Two-dimensional photonic-crystal surface-emitting laser

Abstract

A two-dimensional photonic-crystal surface-emitting laser 10 includes: a two-dimensional photonic crystal (two-dimensional photonic crystal layer 12) including a plate-shaped base body 121 having a predetermined size in which modified refractive index areas 122 whose refractive index differs from the base body are periodically arranged in a two-dimensional pattern; an active layer 11 provided on one side of the two-dimensional photonic crystal; and first and second electrodes 15 and 16 facing each other across the two-dimensional photonic crystal and the active layer 11, for supplying an electric current to the active layer 11. The modified refractive index areas 122 are provided in such a manner that the in-plane occupancy of those areas 122 in the base body 121 decreases, or the lattice constant for those areas 122 increases, in the direction from an outer edge toward the center of a current passage region 21 which is a region where the electric current passes through the two-dimensional photonic crystal. With this configuration, a stable laser oscillation can be obtained even when a temperature distribution which is lower at the outer edge and higher at the center of the current passage region is formed within the two-dimensional photonic crystal.

Claims

1. A two-dimensional photonic-crystal surface-emitting laser including: a two-dimensional photonic crystal including a plate-shaped base body having a predetermined size in which modified refractive index areas whose refractive index differs from the base body are periodically arranged in a two-dimensional pattern; an active layer provided on one side of the two-dimensional photonic crystal; and a pair of electrodes facing each other across the two-dimensional photonic crystal and the active layer, for supplying an electric current to the active layer, wherein: the modified refractive index areas are provided in such a manner that an in-plane occupancy of the modified refractive index areas in the base body increases in a direction from an outer edge toward a center of a current passage region which is a region where the electric current passes through the two-dimensional photonic crystal.

2. The two-dimensional photonic-crystal surface-emitting laser according to claim 1, wherein a difference f(x, y) between the in-plane occupancy f(x, y) at any in-plane position within the current passage region and the in-plane occupancy f.sub.b at the outer edge, i.e. f(x, y)=f(x, y)f.sub.b, is proportional to a difference T(x, y) between a temperature T(x, y) at the in-plane position concerned and the temperature T.sub.b at the outer edge, i.e. T(x, y)=T(x, y)T.sub.b (>0), with a positive proportionality coefficient.

3. The two-dimensional photonic-crystal surface-emitting laser according claim 1, wherein the modified refractive index areas are provided in such a manner that the in-plane occupancy concentrically decreases from the center of the current passage region.

4. A two-dimensional photonic-crystal surface-emitting laser including: a two-dimensional photonic crystal including a plate-shaped base body having a predetermined size in which modified refractive index areas whose refractive index differs from the base body are periodically arranged in a two-dimensional lattice pattern; an active layer provided on one side of the two-dimensional photonic crystal; and a pair of electrodes facing each other across the two-dimensional photonic crystal and the active layer, for supplying an electric current to the active layer, wherein: the modified refractive index areas are arranged in such a manner that a lattice constant decreases in a direction from an outer edge toward a center of a current passage region which is a region where the electric current passes through the two-dimensional photonic crystal.

5. The two-dimensional photonic-crystal surface-emitting laser according to claim 4, wherein a difference a(x, y) between the lattice constant a(x, y) at any in-plane position within the current passage region and the lattice constant a.sub.b at the outer edge, i.e. a(x, y)=a(x, y)a.sub.b, is proportional to a difference T(x, y) between a temperature T(x, y) at the in-plane position concerned and the temperature T.sub.b at the outer edge, T(x, y)=T(x, y)T.sub.b (>0), with a negative proportionality coefficient.

6. The two-dimensional photonic-crystal surface-emitting laser according to claim 4, wherein the modified refractive index areas are provided in such a manner that the lattice constant concentrically increases from the center of the current passage region.

7. The two-dimensional photonic-crystal surface-emitting laser according to claim 2, wherein the modified refractive index areas are provided in such a manner that the in-plane occupancy concentrically decreases from the center of the current passage region.

8. The two-dimensional photonic-crystal surface-emitting laser according to claim 5 wherein the modified refractive index areas are provided in such a manner that the lattice constant concentrically increases from the center of the current passage region.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a perspective view showing one embodiment of the two-dimensional photonic-crystal surface-emitting laser according to the present invention.

(2) FIG. 2 is a diagram schematically showing the current passage region of the two-dimensional photonic-crystal layer in the two-dimensional photonic-crystal surface-emitting laser according to the embodiment.

(3) FIG. 3 is a plan view showing one example of the two-dimensional photonic-crystal layer in the two-dimensional photonic-crystal surface-emitting laser according to the embodiment, in which the in-plane occupancy of the modified refractive index areas increases in the direction from the outer edge toward the center.

(4) FIG. 4 is a graph showing the result of a simulation of the temperature distribution in a two-dimensional photonic-crystal layer (the data indicated by the solid lines) as well as the temperature distribution on the surface of a two-dimensional photonic-crystal surface-emitting laser (the data indicated by the broken lines).

(5) FIG. 5 is a graph showing the result of a simulation of the temperature distribution on the surface of a two-dimensional photonic-crystal layer in the case where a substrate having a higher thermal conductivity than the one in the case of FIG. 4 was used.

(6) FIG. 6 is a plan view showing another example of the two-dimensional photonic-crystal layer in the two-dimensional photonic-crystal surface-emitting laser according to the embodiment, in which the lattice constant for the modified refractive index areas increases in the direction from the center toward the outer edge.

(7) FIG. 7 is a graph showing the result of a calculation of the value of a threshold gain difference with respect to the temperature difference between the center and the outer edge of the two-dimensional photonic crystal in the two-dimensional photonic-crystal surface-emitting laser in the embodiment as well as a comparative example.

(8) FIG. 8 is a graph showing the result of a simulation calculation of the value of a threshold gain difference with respect to the temperature difference between the center and the outer edge of the two-dimensional photonic crystal in the two-dimensional photonic-crystal surface-emitting laser according to the embodiment, where the calculation was performed with approximations in one case and without approximations in another case.

(9) FIGS. 9A-9G show the result of a simulation of the oscillation mode of light for a conventional two-dimensional photonic-crystal surface-emitting laser in the case where an unevenness in the temperature distribution occurs in the plane of the two-dimensional photonic crystal.

DESCRIPTION OF EMBODIMENTS

(10) An embodiment of the two-dimensional photonic-crystal surface-emitting laser according to the present invention is hereinafter described using FIGS. 1-8.

(11) As shown in FIG. 1, the two-dimensional photonic-crystal surface-emitting laser 10 in the present embodiment includes a first electrode 15, first cladding layer 141, active layer 11, spacer layer 13, two-dimensional photonic-crystal layer 12 (which corresponds to the two-dimensional photonic crystal mentioned earlier), second cladding layer 142, and second electrode 16 sequentially stacked in the mentioned order. The active layer 11 and the two-dimensional photonic-crystal layer 12 may be transposed. For convenience, the two-dimensional photonic-crystal surface-emitting laser 10 shown in FIG. 1 have the first and second electrodes 15 and 16 located on its upper and lower sides, respectively. However, the direction of the laser in use is not limited to the shown example. The configuration of each layer is hereinafter described.

(12) The active layer 11 emits light within a specific wavelength band upon receiving electric charges injected from the first and second electrodes 15 and 16. The material used for the active layer 11 in the present embodiment is a multiple quantum well of InGaAs/AlGaAs (emission wavelength band: 935-945 nm). However, the material for the active layer in the present invention is not limited to this example. The active layer 11 has a square shape with a thickness of approximately 2 m. The one-side length of this square is equal to or slightly larger than that of the outer contour of the frame portion 162 of the second electrode 16 (which will be described later). The active layer 11 in the present invention is not limited to these dimensions. Its shape may also be changed, such as a circular or hexagonal shape.

(13) As shown in FIG. 3, the two-dimensional photonic-crystal layer 12 includes a plate-shaped main body 121 in which modified refractive index areas 122 whose refractive index differs from that of the main body are periodically arranged. The material used for the main body 121 in the present embodiment is GaAs. However, the material for the main body in the present invention is not limited to this example. The modified refractive index areas 122 in the present embodiment are holes (air or vacuum). Detailed descriptions of the shape and arrangement of the modified refractive index areas 122 will be given later.

(14) The spacer layer 13 is provided to connect the active layer 11 and the two-dimensional photonic-crystal layer 12, which are made of different materials. The material used for the spacer layer 13 in the present embodiment is AlGaAs, which should be appropriately changed depending on the materials used for the active layer 11 and the two-dimensional photonic-crystal layer 12.

(15) The first and second cladding layers 141 and 142 have the functions of connecting the first electrode 15 with the active layer 11 and the second electrode 16 with the two-dimensional photonic crystal layer 12, respectively, as well as facilitating the injection of the electric current from the first and second electrodes 15 and 16 into the active layer 11. In order to enable the cladding layers to perform those functions, a p-type semiconductor is used as the material for the first cladding layer 141, while an n-type semiconductor is used as the material for the second cladding layer 142. The first cladding layer 141 has a two-layer structure consisting of a p-GaAs layer and p-AlGaAs layer arranged from the first electrode 15. Similarly, the second cladding layer 142 has a two-layer structure consisting of a n-GaAs layer and n-AlGaAs layer arranged from the second electrode 16 (those two-layer structures are not shown in the figure). The materials for the first and second cladding layers 141 and 142 in the present invention are not limited to the mentioned examples. The planar dimensions of the first and second cladding layers 141 and 142 are the same as those of the active layer 11 and the base body 121 of the two-dimensional photonic-crystal layer 12. The thickness of the first cladding layer 141 is 2 m, while that of the second cladding layer is 200 m.

(16) As just described, the first cladding layer 141 is much thinner than the second cladding layer 142. Accordingly, the distance between the two-dimensional photonic-crystal layer 12 and the first electrode 15 is much smaller than the distance between the two-dimensional photonic-crystal layer 12 and the second electrode 16. Consequently, as shown in FIG. 2, the current passage region 21, where the electric current flowing between the first and second electrodes 15 and 16 passes through the two-dimensional photonic-crystal layer 12, becomes almost the same as the region where the first electrode 15 is provided. Furthermore, since the distance between the active layer 11 and the two-dimensional photonic-crystal layer 12 in the present embodiment is much smaller than the distance between the two-dimensional photonic-crystal layer 12 and the second electrode 16, the region within which carriers are injected into the active layer 11 becomes almost the same as the current passage region 21 in the two-dimensional photonic-crystal layer 12.

(17) The first electrode 15 has a square planar shape whose one-side length is 200 m and is shorter than those of the other layers. Therefore, the current passage region 21 can also be approximated by a square whose one-side length is 200 m. The second electrode 16 is a square plate member having a square hollow portion formed inside. This hollow portion of the plate member is hereinafter called the window portion 161, while the remaining portion of the plate member is called the frame portion 162. The one-side length of the square plate member (outer side of the frame portion 162) is 800 m, and that of the square window portion 161 is 600 m. The laser light amplified within the two-dimensional photonic-crystal layer 12 oscillates in this layer, to be emitted through the window portion 161 to the outside of the two-dimensional photonic-crystal surface-emitting laser 10. The material used for the first electrode 15 and the frame portion 162 of the second electrode 16 may be a good conductor (e.g. gold) or a semiconductor having the same polarity as the neighboring cladding layer (a p-type semiconductor for the first electrode 15, and an n-type semiconductor for the second electrode 16).

(18) The shape and arrangement of the modified refractive index areas 122 in the two-dimensional photonic-crystal layer 12 will be hereinafter described. As shown in FIG. 3, the modified refractive index areas 122 within the current passage region 21 are divided by virtual square lines (thick broken lines in FIG. 3) into five zones 1231-1235 from the central zone 1231 to the end zone 1235 concentrically arranged from the center of the in-plane position. Within each zone, the modified refractive index areas 122 are arranged in a square lattice pattern. The spatial interval of the modified refractive index areas 122 (lattice constant) is the same in all zones. In any of these zones, the modified refractive index areas 122 have a right-angular planar shape and are arranged in such a manner that the two orthogonally intersecting sides of the right triangle are aligned with the orthogonally intersecting grid lines of the square lattice.

(19) The in-plane occupancy f(x, y) of the modified refractive index areas 122 is f(x, y)=f.sub.b=0.15600 (15.600%) in the end zone 1235 and is gradually increased in the direction from the end zone 1235 toward the central zone 1231. Any two zones neighboring each other has a difference in the in-plane occupancy f(x, y) by an amount of 6f(x, y)=f(x, y)/T(x, y)=0.00048 (0.048%). (In FIG. 3, for ease of understanding, the difference in the in-plane occupancy between the mutually neighboring zones is overdrawn, and the number of modified refractive index areas 122 shown in the figure is fewer than their actual number.) This value of 6f(x, y) has been calculated from equation (1) on the assumption that a temperature difference of 4 C. occurs between the central zone 1231 and the end zone 1235, with a temperature difference of 1 C. between any two zones neighboring each other, when the two-dimensional photonic-crystal surface-emitting laser 10 is in use. The value used as the numerator of the fraction in equation (1) was 2.6710 [K.sup.1], which is an approximated value for GaAs used as the material for the base body 121. The value used as the denominator was 0.56, which was determined by a simulation based on the coupled-wave theory for the case where the laser oscillation occurs in the so-called band edge A oscillation mode.

(20) The temperature difference of 4 C. between the central zone 1231 and the end zone 1235 has been chosen based on a simulation of the temperature distribution: As shown in FIG. 4, when an electric current of 1000 mA is passed between the first and second electrodes 15 and 16, the temperature difference T.sub.m between the center (x=0 on the x axis) and outer edges (x=100 m) of the current passage region 21 becomes 4 C. As can be seen in FIG. 4, an increase in the current value leads to a greater value of T.sub.m. Based on this relationship, the temperature difference T.sub.m between the central zone 1231 and the end zone 1235 can be appropriately set according to the current value. In FIG. 4, the data indicated by the solid lines show the temperature distribution in the two-dimensional photonic-crystal layer 12, while those indicated by the broken lines show the temperature distribution on the surface of the two-dimensional photonic-crystal surface-emitting laser 10.

(21) The value of the temperature difference T.sub.m can be decreased by improving the heat dissipation capability of the two-dimensional photonic-crystal surface-emitting laser 10. FIG. 5 shows the result of a simulation of the temperature distribution on the surface of the two-dimensional photonic-crystal layer 12 in the case where a substrate that is made to be in contact with the first cladding layer 141 for the installation of the two-dimensional photonic-crystal surface-emitting laser 10 is made of a material having a higher thermal conductivity than the one used in the case of FIG. 4. The temperature distribution within the current passage region (approximately 200 m) is flatter than in FIG. 4. The temperature difference T.sub.m is also smaller than in FIG. 4; its largest value is approximately 3 C.

(22) Though not shown, the modified refractive index areas 122 outside the current passage region 21 are arranged with the same in-plane occupancy and lattice constant as those used in the end zone 1235 inside the current passage region 21.

(23) FIG. 6 shows a two-dimensional photonic-crystal layer 12A as another example. The two-dimensional photonic-crystal layer 12A is identical to the previously described two-dimensional photonic-crystal layer 12 in that the base body 121 is divided by virtual square lines (thick broken lines in FIG. 6) into five zones 1231A-1235A from the end zone 1235A to the central zone 1231A concentrically arranged from the center of the in-plane position, and the modified refractive index areas 122A are arranged in a square lattice pattern within each zone. The two-dimensional photonic-crystal layer 12A differs from the previous example in that the modified refractive index areas 122A have the same planar area in all zones, while their lattice constant a(x, y) is gradually decreased in the direction from the end zone 1235A toward the central zone 1231A. The value of the lattice constant a(x, y) is a(x, y)=a.sub.b=294.000 nm in the end zone 1235A and is changed by an amount of a=a/T=0.027 nm for each zone on the assumption that a temperature difference of 1 C. occurs between any two zones neighboring each other. (In FIG. 6, for ease of understanding, the difference in the lattice constant between the mutually neighboring zones is overdrawn, and the number of modified refractive index areas 122A shown in the figure is fewer than their actual number.) The aforementioned value, 0.027 nm, has been calculated from equation (2) on the assumption that a temperature difference of 4 C. occurs between the central zone 1231A and the end zone 1235A, with a temperature difference of 1 C. between any two zones neighboring each other, when the two-dimensional photonic-crystal surface-emitting laser 10 is in use. The value used as the numerator of the fraction in equation (2) is 2.6710.sup.4 [K.sup.1], i.e. the same value as used in the previous example. The value used as the denominator n.sub.eff.sup.(0) is 2.92, which has been calculated from the refractive index of GaAs (3.28) taking into account the in-plane occupancy of the modified refractive index areas 122A in the central zone 1231A.

(24) A calculation for confirming the stability of the laser oscillation was performed for the two-dimensional photonic-crystal surface-emitting laser 10 in the present embodiment. Specifically, the possible modes of oscillation of the light within the two-dimensional photonic crystal were calculated, and a threshold gain difference (unit: cm.sup.1) was determined, which is the difference between the lasing threshold for the fundamental mode in which the laser oscillation is achieved at the lowest energy level and the lasing threshold for the next-order mode in which the laser oscillation is achieved at the second lowest energy level. A greater value of the threshold gain difference means that the next-order mode of oscillation is less likely to occur, and a stable laser oscillation will be obtained. The threshold gain difference was calculated with respect to the temperature difference T.sub.m between the center and the outer edge of the current passage region 21 (which is hereinafter simply called the temperature difference T.sub.m), with T.sub.m varied from 0 C. to 6 C. in steps of 1 C. As mentioned earlier, T.sub.m=4 C. corresponds to the temperature difference assumed in the designing of the two-dimensional photonic-crystal surface-emitting laser 10. When the temperature difference T.sub.m is within a range of 5-6 C., it means that the temperature difference is larger than expected. For comparison, a similar calculation was also performed for a device which had the same in-plane occupancy f and lattice constant a over the entire area of the two-dimensional photonic-crystal layer.

(25) The graph in FIG. 7 shows the calculated result of the threshold gain difference . The calculation yields the same result in both the case where the two-dimensional photonic-crystal layer 12 (with the adjusted in-plane occupancy f(x, y)) is used and the case where the two-dimensional photonic-crystal layer 12A (with the adjusted lattice constant a(x, y)) is used. When the temperature difference T.sub.m is 4 C., the value of threshold gain difference in the present embodiment is larger than in the comparative example for the same temperature difference, and is equal to the value for a temperature difference of T.sub.m=0 in the comparative example. This is because the two-dimensional photonic-crystal surface-emitting laser 10 is designed to be in an optimum state when the temperature difference T.sub.m is 4 C. When the temperature difference T.sub.m increases 6 C., the oscillation mode in the comparative example changes from the one at a temperature difference T.sub.m of 5 C. or less (and the value of the threshold gain difference increases along with that change). In the present embodiment, the oscillation mode is the same as when the temperature difference T.sub.m is 5 C. or less, and yet a higher threshold gain difference is achieved than when the temperature difference T.sub.m is 4 C.

(26) A brief description on the derivation of equations (1) and (2) is as follows.

(27) Consider a two-dimensional photonic-crystal layer which has neither the spatial distribution of the in-plane occupancy f nor the spatial distribution of the lattice constant a. If a spatial distribution of the temperature occurs in this two-dimensional photonic-crystal layer, a corresponding spatial distribution of the effective refractive index n.sub.eff occurs in the same layer. In this situation, the wave-number offset .sup.(T), which indicates the displacement of the wave number of the standing wave formed within the two-dimensional photonic-crystal layer from a value computed from the lattice constant, is given by:
.sup.(T)=.sup.(0)+n.sub.eff.sup.(T).sup.(T)/c(3)
where .sup.(0) is a constant, n.sub.eff.sup.(T) is a change in the effective refractive index n.sub.eff with respect to a temperature change, .sup.m is the frequency under the influence of the spatial distribution of the temperature, and c is the speed of light. The second term on the right side of equation (3) indicates the influence of the spatial distribution of the temperature. This term, which is hereinafter denoted by .sup.(T), can be rewritten as follows:
.sup.(T)(x,y)=n.sub.eff.sup.(T).sup.(T)/c
=n.sub.eff.sup.(T).sub.0(.sup.(T)/.sub.0)/c
n.sub.eff.sup.(T).sub.0/c (with the approximation of .sup.(T)/.sub.01)
(n.sub.eff.sup.(0)/T).Math.T(x,y).Math..sub.0/c(4)
where .sub.0 is the frequency with no influence of the spatial distribution of the temperature.

(28) In the case of a two-dimensional photonic-crystal layer which has a spatial distribution in the in-plane occupancy f(x, y), the wave-number offset .sup.(f) is given by:
.sup.(f)(x,y)(n.sub.eff.sup.(0).sup.(f)/c+f.Math.(n.sub.eff.sup.(0).sup.(f)/c)f)(.sub.0/c).sup.(0)+(.sub.0/c).Math.(n.sub.eff.sup.(0)/f+(n.sub.eff.sup.(0).sub.0).Math.(/f).Math.f(x,y)(5)
The second term on the right side of equation (5) indicates the influence of the spatial distribution of the in-plane occupancy f(x, y). This term is hereinafter denoted by .sup.(f)(x, y), i.e.:
.sup.(f)(x,y)=(.sub.0/c).Math.(n.sub.eff.sup.(0)/f+(n.sub.eff.sup.(0)/.sub.0).Math.(/f).Math.f(x,y)(6)

(29) From equations (4) and (6), the influence of the spatial distribution of the temperature can be cancelled by the spatial distribution of the in-plane occupancy f when the following equation holds true:
.sup.(T)(x,y)+.sup.(f)(x,y)=0(7)
i.e.,
(n.sub.eff.sup.(0)/T)T(x,y).Math..sub.0/c+(.sub.0/c).Math.(n.sub.eff.sup.(0)/f)+(n.sub.eff.sup.(0)/.sub.0).Math.(/f).Math.f(x,y)=0 (8)
By transforming this equation (8), equation (1) can be obtained.

(30) In the case of a two-dimensional photonic-crystal layer which has a spatial distribution in the lattice constant a(x, y), the wave-number offset .sup.(a) is given by:
.sup.(a)(x,y)=.sup.(0)+(.sub.0/c).Math.(1(a.sup.(0)/a(x,y)))(9)
The second term on the right side of equation (9) indicates the influence of the spatial distribution of the lattice constant a. This term is hereinafter denoted by .sup.(a), i.e.:
.sup.(a)(x,y)=(.sub.0/c).Math.((a.sup.(0)/a(x,y))1)(10)

(31) From equations (4) and (10), the influence of the spatial distribution of the temperature can be cancelled by the spatial distribution of the lattice constant a when the following equation holds true:
.sup.(T)(x,y)+(x,y)=0(11)
i.e.,
(n.sub.eff.sup.(0)/T).Math.T(x,y).Math..sub.0/c(.sub.0/c).Math.((a.sup.(0)/a(x,y))1)=0(12)
By transforming this equation (12), equation (2) can be obtained.

(32) Several approximations have been made for the derivation of equations (1) and (2). In order to confirm that those approximations have only a minor effect, the threshold gain difference has been calculated by simulation with the approximations as well as without the approximations. FIG. 8 shows the calculated result.

(33) The present invention is not limited to the previous embodiment but allows for various modifications.

(34) For example, the two-dimensional photonic-crystal layers 12 and 12A in the examples of FIGS. 3 and 6 are divided into five zones between the center and the outer edge. The number of zones may be increased (in which case the temperature difference between the neighboring zones becomes smaller) or decreased (in which case the temperature difference between the neighboring zones becomes larger). It is also possible to simultaneously vary both the in-plane occupancy and the lattice constant for each zone. Furthermore, the division into zones may be omitted (or the number of zones may be infinitely increased); i.e. the in-plane size (in-plane occupancy) of the neighboring modified refractive index areas 122 may be gradually decreased, or the spatial interval (lattice constant) of the neighboring lattice points may be gradually increased, in the direction from the center toward the outer edge of the two-dimensional photonic-crystal layer 12.

(35) In the previous embodiment, either the in-plane occupancy or lattice constant is varied depending on the position. It is possible to vary both the in-plane occupancy and the lattice constant depending on the position.

(36) In place of the holes used in the previous embodiment, members made of a material different from the base body 121 may be used as the modified refractive index areas. The planar shape of the modified refractive index areas may be variously changed, such as a circular, equilateral triangular, isosceles triangular or square shape in place of the right triangular shape in the previous embodiment. The arrangement pattern of the modified refractive index areas, which is a square lattice in the previous embodiment, may be changed to a triangular lattice, rectangular lattice or other appropriate patterns.

REFERENCE SIGNS LIST

(37) 10 . . . Two-Dimensional Photonic-Crystal Surface-Emitting Laser 11 . . . Active Layer 12, 12A . . . Two-Dimensional Photonic-Crystal Layer 121 . . . Base Body 122, 122A . . . Modified Refractive Index Area 1231-1235, 1231A-1235A . . . Zone in Which Modified Refractive Index Areas Having the Same In-Plane Occupancy and Lattice Constant Are Arranged 13 . . . Spacer Layer 141 . . . First Cladding Layer 142 . . . Second Cladding Layer 15 . . . First Electrode 16 . . . Second Electrode 21 . . . Current Passage Region