A photonic crystal structure, optical waveguide and corner state structure

Abstract

The present application relates to a kind of energy valley photonic crystal structure, optical waveguide and angular state structure.The energy valley photonic crystal structure described in the present application realizes energy band inversion by changing the ring width of circular ring silicon dielectric column, and has higher stability without changing unit cell position.The optical waveguide proposed in the present application has selectivity to left-handed circularly polarized light and right-handed circularly polarized light, and can realize valley polarization light selective coupling and transmission of pseudo-spin and energy valley locking;It also has high efficient light transmission characteristics and anti-scattering robustness, and its transmission efficiency can reach 98% in the frequency range of 155-173THz.The angular state structure proposed in the present application can realize four different frequency topological angular states, and the four topological angular states can not only be realized singly, but also can coexist in fixed photonic band gap through structure design.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of photonic crystals, in particular to an energy valley photonic crystal structure, an optical waveguide and an angular state structure. BACKGROUND

[0002] In recent years, high-order topological insulator (HOTI) has attracted extensive attention due to its unique bulk-edge correspondence. For example, in a two-dimensional system, a two-dimensional topological insulator can have one-dimensional topological edge states and zero-dimensional topological corner states. Subsequently, researchers introduced the concept of topology into photonic crystals and conducted in-depth research, realizing new transmission phenomena such as wideband unidirectional transmission and anti-scattering transmission in topological optical structures. At the same time, for the topological optical structure, defects and other disturbances will only cause local parameter changes and will not affect the global properties of the structure. Therefore, the properties of the photonic states of the topological optical structure are very stable, and have a high tolerance to micro-nano preparation errors, thereby having great research significance. The energy valley topological transmission waveguide and the topological corner state can be constructed by using the topological photonic crystal, which has potential applications in topological laser, robust optical delay line, optical waveguide device and other micro-nano integrated devices. In order to make the energy band of the energy valley photonic crystal have different properties at different energy valleys, it is necessary to break the spatial inversion symmetry of the structure while keeping the time inversion symmetry unchanged. The traditional method is to rotate the unit cell to open the photonic band gap and realize the energy band inversion and topological phase transition. In the process of rotating the unit cell, problems such as deviation of the rotation angle of the dielectric column and micro changes in the internal structure of the device are prone to occur. SUMMARY

[0003] To solve the above technical problems, the present application provides an energy valley photonic crystal structure, an optical waveguide and an angular state structure.

[0004] An energy valley photonic crystal structure is formed by arranging a plurality of regular hexagonal unit cells in an array manner with their cross-sectional centers diverging in six directions around them, and the distance between the centers of adjacent regular hexagonal unit cells is a lattice constant a; a single regular hexagonal unit cell is composed of a first type of circular ring silicon dielectric column and a second type of circular ring silicon dielectric column uniformly placed in air, and the first type of circular ring silicon dielectric column and the second type of circular ring silicon dielectric column are arranged in a triangular lattice staggered manner to form a regular hexagonal basic unit, i.e., the first type of circular ring silicon dielectric column and the second type of circular ring silicon dielectric column are arranged alternately at the six vertices of the regular hexagon.

[0005] Wherein, the outer radii of the first type of circular ring silicon dielectric column and the second type of circular ring silicon dielectric column are the same, and the inner diameter of the first type of circular ring silicon dielectric column is smaller than the inner diameter of the second type of circular ring silicon dielectric column.

[0006] Preferably, the unit cell of the upper vertex of the regular hexagon is denoted as VPC1 when it is a first type of circular ring silicon dielectric column, and the unit cell of the upper vertex of the regular hexagon is denoted as VPC2 when it is a second type of circular ring silicon dielectric column.

[0007] An optical waveguide composed of a valley optical photonic crystal structure as described above, comprising a first crystal unit composed of a plurality of unit cells VPC1 and a second crystal unit composed of a plurality of unit cells VPC2; the splicing boundary of the first crystal unit and the second crystal unit is in a "zig-zag" type or a "Bridge" type.

[0008] When the boundary is in a "zig-zag" type, the boundary formed by the unit cell VPC1 above the unit cell VPC2 is a first edge state, and the boundary formed by the unit cell VPC2 above the unit cell VPC1 is a second edge state; when the boundary is in a "Bridge" type, the boundary formed by the unit cell VPC1 above the unit cell VPC2 is a third edge state, and the boundary formed by the unit cell VPC2 above the unit cell VPC1 is a fourth edge state.

[0009] An angle state structure composed of an optical waveguide as described above, the angle state structure comprising:

[0010] An inner layer crystal unit composed of one of the unit cells VPC1 and VPC2;

[0011] An outer layer crystal unit located outside the region boundary of the inner layer crystal unit, composed of one of the unit cells VPC1 and VPC2, and the unit cells constituting the outer layer crystal unit are different from the unit cells constituting the inner layer crystal unit;

[0012] Wherein, the top angle of the region boundary of the inner layer crystal unit is 60°.

[0013] Preferably, the region boundary of the inner layer crystal unit is a regular triangle.

[0014] Preferably, the boundary state at the boundary where the inner layer crystal unit and the outer layer crystal unit are spliced is a first edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure, forming a T-I type angle state structure.

[0015] Preferably, the boundary state at the boundary where the inner layer crystal unit and the outer layer crystal unit are spliced is a second edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure, forming a T-II type angle state structure.

[0016] Preferably, the boundary state at the boundary where the inner layer crystal unit and the outer layer crystal unit are spliced is a third edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure, forming a T-III type angle state structure.

[0017] Preferably, the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit is a fourth edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure, and a T-IV type corner state structure is formed.

[0018] Preferably, the area boundary of the inner layer crystal unit is an hourglass shape formed by superimposing two equilateral triangles, and the corner state structure is divided into a first quadrant, a second quadrant, a third quadrant and a fourth quadrant with the center of the corner state structure as the origin.

[0019] Preferably, the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the first quadrant is a third edge state, the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the second quadrant is a first edge state, the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the third quadrant is a fourth edge state, and the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the fourth quadrant is a second edge state.

[0020] The above technical solutions of the present application have the following advantages compared with the prior art:

[0021] 1. The energy valley photonic crystal structure can realize energy band inversion by changing the ring width of the circular ring-shaped silicon dielectric column, and has higher stability without changing the unit cell position.

[0022] 2. The optical waveguide proposed in the present application has selectivity for left circularly polarized (LCP) light and right circularly polarized (RCP) light, and can realize valley polarization light selective coupling and transmission of pseudo-spin and energy valley locking.

[0023] 3. The optical waveguide proposed in the present application has high efficient light transmission characteristics and anti-scattering robustness, and the transmission efficiency can reach 98% in the frequency range of 155-173 THz.

[0024] 4. The corner state structure proposed in the present application can realize four different frequency topological corner states, and the four topological corner states can not only be realized singly, but also can coexist in a fixed photonic band gap through structure design. BRIEF DESCRIPTION OF DRAWINGS

[0025] In order to make the content of the present application more easily understood, the present application will be further described in detail below according to specific embodiments of the present application and in combination with the drawings.

[0026] Figure 1 (a) is a schematic diagram of a two-dimensional honeycomb energy valley photonic crystal structure; (b) is a structure schematic diagram of a primitive cell, a unit cell VPC1 and a unit cell VPC2.

[0027] Figure 2(a) is a photonic band structure diagram of a primitive cell; (b) is a photonic band structure diagram of a unit cell VPC1 and a unit cell VPC2.

[0028] Figure 3 (a) is a first edge state; (b) is a second edge state; (c) is a third edge state; (d) is a fourth edge state.

[0029] Figure 4 (a) is a supercell structure; (b) is a photonic band structure of a supercell; (c) is a photonic band structure of a supercell with a defect. Figure 4 (b) is the intrinsic field E of the three points A, B, and C z ; (d) is the Poynting vector distribution of the energy of the three points A, B, and C.

[0030] Figure 5 (a) is a straight waveguide structure constructed; (b) is the Ez electric field intensity distribution of the straight waveguide; (c) and (d) are the Ez electric field intensity distributions corresponding to the positions of the LCP light source and the RCP light source at the center of the boundary, respectively; (e) is a Z-shaped waveguide structure constructed with a 60° sharp bend; (f) is the Ez electric field intensity distribution of the Z waveguide; (g) is a Z-shaped defect waveguide in which cavities, disorder, confusion, impurities, and other defects are introduced in sequence on the transmission path; (h) is the Ez electric field intensity distribution of the Z-shaped defect waveguide structure; (i) is the transmission efficiency curve of the straight waveguide, the Z waveguide, and the Z-shaped defect waveguide.

[0031] Figure 6 (a) is a schematic diagram of a T-I type corner state structure; (b) is the intrinsic frequency of the T-I type corner state structure; (c) is the frequency and the corresponding E z electric field intensity distribution of the three C1 type corner states.

[0032] Figure 7 (a) is a schematic diagram of a T-II type corner state structure; (b) is the intrinsic frequency of the T-II type corner state structure; (c) is the frequency and the corresponding E z electric field intensity distribution of the three C2 type corner states.

[0033] Figure 8 (a) is a schematic diagram of a T-III type corner state structure; (b) is the intrinsic frequency of the T-III type corner state structure; (c) is the frequency and the corresponding E z electric field intensity distribution of the three C3 type corner states.

[0034] Figure 9 (a) is a schematic diagram of a T-IV type corner state structure; (b) is the intrinsic frequency of the T-IV type corner state structure; (c) is the frequency and the corresponding E z electric field intensity distribution of the three C4 type corner states.

[0035] Figure 10(a) is a schematic diagram of hourglass-shaped corner state structure; (b) is intrinsic frequency of hourglass-shaped corner state structure; (c) is frequency and corresponding E of C1, C2, C3 and C4 type corner state z Electric field intensity distribution; (d) is corresponding E of C1, C2, C3 and C4 type corner state z Electric field intensity curve.

[0036] Description of the figures: 10, primitive cell; 11, unit cell VPC1; 12, unit cell VPC2; 13, first type of circular ring silicon dielectric column; 14, second type of circular ring silicon dielectric column; 21, first crystal unit; 22, second crystal unit; 231, first edge state; 232, second edge state; 233, third edge state; 234, fourth edge state. DETAILED DESCRIPTION

[0037] The present application will be further described below in conjunction with the drawings and specific examples, so that those skilled in the art can better understand the present application and implement it, but the examples are not limiting to the present application.

[0038] As shown in the drawings, Figure 1 The present application provides a valley photonic crystal structure, which is formed by a plurality of regular hexagonal unit cells arranged in an array manner with the center of the cross section thereof diverging in six directions around it, the distance between the centers of adjacent regular hexagonal unit cells being a lattice constant a; a single regular hexagonal unit cell is formed by a first type of circular ring silicon dielectric column 13 and a second type of circular ring silicon dielectric column 14 uniformly placed in air, the first type of circular ring silicon dielectric column 13 and the second type of circular ring silicon dielectric column 14 being respectively arranged in a triangular lattice staggered manner to form a regular hexagonal basic unit, i.e., the first type of circular ring silicon dielectric column 13 and the second type of circular ring silicon dielectric column 14 are arranged alternately at the six vertices of the regular hexagon; wherein the outer radius of the first type of circular ring silicon dielectric column 13 is the same as that of the second type of circular ring silicon dielectric column 14, and the inner diameter of the first type of circular ring silicon dielectric column 13 is smaller than that of the second type of circular ring silicon dielectric column 14.

[0039] The valley photonic crystal structure of the present application is derived from a two-dimensional honeycomb valley photonic crystal structure. As shown in Figure 1 (a), the two-dimensional honeycomb valley photonic crystal structure is formed by circular ring-shaped silicon dielectric columns with a ring width W = R' - R uniformly placed in air with a period of a, a being a lattice constant, R' being the outer radius of the circular ring, and R being the inner radius of the circular ring. The regular hexagonal region represents a valley photonic crystal primitive cell 10, each primitive cell 10 containing six identical dielectric columns and having C6 rotational symmetry. A single honeycomb lattice can also be regarded as a composite of two triangular lattices, each lattice containing only A or B type atomic sites (rhombus region). In order to make the energy band of the valley photonic crystal have different properties at different valleys, it is necessary to break the spatial inversion symmetry of the structure while keeping the time inversion symmetry unchanged. As shown inFigure 1 (b) shown, all the medium column outer radius R' in the valley photonic crystal, the radius of the medium column in one of the triangular lattice of the unit cell is reduced so that the ring width is larger, the first type of ring silicon medium column 13 is obtained; the radius of the medium column in another triangular lattice of the unit cell is expanded so that the ring width is smaller, the second type of ring silicon medium column 14 is obtained. The unit cell when the upper vertex of the regular hexagon is the first type of ring silicon medium column is recorded as the unit cell VPC111, and the unit cell when the upper vertex of the regular hexagon is the second type of ring silicon medium column is recorded as the unit cell VPC212.

[0040] In an optional embodiment, the outer radius R' of the two-dimensional honeycomb valley photonic crystal structure is 100 nm, the inner radius R is 50 nm, and a is 600 nm. The inner radius R1 of the first type of ring silicon medium column is 19 nm, and R2 is 86 nm.

[0041] Figure 2 The photonic band structure diagrams of the unit cell, the unit cell VPC1 and the unit cell VPC2 are shown in Figure 2 (a) shown, at this time, the system is protected by time reversal and space reversal symmetries, the first and second energy bands are doubly degenerate at the K(K') point, thereby a Dirac point with a normalized frequency of 0.345c / a is generated. Figure 2 (a) is a schematic diagram of the first Brillouin zone of the honeycomb lattice unit cell, b1 and b2 are the reciprocal lattice vectors of the unit cell in the reciprocal space, Γ, K, K' and M are high symmetry points in the first Brillouin zone. The C6 rotational symmetry of the honeycomb lattice ensures that there is always a Dirac cone with a linear dispersion relationship near the K(K') point in the first Brillouin zone, which provides a platform for realizing topological valley transport of pseudo-spin and energy valley locking. The photonic band structure diagrams of the unit cell VPC1 and the unit cell VPC2 obtained by adjusting the ring width are shown in Figure 2 (b) shown, a photonic band gap with a normalized frequency of 0.309-0.439c / a is formed between the first and second energy bands.

[0042] As shown in Figure 3 The application further provides an optical waveguide composed of the topological photonic crystal structure as described above, which comprises a first crystal unit composed of a plurality of unit cells VPC1 and a second crystal unit composed of a plurality of unit cells VPC2.

[0043] As shown in Figure 3 (a) shown, the splicing boundary of the first crystal unit and the second crystal unit is in a "zig-zag" type, and the splicing boundary formed by the unit cell VPC1 above the unit cell VPC2 is a first edge state 231, recorded as Interface I; as Figure 3(b) as shown, the first crystal unit and the second crystal unit are "zig-zag" type at the splicing boundary, the cell VPC2 is above the cell VPC1 to form a splicing boundary, which is the second edge state 232, recorded as Interface II; in the "zig-zag" type splicing boundary, the medium column at the boundary of the cell VPC1 and the cell VPC2 is shared, and the medium column at the shared place is replaced for the convenience of manufacturing according to the principle of minority yielding to majority. The following is an example, such as Figure 3 (a) as shown, in the first edge state, the medium column at the boundary framed out is shared by two cell VPC1 and one cell VPC2; as the cell VPC1, the medium column at the place is the first type of circular ring silicon medium column; as the cell VPC2, the medium column at the place is the second type of circular ring silicon medium column, so after the cell VPC2 is spliced with the cell VPC1, the second type of circular ring silicon medium column in the cell VPC2 at the place is replaced by the first type of circular ring silicon medium column.

[0044] As shown in Figure 3 (c) as shown, the first crystal unit and the second crystal unit are "Bridge" type at the splicing boundary, the cell VPC1 is above the cell VPC2 to form a splicing boundary, which is the third edge state 233, recorded as Interface III; as shown in Figure 3 (d) as shown, the first crystal unit and the second crystal unit are "Bridge" type at the splicing boundary, the cell VPC2 is above the cell VPC1 to form a splicing boundary, which is the fourth edge state 234, recorded as Interface IV.

[0045] In order to verify the assumption of the existence of topological boundary state, the cell VPC1 and the cell VPC2 are spliced with each other to form a supercell structure as shown in Figure 4 (a) as shown, the splicing boundary of the supercell is "zig-zag" type. Figure 4 (b) is the photonic band structure of the supercell, there are two topological boundary states (blue dashed line and red dashed line) through the whole photonic band gap, and the gray line part is the bulk state. The slope of the curve represents the propagation direction of the topological boundary state, and the two topological boundary states have opposite slopes at the K valley and the K' valley, that is, the frequency of the pseudo-spin downward state is higher than that of the pseudo-spin upward state at the K valley, and the frequency of the pseudo-spin upward state is higher than that of the pseudo-spin downward state at the K' valley.

[0046] In order to explore the characteristics of the topological boundary state, A, B and C points in Figure 4 (b) are analyzed for their intrinsic fields E z As shown in Figure 4(c) are shown. As can be seen from the figures, the electric field of the A point eigenstate is mainly localized at the first edge state, and the electric field of the B point and C point eigenstates is mainly localized at the second edge state. In both cases, the energy is concentrated at the interface of the photonic crystal with different topological properties, and rapidly decays along the inside of the crystal from the middle to both sides, thereby realizing the localization of the optical field.

[0047] Figure 4 (d) are the Poynting vector distributions of the energies of the A, B and C points. As can be seen from the figures, the pseudo-spin downward state of the K valley only transmits along the Γ-K direction, that is, to the left, and the pseudo-spin upward state of the K' valley only transmits along the Γ-K' direction, that is, to the right. Thus, valley polarization light selectivity appears, that is, the K valley and the K' valley are selective to left circular polarization (LCP) light and right circular polarization (RCP) light, respectively, and thus the valley polarization light selective coupling and transmission of the pseudo-spin and the energy valley can be realized.

[0048] In order to verify that the structure has stable anti-scattering unidirectional transmission capability and strong robustness, the present application sequentially constructs a straight waveguide, a Z waveguide and a Z-defect waveguide formed by simultaneously introducing four defects, and places four point light sources at the interface of VPC1 and VPC2. The four point light sources are uniformly distributed on a circle with a radius of 0.03a, and by controlling their phase difference, LCP or RCP light can be formed as an excitation source of electric field. Figure 5 (a) is a straight waveguide structure constructed; Figure 5 (b) is the Ez electric field intensity distribution of the straight waveguide when the frequency of the excitation source is 156.9THz, wherein the yellow pentagram indicates the position of the RCP light source. It can be seen that the RCP light transmits to the right along the boundary, and has stable anti-scattering characteristics; Figure 5 (c) and Figure 5 (d) are the Ez electric field intensity distributions corresponding to the positions of the LCP light source and the RCP light source at the center of the boundary, respectively. The LCP light transmits to the left, and the RCP light transmits to the right, thereby showing good unidirectionality.

[0049] When light is transmitted in a traditional micro-nano photonic device, it will inevitably encounter disturbances such as large-angle turning and defects, which will reduce the transmission efficiency of light in the photonic device, while the topological photonic device has strong robustness to the above problems. Figure 5 (e) is a Z-shaped waveguide structure with a 60° sharp bend constructed, Figure 5 (f) shows the Ez transmission electric field of the Z-shaped waveguide, which fully proves the anti-interference characteristics of the structure in the case of large-angle turning. As Figure 5 (g) shows that cavities are sequentially introduced on the transmission path of the Z-shaped waveguide,Figure 5 (g) in ①), disorder Figure 5 (g) in ②), confusion Figure 5 (g) in ③), impurities Figure 5 (g) in ④) and other defects, forming a Z-shaped defect waveguide structure; Figure 5 (h) embodies that the structure can still maintain stable transmission capacity. Finally, from Figure 6 (i) it can be seen that the transmission efficiency of the three waveguides can reach more than 98% in the frequency range of 155-173 THz, having strong transmission capacity.

[0050] The application further provides an angular state structure composed of the optical waveguide, the angular state structure comprising: an inner layer crystal unit composed of one of the unit cells VPC1 and the unit cell VPC2; and an outer layer crystal unit arranged around the inner layer crystal unit and composed of one of the unit cells VPC1 and the unit cell VPC2, and the unit cell constituting the outer layer crystal unit is different from the unit cell constituting the inner layer crystal unit; wherein the top angle of the boundary where the inner layer crystal unit and the outer layer crystal unit are spliced is 60°.

[0051] In an optional embodiment, the area boundary of the inner layer crystal unit is a regular triangle.

[0052] In order to better observe the topological angular state, a double-layer equilateral triangle supercell structure is constructed, and the area boundary of the inner layer crystal unit of the structure has three 60° top angles. The structure is composed of 45 VPC1 surrounded by 145 VPC2, and the inner layer side length is 10a and the outer layer side length is 20a. The reason for designing this shape is that the formation of the angular state has a selective rule for the internal angle of the structure, which can be explained as the result of the interaction between the valleys. And this structure contains 3 60° angles, and each angle can form an angular state.

[0053] As Figure 6 shown, the boundary state at the boundary where the inner layer crystal unit and the outer layer crystal unit are spliced is a first edge state, a perfect electric conductor (Performance, Efficiency and Comfort, PEC) boundary condition is applied to the outermost part of the structure, and a T-I type angular state structure is formed, as Figure 6 (a) shown. Figure 6 (b) is the intrinsic frequency of the T-I type angular state structure, and the boundary state (blue dot) and the angular state (red dot) exist between the whole body state (gray dot) photonic bandgap (the upper body state appears outside the given frequency coordinate range), and the angular state is isolated. Three C1 type angular states of the T-I type angular state structure are marked as C11, C12 and C13. Figure 7 (c) shows the frequency (178.6 THz) and Ez The electric field of each corner state is only localized in the sublattice on the corner and presents exponential decay along the region away from the corner. Due to the mutual interference of the spatial electric fields of the three corner states in the tight-binding model, the frequencies of the three C1-type corner states are not completely degenerate, and there is a slight frequency difference. However, the good corner localization characteristics, which are significantly different from the boundary state, are fully embodied.

[0054] As shown in Figure 7 , the boundary state at the boundary where the inner crystal unit and the outer crystal unit are spliced is a second edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure, and a T-II type corner state structure is formed, as shown in Figure 7 (a). Figure 7 (b) is the eigenfrequency of the T-II type corner state structure, and the three C2-type corner states of the T-II type corner state structure are marked as C21, C22, and C23, respectively. Figure 8 (c) shows the frequencies (166.8 THz) and E z electric fields of the three C2-type corner states. As can be seen from the figure, the C2-type corner state still exists in isolation, but compared with the C1-type corner state, the frequency has a great change. We found in our previous research on corner states that although the generation of corner states has different principles, all corner states will appear in the photonic band gap of the whole bulk state, so we can generally consider that changing the boundary type of the topological structure will not only change the frequency range of the boundary state, but also change the frequency of the corner state.

[0055] As shown in Figure 8 , the boundary state at the boundary where the inner crystal unit and the outer crystal unit are spliced is a third edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure, and a T-III type corner state structure is formed, as shown in Figure 8 (a). Figure 8 (b) is the eigenfrequency of the T-III type corner state structure, and the three C3-type corner states of the T-III type corner state structure are marked as C31, C32, and C33, respectively. Figure 9 (c) shows the frequencies (188.6 THz) and E z electric fields of the three C3-type corner states. As can be seen from the figure, changing the boundary type of the topological structure will change the frequency of the corner state.

[0056] As shown in Figure 9 , the boundary state at the boundary where the inner crystal unit and the outer crystal unit are spliced is a fourth edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure, and a T-IV type corner state structure is formed, as shown in Figure 9 (a). Figure 9(b) is the eigenfrequency of the T-IV type corner state structure, and the three C4 type corners of the T-IV type corner state structure are marked as C41, C42 and C43 respectively. Figure 10 (c) shows the frequency (169.2 THz) and E z electric field. As can be seen from the figure, changing the boundary type of the topological structure will change the frequency of the corner state.

[0057] In another optional embodiment, as shown in Figure 10 (a), the area boundary of the inner layer crystal unit is a sandglass shape formed by superimposing two equilateral triangles, and the sandglass shape has four 60° corners. The corner state structure is divided into a first quadrant, a second quadrant, a third quadrant and a fourth quadrant with the center of the corner state structure as the origin, wherein the boundary state at the boundary between the inner layer crystal unit and the outer layer crystal unit in the first quadrant is a third edge state, the boundary state at the boundary between the inner layer crystal unit and the outer layer crystal unit in the second quadrant is a first edge state, the boundary state at the boundary between the inner layer crystal unit and the outer layer crystal unit in the third quadrant is a fourth edge state, and the boundary state at the boundary between the inner layer crystal unit and the outer layer crystal unit in the fourth quadrant is a second edge state. Figure 10 (b) is the eigenfrequency of the sandglass type corner state structure obtained by calculation, wherein the corner state in the first quadrant is marked as C1, the corner state in the second quadrant is marked as C2, the corner state in the third quadrant is marked as C3, and the corner state in the fourth quadrant is marked as C4; Figure 10 (c) is the frequency and E z electric field of the C1, C2, C3 and C4 type corner states. The four corner states can be selectively excited on the corresponding inner corner region of the funnel type boundary. ​ (d) is the E z electric field intensity curve measured by placing a domain probe on each inner corner. As can be seen from the figure, each topological corner state has a unique high-intensity electric field at the corresponding frequency, proving its excellent corner localization characteristics.

[0058] Obviously, the above embodiments are only examples for the purpose of clarity, and are not limiting of the embodiments. For those skilled in the art, other different forms of changes or variations can be made on the basis of the above description. Here, it is not necessary and impossible to exhaust all the embodiments. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. An optical waveguide, characterized by, The photonic crystal structure is composed of a plurality of hexagonal cells arranged in an array with the center of the cross section diverging to the surrounding six directions, and the distance between the centers of adjacent hexagonal cells is a lattice constant a; each of the hexagonal cells is composed of a first type of circular ring silicon dielectric column and a second type of circular ring silicon dielectric column uniformly placed in air, and the first type of circular ring silicon dielectric column and the second type of circular ring silicon dielectric column are arranged in a triangular lattice staggered manner to form a hexagonal basic unit, that is, the first type of circular ring silicon dielectric column and the second type of circular ring silicon dielectric column are arranged alternately at the six vertices of the hexagon; wherein the outer radius of the first type of circular ring silicon dielectric column and the second type of circular ring silicon dielectric column is the same, and the inner diameter of the first type of circular ring silicon dielectric column is smaller than the inner diameter of the second type of circular ring silicon dielectric column; the cell at the upper vertex of the hexagon is denoted as VPC1 when the first type of circular ring silicon dielectric column is arranged at the upper vertex of the hexagon, and the cell at the upper vertex of the hexagon is denoted as VPC2 when the second type of circular ring silicon dielectric column is arranged at the upper vertex of the hexagon; the optical waveguide comprises a first crystal unit composed of a plurality of cells VPC1 and a second crystal unit composed of a plurality of cells VPC2; the splicing boundary of the first crystal unit and the second crystal unit is in a "zig-zag" type or a "Bridge" type; When the boundary is in a "zig-zag" type, the boundary formed by the cell VPC1 above the cell VPC2 is a first edge state, and the boundary formed by the cell VPC2 above the cell VPC1 is a second edge state; when the boundary is in a "Bridge" type, the boundary formed by the cell VPC1 above the cell VPC2 is a third edge state, and the boundary formed by the cell VPC2 above the cell VPC1 is a fourth edge state; the optical waveguide is one of a straight waveguide, a Z waveguide or a Z type defect waveguide.

2. An angular structure, characterized in that The optical waveguide is composed of the optical waveguide of claim 1, and the corner state structure comprises: an inner layer crystal unit composed of one of the cell VPC1 and the cell VPC2; an outer layer crystal unit located outside the boundary of the region of the inner layer crystal unit and composed of one of the cell VPC1 and the cell VPC2, and the cell constituting the outer layer crystal unit is different from the cell constituting the inner layer crystal unit; wherein the top angle of the boundary of the region of the inner layer crystal unit is 60°.

3. The angular structure of claim 2, wherein, The boundary of the region of the inner layer crystal unit is a regular triangle.

4. The angular structure of claim 3, wherein, The boundary state at the boundary of the splicing of the inner layer crystal unit and the outer layer crystal unit is a first edge state, a perfect electrical conductor boundary condition is applied to the outermost part of the structure to form a T-I type corner state structure; when the excitation frequency is 178.61 THz, the corner state C11 is excited; when the excitation frequency is 178.62 THz, the corner state C12 or the corner state C13 is excited; the corner state C11, the corner state C12 and the corner state C13 are respectively located at the three vertices of the regular triangle.

5. The angular structure of claim 3, wherein, The boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit is a second edge state, perfect electric conductor boundary conditions are applied to the outermost part of the structure, and a T-II type corner state structure is formed; when the excitation frequency is 166.80 THz, the corner state C21 is excited, and the corner state C21 is located at one vertex of the equilateral triangle; when the excitation frequency is 166.86 THz, the corner state C22 is excited; when the excitation frequency is 166.88 THz, the corner state C23 is excited; the corner states C22 and C23 are located at the other two vertices different from the corner state C21.

6. The angular structure of claim 3, wherein, The boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit is a third edge state, perfect electric conductor boundary conditions are applied to the outermost part of the structure, and a T-III type corner state structure is formed; when the excitation frequency is 188.59 THz, the corner state C31 is excited, and the corner state C31 is located at two vertices of the equilateral triangle; when the excitation frequency is 188.60 THz, the corner state C32 is excited, and the corner state C32 is located at one vertex of the equilateral triangle different from the corner state C31; when the excitation frequency is 188.61 THz, the corner state C33 is excited, and the corner state is located at three vertices of the equilateral triangle.

7. The angular structure of claim 3, wherein, The boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit is a fourth edge state, perfect electric conductor boundary conditions are applied to the outermost part of the structure, and a T-IV type corner state structure is formed; when the excitation frequency is 169.24 THz, the corner state C41 is excited, and the corner state C41 is located at one vertex of the equilateral triangle; when the excitation frequency is 169.25 THz, the corner state C42 or the corner state C43 is excited, and the corner states C42 and C43 are located at the other two vertices different from the corner state C41.

8. The angular structure of claim 2, wherein, The region boundary of the inner layer crystal unit is a sandglass shape formed by superimposing two equilateral triangles, and the corner state structure is divided into a first quadrant, a second quadrant, a third quadrant and a fourth quadrant with the center of the corner state structure as the origin; Wherein, the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the first quadrant is a third edge state, the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the second quadrant is a first edge state, the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the third quadrant is a fourth edge state, and the boundary state at the boundary where the inner layer crystal unit is spliced with the outer layer crystal unit in the fourth quadrant is a second edge state; when the excitation frequency is 178.62 THz, the corner state C1 in the first quadrant is excited; when the excitation frequency is 188.59 THz, the corner state C3 in the second quadrant is excited; when the excitation frequency is 169.28 THz, the corner state C4 in the third quadrant is excited; when the excitation frequency is 166.97 THz, the corner state C2 in the fourth quadrant is excited.

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