JP2021114485A - Semiconductor light-emitting element - Google Patents

Abstract

To provide a semiconductor laser element capable of reducing 0th-order light.SOLUTION: In individual unit constitution regions sectioned in a second virtual square lattice, lattice points of a first virtual square lattice are aligned with gravity center positions of the unit constitution regions, and gravity center positions of main different-refractive-index regions 6BM are arranged at the gravity center positions of the unit constitution regions, wherein each unit constitution region includes one main different-refractive-index region 6BM, and each unit constitution region include one gravity center of a sub different-refractive-index region 6BS. The gravity center position of the sub different-refractive-index region 6BS is a distance r apart from the gravity center position of the main different-refractive-index region 6BM, and 0.38≤(r/a)≤0.5 holds for a lattice constant a of the first virtual square lattice. The main different-refractive-index region 6BM has a periodic structure in an XY plane, and the sub different-refractive-index region 6BS has an aperiodic structure having no uniaxial array in the XY plane.SELECTED DRAWING: Figure 3

Description

The present invention relates to a semiconductor light emitting device.

The inventors of the present application have developed the semiconductor light emitting device described in Patent Document 1 below (see Patent Document 1). This semiconductor light emitting element is a semiconductor light emitting element including an active layer, a pair of clad layers sandwiching the active layer, and a phase modulation layer optically coupled to the active layer. The different refractive index regions are located in the vicinity of the respective lattice points of the virtual square lattice. Other related techniques are described in Patent Documents 2 to 9.

U.S. Pat. No. 9,74873 Japanese Unexamined Patent Publication No. 2007-208127 Japanese Unexamined Patent Publication No. 2012-119635 Japanese Unexamined Patent Publication No. 2010-056446 JP-A-2007-180120 Japanese Unexamined Patent Publication No. 2004-296538 Japanese Unexamined Patent Publication No. 2003-298183 Japanese Unexamined Patent Publication No. 2009-076900 Japanese Unexamined Patent Publication No. 2003-0231993

In a semiconductor light emitting device having a phase modulation layer, 0th-order light is observed on a vertical extension line of the light emitting surface. The inventors of the present application have diligently studied a method for reducing this 0th-order light. The present invention has been made in view of such a problem, and an object of the present invention is to provide a semiconductor laser device capable of reducing 0th-order light.

In order to solve the above-mentioned problems, the first semiconductor light emitting element is a laser element including a phase modulation layer on which laser light is incident, and the phase modulation layer is a basic layer made of a first refractive index medium and the above. The first refractive index medium is composed of a second refractive index medium having a different refractive index, and includes a plurality of different refractive index regions existing in the basic layer, and the plurality of different refractive index regions have a substantially circular planar shape. Alternatively, it is a substantially square or a roughly polygonal shape having a rotational symmetry of 90 °, and has a main different refractive index region having a first area perpendicular to the thickness direction and a secondary different refractive index region having a second area perpendicular to the thickness direction. The position of the center of gravity of the main different refractive index region is located at the grid point of the square lattice, the second area is larger than the first area, and the unit constituent region is one of the main different refractive indexes. It is composed of a rate region and one of the sub-refractive index regions provided closest to the ratio region, and only these pair of different refractive index regions exist in each unit constituent region and are adjacent to each other closest to each other. A line segment connecting the positions of the center of gravity of the main different refractive index region is defined, and the smallest region surrounded by the perpendicular bisectors of this line segment is each of the unit constituent regions, and this unit constituent region Within, all of the pair of different refractive index regions are located, and the rotation angle of the sub-differential refractive index region with respect to the main different refractive index region in the unit constituent region is φ, and the X-axis and Y A plurality of the unit constituent regions are arranged two-dimensionally in the XY plane including the axis, and the XY coordinates of each of the unit constituent regions are given at the position of the center of gravity of each of the principal different refractive index regions. The position of the center of gravity of the sub-refractive index region is separated from the position of the center of gravity of the main refractive index region by a distance r, and assuming that the lattice constant of the square lattice is a, 0.38 ≦ (r / a). ≤0.5, the principal index of refractive index region has a periodic structure in the XY plane, and the sub-refractive index region is aperiodic in the XY plane, which is not aligned along the uniaxial direction. It has a structure and is characterized by emitting a beam pattern other than the 0th-order light in a direction not perpendicular to the light emitting surface.

That is, when the separation distance (r / a) converted into the lattice constant a is 0.38 or more while satisfying the above-mentioned lattice conditions, a beam pattern other than the 0th-order light is emitted in a direction not perpendicular to the light emitting surface. However, a phenomenon was observed in which the intensity of the 0th-order light contained in the emitted light became 0 or less, and a low intensity of the 0th-order light was observed up to 0.5 or less.

_{The larger the second area (sub-area SS} ) of each sub-differential refractive index region, the larger the diffraction intensity. Further, if the areas are the same, the 0th-order light intensity in the sub-differential refractive index region does not exceed the 0th-order light intensity in the main different refractive index region, so that the sub-area _SS (second area)> main area. In _{the case of SM} (first area), the 0th-order light can be effectively suppressed.

In the second semiconductor light emitting element, the beam pattern is a far-field field obtained by two-dimensional Fourier transforming a two-dimensional field strength distribution in real space formed on a light emitting surface parallel to the XY plane in the phase modulation layer. The complex amplitude f (x, y) obtained by two-dimensional inverse Fourier transformation of the far-field image is an image, the imaginary unit is j, the amplitude term is A (x, y), and the phase term is P (x, y). As y), it is given by f (x, y) = A (x, y) × exp [jP (x, y)], and the center of gravity of the sub-Cartesian index region and its sub The angle φ formed by the line segment connecting the grid points (center of gravity) of the unit constituent region including the different refractive index region with the X axis is φ (x, y) = C, where C is the proportional constant and B is the constant. It is characterized in that it is given by × P (x, y) + B.

In the third semiconductor light emitting device, the far field pattern, two-dimensional electric field distribution coordinates in Fourier space that is two-dimensional Fourier transform of the real space (k _{x, k y)} in a plurality of image regions FR (k _x, consists _{k y),} the image area FR _(k x, k _y) are each square, M2 or in the Kx-axis direction to provide a wave number _{k x} normalized in wavenumber space (M2 is one or more integer), N2 or the Ky-axis direction to provide a wave number k _y normalized (N2 is an integer of 1 or more), so as to be arranged, are arranged two-dimensionally, gives the complex amplitude f (x, y) and The two-dimensional reciprocal Fourier transform is given by the following equation.

In the fourth semiconductor light emitting element, the spherical coordinates (r, θtilt, θrot) indicating the coordinates (x, y, z) in the XYZ Cartesian coordinate system are the length r of the radius and the motion from the Z axis. The following relationship is satisfied by using the inclination angle θtilt of the diameter and the rotation angle θrot of the line segment whose radius is projected on the XY plane from the X axis.

x = r · sinθ _tilt · cosθ _rot ,
y = r · sinθ _tilt · sinθ _rot ,
z = r · cosθ _tilt .

Assuming that a set of bright spots formed by a group of beams emitted from the semiconductor light emitting element at an inclination angle θtilt and a rotation angle θrot is a far-field image, the far-field image on the Kx−Ky plane is normalized on the Kx axis. wave number k _y normalized at wave numbers k _x and Ky axis is the oscillation wavelength of the semiconductor light emitting device as lambda, satisfy the following relationship.

k _x = (a / λ) ・ sinθ _tilt・ cosθ _rot ,
_{k y = (a / λ)} · sinθ tilt · sinθ rot.

The fifth semiconductor light emitting device is characterized by having a first clad layer and a second clad layer sandwiching an active layer optically bonded to the phase modulation layer. Since there is a clad layer, light can be efficiently collected in the active layer, and the laser light intensity can be improved.

According to the semiconductor light emitting device of the present invention, the 0th order light can be reduced.

FIG. 1 is a diagram showing a vertical cross-sectional configuration of a semiconductor laser device. FIG. 2 is a perspective view of the phase modulation layer according to the embodiment. FIG. 3 is a plan view of the phase modulation layer according to the embodiment. FIG. 4 is a plan view of the phase modulation layer according to the embodiment. FIG. 5 is a graph showing the position of the different refractive index region in (A) embodiment and the position of the different refractive index region in (B) Comparative Example A. FIG. 6 is a graph showing the relationship between the shift amount (r / a) from the lattice point position in the sub-differential refractive index region and the output beam intensity (arbitrary unit). FIG. 7 is a plan view of the phase modulation layer according to the first comparative example. FIG. 8 is a plan view of the phase modulation layer according to the second comparative example. FIG. 9 is a plan view of the phase modulation layer according to the third comparative example. FIG. 10 is a plan view of the phase modulation layer according to the fourth comparative example. FIG. 11 is a diagram showing a vertical cross-sectional configuration of the semiconductor laser device. FIG. 12 is a diagram for explaining coordinate conversion from spherical coordinates (r, θ _tilt , θ _rot ) to XYZ Cartesian coordinates (x, y, z).

Hereinafter, the semiconductor laser device (semiconductor light emitting device) and the laser device according to the embodiment will be described. The same reference numerals will be used for the same elements, and duplicate description will be omitted.

FIG. 1 is a diagram showing a vertical cross-sectional configuration of a semiconductor laser device.

The semiconductor laser element LD selects the laser beam from the active layer 4 and outputs it to the outside. The structure of the semiconductor laser element LD may be such that laser light is incident and coupled into the phase modulation layer 6 from another semiconductor laser element having an active layer via an optical fiber or directly. good. The laser beam incident on the phase modulation layer 6 forms a predetermined mode in the phase modulation layer 6 according to the lattice of the phase modulation layer, and has a desired pattern in the direction perpendicular to the surface of the phase modulation layer 6. Is emitted to the outside.

The phase modulation layer 6 is optically coupled to the active layer 4. Here, an XYZ three-dimensional Cartesian coordinate system is set in which the thickness direction of the phase modulation layer 6 is the Z-axis direction, the axis perpendicular to the Z-axis is the X-axis, and the axis perpendicular to both of these two axes is the Y-axis. .. The phase modulation layer 6 is composed of a basic layer 6A made of a first refractive index medium and a second refractive index medium having a refractive index different from that of the first refractive index medium, and a plurality of different refractive index regions 6B existing in the basic layer 6A. And have.

The semiconductor laser element LD is a laser light source that forms a standing wave in the XY in-plane direction and outputs a plane wave whose phase is controlled in the Z-axis direction, and sandwiches the active layer 4 that generates the laser light and the active layer 4. The upper clad layer 7 and the lower clad layer 2 are provided between them, and the upper optical guide layer 5 and the lower optical guide layer 3 that sandwich the active layer 4 are provided between the upper clad layer 7 and the active layer 4. Is provided with a phase modulation layer 6. In the structure shown in FIG. 1, the second electrode E2 is provided in the central region of the contact layer 8.

In this structure, the lower clad layer 2, the lower optical guide layer 3, the active layer 4, the upper optical guide layer 5, the phase modulation layer 6, the upper clad layer 7, and the contact layer 8 are sequentially laminated on the semiconductor substrate 1. The first electrode E1 is provided on the lower surface of the semiconductor substrate 1, and the second electrode E2 is provided on the upper surface of the contact layer 8. When a driving current is supplied between the first electrode E1 and the second electrode E2, recombination of electrons and holes occurs in the active layer 4, and the active layer 4 emits light. The carriers contributing to these light emission and the generated light are efficiently trapped between the upper light guide layer 5 and the lower light guide layer 3 and the upper clad layer 7 and the lower clad layer 2. The refractive indexes of the upper clad layer 7 (second clad layer) and the lower clad layer 2 (first clad layer) are both lower than the refractive index of the active layer 4, and these layers sandwich the active layer 4.

The laser beam emitted from the active layer 4 enters the inside of the phase modulation layer 6 to form a predetermined mode. The laser beam incident on the phase modulation layer 6 is emitted to the outside as a laser beam perpendicular to the substrate surface via the upper clad layer 7, the contact layer 8, and the second electrode E2. When the effective refractive index of the phase modulation layer 6 is n, the wavelength λ ₀ (= a × n) selected by the phase modulation layer 6 is included in the emission wavelength range of the active layer 4. The phase modulation layer (diffraction grating layer) can _{select the wavelength λ 0} of the emission wavelengths of the active layer and output it to the outside.

In the oscillation state at this time, when all the different refractive index regions 6B are arranged while maintaining the periodic structure without fluctuation, that is, as in the first comparative example (FIG. 7), the different refractive index regions 6B are arranged. When it consists only of the main refractive index region 6BM arranged at the grid point position of the square grid, it corresponds to the Γ point oscillation of the square grid, and the wave vector of the fundamental wave is lateral in the plane of the phase modulation layer 6. A standing wave is formed in which the main light wave travels in four directions along the grid lines of the square lattice, facing the direction (Γ-X direction) and the vertical direction (Γ-Y direction) (Γ-point oscillation). When the phase modulation layer 6 having a periodic structure as shown in the first comparative example (FIG. 7) is used, in the far-field image of the output laser light, the 0th-order light is observed at the center position of the luminous flux. On the other hand, in the phase modulation layer according to the embodiment, the intensity of the 0th order light is suppressed.

FIG. 2 is a perspective view of the phase modulation layer according to the embodiment, and FIG. 3 is a plan view of the phase modulation layer 6 according to the embodiment.

The phase modulation layer 6 is composed of a basic layer 6A made of a first refractive index medium and a second refractive index medium having a refractive index different from that of the first refractive index medium, and a plurality of different refractive index regions existing in the basic layer 6A. It is equipped with 6B. The plurality of different refractive index regions 6B are composed of a plurality of main different refractive index regions 6BM and a plurality of sub-differential refractive index regions 6BS. The plurality of main different refractive index regions 6BM are arranged at the lattice point positions of the square lattice to form a periodic structure. On the other hand, the sub-refractive index region 6BS is arranged on a circular orbit around each main refractive index region 6BM. Focusing on one major refractive index region 6BM, one sub-refractive index region 6BS is located like the planet, and the main refractive index region 6BM has a periodic structure in the XY plane. On the other hand, the sub-refractive index region 6BS has an aperiodic structure and is not aligned and arranged on one axis.

Incidentally, in the XY plane in FIG. 3, the area of each of the main modified refractive index region 6BM mainly area S _M, the area of the respective sub-modified refractive index areas 6BS and by-area S _S.

Incidentally, the sub-area _{S S} is greater than the main area _{S M.}

The phase modulation layer 6 has a square lattice for determining the arrangement position of the different refractive index region. The main different refractive index region 6BM is arranged at the lattice point position of this square lattice. More specifically, the position of the center of gravity of the main different refractive index region 6BM is arranged at the lattice point position of the square lattice.

Each main refractive index region 6BM is located in the unit constituent region to which it belongs. One main different refractive index region 6BM is located in one unit constituent region, and the shape of the unit constituent region is square.

These unit constituent regions define a line segment connecting the positions of the centers of gravity of the main different refractive index regions 6BM that are adjacent to each other closest to each other, and are defined by the unit constituent region boundaries defined by the perpendicular bisectors of this line segment. It is partitioned.

Within each unit constituent area partitioned by the unit constituent region boundary (dashed line), all of the following conditions are satisfied.

-The grid points of the square grid (dotted line) coincide with the position of the center of gravity of the unit constituent area (dashed line).
-The center of gravity position of the main different refractive index region 6BM is arranged at the center of gravity position of the unit constituent region (dashed line).
-The number of main different refractive index regions 6BM included in one unit constituent region (dashed line) is one.
The number of centers of gravity of the sub-differential refractive index region 6BS included in one unit constituent region is one.
The position of the center of gravity of the sub-differential refractive index region 6BS is separated from the position of the center of gravity of the main different refractive index region 6BM by a distance r.
-If the lattice constant of the first virtual square lattice (dotted line) is a, 0.38 ≤ (r / a) ≤ 0.5 is satisfied.-The sub-differential refractive index region 6BS is not aligned along the uniaxial direction. It has a periodic structure.

This semiconductor laser device emits a beam pattern other than the 0th-order light in a direction not perpendicular to the light emitting surface. The position of the center of gravity of the sub-differential refractive index region 6BS is not located outside the unit constituent region, and is configured so that the adjacent sub-differential refractive index regions 6BS do not merge.

The arrangement of the sub-refractive index region 6BS is set as follows.

First, assuming that the Fourier transform is indicated by F and the inverse Fourier transform is ^{indicated by F-1} , the two-dimensional electric field strength FR (x, y) of the far-field image of the target laser beam is subjected to the two-dimensional inverse Fourier transform (=). F ^-1 {FR (x, y)}), obtain a near-field image. In order to output this near-field image from the phase modulation layer 6, the distance from the center of gravity position of the main different refractive index region 6BM to the center of gravity position of the sub-differential refractive index region 6BS in each unit constituent region in the XY plane. The r, the line segment connecting the positions of the center of gravity, and the angle φ formed by the X-axis may satisfy the following conditions. However, Imag means a function that extracts only the imaginary part of the complex number. In addition, log means a logarithmic function whose base is the natural logarithm. Note that P (x, y) is a phase term described later.

P (x, y) = Imag [log (F ^-1 {FR (x, y)})],
(R / a) ≤0.5
However, P (x, y) is expressed in radian.

A phenomenon in which the intensity of the 0th-order light contained in the emitted light of the laser light becomes 0 or less when the separation distance (r / a) converted into the lattice constant a is 0.38 or more while satisfying these lattice conditions. Is observed, and low intensity of 0th order light is observed up to 0.5 or less.

FIG. 4 is a plan view in which a circular auxiliary line is added to the phase modulation layer shown in FIG.

The sub-refractive index region 6BS is arranged on a circular auxiliary line surrounding the main refractive index region 6BM. The sub-refractive index region 6BS is not aligned on one axis or arranged with periodicity, but the distance r (from the main refractive index region 6BM) of all the sub-refractive index regions 6BS The distance between the centers of gravity) is the same.

The beam pattern (far-field image) of the laser beam emitted from the semiconductor light emitting device can include at least one spot, a straight line, a cross, a figure, a photograph, a CG (computer graphics), or a character. For example, when the letter "A" is to be displayed, the beam pattern (far-field image) is subjected to a two-dimensional inverse Fourier transform, and the position of the center of gravity of the different refractive index region is performed in the direction of the angle φ corresponding to the phase of the complex amplitude. G may be shifted from the grid point position O of the virtual square grid. By adjusting the angle φ, it is possible to obtain an arbitrary beam pattern or a pair of diagonal single peak beams. The far-field image after Fourier transform of the laser beam shall take various shapes such as a single or multiple spot shape, an annulus shape, a linear shape, a character shape, a double annulus shape, or a Laguerre Gaussian beam shape. Can be done.

Further, since the beam direction can also be controlled, it can be used for a laser processing machine or the like that electrically performs high-speed scanning by arranging the laser elements in one dimension or two dimensions.

Further, as a method of obtaining the intensity distribution and the phase distribution from the complex amplitude distribution obtained by the Fourier transform or the inverse Fourier transform, for example, for the intensity distribution I (x, y), the abs of the numerical analysis software "MATLAB" of MathWorks Co., Ltd. It can be calculated by using a function, and the phase distribution P (x, y) can be calculated by using the angular function of MATLAB.

The complex amplitude F (X, Y) obtained by two-dimensional inverse Fourier transformation of a specific region of the beam pattern (far-view image) in the XY plane is the intensity distribution I (X, Y) in the XY plane with j as an imaginary unit. And, using the phase distribution P (X, Y) in the XY plane, it is given by F (X, Y) = I (X, Y) × exp {P (X, Y) j}, and the phase modulation layer 6 In, the angle formed by the X-axis and the direction from each lattice point of the first virtual square lattice toward the center of gravity of each corresponding sub-Cartesian refractive index region 6BS is φ, the constant is C, and the X-axis direction. If the position of the x-th and y-th virtual square grid points in the Y-axis direction is (x, y) and the angle at the position (x, y) is φ (x, y), then φ (x, y) ) = C × P (X, Y) is satisfied.

FIG. 5 is a schematic view showing the position of the different refractive index region in (A) embodiment and the position of the different refractive index region in (B) Comparative Example A.

In the embodiment, it is assumed that the position of the center of gravity of an arbitrary main Cartesian refractive index region 6BM exists at the position of the origin O on the XY plane, and the distance in the X-axis direction from this temporary origin O is set in the x and Y-axis directions. Assuming that the distance is y, the center of gravity position G of the sub-differential refractive index region 6BS is located at a distance r (x, y) from the position of the center of gravity of the main different refractive index region 6BM (r = (x ² + y ^{2 ) 1} ). ^{/ 2} ). Let φ (x, y) be the angle formed by the line segment connecting the origin O and the position G of the center of gravity with the X axis. The diameter of the sub-refractive index region 6BS is D.

In Comparative Example A, in the embodiment, the structure is such that the main different refractive index region 6BM existing at the position of the origin O is removed. In the embodiment, the intensity of the 0th-order light is low, but when the pattern in the case of Comparative Example A is obtained, the 0th-order light cannot be canceled and the 0th-order light cannot be suppressed in principle. .. In other words, the arrangement of Comparative Example A does not produce the effect of the present invention.

FIG. 6 shows the shift amount (r / a) when the sub-differential refractive index region is shifted from the lattice point position (origin O) of the first virtual square lattice in the above-mentioned semiconductor laser according to the embodiment. It is a graph which shows the relationship with the intensity I (arbitrary unit) of an output light.

As shown in the figure, the intensity I of the output light changes as the shift amount (r / a) increases. That is, the 0th-order light has a maximum value of 1.0 when the shift amount (r / a) is 0, decreases as the shift amount (r / a) increases, and becomes 0 at 0.38. Become. This is because the plane wave caused by the different refractive index region, which has a main-sub relationship, causes vanishing interference, and the 0th-order light intensity is reduced. Therefore, in order to reduce the intensity of the 0th order light, the above range is preferable. As the shift amount (r / a) increases, the intensity of the primary light increases and the intensity of the -1st order light also increases, and the maximum value when the shift amount (r / a) is 0.3, respectively. And a minimum value, and if the shift amount (r / a) is more than this, the intensity decreases.

Since the diameter of the sub-modified refractive index areas 6BS is a D, the sub-area _{S S} becomes π (D / ²⁾ 2. Incidentally, if the diameter of the main modified refractive index region 6BM and M, the main area _{S M} becomes π (M / ²⁾ 2. Here, further preferably satisfies 1.0 ≦ sub area _{S S} / main area _{S M.} If towards the sub-area S _S is larger than the main area S _M, 0 the effect of the primary light suppression can be sufficiently expected, in particular, the strength of the opposite phase 0-order light caused to be smaller than the lower limit by the secondary modified refractive index area Is smaller than the intensity of the 0th-order light generated by the main different refractive index region, and a sufficient 0th-order light suppression effect cannot be expected.

Next, the material of each layer shown in FIG. 1 will be described.

The contact layer 8 located at the upper part is made of GaAs, the conductive type is P type, and the thickness is 50 nm to 500 nm (preferably 200 nm). The upper clad layer 7 is made of AlGaAs, the conductive type is P type, and the thickness is 1 × 10 ^{3 nm to 3} × 10 3 nm (preferably 2 × 10 ³ nm). The phase modulation layer 6 (diffraction grating layer) includes a basic layer 6A and a different refractive index region 6B. The basic layer 6A is made of GaAs, the conductive type is I type, and the thickness is 50 nm to 20 nm (preferably 100 nm), the different refractive index region 6B is made of AlGaAs, the conductive type is I type, and the thickness is 50 nm. It is ~ 20 nm (preferably 100 nm). The upper optical guide layer 5 has a two-layer structure, the upper layer is made of GaAs, the conductive type is type I, the thickness is 10 nm to 200 nm (preferably 50 nm), and the lower layer is made of AlGaAs and is conductive. The type is P type or I type, and the thickness is 10 nm to 100 nm (preferably 50 nm).

The active layer 4 has a multiple quantum well structure MQW (barrier layer: I-type AlGaAs / well layer: I-type InGaAs) in which barrier layers and well layers having a thickness of about 5 nm to 20 nm are alternately laminated. The thickness is 10 nm to 100 nm (preferably 30 nm). The lower optical guide layer 3 is made of AlGaAs, the conductive type is type I, and the thickness is 0 to 300 nm (preferably 150 nm). The lower clad layer 2 is made of AlGaAs, the conductive type is N type, and the thickness is 1 × 10 ^{3 nm to 3} × 10 3 nm (preferably 2 × 10 ³ nm). The semiconductor substrate 1 is made of GaAs, the conductive type is N type, and the thickness is 80 μm to 350 μm (preferably 150 μm). In this way, impurities of the first conductive type (N type) or impurities of the second conductive type (P type) are added to each layer (impurity concentration is 1 × 10 ¹⁷ to 1 × 10 ²¹ / cm. ³ ) The region where no impurities are intentionally added is true (type I). The concentration of type I impurities is 1 × 10 ¹⁵ / cm ³ or less.

Hereinafter, the superiority of the structure of the embodiment over various comparative examples will be described.

FIG. 7 is a plan view of the phase modulation layer according to the first comparative example.

This structure is a structure in which the sub-differential refractive index region 6BS is excluded from the structure shown in FIG. When the phase modulation layer having this structure is adopted for the semiconductor laser device of FIG. 1, high-intensity 0th-order light is observed.

FIG. 8 is a plan view of the phase modulation layer according to the second comparative example.

This structure is a structure in which the sub-differential refractive index region 6BS is periodically and regularly arranged at a position where the shift amount (r / a) = 0.5 in the structure shown in the first comparative example. The smaller sub-refractive index regions 6BS are _{arranged at equal intervals along each straight line on a straight line of Y = X + b 0} + Nb (b ₀ is a constant, b is a variable, and N is an integer). When the phase modulation layer having this structure is adopted for the semiconductor laser device of FIG. 1, the apparent output is the same as that of the first comparative example. That is, only a point beam in a direction perpendicular to the light emitting surface can be obtained, and the effect of the present invention of outputting a two-dimensional beam pattern having an arbitrary shape cannot be obtained.

FIG. 9 is a plan view of the phase modulation layer according to the third comparative example.

This structure is a structure in which the sub-differential refractive index region 6BS is periodically and regularly arranged next to each main different refractive index region in the structure shown in the first comparative example. When the phase modulation layer having this structure is adopted for the semiconductor laser device of FIG. 1, the apparent output is the same as that of the first comparative example. That is, only a point beam in a direction perpendicular to the light emitting surface can be obtained, and the effect of the present invention of outputting a two-dimensional beam pattern having an arbitrary shape cannot be obtained.

FIG. 10 is a plan view of the phase modulation layer according to the fourth comparative example.

In the structure shown in the first comparative example, this structure has a periodic and regular sub-refractive index region at positions where the shift amounts in the X and Y directions are (r / a) = 0.5, respectively. It is a structure in which 6BS is arranged. The smaller sub-refractive index region 6BS is _{arranged at equal intervals along each straight line on a straight line of Y = X + b 0} + Nb (b ₀ is a constant, b is a variable, N is an integer), and the main refraction The position of the rate region 6BM and the position of the sub-refractive index region 6BS have a relationship of having the same structure even if they are replaced with each other. When a phase modulation layer having this structure is adopted for the semiconductor laser device of FIG. 1, only a point beam in a direction perpendicular to the light emitting surface can be obtained, but the output is weaker than that of the first comparative example. Is observed.

The semiconductor laser device can have a plurality of conventionally known structures. For example, FIG. 11 is a diagram showing a vertical cross-sectional configuration of the semiconductor laser element, and the difference from that shown in FIG. 1 is that the laser beam is emitted from the back surface of the semiconductor substrate 1.

When the first electrode E1 is open in the region of the lower surface of the semiconductor substrate 1 facing the second electrode E2, the laser beam is emitted from the lower surface to the outside. In this case, the first electrode E1 provided on the lower surface of the semiconductor substrate 1 is an opening electrode having an opening in the center, and an antireflection film (first insulating film IN1) is formed in and around the opening of the first electrode E1. ) May be provided. In this case, the antireflection film is composed of a dielectric single layer film such as silicon nitride (SiN) or silicon dioxide (SiO _{2) or a dielectric multilayer film.} Examples of the dielectric multilayer film include titanium oxide (TiO ₂ ), silicon dioxide (SiO ₂ ), silicon monoxide (SiO), niobium oxide (Nb ₂ O ₅ ), tantalum pentoxide (Ta ₂ O ₅ ), and foot. Dielectric layers such as magnesium _{oxide (MgF 2} ), titanium oxide (TIO ₂ ), aluminum oxide (Al ₂ O ₃ ), cerium oxide (CeO ₂ ), indium oxide (In ₂ O ₃ ), zirconium oxide (ZrO ₂₎ A film in which two or more kinds of dielectric layers selected from the group are appropriately laminated can be used. For example, a film having a thickness of λ / 4 is laminated with an optical film thickness for light having a wavelength of λ. The reflective film and the antireflection film can be formed by using a sputtering method.

A second electrode E2 is provided on the upper surface of the contact layer 8, but a region other than the region where the second electrode E2 is formed is an insulating film (third) such as _{SiO 2 or silicon nitride, if necessary.} 1 The surface can be protected by covering with an insulating film IN2).

Next, a little description will be given about the method for manufacturing the above-mentioned semiconductor laser device.

In the production of the above-mentioned laser device, each compound semiconductor layer uses a metalorganic vapor phase growth (MOCVD) method. Crystal growth is carried out on the (001) plane of the semiconductor substrate 1, but the present invention is not limited to this. Further, in the manufacture of the laser element using AlGaN described above, the growth temperature of AlGaAs is 500 ° C. to 850 ° C., and 550 to 700 ° C. is adopted in the experiment, and TMA (trimethylaluminum) is used as the Al raw material during growth. ), TMG (trimethyl gallium) and TEG (triethyl gallium as a gallium raw material), AsH ₃ as the as raw material (arsine), Si ₂ H ₆ as a raw material for N-type impurity (disilane), DEZn as a raw material for P-type impurity (Diethylzinc) is used. In the growth of GaAs, TMG and arsine are used, but TMA is not used. InGaAs is manufactured using TMG, TMI (trimethylindium) and arsine. The insulating film may be formed by sputtering a target using the constituent substance as a raw material.

That is, in the above-mentioned laser element, first, the activity of the N-type clad layer (AlGaAs) 2, the guide layer (AlGaAs) 3, and the multiple quantum well structure (InGaAs / AlGaAs) on the N-type semiconductor substrate (GaAs) 1 is performed. The layer 4, the optical guide layer (GaAs / AaGaAs) 5, and the basic layer (GaAs) 6A to be the phase modulation layer are sequentially epitaxially grown by using the MOCVD (metalorganic vapor phase growth) method. Next, in order to perform alignment after epitaxial growth, a SiN layer is formed on the basic layer 6A by a PCVD (plasma CVD) method, and then a resist is formed on the SiN layer. Further, the resist is exposed and developed, the SiN layer is etched using the resist as a mask, and a part of the SiN layer remains to form an alignment mark. Remove the remaining resist.

Next, another resist is applied to the basic layer 6A, a two-dimensional fine pattern is drawn on the resist with an electron beam drawing device based on the alignment mark, and the two-dimensional fine pattern is formed on the resist by developing the resist. .. Then, using the resist as a mask, a two-dimensional fine pattern having a depth of about 100 nm is transferred onto the basic layer 6A by dry etching to remove the resist that forms holes. The depth of the holes is 100 nm. In the pores, a compound semiconductor having a different refractive index region 6B (AlGaAs) is re-grown to a depth equal to or greater than the depth of the pores. Next, the upper clad layer (AlGaAs) 7 and the contact layer (GaAs) 8 are sequentially formed by MOCVD, and an appropriate electrode material is formed on the upper and lower surfaces of the substrate by a vapor deposition method or a sputtering method to form the first and second electrodes. Form. Further, if necessary, an insulating film can be formed on the upper and lower surfaces of the substrate by a sputtering method or the like.

When the phase modulation layer is provided below the active layer, the phase modulation layer may be formed on the lower clad layer before the active layer and the lower optical guide layer are formed.

Further, a columnar different refractive index region may be used as a void, and a gas such as air, nitrogen or argon may be enclosed. The spacing between the vertical and horizontal grid lines in the above-mentioned virtual square grid is about the wavelength divided by the equivalent refractive index or the wavelength divided by the equivalent refractive index and √2, specifically 300 nm. It is preferably set to about 210 nm. In the case of a square lattice with a lattice spacing a, if the unit vectors of Cartesian coordinates are x and y, the basic translation vectors a ₁ = ax and a ₂ = ay, and the basic reciprocal lattice vectors with respect to the _{translation vectors a 1} and a _2. b ₁ = (2π / a) y, b ₂ = (2π / a) x. When the wave vector of the wave existing in the lattice is k = Nb ₁ + Mb ₂ (N and M are arbitrary integers), the wave number k exists at the Γ point, but the magnitude of the wave vector is basically the reverse. When it is equal to the magnitude of the lattice vector, a resonance mode (standing wave in the XY plane) in which the lattice spacing a is equal to the wavelength λ is obtained. Considering the TE mode in which an electric field exists in a plane parallel to the square lattice, there are four modes in the standing wave state where the lattice spacing and wavelength are equal, due to the symmetry of the square lattice. Similarly, a desired beam pattern can be obtained when oscillating in any mode of the standing wave state.

The standing wave in the phase modulation layer described above is scattered by the hole shape, and the wavefront obtained in the direction perpendicular to the plane is phase-modulated to obtain a desired beam pattern. Therefore, a desired beam pattern can be obtained without a polarizing plate. This beam pattern is not only a pair of single peak beams (spots), but as described above, a character shape, two or more spots having the same shape, or a vector in which the phase and intensity distribution are spatially non-uniform. It can also be a beam or the like.

The refractive index of the basic layer 6A is preferably 3.0 to 3.5, and the refractive index of the different refractive index region 6B is preferably 1.0 to 3.4. Further, as described above, the phase of the laser light caused by the main different refractive index region 6BM and the phase of the laser light of the sub-differential refractive index region 6BS tend to be inverted and canceled at the 0th order light position.

In the above-mentioned structure, pores are periodically formed by etching at a plurality of locations of the basic layer 6A, and the different refractive index region 6B is formed in the formed pores by an organic metal vapor phase growth method, a sputtering method, or a sputtering method. Although it is embedded by using an epitaxial method, after embedding the different refractive index region 6B in the pores of the basic layer 6A, a different refractive index coating layer made of the same material as the different refractive index region 6B is further deposited on it. You may.

In the above-mentioned structure, if the structure includes the active layer 4 and the phase modulation layer 6, the material system, the film thickness, and the layer structure have a degree of freedom. Here, the scaling law holds for the so-called square lattice photonic crystal laser when the perturbation from the virtual square lattice is 0. That is, when the wavelength becomes a constant α times, the same standing wave state can be obtained by multiplying the entire cubic lattice structure by α. Similarly, in the present invention, the structure of the phase modulation layer can be determined by the scaling law even at wavelengths other than those disclosed in the embodiment. Therefore, it is also possible to realize a semiconductor light emitting device that outputs visible light by using an active layer that emits light such as blue, green, or red and applying a scaling law according to a wavelength.

Further, the oscillation of the above-mentioned semiconductor laser element is Γ point oscillation, and when the effective refractive index of the phase modulation layer 6 is n, the wavelength λ ₀ (= lattice constant a × effective refractive index) selected by the phase modulation layer 6 is selected. n) is included in the emission wavelength range of the active layer 4. _{The phase modulation layer 6 can select the wavelength λ 0} of the emission wavelengths of the active layer 4 and output it to the outside.

As described above, the semiconductor light emitting element according to the above-described embodiment is a semiconductor light emitting element provided with a phase modulation layer 6 optically coupled to the active layer 4, and the thickness direction of the phase modulation layer 6 is in the Z-axis direction. The XYZ three-dimensional Cartesian coordinate system is set, and the phase modulation layer 6 is composed of a basic layer 6A composed of a first refractive index medium and a second refractive index medium having a refractive index different from that of the first refractive index medium. and a plurality of modified refractive index area 6B that exists among a plurality of modified refractive index areas. 6B, sub area S _S as larger than that of the main area S _M, in the XY plane, each main area S XY comprising a first group of main modified refractive index region 6BM with _M, in the XY plane, and a second group, each composed of a sub-modified refractive index areas 6BS having sub area S _S, a base layer 6A In the plane, a first virtual square grid consisting of grid lines extending in the X-axis direction and the Y-axis direction is set, and in the XY plane including the basic layer 6A, in the X-axis direction in the first virtual square grid. Passing through the midpoint of the line segment connecting adjacent grid points along the line segment and passing through the midpoint of the vertical bisector line group perpendicular to the line segment and the line segment connecting adjacent grid points along the Y-axis direction A second virtual square grid consisting of a grid line group (VL2 in FIG. 3) consisting of a group of vertically bisected lines perpendicular to the line segment is set, and individual unit constituent areas partitioned by the second virtual square grid are set. Within, the grid points of the first virtual square lattice coincide with the position of the center of gravity of the unit constituent area, and the position of the center of gravity of the main Cartesian coordinate region 6BM is arranged at the position of the center of gravity of the unit constituent region, and one. The number of main Cartesian refractive index regions included in the unit constituent region is one, and the number of center of gravity of the sub Cartesian refractive index region 6BS included in one unit constituent region is one, and the sub The position of the center of gravity of the Cartesian coordinate region 6BS is separated from the position of the center of gravity of the main Cartesian coordinate region 6BM by a distance r, and assuming that the lattice constant of the first virtual square lattice is a, 0.38 ≦ (r / a). ) ≤ 0.5, the sub-Cartesian refraction region 6BS has an aperiodic structure that is not aligned along the uniaxial direction, and emits a beam pattern other than the 0th order light in a direction not perpendicular to the light emitting surface. .. At this time, a two-dimensional beam pattern having an arbitrary shape may be output.

When attempting to generate an arbitrary beam pattern, the sub-refractive index region has an aperiodic structure that is not aligned along the uniaxial direction. In the case of FIG. 8, the sub-refractive index regions are arranged in the space period 2a, and on the reciprocal lattice space, point-like diffraction derived from the sub-refractive index region exists on the Brillouin boundary. Since the Brillouin boundary always corresponds to the part outside the light line, that is, the part that is totally reflected and the light does not come out to the upper surface of the device, in the case of FIG. 8, only the 0th-order light derived from the main different refractive index region is used. Is output, no beam pattern other than the 0th-order light is output, and it cannot be a semiconductor light emitting device capable of outputting an arbitrary beam pattern. Further, in the case of FIG. 9, all the unit lattices have the same shape, which corresponds to the case where the phase distribution is constant. Also in this case, only the 0th-order light is output, no beam pattern other than the 0th-order light is output, and the semiconductor light emitting device cannot output an arbitrary beam pattern. Further supplementing, when the spatial phase distribution is uniform, the inverse Fourier transform corresponds to a point, and it is not possible to obtain an arbitrary two-dimensional beam pattern.

When the shift amount (r / a), which is the separation distance converted to the lattice constant a, is 0.38 or more while satisfying the above-mentioned lattice conditions, the intensity of the 0th-order light contained in the emitted light becomes 0 or less. The phenomenon was observed, and low intensity of 0th order light was observed up to 0.5 or less.

FIG. 12 is a diagram _{for explaining coordinate conversion from spherical coordinates (r, θ tilt} , θ _rot ) to coordinates (x, y, z) in the XYZ Cartesian coordinate system. Note that r here is a parameter of an appropriate length used to explain the coordinate transformation.

The spherical coordinates (r, θtilt, θrot) indicating the coordinates (x, y, z) in the XYZ Cartesian coordinate system are the length r of the radius, the inclination angle θtilt of the radius from the Z axis, and the said. The following relationship is satisfied by using the rotation angle θrot of the line segment whose radius is projected on the XY plane from the X axis.

x = r · sinθ _tilt · cosθ _rot ,
y = r · sinθ _tilt · sinθ _rot ,
z = r · cosθ _tilt.

Assuming that a set of bright spots formed by a group of beams emitted from a semiconductor light emitting element at an inclination angle θtilt and a rotation angle θrot is a far-field image, the far-field image on the Kx-Ky plane has a normalized wave number on the Kx axis. wave number k _y normalized in k _x and Ky axis is the oscillation wavelength of the semiconductor light emitting device as lambda, satisfy the following relationship. Note that a is a lattice constant of the first virtual square lattice.

k _x = (a / λ) ・ sinθ _tilt・ cosθ _rot ,
_{k y = (a / λ)} · sinθ tilt · sinθ rot.

The coordinates (x, y, z) represent a design optical image on a predetermined plane set in the XYZ Cartesian coordinate system in real space. Incidentally, k _x is the coordinate on the Kx-axis corresponding to the X axis a normalized wave number, k _y together with corresponding to the Y-axis a normalized wavenumber, on Ky axis orthogonal to Kx axis Coordinates.

The standardized wavenumber means the wavenumber standardized with the wavenumber corresponding to the grid spacing of the virtual square lattice as 1.0. At this time, in the wavenumber space defined by the Kx axis and the Ky axis, the specific wavenumber range including the beam pattern corresponding to the light image is square M2 (integer of 1 or more) × N2 (integer of 1 or more), respectively. ) Consists of image area FR. The integer M2 does not have to match the integer M1. Similarly, the integer N2 does not have to match the integer N1. Equations (4) and (5) also include, for example, "Y. Kurosaka et al.," Effects of non-lasing band intwo-dimensional photonic-crystal lasers clarified using omnidirectional bandstructure, "Opt. Express 20, 21773-. 21783 (2012) ”.

When the pattern in the real space is Fourier transformed, the component of the wave number (or frequency) is obtained, and the obtained wave number space (k space) shows what kind of frequency component the pattern in the real space is formed of. Is done. Both the physical pattern and the electromagnetic field distribution pattern in the real space can be Fourier transformed, but in the semiconductor laser, the beam pattern of the far-field image is the electromagnetic field distribution on the light emitting surface (XY plane). It is a two-dimensional Fourier transform of the near-field image).

In Fourier space, Kx axis direction of the coordinate component _k x (1 or M2 below integer) coordinate components of Ky axis _k y (1 or N2 an integer) the de image area FR are identified _{(k x,} k _y ) Each unit configuration on the XY plane specified by the coordinate component x in the X-axis direction (an integer of 1 or more and M1 or less) and the coordinate component y in the Y-axis direction (an integer of 1 or more and N1 or less). When the two-dimensional inverse Fourier transformation (F ^-1 ) is performed on the region R (x, y), the complex amplitude f (x, y) in the real space is obtained. That is, the far-field pattern, the coordinates in the two-dimensional electric field distribution of the two-dimensional Fourier transformed Fourier space in the real space (k _{x, k y)} in, is composed of a plurality of image regions FR (k x, _{k y)} image area FR _(k x, _{k y)} are each square, M2 or in the Kx-axis direction to provide a wave number _{k x} normalized in wavenumber space (M2 is an integer of 1 or more), the wave number k obtained by normalizing Two N2s (N2 is an integer of 1 or more) are arranged two-dimensionally in the Ky-axis direction that gives _{y, and the two-dimensional reciprocal Fourier transform that gives the complex amplitude f (x, y) sets j.} It is given by the following formula as an imaginary unit.

The beam pattern of the far-field image is a two-dimensional Fourier transform of the two-dimensional electric field strength distribution in the real space formed on the light emitting surface parallel to the XY plane in the phase modulation layer, and is a far-field image. The complex amplitude f (x, y) obtained by two-dimensional inverse Fourier transform is given by the following equation, where the imaginary unit is j, the amplitude term is A (x, y), and the phase term is P (x, y). Given.

f (x, y) = A (x, y) x exp [jP (x, y)].

Further, a line segment (r in FIG. 5) connecting the center of gravity of the sub-differential refractive index region in the unit constituent region and the lattice point (center of gravity) of the unit constituent region including this sub-differential refractive index region is the X-axis. The angle φ formed by is given by the following equation, where C is the proportionality constant and B is the constant.

φ (x, y) = C × P (x, y) + B.
However, φ (x, y) is expressed as degree.

The phase modulation layer is configured to satisfy the following first and second conditions. That is, the first condition is that the center of gravity G of the sub-refractive index region 6BS is separated from the lattice point O (x, y) which is the center of gravity of the main refractive index region 6BM in the unit constituent region R (x, y). It is arranged in a state of refraction. The second condition is from the grid point O (x, y), which is the center of gravity of the main different refractive index region 6BM, to the center of gravity G of the sub-differential refractive index region 6BS in the unit constituent region to which the grid point O belongs. In a state where the line segment length r (x, y) (r in FIG. 5) is set to a common value in each of the unit constituent regions R of M1 × N1, the line segment length r (x, y) is set. The corresponding sub-refractive index region 6BS is the unit constituent region R (x, y) so that the angle φ (x, y) formed by the given line segment and the X-axis satisfies the relationship of the above equation of φ (x, y). It is arranged in y).

Note that C is a proportional constant and is, for example, 180 ° / π, and B is an arbitrary constant and is, for example, 0. Note that P (x, y) is a phase term of the complex amplitude f (x, y).

That is, when a desired optical image is to be obtained, the optical image formed on the Kx−Ky plane projected on the wave number space is formed on the unit constituent region R (x, y) on the XY plane on the phase modulation layer. Two-dimensional reciprocal Fourier transform is performed, and the rotation angle φ (x, y) corresponding to the phase term P (x, y) of the complex amplitude f (x, y) is set in the unit constituent region R (x, y). It may be given to the sub-reciprocal refractive index region 6BS arranged in. The far-field image of the laser beam after the two-dimensional Fourier transform has various spot shapes, a ring shape, a linear shape, a character shape, a double ring shape, a Laguerre Gaussian beam shape, and the like. Can take shape. Since the beam pattern is represented by wave number information in the wave number space (on the Kx-Ky plane), in the case of a bitmap image or the like in which the target beam pattern is represented by two-dimensional position information. In order to do so, it is advisable to perform a two-dimensional reciprocal Fourier transform after converting the wave number information once.

As a method of obtaining the intensity distribution and the phase distribution from the complex amplitude distribution on the XY plane obtained by the two-dimensional inverse Fourier transform, for example, the intensity distribution (amplitude term A (x, y) on the XY plane) The distribution) can be calculated by using the abs function of the numerical analysis software "MATLAB" of MATLABs, and the phase distribution (distribution of the phase term P (x, y) on the XY plane) can be calculated. It can be calculated by using the MATLAB angle function.

1 ... Semiconductor substrate, 2 ... Lower clad layer, 3 ... Lower optical guide layer, 4 ... Active layer, 5 ... Upper optical guide layer, 6 ... Phase modulation layer, 6A ... Basic layer, 6B ... Different refractive index region, 6BM ... Main different refractive index region, 6BS ... minor different refractive index region, 7 ... upper clad layer, 8 ... contact layer, E1 ... first electrode, E2 ... second electrode, LD ... semiconductor laser element.

Claims (5)

In a laser device provided with a phase modulation layer on which laser light is incident,
The phase modulation layer is
The basic layer consisting of the first refractive index medium and
A plurality of different refractive index regions existing in the basic layer, which are composed of a second refractive index medium having a different refractive index from the first refractive index medium,
With
The plurality of different refractive index regions
The planar shape is approximately circular or approximately square or approximately polygonal with rotational symmetry of 90 °, and has a main different refractive index region having a first area perpendicular to the thickness direction and a second area perpendicular to the thickness direction. Sub-differential index region and
With
The position of the center of gravity of the main different refractive index region is located at the lattice point of the square lattice.
The second area is larger than the first area,
The unit constituent region is composed of one main different refractive index region and one sub-differentred refractive index region provided closest to the main different refractive index region, and only these pair of different refractive index regions are configured for each unit. Exists in the area and
A line segment connecting the positions of the centers of gravity of the main different refractive index regions adjacent to each other is defined, and the smallest region surrounded by the perpendicular bisectors of this line segment is each of the unit constituent regions. In this unit constituent region, all of the pair of different refractive index regions are located.
Let φ be the rotation angle of the sub-differential refractive index region with respect to the main different refractive index region in the unit constituent region.
A plurality of the unit constituent regions are two-dimensionally arranged in the XY plane including the X-axis and the Y-axis.
The XY coordinates of each of the unit constituent regions are given at the position of the center of gravity of each of the principal different refractive index regions.
Assuming that the position of the center of gravity of the sub-differential refractive index region is separated from the position of the center of gravity of the main different refractive index region by a distance r, and the lattice constant of the square lattice is a.
0.38 ≤ (r / a) ≤ 0.5,
The filling,
The main different refractive index region has a periodic structure in the XY plane.
The sub-refractive index region has an aperiodic structure that is not aligned along the uniaxial direction in the XY plane, and emits a beam pattern other than the 0th-order light in a direction that is not perpendicular to the light emitting surface.
A semiconductor light emitting device characterized by this. The beam pattern is
This is a far-field image obtained by two-dimensional Fourier transforming a two-dimensional electric field strength distribution in real space formed on a light emitting surface parallel to the XY plane in the phase modulation layer.
The complex amplitude f (x, y) obtained by two-dimensional inverse Fourier transform of the far-field image has an imaginary unit of j, an amplitude term of A (x, y), and a phase term of P (x, y).
f (x, y) = A (x, y) x exp [jP (x, y)],
Given in
The angle φ formed by the line segment connecting the center of gravity of the sub-Cartesian index region and the lattice point (center of gravity) of the unit constitutive region including the sub-Cartesian index region in the unit constituent region with respect to the X axis is Let C be the constant of proportionality and B be the constant.
φ (x, y) = C × P (x, y) + B,
The semiconductor light emitting device according to claim 1, wherein the semiconductor light emitting device is given by. The far field pattern, in a two-dimensional electric field distribution coordinates in Fourier space that is two-dimensional Fourier transform of the real space _{(k x,} k _y), a plurality of image regions FR _(k x, k _y) is composed of, the image area FR _(k x, _{k y)} are each square, M2 or in the Kx-axis direction to provide a wave number _{k x} normalized in wavenumber space (M2 is an integer of 1 or more), the wave number k obtained by normalizing N2 pieces (N2 is an integer of 1 or more) are arranged two-dimensionally in the direction of the Ky axis that gives _y.
The two-dimensional inverse Fourier transform that gives the complex amplitude f (x, y) is based on the following equation:

The semiconductor light emitting device according to claim 2, wherein the semiconductor light emitting device is given by. The spherical coordinates (r, θtilt, θrot) indicating the coordinates (x, y, z) in the XYZ Cartesian coordinate system are the length r of the radius, the inclination angle θtilt of the radius from the Z axis, and the radius. Satisfies the following relationship using the rotation angle θrot of the line segment projected on the XY plane from the X axis.
x = r · sinθ _tilt · cosθ _rot ,
y = r · sinθ _tilt · sinθ _rot ,
z = r · cosθ _tilt ,
Assuming that a set of bright spots formed by a group of beams emitted from the semiconductor light emitting device at an inclination angle θtilt and an angle of rotation θrot is a far-field image.
The far field pattern in the Kx-Ky plane, wave number k _y normalized at wave numbers k _x and Ky-axis normalized at the Kx-axis is the oscillation wavelength of the semiconductor light emitting device as lambda, satisfy the following relationship ,
k _x = (a / λ) ・ sinθ _tilt・ cosθ _rot ,
_{k y = (a / λ)} · sinθ tilt · sinθ rot,
The semiconductor light emitting device according to claim 3. The semiconductor light emitting device according to any one of claims 1 to 4, further comprising a first clad layer and a second clad layer that sandwich an active layer optically coupled to the phase modulation layer.

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