustrating the above operation. As shown in the figure, by adding the diffraction vector V to the in-plane wave vectors K6 to K9 excluding the wave number spread Δk, the magnitude of at least one of the in-plane wave vectors K6 to K9 is made smaller than {(2π/λ)-Δk}. In the figure, region LL2 is a circular region with a radius of {(2π/λ)-Δk}. Note that the in-plane wave vectors K6 to K9 shown by dashed lines in Figure 26 represent the state before the diffraction vector V is added, and the in-plane wave vectors K6 to K9 shown by solid lines represent the state after the diffraction vector V is added. Region LL2 corresponds to the total reflection condition, and wave vectors whose magnitude falls within region LL2 will also propagate in the direction perpendicular to the surface (Z direction).

ここで、回折ベクトルＶを前述した数式（１６）のように表したとき、回折ベクトルＶが加えられた後の面内波数ベクトルＫ６～Ｋ９は下記の数式（３０）～（３３）となる。

数式（３０）～（３３）において面内波数ベクトルＫ６～Ｋ９のいずれかが領域ＬＬ２内に収まることを考慮すると、下記の数式（３４）の関係が成り立つ。

すなわち、数式（３４）を満たす回折ベクトルＶを加えることにより、波数拡がりΔｋを除いた面内波数ベクトルＫ６～Ｋ９のいずれかが領域ＬＬ２内に収まる。このような場合であっても、０次光を出力しないまま、１次光及び－１次光の一部を出力することができる。 In this modification, the magnitude and direction of the diffraction vector V for placing at least one of the in-plane wave vectors K6 to K9 within the region LL2 will be described. The following formulas (26) to (29) show the in-plane wave vectors K6 to K9 before the diffraction vector V is added.

Here, when the diffraction vector V is expressed as in the above-mentioned formula (16), the in-plane wave number vectors K6 to K9 after the diffraction vector V is added become the following formulas (30) to (33).

In formulas (30) to (33), if it is considered that any of the in-plane wave vectors K6 to K9 falls within the region LL2, the relationship of the following formula (34) holds.

That is, by adding the diffraction vector V that satisfies the formula (34), any of the in-plane wave vectors K6 to K9 excluding the wave number spread Δk falls within the 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.

(Second Modification)
27, 28 and 29 are diagrams showing other examples of the planar shape of the modified refractive index area 25b in the first embodiment. In the example shown in FIG. 27, as in the above embodiment, the planar shape of the modified refractive index area 25b is a C-shape with the lattice point O as the center of the inner and outer arcs. However, in this modified example, the line segment 153 connecting one end of the inner arc 151 and one end of the outer arc 152 and the line segment 154 connecting the other end of the arc 151 and the other end of the arc 152 are parallel to each other. Therefore, the central angle of the outer arc 152 is slightly larger than the central angle of the inner arc 151. Even when the modified refractive index area 25b has such a planar shape, it is possible to achieve the same effect as the above embodiment.

In the example shown in FIG. 28, the planar shape of the modified refractive index area 25b is a circle with the corresponding lattice point O located outside of it. In the example shown in FIG. 29, the planar shape of the modified refractive index area 25b is a polygon with the corresponding lattice point O located outside of it. Even with these shapes, when the modified refractive index area 25b is virtually rotated once around the lattice point O as the rotation center, a circular ring shape defined by the inner circle C1 and the outer circle C2 is preferably obtained. And, the light diffraction layer 25A includes a large number of modified refractive index areas 25b, and the angle θ is set individually for each modified refractive index area 25b. Therefore, in considering the diffraction action in the light diffraction layer 25A, each modified refractive index area 25b can be approximately regarded as a two-dimensional photonic crystal having this circular ring shape. Therefore, even if the modified refractive index area 25b has these planar shapes, the same action and effect as the above embodiment can be achieved. In these cases, the distance between the lattice point O and the point closest to the lattice point O on the outer periphery of the modified refractive index area 25b corresponds to the radius _r1 of the inner circle, and the distance between the lattice point O and the point farthest from the lattice point O on the outer periphery of the modified refractive index area 25b corresponds to the radius _r2 of the outer circle.

(Third Modification)
30 is a diagram showing another example of the planar shape of the modified refractive index area 25b in the first embodiment. In the example shown in FIG. 30, the planar shape of the modified refractive index area 25b is a sector shape with the corresponding lattice point O as the center of the arc. Specifically, the planar shape of the modified refractive index area 25b is defined by an arc 161, a line segment 162 connecting one end of the arc 161 to the lattice point O, and a line segment 163 connecting the other end of the arc 161 to the lattice point O. The arc 161 is a major arc. In other words, the central angle of the arc 161 is greater than 180°. The central angle of the arc 161 is, for example, in the range of 300° or more and less than 360°. The line segments 162 and 163 extend along the radial direction of the arc 161.

In this example, the angle θ(x, y) between the vector starting from the lattice point O and the center of the sector-shaped cutout and the X-axis is defined. Adding 180° to this angle θ(x, y) equals the angle between the vector from the lattice point O toward the center of gravity G and the X-axis. Therefore, even in this example, the angle θ(x, y) can be considered to correspond to the angle between the vector from the lattice point O toward the center of gravity G and the X-axis. The angle of the vector connecting the center of gravity G of each modified refractive index area 25b and the lattice point O can be set arbitrarily by changing the circumferential position of the sector-shaped cutout. The distance between the lattice point O and the center of gravity G is constant regardless of x and y (throughout the entire light diffraction layer 25A). Note that the optical image obtained does not change even if a constant is added to the phase angle, so the phase angle may be designed without adding 180°.

When this sector is virtually rotated once around the lattice point O as the center of rotation, a circle with a radius r ₃ is obtained, unlike the above embodiment. In the case of M-point oscillation, the Fourier coefficient of the circle is obtained by the formula (25) as described in the above embodiment. When the (±1, ±1)-order Fourier coefficient calculated by this formula (25) is zero or close to zero, one-dimensional diffraction can be suppressed to achieve the same effect as the above embodiment. The preferred range of the (±1, ±1)-order Fourier coefficient of the modified refractive index area 25b of this modification is the same as the above embodiment. The preferred size of the radius r ₃ that realizes such a Fourier coefficient is shown in FIG. 19. That is, the radius r ₃ of the circle is preferably 0.43 times or more and 0.44 times or less of the lattice interval a. In the case of M-point oscillation, the Fourier coefficient of the circle becomes zero when the radius r ₃ is a certain value within the range of 0.43 times to 0.44 times the lattice interval a. Therefore, in this case, the Fourier coefficient of the planar shape of the modified refractive index area 25b can be brought close to zero, and one-dimensional local oscillation can be more effectively reduced.

In addition, since a sector with a major arc is close to a circle, the Fourier coefficients of the planar shape of each modified refractive index area 25b can be made to accurately approximate the Fourier coefficients of a circle.

In this modified example, unlike the first embodiment, the width of the hole in the modified refractive index area 25b is increased. Therefore, when covering the hole with another semiconductor layer, it is advisable to increase the ratio of the width to the depth of the hole (aspect ratio) in order to prevent the hole from being filled with the other semiconductor layer. For this reason, only the outline portion of the modified refractive index area 25b described above may be made a hole, and an area made of the same material as the basic layer 25a may be provided inside it, thereby narrowing the hole while maintaining the outer shape of the modified refractive index area 25b.

(Fourth Modification)
31, 32, and 33 are diagrams showing other examples of the planar shape of the modified refractive index area 25b in the first embodiment. In the example shown in FIG. 31, the planar shape of the modified refractive index area 25b is a circle centered on the corresponding lattice point O and has a linear notch in the radial direction. Specifically, the planar shape of the modified refractive index area 25b is defined by an arc 171 and a rectangular concave portion 172 extending from the opening of the arc 171 toward the lattice point O. The arc 171 is a major arc. In other words, the central angle of the arc 171 is greater than 180°. The central angle of the arc 171 is, for example, greater than or equal to 300° and less than 360°. A pair of line segments 173 and 174 extending from one end and the other end of the arc 171, respectively, and forming the concave portion 172 are parallel to each other.

31 also defines an angle θ(x, y) between the X-axis and a vector starting from lattice point O and running along the center of the recessed portion 172. The angle of the vector connecting the center of gravity G of each modified refractive index area 25b and lattice point O can be set arbitrarily by changing the circumferential position of the recessed portion 172. When this shape is virtually rotated once around the lattice point O as the center of rotation, a circle with a radius _r3 is obtained. The preferable size of radius _r3 is the same as in the third modified example.

In the example shown in FIG. 32, the planar shape of the modified refractive index area 25b is a circle with the corresponding lattice point O located inside. In the example shown in FIG. 33, the planar shape of the modified refractive index area 25b is a polygon with the corresponding lattice point O located inside. Even with these shapes, when the modified refractive index area 25b is virtually rotated once around the lattice point O as the rotation center, a circle C3 can be suitably obtained. Since the light diffraction layer 25A includes many modified refractive index areas 25b and the angle θ is set individually for each modified refractive index area 25b, when considering the diffraction action in the light diffraction layer 25A, each modified refractive index area 25b can be approximately regarded as a two-dimensional photonic crystal having this circle C3. Therefore, even if the modified refractive index area 25b has these planar shapes, the same effect as the above embodiment can be achieved. In these cases, the distance between the lattice point O and the point farthest from the lattice point O on the outer periphery of the modified refractive index area 25b coincides with the radius _r3 of the circle C3. The preferable radius _r3 is the same as that of the third modified example.

Second Embodiment
Fig. 34 is a perspective view showing a schematic configuration of a light source device 1B according to a second embodiment of the present disclosure. In Fig. 34 as well, a coordinate system is defined in which the stacking direction of the light source device 1B is the Z direction, and the X direction, the Y direction, and the Z direction are mutually orthogonal.

The light source device 1B of this embodiment includes a light guide section 20B instead of the light guide section 20A of the first embodiment. The other configurations of the light source device 1B are the same as those of the light source device 1A of the first embodiment. The difference between the light guide section 20B and the light guide section 20A of the first embodiment is the configuration of the light diffraction layer. Figure 35 is a plan view of the light diffraction layer 25B of the light guide section 20A of this embodiment. The light diffraction layer 25B also includes a basic layer 25a made of a first refractive index medium and a plurality of modified refractive index areas 25b made of a second refractive index medium having a refractive index different from that of the first refractive index medium. A virtual square lattice in the XY plane is also set in the light diffraction layer 25B. One side of the square lattice is parallel to the X axis, and the other side is parallel to the Y axis. The multiple modified refractive index areas 25b are provided, for example, one by one in each unit configuration region R.

Figure 36 is an enlarged view of one unit constituent region R. As shown in Figure 36, the planar shape of the modified refractive index area 25b is, for example, a circular ring shape with the lattice point O as the center of the inner and outer circles. Specifically, the planar shape of the modified refractive index area 25b is defined by an inner circumferential circle 181 and an outer circumferential circle 182. The centers of the inner circumferential circle 181 and the outer circumferential circle 182 coincide with the lattice point O.

The optical diffraction layer 25B has a configuration as a photonic crystal laser that oscillates at the Γ point. That is, the lattice spacing a of the virtual square lattice and the emission wavelength λ of the active layer 13 (i.e., the wavelength of the light Lin) satisfy the conditions for Γ point oscillation. The conditions for Γ point oscillation are as described in the first embodiment. Therefore, as shown in FIG. 34, light Lout is output from the optical diffraction layer 25B in the direction perpendicular to the surface (Z direction).

The conditions for reducing one-dimensional local oscillation in the light diffraction layer 25B will be considered. In the case of Γ-point oscillation, the Fourier orders that directly contribute to one-dimensional diffraction are (±2,0) and (0,±2), and the closer the (±2,0) and (0,±2) Fourier coefficients of the fundamental wave are to zero, the more the one-dimensional diffraction in the 180° direction of the light Lin incident on the light diffraction layer 25B is suppressed. Note that the (±2,0) and (0,±2) Fourier coefficients approaching zero means that the four Fourier coefficients of (+2,0), (-2,0), (0,+2), and (0,-2) are to zero. The planar shape of the modified refractive index area 25b of this embodiment is a circular ring shape with the lattice point O as the center of the inner and outer circles, as shown in FIG. 36. The radius (inner diameter) of the inner circle of this circular ring shape is r ₁ , and the radius (outer diameter) of the outer circle is r ₂ . The relationship between the Fourier coefficients and the radius of the circle is expressed by the above-mentioned formula (22). Moreover, the Fourier coefficient of the annular shape is a value obtained by subtracting the Fourier coefficient of the inner circle from the Fourier coefficient of the outer circle, and is expressed by the above-mentioned formula (24). Here, _R1 is the inner radius (= _r1 ), and _R2 is the outer radius (= _r2 ).

When the light diffractive layer 25B is Γ-point oscillated, the lattice interval a is determined so that the wave number of the fundamental wave is k=2nπ/λ=2π/a. Therefore, in the case of Γ-point oscillation, the Fourier coefficient of the circle shown in formula (22) is expressed by the following formula (35) since the absolute value of the Fourier order is ρ=2 for the orders (±2, 0) or (0, ±2) that contribute to one-dimensional diffraction. Here, r is the radius of the circle. The radius r is a value normalized by the lattice interval a.

Figure 37 is a graph of the relationship in equation (35). In Figure 37, the vertical axis represents the Fourier coefficient, and the horizontal axis represents the magnification of the circle radius to the lattice interval a. As shown in the figure, the Fourier coefficient in the Γ-point oscillation reaches a maximum value (0.05) when the circle radius is 0.19 times the lattice interval a. The Fourier coefficient increases and decreases with approximately the same slope before and after the maximum value. The Fourier coefficient in the Γ-point oscillation reaches a minimum value (-0.075) when the circle radius is 0.44 times the lattice interval a. The Fourier coefficient decreases and increases with approximately the same slope before and after the minimum value.

When the plane shape of the modified refractive index area 25b has a circular ring shape, if the Fourier coefficient of the inner circle and the Fourier coefficient of the outer circle are equal to each other, the Fourier coefficient of the circular ring shape will be zero. Therefore, in order to make the Fourier coefficient of the circular ring shape zero, as shown in FIG. 37, it is good to set each of the two radii corresponding to a certain Fourier coefficient Fb to the inner radius _r1 and the outer radius _r2 . In this case, the inner radius _r1 is smaller than 0.19 times the lattice interval a, and the outer radius _r2 is larger than 0.19 times the lattice interval a. Alternatively, each of the two radii corresponding to a certain Fourier coefficient Fc may be set to the inner radius _r1 and the outer radius _r2 . In this case, the inner radius _r1 is smaller than 0.44 times the lattice interval a, and the outer radius _r2 is larger than 0.44 times the lattice interval a.

In the above description, the one-dimensional local oscillation is suppressed by making the Fourier coefficient zero, but even if the Fourier coefficient is not strictly zero, the one-dimensional local oscillation can be suppressed by making its absolute value extremely small.Specifically, if the absolute value of the (±2,0) order and (0,±2) order Fourier coefficients of the annular shape of the modified refractive index area 25b is 0.01 or less, or is 20% or less of the maximum peak value (0.05 in the example of FIG. 37) of the circular (±2,0) order and (0,±2) order Fourier coefficients, the one-dimensional local oscillation can be effectively suppressed.In addition, if the ratio (F2/F1) of the (±2,0) order and (0,±2) order Fourier coefficients _F1 of the inner circle that defines the annular shape to the (±2,0) order and (0,±2) order Fourier coefficients _F2 of the outer circle that defines the _annular shape is 0.99 or more and _1.01 or less, the one-dimensional local oscillation can be effectively suppressed. In one embodiment, the inner radius _r1 is 0.085 times the lattice spacing a, and the outer radius _r2 is 0.28 times the lattice spacing a. In another embodiment, the inner radius _r1 is 0.41 times the lattice spacing a, and the outer radius _r2 is 0.47 times the lattice spacing a.

In this embodiment, the structure of the light diffraction layer 25B can be determined by a scaling law according to the wavelength. The light source device 1B can be manufactured by a method similar to the manufacturing method of the light source device 1A of the first embodiment.

The effects obtained by the light source device 1B and the optical waveguide section 20B of the present embodiment described above will be described. In this optical waveguide section 20B, the lattice spacing a of the virtual square lattice and the wavelength λ of the light satisfy the condition for Γ-point oscillation. With such a structure, the light Lin input along the XY plane can be diffracted in a direction perpendicular to the XY plane. In addition, in this optical waveguide section 20B, each modified refractive index area 25b has a circular ring shape centered on the corresponding lattice point O. The absolute values of the (±2,0)-order and (0,±2)-order Fourier coefficients of the circular ring shape are 0.01 or less, or 20% or less of the maximum peak value of the (±2,0)-order and (0,±2)-order Fourier coefficients of the circular shape. In this way, the (±2,0)-order and (0,±2)-order Fourier coefficients of each modified refractive index area 25b have extremely small values, so that one-dimensional local oscillation can be reduced. Therefore, with this optical waveguide section 20B, phenomena such as mode localization due to one-dimensional diffraction and flat-band diffraction can be suppressed, the light intensity distribution can be made closer to uniform, and the area in which output can be achieved in a single mode can be increased, resulting in high resolution and quality of the emitted optical image.

As mentioned above, the (±2, 0) and (0, ±2) Fourier coefficients of the annular shape of each modified refractive index area 25b may be zero. In this case, the above-mentioned effect can be more pronounced.

As described above, the ratio (F2/F1) between the (±2,0) and (0,±2) Fourier coefficients _F1 of the inner circle that defines the annular shape of each modified refractive index area 25b and the (±2,0) and (0,±2) Fourier coefficients _F2 of the outer circle may be 0.99 or more and _1.01 or less. As described above, the Fourier coefficient of the annular shape is calculated as the difference between the Fourier coefficient _F2 of the outer circle that defines the annular shape and the Fourier coefficient _F1 of the inner circle that defines the annular shape. Therefore, since the Fourier coefficient _F2 of the outer circle and the Fourier coefficient _F1 of the inner circle are close to each other in this way, the Fourier coefficient of the annular shape can be brought close to zero, so _that one-dimensional local oscillation can be more effectively reduced.

As described above, the (±2,0)-order and (0,±2)-order Fourier coefficients _F1 of the inner circle that defines the annular shape of each modified refractive index area 25b and the (±2,0)-order and (0,±2)-order Fourier coefficients _F2 of the outer circle may be equal to each other. In this case, the annular Fourier coefficients become sufficiently small, so that the above-mentioned effect can be achieved.

As described above, the radius _r1 of the inner circle of the annular shape of each modified refractive index area 25b may be smaller than 0.19 times the lattice interval a, and the radius _r2 of the outer circle may be larger than 0.19 times the lattice interval a. Alternatively, the radius _r1 of the inner circle may be smaller than 0.44 times the lattice interval a, and the radius _r2 of the outer circle may be larger than 0.44 times the lattice interval a. As shown in FIG. 37, in the Γ-point oscillation structure, the circular Fourier coefficient takes an extreme value when its radius is 0.19 or 0.44 times the lattice interval a. Therefore, by making the radius _r1 of the inner circle smaller than 0.19 (or 0.44) times the lattice interval a, and making the radius _r2 of the outer circle larger than 0.19 (or 0.44) times the lattice interval a, it is easy to make the Fourier coefficient _F1 of the inner circle and the Fourier coefficient _F2 of the outer circle closer to each other.

(Fifth Modification)
FIG. 38 is a diagram showing another example of the planar shape of the modified refractive index area 25b in the second embodiment. In the example shown in FIG. 38, the planar shape of the modified refractive index area 25b is a circle with a radius r ₃ centered on the corresponding lattice point O. As described above, the Fourier coefficient of the circle is obtained by the formula (35). When the (±2,0)-order and (0,±2)-order Fourier coefficients calculated by this formula (35) are zero or close to zero, one-dimensional diffraction can be suppressed to achieve the same effect as in the second embodiment. The preferred range of the (±2,0)-order and (0,±2)-order Fourier coefficients of the modified refractive index area 25b of this modification is the same as in the second embodiment. The preferred size of the radius r ₃ that realizes such a Fourier coefficient is shown in FIG. 37. That is, it is preferable that the radius r ₃ of the circle is 0.30 times or more and 0.31 times or less the lattice interval a. In the case of Γ-point oscillation, the Fourier coefficient of the circular shape becomes zero when its radius _r3 is a certain value within the range of 0.30 to 0.31 times the lattice spacing a. Therefore, in this case, the Fourier coefficient of the planar shape of the modified refractive index area 25b can be made close to zero, and one-dimensional local oscillation can be more effectively reduced.

Third Embodiment
FIG. 39 is a perspective view showing a light source device 1C according to a third embodiment of the present disclosure. As shown in the figure, the light source device 1C includes a plurality of light source devices 1A. The plurality of light source devices 1A are arranged side by side along the XY plane with the normal direction (Z direction) of the main surface 3a of each substrate 3 aligned. In the illustrated example, the plurality of light source devices 1A are arranged side by side in a direction intersecting the arrangement direction of the laser oscillation section 10A and the optical waveguide section 20A, and may be in contact with each other, or may be separated or shielded from each other if it is necessary to reduce optical and electrical crosstalk. The substrates 3 of the plurality of light source devices 1A may be common to each other. Each semiconductor layer constituting the laser oscillation section 10A of the plurality of light source devices 1A may be common between the plurality of light source devices 1A.

According to the light source device 1C of this embodiment, by providing multiple light source devices 1A with the same light output direction, it is possible to output light Lout with even greater light intensity. Alternatively, by switching between multiple light source devices 1A, it is possible to electrically select and output multiple light Louts with different beam patterns. Note that, instead of multiple light source devices 1A, multiple light source devices 1B of the second embodiment may be arranged in a similar manner.

Fourth Embodiment
FIG. 40 is a perspective view showing a light source device 1D according to a fourth embodiment of the present disclosure. FIG. 41 is a diagram showing a stacked structure of the light source device 1D. As shown in these figures, the light source device 1D includes a substrate 3, a laser oscillator 10B, and an optical waveguide 20C. The laser oscillator 10B corresponds to the light emitting section in the present disclosure. The optical waveguide 20C corresponds to the optical waveguide structure in the present disclosure. The laser oscillator 10B and the optical waveguide 20C are arranged in a direction along the XY plane and are provided adjacent to each other on a common substrate 3. The laser oscillator 10B is an M-point oscillation type photonic crystal laser, and outputs spatially coherent laser light Lin along the XY plane. The laser oscillator 10B inputs the laser light Lin to the optical waveguide 20C. The optical waveguide 20C outputs light Lout in a direction intersecting the XY plane by diffracting the input laser light Lin. The light source device 1D may include the optical waveguide section 20B of the second embodiment instead of the optical waveguide section 20C.

The semiconductor laminate 11B of the laser oscillator 10B has a photonic crystal layer 19 instead of the light confinement layer 14 of the laser oscillator 10A of the first embodiment. The photonic crystal layer 19 is disposed between the active layer 13 and the upper cladding layer 15. The photonic crystal layer 19 includes a basic layer 19a and a plurality of modified refractive index areas 19b that have a different refractive index from the basic layer 19a and are distributed two-dimensionally in the XY plane, similar to the optical diffraction layer 25A. When the semiconductor laminate 11B is made of a GaAs-based semiconductor, the basic layer 19a is, for example, an i-type GaAs layer. The plurality of modified refractive index areas 19b are, for example, holes. When a virtual square lattice is set in the XY plane, the center of gravity of each modified refractive index area 19b coincides with the corresponding lattice point. The lattice interval of the virtual square lattice and the wavelength of the light Lin satisfy the above-mentioned condition for M-point oscillation. The planar shape of each modified refractive index area 19b is, for example, a circle.

The semiconductor laminate 21B of the optical waveguide 20C does not have the optical confinement layer 24 of the first embodiment. The optical diffraction layer 25A (or 25B) is disposed on the active layer 23 without an optical confinement layer. Between the modified refractive index region 25b of the optical diffraction layer 25A (or 25B) and the active layer 23, a layer having a thickness of about 100 nm and consisting of only the base layer 25a is provided.

When manufacturing this light source device 1D, first, the lower cladding layers 12, 22, the active layers 13, 23, and the semiconductor layers that will become the basic layer 19a of the photonic crystal layer 19 and the basic layer 25a of the optical diffraction layer 25A (or 25B) are epitaxially grown in sequence on the main surface 3a of the substrate 3 using the MOCVD (metal organic chemical vapor deposition) method. Next, the portion that will become the basic layer 25a is covered, and only the portion that will become the basic layer 19a is slightly etched (etched back). The etching depth is, for example, 100 nm. Then, a resist is applied to the semiconductor layer that will become the basic layer 19a, and a two-dimensional fine pattern is drawn on the resist using an electron beam drawing device, and developed to form a two-dimensional fine pattern on the resist. After that, using the resist as a mask, the two-dimensional fine pattern is transferred onto the basic layer 19a by dry etching, and holes (holes) are formed, and the resist is then removed. These holes are made into the modified refractive index areas 19b, or these holes are made into the modified refractive index areas 19b. A semiconductor that will become the modified refractive index region 19b is regrown in the hole to a depth equal to or greater than the depth of the hole. When the hole is used as the modified refractive index region 19b, the hole may be filled with a gas such as air, nitrogen, hydrogen, or argon. The upper cladding layer 15 and the contact layer 16 are then epitaxially grown in sequence using the MOCVD method. Next, the region on the contact layer 16 that will become the laser oscillation section 10B is covered with a silicon compound such as SiN, and the contact layer 16 and the upper cladding layer 15 in the region that will become the optical waveguide section 20C are etched to expose the base layer 25a. The subsequent steps are the same as those in the first embodiment.

According to this embodiment, the laser light from the laser oscillator 10B, which is a photonic crystal laser, can be input to the optical diffraction layer 25A (or 25B) along the XY plane. The photonic crystal laser can be made larger in area than an end-face resonating type laser, and can provide coherent and wide light to the optical diffraction layer 25A (or 25B). Therefore, the light emission diameter can be increased while the intensity of the light Lout output by diffraction from the optical diffraction layer 25A (or 25B) is made closer to uniform, and a narrow radiation beam with little diffraction spread can be output.

An example of the light source device 1D of this embodiment is shown. The following Table 3 shows an example of the thickness and refractive index of each layer constituting the laser oscillation section 10B. FIG. 42 is a graph showing the refractive index distribution G31 and mode distribution G32 of the laser oscillation section 10B having the configuration of Table 3. In the figure, the section T11 corresponds to the lower cladding layer 12, the section T12 corresponds to the active layer 13, the section T17 corresponds to the photonic crystal layer 19, the section T14 corresponds to the upper cladding layer 15, the section T15 corresponds to the contact layer 16, and the section T16 corresponds to air. Table 4 is a table showing an example of the thickness and refractive index of each layer constituting the optical waveguide section 20C. FIG. 43 is a graph showing the refractive index distribution G41 and mode distribution G42 of the optical waveguide section 20C having the configuration of Table 4. In the figure, section T21 corresponds to the lower cladding layer 22, section T22 corresponds to the active layer 23, section T25 corresponds to a layer of the optical diffraction layer 25A (or 25B) consisting only of the basic layer 25a, section T26 corresponds to a layer of the optical diffraction layer 25A (or 25B) in which the basic layer 25a and the modified refractive index area 25b (holes) are mixed, and section T24 corresponds to air.

Figure 44 is a graph in which the mode distribution G32 shown in Figure 42 and the mode distribution G42 shown in Figure 43 are superimposed. As shown in Figure 44, according to this embodiment, the mode distribution G32 of the laser oscillator 10B and the mode distribution G42 of the optical waveguide 20C almost coincide with each other, and it can be seen that high coupling efficiency between the laser oscillator 10B and the optical waveguide 20C can be obtained. In this embodiment, the coupling efficiency is 0.946.

(Sixth Modification)
45 is a diagram showing a schematic view of a laminated structure of a light source device 1E according to a modification of the fourth embodiment described above. The light source device 1E of this modification includes an optical waveguide 20D instead of the optical waveguide 20C of the fourth embodiment. The semiconductor laminated portion 21C of this optical waveguide 20D does not have the active layer 23 of the first embodiment. The optical confinement layer 24 is disposed on the lower cladding layer 22 without an active layer. The configuration of the laser oscillation portion 10B and the configuration of the semiconductor laminated portion 21C except for the above are the same as those of the fourth embodiment. The optical confinement layer 24 of this modification has the same thickness as that of the active layer 13, for example.

When manufacturing this light source device 1E, the process up to epitaxial growth of the contact layer 16 is the same as in the fourth embodiment. In this modification, the area on the contact layer 16 that will become the laser oscillation section 10B is then covered with a silicon compound such as SiN, and the area that will become the optical waveguide section 20D is etched until the lower cladding layer 22 is exposed. Then, the optical confinement layer 24 and the base layer 25a are epitaxially grown in that order. The subsequent processes are the same as in the fourth embodiment.

An example of the light source device 1E of this modification is shown. Table 5 below shows an example of the thickness and refractive index of each layer constituting the laser oscillation section 10B. FIG. 46 is a graph showing the refractive index distribution G51 and mode distribution G52 of the laser oscillation section 10B having the configuration of Table 5. The definitions of sections T11 to T16 are the same as those of FIG. 42. Table 6 is a table showing an example of the thickness and refractive index of each layer constituting the optical waveguide section 20D. FIG. 47 is a graph showing the refractive index distribution G61 and mode distribution G62 of the optical waveguide section 20D having the configuration of Table 6. In the figure, section T27 corresponds to the optical confinement layer 24. The definitions of sections T21, T24 to T26 are the same as those of the fourth embodiment.

Figure 48 is a graph in which the mode distribution G52 shown in Figure 46 and the mode distribution G62 shown in Figure 47 are superimposed. As shown in Figure 48, according to this embodiment, the mode distribution G52 of the laser oscillator 10B and the mode distribution G62 of the optical waveguide 20D almost coincide with each other, and it can be seen that a high coupling efficiency between the laser oscillator 10B and the optical waveguide 20D can be obtained. In this embodiment, the coupling efficiency is 0.946.

Fifth Embodiment
FIG. 49 is a perspective view showing a light source device 1F according to a fifth embodiment of the present disclosure. As shown in the figure, the light source device 1F includes a laser oscillator 10B, which is a photonic crystal laser, and a plurality of (four in the illustrated example) optical waveguides 20C. Unlike the laser oscillator 10A of the first embodiment, the laser oscillator 10B can resonate laser light in two mutually orthogonal directions along the XY plane. The laser oscillator 10B outputs light Lin in four directions from both ends in one direction along the XY plane and both ends in the other direction along the XY plane. The configuration of the optical waveguide 20C is the same as that of the fourth embodiment.

The four optical waveguides 20C are arranged side by side in the circumferential direction of the laser oscillator 10B in the XY plane. In other words, two optical waveguides 20C are arranged at positions sandwiching the laser oscillator 10B in one direction along the XY plane, and the other two optical waveguides 20C are arranged at positions sandwiching the laser oscillator 10B in the other direction along the XY plane. Light Lin is input from the laser oscillator 10B along the XY plane to the optical diffraction layers 25A of these optical waveguides 20C.

The substrate 3 of the multiple optical waveguides 20C may be common to each other. Each semiconductor layer constituting the multiple optical waveguides 20C may be common to the multiple optical waveguides 20C.

According to this light source device 1F, since it has a plurality of optical waveguides 20C having the same configuration as the first embodiment, the light Lin input from the laser oscillator 10B to the light diffraction layer 25A along the XY plane can be diffracted in a direction intersecting the XY plane and output. In addition, according to this light source device 1F, since it has a plurality of optical waveguides 20C having the same configuration as the fourth embodiment, one-dimensional local oscillation can be reduced. Therefore, it is possible to suppress phenomena such as mode localization due to one-dimensional diffraction and flat band diffraction, to make the light intensity distribution closer to uniform, and to increase the area of the region that can be output in a single mode, so that the emitted light image can have high resolution and high image quality. Note that instead of the plurality of optical waveguides 20C, the optical waveguides 20A of the first embodiment, the optical waveguides 20B of the second embodiment, or the optical waveguides 20D of the sixth modified example may be arranged in a similar manner.

The optical waveguide structure and light source device according to the present disclosure are not limited to the above-described embodiment, and various other modifications are possible. For example, the above embodiment illustrates an optical waveguide structure made of GaAs-based, InP-based, and nitride-based (particularly GaN-based) compound semiconductors, but the present disclosure can be applied to optical waveguide structures made of various other semiconductor materials.

In addition, in the above embodiment, the light emitting section is provided on a common substrate with the optical waveguide structure, but in the present disclosure, the light emitting section may be provided separately from the optical waveguide structure. As long as the light emitting section is optically coupled to the optical waveguide structure and supplies light to the optical diffraction layer, even with such a configuration, the same effects as those of the above embodiment can be preferably achieved.

In addition, in the above embodiment, an example in which an optical waveguide structure and a light emitting unit are provided in a one-to-one relationship and an example in which multiple optical waveguide structures are provided for one light emitting unit are shown, but multiple light emitting units may be provided for one optical waveguide structure. For example, an optical waveguide unit 20C may be arranged in place of the laser oscillator unit 10B shown in FIG. 49, and a laser oscillator unit 10B may be provided in place of the optical waveguide unit 20C around it. In this case, the light intensity of the light Lout output from the single optical waveguide unit 20C can be increased.

1A to 1F...light source device, 3...substrate, 3a...main surface, 3b...rear surface, 10A, 10B...laser oscillation section, 11A, 11B...semiconductor laminate section, 12...lower cladding layer, 13...active layer, 14...light confinement layer, 15...upper cladding layer, 16...contact layer, 17, 18...electrodes, 19...photonic crystal layer, 19a...basic layer, 19b...modified refractive index area, 20A to 20D...optical waveguide section, 21A to 21C...semiconductor laminate section, 22...lower cladding layer, 23...active layer, 24...light confinement layer, 25A, 25B...optical diffraction layer, 25a...basic layer, 25b...modified refractive index area, 31, 32...protective film, 151, 152, 161, 171...arc , 153, 154, 162, 163, 173, 174...line segment, 172...concave portion, 181...inner circle, 182...outer circle, B1...primitive reciprocal lattice vector, FR...image region, G...center of gravity, G11, G21, G31, G41, G51, G61...refractive index distribution, G12, G22, G32, G42, G52, G62...mode distribution, K1 to K4, K6 to K9...in-plane wave vector, Ka, Kb...wave vector, Lin, Lout...light, LL...light line, LL2...region, LM...beam pattern, O...lattice point, R...unit constituent region, RIN...inner region, ROUT...outer region, SP...wave number spread, V...diffraction vector, φ _A , φ _B ...phase value.

Claims (25)

a light diffractive layer that diffracts light input along the imaginary plane in a direction intersecting the imaginary plane and outputs the light, the light diffracting layer having a thickness direction perpendicular to the imaginary plane;
the optical diffraction layer includes a base layer and a plurality of modified refractive index areas having a refractive index different from that of the base layer and two-dimensionally distributed within the imaginary plane,
When a virtual square lattice is set in the virtual plane, a center of gravity of each modified refractive index area is disposed away from a corresponding lattice point, and an angle of a vector connecting the corresponding lattice point and the center of gravity is set individually for each modified refractive index area,
the lattice spacing a of the virtual square lattice and the wavelength λ of the light satisfy the condition for M-point oscillation,
the distribution of angles satisfies a condition for the light to be output in a direction intersecting the imaginary plane,
When each modified refractive index area is virtually rotated around the corresponding lattice point as a rotation center, a ring shape or a circle shape is obtained,
an absolute value of the annular or circular (m, n)-th order Fourier coefficient (where (m, n)=(±1, ±1)) is 0.01 or less, or 10% or less of the maximum peak value of the circular (m, n)-th order Fourier coefficient. The optical waveguide structure of claim 1, wherein the (m, n)th order Fourier coefficient of the annular or circular shape is zero. 3. The optical waveguide structure according to claim 1, wherein a ratio (F2/F1) of a (m, n)-th Fourier coefficient _F1 of an inner circle defining the annular shape _to a (m, _n )-th Fourier coefficient _F2 of an outer circle defining the annular shape is 0.99 or more and 1.01 or less. The optical waveguide structure according to claim 3 , wherein the Fourier coefficient F ₁ and the Fourier coefficient F ₂ are equal to each other. The optical waveguide structure according to claim 3 or 4, wherein the radius of the inner circle is smaller than 0.27 times the lattice spacing a, and the radius of the outer circle is larger than 0.27 times the lattice spacing a. The optical waveguide structure according to any one of claims 1 to 5, wherein the planar shape of each modified refractive index area is a C-shape with the corresponding lattice point as the center of the inner and outer arcs. The optical waveguide structure according to any one of claims 1 to 5, wherein the planar shape of each modified refractive index area is a circle with the corresponding lattice point located outside it. The optical waveguide structure according to any one of claims 1 to 5, wherein the planar shape of each modified refractive index area is a polygon with the corresponding lattice point located outside it. The optical waveguide structure according to claim 1 or 2, wherein the radius of the circular shape is 0.43 to 0.44 times the lattice spacing a. The optical waveguide structure according to claim 1, 2 or 9, wherein the planar shape of each modified refractive index area is a sector with the corresponding lattice point as the center of an arc, and the arc is a major arc. The optical waveguide structure according to claim 1, 2 or 9, wherein the planar shape of each modified refractive index area is a circle with the corresponding lattice point located inside it. The optical waveguide structure according to claim 1, 2 or 9, wherein the planar shape of each modified refractive index area is a polygon inside which the corresponding lattice point is located. The optical waveguide structure according to any one of claims 1 to 12, wherein the condition for the light to be output in a direction intersecting the virtual plane is that the magnitude of at least one of the four in-plane wave vectors in the reciprocal lattice space of the optical diffraction layer, each of which includes the wave number spread due to the distribution of angles, is smaller than 2π/λ. a light diffractive layer that diffracts light input along the imaginary plane in a direction intersecting the imaginary plane and outputs the light, the light diffracting layer having a thickness direction perpendicular to the imaginary plane;
the optical diffraction layer includes a base layer and a plurality of modified refractive index areas having a refractive index different from that of the base layer and two-dimensionally distributed within the imaginary plane,
When a virtual square lattice is set in the virtual plane, the center of gravity of each modified refractive index area coincides with a corresponding lattice point,
the lattice spacing a of the virtual square lattice and the wavelength λ of the light satisfy the condition for Γ-point oscillation,
Each modified refractive index area has an annular or circular shape centered on the corresponding lattice point,
an optical waveguide structure, wherein the absolute value of the annular or circular (m, n)-th order Fourier coefficient (where (m, n)=(±2, 0) and (0, ±2)) is 0.01 or less, or 20% or less of the maximum peak value of the circular (m, n)-th order Fourier coefficient. The optical waveguide structure of claim 14, wherein the (m, n)-th order Fourier coefficient of the annular or circular shape is zero. 16. The optical waveguide structure according to claim 14, wherein a ratio (F2/F1) of a (m, n)-th Fourier coefficient _F1 of an inner circle defining the annular shape _to a (m, _n )-th Fourier coefficient _F2 of an outer circle defining the annular shape is 0.99 or more and 1.01 or less. 17. The optical guiding structure of claim 16, wherein the Fourier coefficient _F1 and the Fourier coefficient _F2 are equal to each other. The optical waveguide structure of claim 16 or 17, wherein the radius of the inner circle is smaller than 0.19 times the lattice spacing a, and the radius of the outer circle is larger than 0.19 times the lattice spacing a. The optical waveguide structure of claim 16 or 17, wherein the radius of the inner circle is smaller than 0.44 times the lattice spacing a, and the radius of the outer circle is larger than 0.44 times the lattice spacing a. The optical waveguide structure according to claim 14 or 15, wherein the radius of the circular shape is 0.30 to 0.31 times the lattice spacing a. The optical waveguide structure according to any one of claims 1 to 20, wherein the modified refractive index area is a hole, and the upper part of the hole is open. An optical waveguide structure according to any one of claims 1 to 21;
a light emitting section that is provided alongside the optical waveguide structure in a direction along the imaginary plane and that inputs light into the optical diffraction layer along the imaginary plane;
A light source device comprising: A plurality of optical waveguide structures, each of which is an optical waveguide structure according to any one of claims 1 to 21;
a light emitting unit that inputs light along the imaginary plane into the optical diffraction layer of each optical waveguide structure;
Equipped with
The light source device, wherein the plurality of optical waveguide structures are arranged side by side in a circumferential direction of the light emitting portion within the imaginary plane. The light source device according to claim 22 or 23, wherein the light is spatially coherent. the light emitting portion is a semiconductor laser including an active layer and a photonic crystal layer,
25. The light source device according to claim 22, wherein the photonic crystal layer exhibits M-point oscillation.

Images