Photonic crystal laser

Abstract

A photonic crystal laser 10 is a laser that has a configuration, in which a light emitting layer (an active layer 12) that generates light including light of wavelength .sub.L, and a two-dimensional photonic crystal layer 11 including different refractive index regions (holes 111) disposed two-dimensionally on a plate-like base material 112, the different refractive index regions having a refractive index different from a refractive index of the base material, so that a refractive index distribution is formed, are stacked. Each different refractive index region in the two-dimensional photonic crystal layer 11 is disposed at a position shifted from each lattice point of a basic two-dimensional lattice that has periodicity defined to generate a resonant state of light of the wavelength .sub.L by forming a two-dimensional standing wave and not to emit light of the wavelength .sub.L to outside. A positional shift vector r representing the shift of the position of the different refractive index region at the each lattice point from the lattice point is expressed by
r=d.Math.sin(G.Math.r+.sub.0).Math.(cos(L(+.sub.0)), sin(L(+.sub.0))) by using a wave number vector k=(k.sub.x, k.sub.y) of light of the wavelength .sub.L in the two-dimensional photonic crystal layer 11, an effective refractive index n.sub.eff of the two-dimensional photonic crystal layer, an azimuth angle from a predetermined reference line extending in a predetermined direction from a predetermined origin of the basic two-dimensional lattice, an arbitrary constant .sub.0, and a reciprocal lattice vector G=(k.sub.x|k|(sin cos )/n.sub.eff, k.sub.y|k|(sin sin )/n.sub.eff) expressed by using a spread angle of a laser beam, the position vector r of the each lattice point, arbitrary constants d and .sub.0, and an integer L excluding 0.

Claims

1. A photonic crystal laser having a configuration, in which a light emitting layer that generates light including light of wavelength .sub.L, and a two-dimensional photonic crystal layer including different refractive index regions disposed two-dimensionally on a plate-like base material, the different refractive index regions having a refractive index different from a refractive index of the plate-like base material, so that refractive index distribution is formed, are stacked, wherein each different refractive index region in the two-dimensional photonic crystal layer is disposed at a position shifted from each lattice point of a basic two-dimensional lattice that has periodicity defined to generate a resonant state of light of the wavelength .sub.L by forming a two-dimensional standing wave and not to emit light of the wavelength .sub.L to outside, and magnitude of a shift of a position of a different refractive index region at the each lattice point from the lattice point has modulation in which the magnitude of the shift changes in a predetermined period from a predetermined origin of the basic two-dimensional lattice in a radial direction and in a predetermined period from the predetermined origin in a circumferential direction, and a direction of the shift from the lattice point is different depending on a direction of a straight line connecting the origin and the lattice point.

2. The photonic crystal laser according to claim 1, wherein a planar shape of the different refractive index region is a circle, an ellipse, or a polygon with three or more vertices.

3. The photonic crystal laser according to claim 2, wherein a planar shape of the different refractive index region is a circle or a polygon with six or more vertices.

4. A photonic crystal laser having a configuration, in which a light emitting layer that generates light including light of wavelength .sub.L, and a two-dimensional photonic crystal layer including different refractive index regions disposed two-dimensionally on a plate-like base material, the different refractive index regions having a refractive index different from a refractive index of the plate-like base material, so that refractive index distribution is formed, are stacked, wherein each different refractive index region in the two-dimensional photonic crystal layer is disposed at a position shifted from each lattice point of a basic two-dimensional lattice that has periodicity defined to generate a resonant state of light of the wavelength .sub.L by forming a two-dimensional standing wave and not to emit light of the wavelength .sub.L to outside, and a positional shift vector r representing a shift of a position of a different refractive index region at the each lattice point from the lattice point is expressed by
r=d.Math.sin(G.Math.r+.sub.0).Math.(cos(L(+.sub.0)), sin(L(+.sub.0))) by using a wave number vector k=(k.sub.x, k.sub.y) of light of the wavelength .sub.L in the two-dimensional photonic crystal layer, an effective refractive index n.sub.eff of the two-dimensional photonic crystal layer, an azimuth angle from a predetermined reference line extending in a predetermined direction from a predetermined origin of the basic two-dimensional lattice, an arbitrary constant .sub.0, and a reciprocal lattice vector G=(k.sub.x|k|(sin cos )/n.sub.eff, k.sub.y|k|(sin sin )/n.sub.eff) expressed by using a spread angle of a laser beam, the position vector r of the each lattice point, arbitrary constants d and .sub.0, and an integer L excluding 0.

5. The photonic crystal laser according to claim 4, wherein a value of L is +1 and a value of .sub.0 is 90.

6. The photonic crystal laser according to claim 5, wherein a planar shape of the different refractive index region is a circle, an ellipse, or a polygon with three or more vertices.

7. The photonic crystal laser according to claim 6, wherein a planar shape of the different refractive index region is a circle or a polygon with six or more vertices.

8. The photonic crystal laser according to claim 4, wherein a planar shape of the different refractive index region is a circle, an ellipse, or a polygon with three or more vertices.

9. The photonic crystal laser according to claim 8, wherein a planar shape of the different refractive index region is a circle or a polygon with six or more vertices.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1A is a diagram for explaining that a basic two-dimensional lattice amplifies light of a wavelength .sub.L, and FIG. 1B is a diagram for explaining a reason why light of the wavelength .sub.L is not emitted to the outside.

(2) FIG. 2 is a schematic configuration diagram showing an embodiment of a photonic crystal laser according to the present invention.

(3) FIG. 3 is a top view showing a two-dimensional photonic crystal layer in the photonic crystal laser of the present embodiment.

(4) FIG. 4 is a partially enlarged view showing a center of gravity of a square lattice which is a basic two-dimensional lattice and a hole in the two-dimensional photonic crystal layer of the photonic crystal laser of the present embodiment.

(5) FIG. 5 is a top view (upper diagram) of the two-dimensional photonic crystal layer and a diagram showing a result (lower diagram) obtained by measuring a polarization direction for three examples in which values of an inclination angle and an azimuth angle are the same and directions of shift of the holes are different.

(6) FIG. 6 is a photograph showing a spot of a laser beam for three examples in which the inclination angle and the directions of the shift of the holes are the same and the values of the azimuth angle are different.

(7) FIG. 7 is a diagram for explaining that a radial annular laser beam can be obtained in the photonic crystal laser of the present embodiment.

(8) FIG. 8 is a diagram for explaining that a circumferential annular laser beam is obtained.

(9) FIG. 9 is a diagram showing a direction of polarization of an annular laser beam in a case of L=2, .sub.0=90.

(10) FIG. 10 is a photograph showing a cross section of a laser beam obtained by the photonic crystal laser of the present embodiment for a case of (a) L=+1, .sub.0=90 and (a) L=1, .sub.0=90.

(11) FIG. 11 is a photograph of a cross section of a laser beam which has passed through a polarizing element taken for a plurality of examples with different directions of the polarizing element for the case of L=+1, .sub.0=90 and a diagram of the explanation.

(12) FIG. 12 is a photograph of a cross section of a laser beam which has passed through a polarizing element taken for a plurality of examples with different directions of the polarizing element for the case of L=1, .sub.0=90 and a diagram of the explanation.

(13) FIG. 13 is a photograph of a cross section of a laser beam obtained by the photonic crystal laser of the present embodiment, for two examples where L=1, .sub.0=90 and a spread angle is different.

(14) FIG. 14 is an SEM photograph showing an example of a produced two-dimensional photonic crystal layer for the photonic crystal laser of the present embodiment.

(15) FIG. 15 is a diagram schematically showing a cross section (a) perpendicular to the radially polarized annular laser beam and one cross section (b) parallel to the radially polarized annular laser beam.

DESCRIPTION OF EMBODIMENTS

(16) An embodiment of the photonic crystal laser according to the present invention will be described with reference to FIGS. 2 to 14.

(17) FIG. 2 is a perspective view of a photonic crystal laser 10 of the present embodiment. The photonic crystal laser 10 includes a lower electrode 151, a lower substrate 141, a lower cladding layer 131, a two-dimensional photonic crystal layer 11, an active layer (light emitting layer) 12, an upper cladding layer 132, an upper substrate 142, and an upper electrode 152 which are stacked in this order. However, the order of the two-dimensional photonic crystal layer 11 and the active layer 12 may be reversed to that described above. Note that, although FIG. 2 shows the two-dimensional photonic crystal layer 11 and the active layer 12 separately in order to show a configuration of the two-dimensional photonic crystal layer 11, they are actually in contact with each other. Similarly, the lower substrate 141 and the lower electrode 151 are also in contact with each other. In the present application, for convenience, the terms upper and lower are used, but these terms do not actually define directions (upper and lower) when the photonic crystal laser is actually used. Further, a member, such as a spacer, may be inserted between the two-dimensional photonic crystal layer 11 and the active layer 12.

(18) First, a configuration of each layer other than the two-dimensional photonic crystal layer 11 will be described. The active layer 12 corresponds to the light emitting layer, and when electric charges are injected by passing a current between the lower electrode 151 and the upper electrode 152, light of a wavelength within a predetermined wavelength range corresponding to a material of the active layer 12 is emitted. For the active layer 12, for example, one having a Multiple-Quantum Well (MQW) including indium gallium arsenide/gallium arsenide (InGaAs/GaAs) can be used. The active layer 12 emits light of a wavelength in the range of 960 to 990 nm. A p-type semiconductor is used for the lower cladding layer 131 and the lower substrate 141, and an n-type semiconductor is used for the upper cladding layer 132 and the upper substrate 142. For example, p-type semiconductor gallium arsenide (GaAs) can be used for the lower substrate 141, n-type GaAs can be used for the upper substrate 142, p-type semiconductor aluminum gallium arsenide (AlGaAs) can be used for the lower cladding layer 131, and n-type AlGaAs can be used for the upper cladding layer 132. Note that, an n-type semiconductor may be used for the lower cladding layer 131 and the lower substrate 141, and a p-type semiconductor may be used for the upper cladding layer 132 and the upper substrate 142.

(19) In the present embodiment, one provided with a window (cavity) 1521 provided at the center of a film made from metal, such as gold, is used for the upper electrode 152. A laser beam generated by the photonic crystal laser 10 is emitted out of the photonic crystal laser 10 through the window 1521. As the upper electrode 152, a transparent electrode made from indium tin oxide (ITO) or the like may be used instead of the one having the window 1521. In the present embodiment, a film made from metal, such as gold, whose area is smaller than that of the window 1521 of the upper electrode 152 is used for the lower electrode 151. A shape of the lower electrode 151 is circular in the present embodiment, but is not considered in particular.

(20) Next, a configuration of the two-dimensional photonic crystal layer 11 will be described. As shown in FIG. 3, the two-dimensional photonic crystal layer 11 is a plate-shaped base material (slab) 112 in which a hole (different refractive index region) 111 is arranged as described later. In the present embodiment, p-type GaAs is used as a material of the base material 112. A shape of the holes 111 is circular in the present embodiment.

(21) The arrangement of the hole 111 in the base material 112 will be described with reference to FIGS. 3 and 4. In the present embodiment, the basic two-dimensional lattice is a square lattice. FIG. 3 is a top view of the two-dimensional photonic crystal layer 11. In this diagram, the hole 111 actually provided on the two-dimensional photonic crystal layer 11 is indicated by a solid line, a square lattice, which is the basic two-dimensional lattice, is indicated by an alternate long and short dashed line, and a broken line indicates a state in which the center of gravity of a hole 111V is disposed virtually at a lattice point of the square lattice. Further, as described later, an origin 1131 serving as a reference for determining the position of the hole 111 is indicated by a cross, and a reference line 1132, which is a straight line extending in one direction from the origin, is indicated by a solid arrow. The origin 1131 is an arbitrary one of lattice points of the basic two-dimensional lattice, and the reference line 1132 is a line parallel to one of lattice lines orthogonal to each other of the square lattice. FIG. 4 shows only the square lattice (alternate long and short dashed line), a center of gravity 111G (black circle) of the hole 111, the origin 1131, and the reference line 1132.

(22) The lattice constant a of the basic two-dimensional lattice is preferably determined so as to be a=2.sup.1/2.sub.L/n.sub.eff, after selecting the wavelength .sub.L for laser oscillation from the wavelength range of 960 to 990 nm in which the active layer 12 emits light. Here, the lattice constant a is preferably determined based on a ratio (filling factor) of the volume occupied by the hole 111 in the two-dimensional photonic crystal layer 11 and a refractive index of a material of the base material 112. In the present embodiment, the effective refractive index n.sub.eff of the two-dimensional photonic crystal layer 11 is 3.4.

(23) In the present embodiment, in order to obtain a radially polarized annular laser beam, in Equation (1) described above, L=+1, .sub.0=90. Further, a spread angle of the laser beam is an arbitrary value (for example, =1). The azimuth angle at each lattice point is represented by an angle formed by a straight line connecting the origin 1131 and the lattice point with respect to the reference line 1132 (FIG. 4).

(24) Since the basic two-dimensional lattice is a square lattice, the reciprocal lattice vector G for each lattice point is obtained by substituting values of the effective refractive index n.sub.eff and the azimuth angle at the lattice point into Equation (2). Then, the positional shift vector r for each lattice point is obtained by substituting L=1 and .sub.0=90, and the position vector r and the reciprocal lattice vector G for each lattice point into Equation (1). Note that the value of d in Equation (1) is arbitrary.

(25) From Equation (1), a direction of the positional shift vector r is generally determined by a vector (cos(L(+.sub.0)), sin(L(+.sub.0)), and is determined by a vector (cos(+)/2), sin(+/2)) in the present embodiment. Therefore, in the present embodiment, the center of gravity 111G of the hole 111 is disposed at a position shifted in a direction rotated by (+/2) radians, that is, (+90) from the direction of the reference line at each lattice point (FIG. 4). For example, the center of gravity 111G of the hole 111 is disposed at a position shifted from a lattice point in a direction perpendicular to the reference line 1132 for a lattice point (=0) on the reference line 1132, in a direction parallel to the reference line 1132 for a lattice point (=90) on a line 1133 orthogonal to the reference line 1132, and in a direction of =135 orthogonal to a line 1134 for a lattice point on the line 1134 crossing the reference line 1132 at an angle of =45. All of these directions of shifts are perpendicular to the straight line connecting the origin and the lattice point.

(26) On the other hand, a distance of a shift of the center of gravity 111G of the hole 111 from the lattice point is determined by d sin(G.Math.r). Since G and r are vectors different for each lattice point, the distance of a shift from the lattice point is also a value different for each lattice point.

(27) Since the hole 111 is disposed at a position shifted from a lattice point as described above at each lattice point, the laser beam generated by the photonic crystal laser 10 becomes a radially polarized annular laser beam. Hereinafter, the reason for the above will be described.

(28) (a) Reason Why the Laser Beam becomes Radially Polarized Light

(29) First, unlike the present embodiment, a case where the holes 111 are shifted in the same direction at all lattice points will be examined. In the upper diagram of FIG. 5, at all the lattice points, vectors (cos(L(+.sub.0)), sin(L(+.sub.0))) representing directions of shifts of the holes 111 are not dependent on the azimuth angle of each lattice point.

(30) In place of a vector, an example in which is 30, is 0, and .sub.0 is 0 in a factor d sin(G.Math.r+.sub.0) representing the magnitude of a shift is shown. The direction of a shift of the hole 111 is the y direction in FIG. 5A, a direction of +45 with respect to the x direction in FIG. 5B, and the x direction in FIG. 5C. All of these examples are the same as the example described in Patent Literature 2. As a result, a laser beam having linearly polarized light in the x direction in FIG. 5A, the direction of +45 with respect to the y direction in FIG. 5B, and they direction in FIG. 5C with respect to the direction of a shift of the hole 111 is obtained, and in all the examples, the linearly polarized light is in a direction of +90 with respect to the direction of a shift of the hole 111 (lower diagram in FIG. 5).

(31) Next, unlike the present embodiment and the example of FIG. 5 described above, FIG. 6 shows a result of photographing an obtained laser beam in a cross section parallel to the two-dimensional photonic crystal layer in a case where directions of shifting the holes 111 from lattice points are set to be the same (here, the x direction) in all lattice points, and the angle in the factor d sin(G.Math.r+.sub.0) representing the magnitude of a shift is different (the angle is the same). In any of cases where the azimuth angle in the factor d sin(G.Math.r+.sub.0) is (a) 0, (b) 45, and (c) 90, a laser beam having an inclination angle with respect to a normal line of a two-dimensional photonic crystal layer at the angle and an azimuth angle at is shown to be emitted.

(32) When the results of FIGS. 5 and 6 are combined, a conclusion described below can be drawn. When the azimuth angle is 0 (FIG. 6A) and the direction of a shift of the hole 111 is the y direction (90, FIG. 5A), as shown in FIG. 7, a spot 201 of a laser beam in a cross section parallel to the two-dimensional photonic crystal layer appears in a direction in which the azimuth angle is 0, and its polarization is in the x direction (0). Similarly, in a case where the azimuth angle is 45 (FIG. 6B) and the direction of a shift of the hole 111 is 135 with respect to the x direction (FIG. 5B), a spot 202 of the laser beam in the cross section appears in a direction in which the azimuth angle is 45, and its polarization is in a direction at 45 with respect to the x direction. Further, in a case where the azimuth angle is 90 (FIG. 6C) and the direction of a shift of the hole 111 is the x direction (180, FIG. 5C), a spot 203 of the laser beam in the cross section appears in a direction in which the azimuth angle is 90, and its polarization is in the y direction (90). In any spot, the polarization is in the same direction as the direction connecting the origin and the spot.

(33) Therefore, when the spots of these laser beams are collected within a range of the azimuth angles from 0 to 360, a laser beam having a cross section of a ring shape is formed (a broken line in FIG. 7). Further, by setting the direction in which the hole 111 shifts from a lattice point to be a direction of 90 with respect to the direction connecting the origin and the spot, the direction of polarization in each spot is the same as the direction connecting the origin and the spot, that is, the radial direction. That is, by combining these conditions, a radially polarized annular laser beam can be obtained. The photonic crystal laser 10 of the present embodiment satisfies the above conditions by changing a value of the azimuth angle in Equations (1) and (2) within the range of 0 to 360 for each lattice point, and shifting the hole 111 from a lattice point in a direction of 90 with respect to the direction connecting the origin and the spot by the vector (cos(+/2), sin(+/2)) that specifies the direction of the positional shift vector r, and a radially polarized annular laser beam can be obtained.

(34) Similarly, as shown in FIG. 8, if the azimuth angle is 0 (FIG. 6A) and the direction of a shift of the hole 111 is the x direction (FIG. 5C), a spot 201A of a laser beam appears in the direction in which the azimuth angle is 0, polarization is y polarization (90), if the azimuth angle is 45 (FIG. 6B) and the direction of a shift of the hole 111 is in the direction of 45 (FIG. 5B) with respect to the x direction, a spot 202A of a laser beam appears in the direction in which the azimuth angle is 45 and the polarization is 135 with respect to the x direction, and if the azimuth angle is 90 (FIG. 6C) and the direction of a shift of the hole 111 is they direction (FIG. 5A), a spot 203A of a laser beam appears in the direction in which the azimuth angle is 90, and becomes x-polarization (180). Therefore, when spots of laser beams with different azimuth angles within the range of 0 to 360 are collected, a laser beam having a cross section of a ring shape is formed (a broken line in FIG. 8). Further, the polarization direction is the circumferential direction of the ring. Therefore, the laser beam obtained in this example is an azimuthally polarized annular laser beam. The conditions mentioned here correspond to the case where L=+1, .sub.0=0 in Equation (1).

(35) Further, when the value of L is an integer other than +1 (the above embodiment) and 0 (out of the range of the present invention), an annular laser beam having polarization corresponding to the value of L can be obtained. FIG. 9 shows a direction of polarized light by an arrow in a case of L=+2 and .sub.0=90. In a case where =0 and the direction of a shift of the hole 111 is the y direction (90), in an obtained spot 201B, the polarized light is in the x direction as in FIG. 7, and this direction is the radial direction. In contrast, as the value of increases, the direction of polarized light rotates by 2. For example, in a case where =30 and the direction of a shift of the hole 111 is 120 with respect to the x direction, the polarized light is rotated by 2 with respect to the x direction, that is, 60 in an obtained spot 202B. Therefore, every time increases by 180, a direction of polarized light rotates 360 and becomes the same direction as when =0. Then, the polarized light is rotated twice by the time increases by 360. Similarly, in a case where L is +3 or more, the direction of the polarized light is rotated 360 every time increases by (360/L), and becomes the same direction as when =0, and the polarized light is rotated L times by the time increases by 360. On the other hand, in a case where L has a negative value, as increases, the direction of polarized light rotates in the opposite direction to a case where L has a positive value.

(36) FIG. 10 shows a photograph of a cross section of a laser beam obtained by the photonic crystal laser 10 manufactured as (a) L=+1, .sub.0=90 (that is, conditions for obtaining a radially polarized annular laser beam), and (b) L=1, .sub.0=90. The spread angle is 1 in all cases. In all the cases, a laser beam having a cross section of a ring shape is obtained. Note that, in the condition (a), since light emission (side lobe) appears also on the outside of the ring of the cross section, FIG. 10A shows a photograph in which the side lobe is blocked. No side lobe appears in (b).

(37) For the laser beams in the cases of L=+1, .sub.0=90 and L=1, .sub.0=90 shown in FIGS. 10A and 10B, the photograph is taken by passing the laser beam through the polarizing element, and changing an orientation of the polarizing element. The results are shown in FIG. 11 for the case of L=+1 and .sub.0=90 and in FIG. 12 for the case of L=1 and .sub.0=90. FIG. 11 and FIG. 12 show four photographs different in the orientation of the polarizing element on the left side. The right side of each of the diagrams shows a direction of polarized light that can pass through the polarizing element in a manner corresponding to each of the four photographs by an outlined arrow, and a direction of polarized light that can be assumed from design (values of L and .sub.0) at each position of a cross section of a ring shape of a laser beam by a black arrow. Further, a portion where the direction of polarized light that can pass through the polarizing element matches with the assumed direction of polarized light is shown by enclosing with a broken line. In either cases of FIG. 11 and FIG. 12, a position of a portion where light appears in the photograph on the left matches with a position of a portion enclosed by a broken line in the diagram on the right. From this result, an annular laser beam having polarized light as designed is considered to be obtained.

(38) FIGS. 13A and 13B show photographs of cross sections of the laser beams obtained by two of the photonic crystal lasers 10 having the spread angles different from each other in the case of L=1 and .sub.0=90. The spread angle is set to 1 in FIG. 13A and 8 in FIG. 13B. A filling factor (FF) is 12.0% in FIG. 13A and 14.0% in FIG. 13B. The other parameters are common between FIGS. 13A and 13B, the lattice constant a is 206 nm, and a diameter of the lower electrode 151 and a thickness of each layer are common between both. FIGS. 13A and 13B are shown on the same scale, and FIG. 13A with a smaller spread angle is shown to have a smaller wheel diameter.

(39) FIG. 14 shows an example of the produced two-dimensional photonic crystal layer 11 by an SEM photograph for the photonic crystal laser 10 of the present embodiment. In this example, L=+1 and .sub.0=90. Each of the holes 111 is disposed at a position shifted from the lattice point of the square lattice, and a direction and size of the shift is different for each of the holes 111.

(40) The present invention is not limited to the above embodiment. For example, although the shape of the hole (different refractive index region) 111 is circular in the above embodiment, it may be various shapes, such as an equilateral triangle or another triangle, a polygon including a triangle, or an ellipse. Further, instead of the hole 111, a member (different refractive index member) having a refractive index different from a refractive index of the base material 112 may be used for the different refractive index region. While a hole is excellent in that it can be easily processed, the different refractive index member is advantageous in a case where there is possibility that the base material is deformed by heating or the like at the time of processing. Furthermore, the basic two-dimensional lattice is not limited to the square lattice, and a triangular lattice, a rectangular lattice, or the like may be used. In a case of using a triangular lattice or a rectangular lattice, the positional shift vector r obtained by substituting the reciprocal lattice vector G shown in any of Equations (3) to (5) into Equation (1) is preferably used to set a position of the different refractive index region.

INDUSTRIAL APPLICABILITY

(41) The photonic crystal laser according to the present invention can obtain an annular laser beam having desired polarization distribution, and can have a large output power since it can resonate in a large area, and has an oscillation mode called TE mode. Due to these excellent features, the photonic crystal laser according to the present invention can be suitably used in many devices, such as a high resolution microscope, various measuring instruments and analyzers, a laser processing machine, and an OCT diagnostic device.

REFERENCE SIGNS LIST

(42) 10 . . . Photonic Crystal Laser 11 . . . Two-dimensional Photonic Crystal Layer 111, 111V . . . Hole (Different Refractive Index Region) 111G . . . Center of Gravity 112 . . . Base Material 1131 . . . Origin 1132 . . . Reference Line 1133 . . . Line Orthogonal to Reference Line 1134 . . . Line Crossing Reference Line at Angle of 45 12 . . . Active Layer (Light Emitting Layer) 131 . . . Lower Cladding Layer 132 . . . Upper Cladding Layer 141 . . . Lower Substrate 142 . . . Upper Substrate 151 . . . Lower Electrode 152 . . . Upper Electrode 1521 . . . Window of Upper Electrode 201, 201A, 201B, 202, 202A, 202B, 203, 203A . . . Spot of Laser Beam 81 . . . Cross Section of Radially Polarized Annular Laser Beam 83 . . . Lens 90 . . . Basic Two-dimensional Lattice 91, 911, 912 . . . Lattice Point