A topologically configured photonic crystal surface-emitting laser
By designing a topological ring structure in a photonic crystal surface-emitting laser, the refractive index and coupling symmetry are broken, solving the problems of polarization instability and insufficient far-field quality. This enables stable single-mode operation and high extinction ratio laser output, making it suitable for fields such as optical communication.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHANGCHUN INST OF OPTICS FINE MECHANICS & PHYSICS CHINESE ACAD OF SCI
- Filing Date
- 2026-04-13
- Publication Date
- 2026-07-31
AI Technical Summary
Existing photonic crystal surface-emitting lasers have shortcomings in polarization stability and far-field beam quality, making it difficult to achieve stable single-mode operation and controllable polarization output. They are also sensitive to process errors, affecting system integration and optical communication performance.
A topologically configured photonic crystal layer is employed. By designing a topological ring structure, the equivalent refractive index and coupling symmetry in the x and y directions are broken, resulting in polarization degeneracy splitting. Combined with the non-uniformity and tilt angle of the ring region, the polarization state of the emitted light can be controlled, avoiding the use of additional polarization elements.
It achieves high polarization stability and high extinction ratio laser output, suppresses multimode competition, and features a concentrated far-field spot, low sidelobes, and small divergence angle, making it suitable for system integration and optical communication applications.
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Figure CN122495151A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of semiconductor laser technology, and particularly relates to a topologically configured photonic crystal surface-emitting laser. Background Technology
[0002] Semiconductor lasers have been widely used in many fields due to their advantages of small size, high electro-optic conversion efficiency and low cost. Among them, the photonic crystal surface-emitting laser (PCSEL) uses a two-dimensional photonic crystal to provide distributed feedback in the waveguide layer, forming a high-Q resonance at the Brillouin zone band edge (commonly the band edge mode near the Γ point), realizing large-area coherent oscillation. At the same time, the light is emitted vertically by the second-order diffraction coupling of the two-dimensional photonic crystal, thereby obtaining a surface-emitting laser output with a small divergence angle, narrow linewidth and scalable high power. Compared with the traditional vertical-cavity surface-emitting laser (VCSEL), PCSEL is easier to maintain a single transverse mode at large apertures and has better far-field quality potential.
[0003] In most two-dimensional photonic crystal PCSEL designs, degenerate or near-degenerate modes exist near the Γ point. When the unit cell has high symmetry (e.g., circular holes, cylinders, etc.) or the device is subject to process disturbances, stress anisotropy, non-uniform injection, etc., the device may exhibit problems such as polarization instability, polarization reversal, insufficient polarization extinction ratio, or uncontrollable polarization direction, which in turn affects system integration (e.g., polarization multiplexing, coherent synthesis, precision measurement, optical communication, projection / display, etc.).
[0004] Currently, there are four main methods for achieving polarization control in PCSELs: 1) Introducing anisotropy by changing the shape of the two-dimensional photonic crystal cell to break degeneracy and "lock" a specific linear polarization; 2) Adding a metasurface to the light-emitting surface to implement high reflectivity / high transmittance selection for a specific polarization; 3) Achieving polarization selection through cavity anisotropy (stress, birefringent layer, asymmetric cladding); 4) Achieving polarization purification through external polarization elements or encapsulated optics, but this introduces volume, cost, and coupling loss. Among the above schemes, although cell anisotropy can lock polarization, the polarization direction is limited, far-field symmetry decreases, and it is sensitive to process errors. Adding an external polarization selection layer may reduce light extraction or introduce additional heat / loss. It is difficult to achieve a balance between "polarization stability / controllability" and "small far-field divergence angle" simultaneously using a single method.
[0005] Specifically, existing laser technologies mainly suffer from the following shortcomings: 1) Polarization instability caused by polarization degeneracy: Symmetric or weakly anisotropic cells are prone to competition between two orthogonal polarization modes, leading to polarization reversal, insufficient extinction ratio, or polarization direction drift; 2) Difficulty in achieving both polarization locking and far-field quality: Although strong geometric anisotropy (such as slits / strips) can lock polarization, it easily disrupts the circular symmetry of the outgoing wavefront, resulting in ellipticization, sidelobe enhancement, or decreased single-lobe quality in the far field; 3) Sensitivity to process and stress disturbances: When polarization selection depends on small differences, etching depth, dimensional errors, material stress, and temperature rise can cause changes in polarization selectivity, reducing batch consistency; 4) Additional polarization elements bring losses and complexity, potentially introducing light extraction losses, increased thermal resistance, and assembly difficulties.
[0006] In summary, the urgent problem to be solved is how to provide a photonic crystal surface-emitting laser that can achieve stable single-mode operation and better beam quality, can realize settable and long-term stable output polarization state, and has a near-Gaussian far-field spot with low sidelobes and small divergence angle. Summary of the Invention
[0007] In view of this, the present invention aims to provide a topologically configured photonic crystal surface-emitting laser to solve the problems faced by the prior art, achieve laser polarization stability, improve single-mode stability, and improve far-field beam quality.
[0008] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A topologically configured photonic crystal surface-emitting laser includes, from bottom to top, an n-electrode, an n-substrate, an n-type cladding, an active layer, a photonic crystal layer, a p-type cladding, a p-type contact layer, and a p-electrode. The photonic crystal layer is composed of multiple periodically arranged unit cells, each unit cell containing a topological ring structure with a refractive index different from that of the parent material. The topological ring structure includes an outer boundary and an inner boundary located within the outer boundary, forming a ring region between the outer and inner boundaries. In the topological ring structure, by breaking the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions, polarization degeneracy splitting is formed near the resonant frequency to achieve the control of the polarization state of the emitted light.
[0009] Furthermore, breaking the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions includes one or more of the following methods: Method 1: Use a topological ring structure that is tilted at an angle θ relative to the lattice axis; Method 2: Set the center of the inner boundary at an offset of Δx and / or Δy relative to the center of the outer boundary; Method 3: Set the ring width of the annular region to be non-uniform in the x and y directions.
[0010] Furthermore, the tilt angle θ of the topological ring structure is set in a partitioned manner, or globally consistent, or radially gradient manner in the photonic crystal layer.
[0011] Furthermore, the topological ring structure has geometric degrees of freedom that can act on the coupling coefficients of the two orthogonal directions respectively, so that the second-order Fourier components and the first-order Fourier components along the two orthogonal lattice directions can be independently balanced within a preset range, thereby taking into account both high threshold difference and surface emission coupling efficiency.
[0012] Furthermore, the intracavity operating modes within the large-aperture resonant cavity formed by the cell array exhibit a circularly symmetrical fundamental mode field distribution, and suppress the transverse multi-peak distribution of higher-order modes.
[0013] Furthermore, the outer and inner boundaries can be elliptical, circular, or triangular in shape; the outer and inner boundaries can be combined in the same or different shapes.
[0014] Furthermore, the outer radius R of the outer boundary of the topological ring structure out The range is from 0.20a to 0.45a, and the inner radius R of the inner boundary is... in The range is from 0.05a to 0.35a; where a is the lattice constant of the photonic crystal layer.
[0015] Furthermore, both the outer and inner boundaries are elliptical, with an ellipticity, i.e., the ratio of the major axis to the minor axis, ranging from 1.0 to 1.6.
[0016] Furthermore, in the topological ring structure, the center of the inner boundary circle is offset by Δx in the x-axis direction and by Δy in the y-axis direction relative to the center of the outer boundary circle.
[0017] Furthermore, the major axis directions of the outer boundary and the inner boundary are set to be the same and coaxial, and the entire topological ring structure is tilted at an angle θ relative to the lattice axis to break the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions; the major axis directions of the outer boundary and the inner boundary are set to be different and non-axial, and an angle β is formed between the major axis of the outer boundary and the major axis of the inner boundary to break the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions.
[0018] Compared with the prior art, the present invention can achieve the following beneficial effects: 1. This scheme achieves resonant polarization degeneracy splitting through the anisotropy of photonic crystals, outputting stable laser with high polarization extinction ratio without the aid of other polarization elements, exhibiting high polarization stability. At the same time, the bidirectional independent control of the coupling coefficient increases the threshold gain difference between the fundamental mode and higher-order modes, suppressing multimode competition and resulting in high single-mode stability.
[0019] 2. In this scheme, the fundamental mode dominates, the far-field spot is concentrated, the side lobes are low, and the divergence angle is small, which is conducive to collimation and system integration. The far-field beam quality is good, and the topological ring structure can obtain the inner and outer elliptical boundaries through a single exposure. The morphology is regular and the repeatability is good. Compared with the complex shapes of porous / polylattice, it is more friendly to the consistency of etching depth. At the same time, it can adapt to different wavebands, different polarization angles and different system requirements. Attached Figure Description
[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 The top view and cross-sectional view of the photonic crystal layer in the laser described in Embodiment 1 of the present invention are shown in Figure (1), and Figure (2) is a cross-sectional view, which is cut from the topological ring structure. Figure 2 This is a three-dimensional structural diagram of the laser described in Embodiment 1 of the present invention; wherein, the S direction is the light emission direction; Figure 3 A top view of the n-electrode in the laser described in Embodiment 1 of the present invention; Figure 4 A cross-sectional structural diagram of the laser described in Embodiment 1 of the present invention; wherein, the S direction is the light emission direction; Figure 5 The graph shows the variation of transmittance and polarization extinction ratio ER of the laser in TE and TM modes as a function of operating temperature in Embodiment 1 of the present invention. Figure 6 This invention creates a mode distribution diagram of the laser described in Embodiment 1; Figure 7 A far-field simulation diagram of the laser described in Embodiment 1 of this invention; Figure 8 This invention creates a far-field amplitude diagram of the laser described in Embodiment 1 of the present invention; Figure 9 The top view and cross-sectional view of the photonic crystal structure in the laser described in Embodiment 2 of the present invention are shown in the figure; wherein, Figure (1) is a top view and Figure (2) is a cross-sectional view, which is cut from the topological ring structure; Figure 10 This is a cross-sectional schematic diagram of the photonic crystal layer in the laser described in Embodiment 3 of the present invention.
[0021] Reference numerals: substrate 101, unit cell 102, outer boundary 102a, inner boundary 102b, n-electrode 201, circular electrode window 201a, square Ni / Au-Ge / Ni / Au metal film 201b, n-substrate 202, n-type cladding 203, active layer 204, photonic crystal layer 101, p-type cladding 205, p-type contact layer 206, p-electrode 207. Detailed Implementation
[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.
[0023] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.
[0024] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.
[0025] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0026] The following will refer to the appendix. Figure 1-10 The invention will be described in detail with reference to the embodiments.
[0027] Example 1 This implementation example Figures 1-8 As shown, a topologically configured photonic crystal surface-emitting laser includes, from bottom to top, an n-electrode 201, an n-substrate 202, an n-type cladding 203, an active layer 204, a photonic crystal layer 101, a p-type cladding 205, a p-type contact layer 206, and an n-electrode 201. The materials of the above layers are, in order: a square Ni / Au-Ge / Ni / Au metal film 201b, GaAs, Al0.7Ga0.3As, InGaAs multiple quantum wells, GaAs, Al0.4Ga0.6As, GaAs, and a square Ti / Pt / Au metal film. A circular electrode window 201a is formed on the square Ni / Au-Ge / Ni / Au metal film 201b.
[0028] The laser is fabricated as follows: an n-cladding layer, an active layer 204, and a photonic crystal layer 101 are grown on an n-substrate 202; a photonic crystal is fabricated on the photonic crystal layer 101; an n-type cladding layer 203 and a p-contact layer are grown; and an n-electrode 201 is grown. An electrically insulating layer (SiO2) is grown before the n-electrode 201 is grown.
[0029] The photonic crystal layer 101 is composed of multiple cells 102 arranged periodically. Each cell 102 contains a topological ring structure with a different refractive index than the parent material 101. The topological ring structure includes an outer boundary 102a and an inner boundary 102b located within the outer boundary 102a. A ring region is formed between the outer boundary 102a and the inner boundary 102b. The topological ring structure has geometric degrees of freedom that can act on the coupling coefficients of two orthogonal directions respectively, so that the second-order Fourier components (corresponding to one-dimensional coupling strength) and the first-order Fourier components (corresponding to vertical radiation constant) along the two orthogonal lattice directions can be independently balanced within a preset range, thereby balancing high threshold difference and sufficient surface emission coupling efficiency.
[0030] The outer boundary 102a and the inner boundary 102b are elliptical, circular or triangular. The outer boundary 102a and the inner boundary 102b can be combined in the same shape or different shapes. In this embodiment, the outer boundary 102a and the inner boundary 102b are both elliptical, and their ellipticity, that is, the ratio of the major axis to the minor axis, ranges from 1.0 to 1.6. The inner ellipse is the inner boundary 102b, and the outer ellipse is the outer boundary 102a.
[0031] In a topological ring structure, by breaking the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions, polarization degeneracy splitting is formed near the resonant frequency, resulting in a lower threshold and locking of a certain linear polarization state. This allows for the control of the polarization state of the outgoing light, increasing the threshold gain difference between the fundamental mode and higher-order modes. Breaking the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions includes one or more of the following methods: Method 1: A topological ring structure is used, tilted at an angle θ relative to the lattice axis. The major axes of the outer and inner ellipses can be in the same direction and tilted at an angle θ relative to the lattice axis. This is used to introduce in-plane anisotropy and split orthogonal polarization modes. In this embodiment, the major axis of the inner ellipse (inner boundary 102b) is in the same direction and coaxial with the major axis of the outer ellipse (outer boundary 102a). Specifically, as shown below... Figure 1 As shown on the L-axis, and at the same time, the angle θ is as follows Figure 1 As shown in the figure, angle θ is the angle between the x-axis and the major axis L of the inner boundary 102b and the outer boundary 102a.
[0032] Method 2: Set the center of the inner boundary 102b at an offset of Δx and / or Δy relative to the center of the outer boundary 102a.
[0033] Method 3: Set the ring width of the annular region to be non-uniform in the x and y directions to achieve PCSEL output polarization state locking.
[0034] The outer radius R of the outer boundary 102a of the topological ring structure out The range is from 0.20a to 0.45a, and the inner radius R of the inner boundary 102b is... in The range is from 0.05a to 0.35a, where a is the lattice constant of the photonic crystal layer 101. In this embodiment, in the topological ring structure, the center of the inner ellipse, i.e., the inner boundary 102b, is offset by a Δx in the x-axis direction and an offset by a Δy in the y-axis direction relative to the center of the outer ellipse, i.e., the outer boundary 102a. Δx and Δy are as follows: Figure 1 As shown.
[0035] In this embodiment, methods one, two, and three are used simultaneously to break the equivalent refractive index symmetry and coupling symmetry between the x and y directions. Those skilled in the art can use one or a combination of two methods according to actual needs.
[0036] In this embodiment, the lattice constant a is set to 276 nm, and the major axis R of the outer ellipse, i.e., the outer boundary 102a, is... out1 Set to 124nm, minor axis R out2 Set to 82nm, the major axis R of the inner ellipse, i.e., the inner boundary 102b, is... in1 Set to 69nm, minor axis R in2 The core diameter is set to 30nm. The major axes of the inner and outer ellipses are in the same direction. The offset of the center of the inner ellipse from the center of the outer ellipse on the x-axis is set to 25nm, and the offset on the y-axis is set to 15nm. The rotation angle θ is set to 60°, the etching depth h is set to 200nm, and the entire photonic crystal resonant cavity is square with a side length of 600μm.
[0037] In this embodiment, the photonic crystal layer 101 adopts a partitioned setting, a globally consistent setting, or a radially gradual setting to set the tilt angle θ of the topological ring structure, so as to realize on-chip rotation of polarization direction, polarization state splicing, or arrayed multi-polarization output. Partitioned setting means that the photonic crystal region is divided into multiple sub-regions, and the unit cells 102 in different sub-regions adopt different tilt angles θ. Global consistency means that the topological ring structure of all unit cells 102 in the entire photonic crystal region adopts the same tilt angle θ. Radial gradual setting means that the value of θ changes continuously or stepwise along the radial direction of the photonic crystal region (from the center to the periphery).
[0038] The working mode inside the large-aperture resonant cavity composed of a 102-cell array exhibits a circularly symmetrical fundamental mode field distribution and suppresses the transverse multi-peak distribution of higher-order modes. Combined with the aforementioned polarization locking and threshold difference enhancement, the far-field beam of the surface-emitting output can remain concentrated with low sidelobes and achieve a near-Gaussian far-field distribution and small divergence angle.
[0039] Figure 6 This implementation scheme uses simulations to show the changes in transmittance and polarization extinction ratio (ER) of TE and TM modes with temperature. Figure 6 As can be seen from the results, this implementation scheme achieves a transmittance of 0.99 for the target polarized light and a polarization extinction ratio of 32dB at a temperature of 15℃. When the temperature changes from -40℃ to 85℃, the extinction ratio fluctuates little, which can fully meet the requirements of practical application scenarios.
[0040] Figure 7 The diagram shows the pattern distribution of this implementation scheme, with a threshold difference Δα between the fundamental mode and higher-order modes of 26.7 cm. -1 It meets the resonant cavity requirements of single-mode lasers. Figure 8 and Figure 9 The far-field simulation diagram and amplitude diagram of this implementation scheme show that the laser can achieve a far-field divergence angle of less than 1° and has a Gaussian-distributed intracavity electromagnetic field intensity.
[0041] Example 2 like Figure 9 As shown, the difference between this embodiment and Embodiment 1 is that in this embodiment, both the outer boundary 102a and the inner boundary 102b are circular, and the annular region formed between the outer boundary 102a and the inner boundary 102b is an eccentric annular region, which realizes polarization degeneracy breaking and polarization locking through broken symmetry.
[0042] Example 3 like Figure 10 As shown, the difference between this embodiment and Embodiment 1 is that in this embodiment, the major axis of the inner ellipse (i.e., the inner boundary 102b) and the major axis of the outer ellipse (i.e., the outer boundary 102a) are in different directions and have different axes. The major axis of the inner boundary 102b is as follows: Figure 10The M-axis shown has a major axis of outer boundary 102a as shown in the figure. Figure 10 The angle between the N-axis of the outer boundary 102a and the M-axis of the inner boundary 102b shown in the figure is β. This embodiment can further break the in-plane coupling symmetry and achieve stable emission of polarized light.
[0043] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.
[0044] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.
Claims
1. A topologically configured photonic crystal surface-emitting laser, characterized in that: The structure includes, from bottom to top, an n-electrode (201), an n-substrate (202), an n-type cladding (203), an active layer (204), a photonic crystal layer (101), a p-type cladding (205), a p-type contact layer (206), and a p-electrode (207). The photonic crystal layer (101) is composed of multiple cells (102) arranged periodically. Each cell (102) contains a topological ring structure with a refractive index different from that of the parent material (101). The topological ring structure includes an outer boundary (102a) and an inner boundary (102b) located within the outer boundary (102a). A ring region is formed between the outer boundary (102a) and the inner boundary (102b). In the topological ring structure, by breaking the equivalent refractive index symmetry and / or coupling symmetry of the x and y directions, a polarization degeneracy split is formed near the resonant frequency to achieve the control of the polarization state of the emitted light.
2. The topologically configured photonic crystal surface-emitting laser according to claim 1, characterized in that: Breaking the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions includes one or more of the following methods: Method 1: Use a topological ring structure that is tilted at an angle θ relative to the lattice axis; Method 2: Set the center of the inner boundary (102b) with an offset of Δx and / or Δy relative to the center of the outer boundary (102a); Method 3: Set the ring width of the annular region to be non-uniform in the x and y directions.
3. The topologically configured photonic crystal surface-emitting laser according to claim 2, characterized in that: The tilt angle θ of the topological ring structure is set by partitioning, global consistency, or radial gradient in the photonic crystal layer (101).
4. The topologically configured photonic crystal surface-emitting laser according to claim 1, characterized in that: The topological ring structure has geometric degrees of freedom that can act on the coupling coefficients of two orthogonal directions respectively, so that the second-order Fourier components and the first-order Fourier components along the two orthogonal lattice directions can be independently balanced within a preset range, thereby balancing high threshold difference and surface emission coupling efficiency.
5. The topologically configured photonic crystal surface-emitting laser according to claim 1, characterized in that: The working mode inside the large-aperture resonant cavity composed of a cell (102) array exhibits a circularly symmetrical fundamental mode field distribution and suppresses the transverse multi-peak distribution of higher-order modes.
6. The topologically configured photonic crystal surface-emitting laser according to claim 1, characterized in that: The outer boundary (102a) and the inner boundary (102b) are elliptical, circular or triangular in shape; the outer boundary (102a) and the inner boundary (102b) can be combined in the same shape or in a combination of different shapes.
7. The topologically configured photonic crystal surface-emitting laser according to claim 1, characterized in that: The outer radius R of the outer boundary (102a) of the topological ring structure out The range is from 0.20a to 0.45a, and the inner radius R of the inner boundary (102b) is... in The range is from 0.05a to 0.35a; where a is the lattice constant of the photonic crystal layer (101).
8. The topologically configured photonic crystal surface-emitting laser according to claim 7, characterized in that: Both the outer boundary (102a) and the inner boundary (102b) are elliptical, and their ellipticity, i.e. the ratio of the major axis to the minor axis, ranges from 1.0 to 1.
6.
9. The topologically configured photonic crystal surface-emitting laser according to claim 8, characterized in that: In the topological ring structure, the center of the inner boundary (102b) is offset by Δx in the x-axis direction and by Δy in the y-axis direction relative to the center of the outer boundary (102a).
10. The topologically configured photonic crystal surface-emitting laser according to claim 9, characterized in that: The major axis of the outer boundary (102a) is set to be the same and coaxial as the major axis of the inner boundary (102b). The topological ring structure is tilted at an angle θ relative to the lattice axis to break the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions. The major axis of the outer boundary (102a) is set to be different and non-axial from the major axis of the inner boundary (102b). An angle β is formed between the major axis of the outer boundary (102a) and the major axis of the inner boundary (102b) to break the equivalent refractive index symmetry and / or coupling symmetry in the x and y directions.