A photonic crystal structure with complex unit cell and optical waveguide
By designing complex unit cell structures and using the methods of compressing, stretching and rotating the dielectric columns, the energy band inversion and topological phase transition of topological photonic crystals are achieved, and the problem of single photonic band gap regulation method in the existing technology is solved, and the problem of enhanced The local performance and application value of optical area.
Patent Information
- Application Number
- CN202210231668.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-09
- Publication Date
- 2024-12-10
- Estimated Expiration
- 2042-03-09
AI Technical Summary
When the existing topological photonic crystal structure realizes energy band inversion and topological phase transition, the dielectric column has a single regulation method, a small photonic band gap, lacks flexibility, and makes it difficult to build rich topological boundary states and practical applications.
A photonic crystal structure of complex unit cells was designed. By compressing and stretching unit cells, changing the cross-sectional diameter and rotating daughter cells of the medium column, band reversing and topological phase transition were achieved, and topological to topological non-mediocre crystal structure was constructed. , increase the size and regulation method of photon band gap.
It achieves higher freedom of topological structure, rich topological phase transition methods, enhances optical local performance, suppresses backscattering, and has greater application value.
Smart Images
Figure CN114660719B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of topological photonic crystals, and in particular to a photonic crystal structure and an optical waveguide with a complex unit cell. Background Art
[0002] The discovery of the optical integer quantum Hall effect and quantum spin Hall effect in condensed matter physics has opened up a new research direction - optical topological insulators. A solution to realize topological states has been proposed. In optical systems, topological photonic crystal research has a strong application prospect, especially the unidirectional transmission and defect immunity properties of topological states, which can be used in topological photonic devices such as differentiators, hubs, and optical isolators.
[0003] The photon spin Hall effect is based on paired topological boundary states protected by time reversal symmetry, and the key is to achieve Kramers degeneracy. Photons do not have spin degrees of freedom, so pseudospins need to be constructed in the photon system. Currently, six dielectric columns are mainly used to construct a honeycomb unit cell with C6 symmetry, and a double Dirac cone is realized in the band gap of the honeycomb unit cell. Compression and stretching of the honeycomb unit cell can achieve band inversion and topological phase transition. This implementation method is too simple, there are not many ways to control the photon band gap, and the opened photon band gap is not large. Summary of the invention
[0004] In view of the shortcomings of the prior art, the present invention designs a photonic crystal structure with a complex unit cell, and an optical waveguide constructed by the photonic crystal structure. Based on the photonic crystal structure with a complex unit cell, three different methods can be used to achieve band inversion and topological phase transition, such as compression and stretching of the unit cell, changing the cross-sectional diameter of the dielectric column, and rotating the unit cell, thereby constructing a topologically mediocre to topologically non-trivial crystal structure; and the photonic band gap is larger and the photon localization performance is strong. Compared with the existing unit cell structure, the complex unit cell proposed by the present invention has a higher degree of freedom, more abundant ways to achieve topological phase transition, and is easier to apply in practice.
[0005] The present invention achieves the above technical objectives through the following technical means:
[0006] A photonic crystal structure with a complex unit cell, characterized in that the complex unit cell is composed of 6 sub-cells arranged in a C6 structure, and the cross-section is a regular hexagonal structure; a plurality of complex unit cells are adjacent to each other and arranged in an array to form the photonic crystal structure, and the distance between the centers of two adjacent complex unit cells is a lattice constant a;
[0007] The sub-cell is formed by parallel arrangement with the axes of a first dielectric column with a cross-sectional diameter of 2r1 and two second dielectric columns with a cross-sectional diameter of 2r2 located at the three vertices of an equilateral triangle respectively, and the side length of the equilateral triangle is L = 0.14a;
[0008] In the complex unit cell, the distance from the center of the complex unit cell to the center of the equilateral triangle of the sub-cell in the complex unit cell is R; it is defined that the placement angle where the first dielectric column in the sub-cell is located at the position closest to the center of the complex unit cell and the distances from the two second dielectric columns to the center of the complex unit cell are the same is 0°, and the angle by which the sub-cell rotates clockwise with the center of the unit cell as the rotation center is θ, and the value range of θ is 0 to 60°.
[0009] Furthermore, the materials of the first dielectric column and the second dielectric column are both silicon, and the lattice constant a = 1000 nm.
[0010] Furthermore, on the premise of r1 = r2 and θ = 0°:
[0011] The photonic crystal structure that satisfies the condition has double Dirac cones;
[0012] The photonic crystal structure that satisfies the condition PC1 has topologically non-trivial properties;
[0013] The photonic crystal structure that satisfies the condition PC2 has topologically trivial properties.
[0014] Furthermore, on the premise of θ = 0°,
[0015] The photonic crystal structure PC3 that satisfies the condition r1 < r2 has topologically non-trivial properties;
[0016] The photonic crystal structure PC4 that satisfies the condition r1 > r2 has topologically trivial properties.
[0017] Furthermore, on the premise of r1 = r2, the premise of
[0018] The photonic crystal structure that satisfies the condition θ = 12° or θ = 48° has double Dirac cones;
[0019] The photonic crystal structure PC5 that satisfies the condition 12° < θ < 48° has topologically trivial properties;
[0020] The photonic crystal structure PC6 that satisfies the conditions 0° < θ < 12° and 48° < θ < 60° has topologically non-trivial properties.
[0021] The optical waveguide constructed with the photonic crystal structure having a complex unit cell is characterized in that it is composed of a photonic crystal structure PC1 having a topologically non-trivial property and a photonic crystal structure PC2 having a topologically trivial property, and there is an interface between the two.
[0022] Furthermore, r1=r2=0.04a, the photonic crystal structure PC1 The photonic crystal structure PC2 The working bandwidth of the optical waveguide is 0.662-0.691 (2πc / a), where c is the speed of light.
[0023] The optical waveguide constructed with the photonic crystal structure having a complex unit cell is characterized in that it is composed of a photonic crystal structure PC3 having a topologically non-trivial property and a photonic crystal structure PC4 having a topologically trivial property, and there is an interface between the two.
[0024] Further, θ=0°, r1=0.09a, r2=0.04a of the photonic crystal structure PC3; r1=0.04a, r2=0.07a of the photonic crystal structure PC4; the working bandwidths of the optical waveguides are 0.485-0.515 (2πc / a) respectively.
[0025] The optical waveguide constructed by the photonic crystal structure with complex unit cells is characterized by being composed of a photonic crystal structure PC5 with topological non-trivial properties and a photonic crystal structure PC6 with topological trivial properties, and having an interface between the two. Further, r1=r2=0.04a, The θ of the photonic crystal structure PC5 is 0°; the θ of the photonic crystal structure PC6 is 15°; the working bandwidths of the optical waveguides are 0.68-0.70 (2πc / a) respectively. In the above scheme, the material used for the circular dielectric column is silicon.
[0026] In the above scheme, the lattice constant a=1000nm.
[0027] Compared with the topological photonic crystal optical waveguide structure previously constructed using simple unit cells, the present invention has the following beneficial effects:
[0028] Traditional topological photonic structures based on the C6 structure can only achieve topological phase transitions by changing the distance between the center of the dielectric column and the unit cell. The complex unit cell proposed in the present invention has a higher degree of freedom and can achieve Dirac degeneracy and topological phase transitions by compressing and stretching the unit cell, changing the cross-sectional diameter of the dielectric column, and rotating the unit cell.
[0029] This complex unit cell structure has a large photonic band gap, which can be changed by adjusting the lattice constant, the size of the dielectric column, the materials of the background and dielectric column, and the angle of the dielectric column. The regulation method is also richer and more flexible, which is more conducive to the construction of topological boundary states and practical applications. Compared with previous studies, this flexible topological system shows richer physical phenomena, enriches the realization of topological photonics, and promotes our research on topological boundary states and the development of topological insulators in practical applications.
[0030] A topological photonic crystal waveguide structure is constructed using topologically trivial and topologically nontrivial unit cells with a larger common photonic band gap constructed using complex unit cells. Electromagnetic waves within the working bandwidth can be transmitted unidirectionally along the topologically trivial and nontrivial interfaces, light localization is enhanced and backscattering is suppressed, and the structure is highly immune to sharp bends and defects.
[0031] Optical waveguide structures constructed using complex unit cells can construct topologically trivial and non-trivial interfaces by changing the size and position of dielectric columns, thereby changing the transmission of electromagnetic waves within the working bandwidth, which has great application value in practice. BRIEF DESCRIPTION OF THE DRAWINGS
[0032] Figure 1 (a) is a schematic diagram of the structure of the complex unit cell constructed by the present invention, wherein the lattice vector and (b) When r1 = r2 = 0.04a, θ = 0°, Energy band diagram of the complex unit cell when .
[0033] Figure 2 (a) is PC1 (r1 = r2 = 0.04a, ) has a topologically trivial property; (b) is the band diagram of PC2 (r1 = r2 = 0.04a, ), which has topological non-trivial properties, and the black rectangle is their common bandwidth. (c) and (d) represent the topological phase transition process from PC1 to PC2.
[0034] Figure 3 (a) is PC3 (r1 = 0.09a, r2 = 0.04a, ) has a topologically trivial property. (b) is the band diagram of PC4 (r1 = 0.04a, r2 = 0.07a, ), which has topological non-trivial properties. The black rectangle is their common bandwidth. (c) and (d) represent the topological phase transition process of PC3-PC4.
[0035] Figure 4 (a) is PC5 (r1 = r2 = 0.04a, θ=0°), which has topological trivial properties; (b) is the band diagram of PC6 (r1=r2=0.04a, The band diagram of θ=15°) has topological non-trivial properties, and the black rectangular part is their common bandwidth. (c) Represents the topological phase transition process of PC5-PC6. (d) When the rotation angle θ and ω p and ω d The relationship between them is that area I represents topological non-trivial, and area II represents topological trivial.
[0036] Figure 5 (a) Phase diagram with rotation angle θ and lattice constant a / R; (b) r2 / r1 and ω pd Phase diagram of the system, and the relationship between r2 / r1 and |Δω|. Region I represents topological nontriviality, and region II represents topological triviality.
[0037] Figure 6 (a)-(c) Dispersion curves of supercells constructed using PC1 and PC2, PC3 and PC4, and PC5 and PC6, respectively. There is a pair of topologically protected edge states in the photonic band gap. (d)-(f) Z-shaped waveguides constructed using PC1 and PC2, PC3 and PC4, and PC5 and PC6 simulate a point source. In the Z-shaped waveguide unidirectional transmission (S + Right circularly polarized light source, S - Left circularly polarized light source). DETAILED DESCRIPTION
[0038] The design of the present invention is further described in detail below in conjunction with the description of the accompanying drawings and specific implementation methods.
[0039] Figure 1 (a) shows the complex unit cell structure designed by the present invention, wherein the complex unit cell is composed of 6 sub-cells arranged in a C6 structure, and the cross-section is a regular hexagonal structure; multiple complex unit cells are adjacent to each other and arranged in an array to form the photonic crystal structure, and the distance between the centers of two adjacent complex unit cells is the lattice constant a.
[0040] The daughter cell is composed of a first medium column with a cross-sectional diameter of 2r1 and two second medium columns with a cross-sectional diameter of 2r2, the axes of which are respectively located at three vertices of an equilateral triangle and arranged in parallel, and the side length of the equilateral triangle is L=0.14a.
[0041] In the complex unit cell, the distance from the center of the complex unit cell to the center of the subcell equilateral triangle in the complex unit cell is R; the first dielectric column in the subcell is located closest to the center of the complex unit cell, and the two second dielectric columns are at the same distance from the center of the complex unit cell. The angle of rotation of the subcell clockwise around the unit cell center is θ, and the value range of θ is 0 to 60°. The key to realizing the photon spin Hall effect is to realize Kramers degeneracy. During the topological phase change, the band gap will undergo a process of opening-merging-opening. The double Dirac cone is the topological phase transition point. When the double Dirac cone separates, a photonic band gap will be opened. If the upper energy band is similar to the d orbital and the lower energy band is similar to the p orbital, the structure behaves as a topologically trivial structure; if the upper energy band is similar to the p orbital and the lower energy band is similar to the d orbital, the structure behaves as a topologically non-trivial structure.
[0042] In this embodiment, the lattice constant a=1000 nm, the materials of the first dielectric column and the second dielectric column are both silicon, and r1=r2=0.04a. Figure 1 (b) is the parameter state and θ=0°, The energy band diagram of the complex unit cell when ω p =ω d , the P band and the d band are degenerate, a double Dirac cone appears, and the structure appears as a honeycomb lattice. Figure 1 As shown in (c), when the rotation angle of the daughter cell is θ = 12°, When , double Dirac cones also appear in the band diagram of its unit cell, and the structure also behaves as a honeycomb lattice.
[0043] Based on the proposed complex unit cell, the present invention statistically analyzes the relationship between the three topological phase transition mechanisms and structural parameters. It is found that Dirac degeneracy and topological phase transition can be achieved by compressing and stretching the unit cell, changing the cross-sectional diameter of the dielectric column, and rotating the subcell. Specifically:
[0044] (1) Compression and stretching of unit cells
[0045] Under the premise of r1=r2:
[0046] Satisfy the conditions The photonic crystal structure with θ = 0° has a double Dirac cone;
[0047] Satisfy the conditions The photonic crystal structure PC1 with θ = 0° has topological nontrivial properties;
[0048] Satisfy the conditions The photonic crystal structure PC2 with θ=0° has topologically trivial properties.
[0049] Specific experimental data such as Figure 2 As shown, by changing the size of R, its topological properties are changed to achieve topological phase transition. When ω p < ω d , PC1 exhibits topologically trivial properties; when ω p > ω d , PC2 exhibits topologically non-trivial properties.
[0050] (2) Changing the cross-sectional diameter of the dielectric column
[0051] Under the premise of θ = 0°:
[0052] The photonic crystal structure PC3 that satisfies the condition r1 < r2 has topologically non-trivial properties;
[0053] The photonic crystal structure PC4 that satisfies the condition r1 > r2 has topologically trivial properties.
[0054] Specific experimental data are as Figure 3 shown. When ω, the topological properties can be changed by changing the size of the dielectric column to achieve topological phase transition. When r1 = 0.09a and r2 = 0.04a, p < ω d , PC3 exhibits topologically trivial properties; when r1 = 0.04a and r2 = 0.07a, p > ω d , PC4 exhibits topologically non-trivial properties.
[0055] (3) Rotating the sub-cell
[0056] Under the premise of r1 = r2, ω,
[0057] The photonic crystal structure PC5 that satisfies the condition 12° ≤ θ < 48° has topologically trivial properties;
[0058] The photonic crystal structure PC6 that satisfies the condition 0° < θ < 12° or 48° < θ < 60° has topologically non-trivial properties.
[0059] Specific experimental data are as Figure 2 (c) shown. By changing the rotation angle θ of the dielectric column, its topological properties are changed to achieve topological phase transition. When θ = 0°, p < ω d , PC5 exhibits topologically trivial properties; when θ = 15°, p > ω d , PC6 exhibits topologically non-trivial properties.
[0060] By compressing and stretching the standard honeycomb unit cell, changing the size of the dielectric column or changing the rotation angle of the dielectric column, the topological properties of the complex unit cell can be changed to achieve a topological phase transition.
[0061] In order to further explore the relationship between the three methods to achieve topologically trivial and non-trivial states and structural parameters, the variable ω is introduced. pd and |Δω|, where |Δω|=|ω d -ω p |,ω d and ω p Respectively represent the characteristic frequencies of the d-band and p-band at the Γ point; ω pd The positive (negative) value of |Δω| indicates topological triviality (non-triviality), and the size of |Δω| indicates the size of the photonic band gap.
[0062] like Figure 5 As shown in (a), for methods (1) and (3), combined with parameters and the rotation angle θ, the topological properties of the structure are explored. Region I represents topological non-triviality, and region II represents topological triviality. When , the structure shows topological trivial properties; when When , the transformation from topological trivial to topological non-trivial can be achieved through rotation.
[0063] For method (2), When pd >0, the structure exhibits topologically trivial properties; when When pd <0, the structure exhibits topological non-trivial properties. When the value of is far away from 1, the value of |Δω| becomes larger and larger, which means that the larger the gap between r1 and r2, the larger the photonic band gap of the structure.
[0064] By combining a photonic crystal structure with topologically nontrivial properties and a photonic crystal structure with topologically trivial properties to construct an optical waveguide with an interface, a topologically protected spiral boundary state will appear at the interface of two different topological properties. The present invention uses PC1 and PC2, PC3 and PC4, and PC5 and PC6 to construct topologically trivial and topologically nontrivial interfaces respectively. Figure 6 As shown in (a)(b)(c), there are spiral boundary states in the photonic band gap, and their operating bandwidths are 0.662-0.691(2πc / a), 0.485-0.515(2πc / a) and 0.68-0.70(2πc / a), respectively, where c is the speed of light.
[0065] The present invention uses PC1 and PC2, PC3 and PC4, and PC5 and PC6 to construct a topological optical waveguide structure. Since the topological boundary state has the property that light is robustly transmitted unidirectionally at the interface of two photonic crystals with different topological properties, light cannot be transmitted at the interface in other regions due to the existence of photonic band gaps. Figure 6 As shown in (d)-(f), an electromagnetic wave excited by a point source carrying negative orbital angular momentum propagates in a unidirectional "Z" shape to the right along the interface. The electromagnetic wave is mainly localized near the interface, is immune to sharp bends, and has almost no backscattering and transmission loss. In practical applications, the size and position of the working bandwidth can be controlled by changing the parameters of the complex unit cell.
[0066] The above is only a specific example of the present invention, but the present invention is not limited to the above embodiment, such as changing the parameters of the complex unit cell, using this structure to design a topological beam splitter and using an encoder to achieve control of the optical flow path transmission, etc. All structures directly associated with the content disclosed in the present invention should be within the protection scope of the present invention.
Claims
1. An optical waveguide constructed with a photonic crystal structure having a complex unit cell, characterized in that: The complex unit cell is formed by arranging 6 sub-cells in a C6 structure, and its cross-section is a regular hexagon structure; multiple complex unit cells are adjacent to each other edge to edge and arranged in an array to form the photonic crystal structure, and the distance between the centers of two adjacent complex unit cells is the lattice constant a; The sub-cell is formed by arranging a first dielectric column with a cross-sectional diameter of 2r1 and two second dielectric columns with a cross-sectional diameter of 2r2 in parallel, and the axes of the two second dielectric columns are located at the three vertices of an equilateral triangle respectively, and the side length of the equilateral triangle is L = 0.14a; In the complex unit cell, the distance from the center of the complex unit cell to the center of the equilateral triangle of the sub-cell in this complex unit cell is R; it is defined that the placement angle when the first dielectric column in the sub-cell is located at the position closest to the center of the complex unit cell and the distances from the two second dielectric columns to the center of the complex unit cell are the same is 0°, and the angle by which the sub-cell rotates clockwise with the center of the unit cell as the rotation center is θ, and the value range of θ is 0 to 60°; On the premise of r1 = r2 and θ = 0°: Satisfy the conditions The photonic crystal structure has a double Dirac cone; Satisfy the conditions The photonic crystal structure PC1 has topological non-trivial properties; Satisfy the conditions The photonic crystal structure PC2 has topologically trivial properties; The optical waveguide is composed of a photonic crystal structure PC1 with topological non-trivial properties and a photonic crystal structure PC2 with topological trivial properties, and there is an interface between the two; r1=r2=0.04a, the photonic crystal structure PC1 The photonic crystal structure PC2 The working bandwidth of the optical waveguide is 0.662(2πc / a) to 0.691(2πc / a), wherein c is the speed of light.
2. An optical waveguide constructed with a photonic crystal structure having a complex unit cell, characterized in that: The complex unit cell is formed by arranging 6 sub-cells in a C6 structure, and its cross-section is a regular hexagon structure; multiple complex unit cells are adjacent to each other edge to edge and arranged in an array to form the photonic crystal structure, and the distance between the centers of two adjacent complex unit cells is the lattice constant a; The sub-cell is formed by arranging a first dielectric column with a cross-sectional diameter of 2r1 and two second dielectric columns with a cross-sectional diameter of 2r2 in parallel, and the axes of the two second dielectric columns are located at the three vertices of an equilateral triangle respectively, and the side length of the equilateral triangle is L = 0.14a; In the complex unit cell, the distance from the center of the complex unit cell to the center of the equilateral triangle of the sub-cell in this complex unit cell is R; it is defined that the placement angle when the first dielectric column in the sub-cell is located at the position closest to the center of the complex unit cell and the distances from the two second dielectric columns to the center of the complex unit cell are the same is 0°, and the angle by which the sub-cell rotates clockwise with the center of the unit cell as the rotation center is θ, and the value range of θ is 0 to 60°; exist On the premise of The photonic crystal structure PC3 that satisfies the condition r1 < r2 has topological non-trivial properties; The photonic crystal structure PC4 that satisfies the condition r1 > r2 has topological trivial properties; The optical waveguide is composed of a photonic crystal structure PC3 with topological non-trivial properties and a photonic crystal structure PC4 with topological trivial properties, and there is an interface between the two; The photonic crystal structure PC3 has r1==0.09a, r2=0.04a; the photonic crystal structure PC4 has r1=0.04a, r2=0.07a; the working bandwidth of the optical waveguide is 0.485 (2πc / a) to 0.515 (2πc / a).
3. An optical waveguide constructed with a photonic crystal structure having a complex unit cell, characterized in that: The complex unit cell is formed by arranging 6 sub-cells in a C6 structure, and its cross-section is a regular hexagon structure; multiple complex unit cells are adjacent to each other edge to edge and arranged in an array to form the photonic crystal structure, and the distance between the centers of two adjacent complex unit cells is the lattice constant a; The sub-cell is formed by arranging a first dielectric column with a cross-sectional diameter of 2r1 and two second dielectric columns with a cross-sectional diameter of 2r2 in parallel, and the axes of the two second dielectric columns are located at the three vertices of an equilateral triangle respectively, and the side length of the equilateral triangle is L = 0.14a; In the complex unit cell, the distance from the center of the complex unit cell to the center of the subcell equilateral triangle in the complex unit cell is R; the placement angle at which the first dielectric column in the subcell is located closest to the center of the complex unit cell and the two second dielectric columns are at the same distance from the center of the complex unit cell is defined as 0°, and the angle at which the subcell rotates clockwise with the unit cell center as the rotation center is θ, and the value range of θ is 0 to 60°; When r1=r2, On the premise of The photonic crystal structure that meets the condition of θ=12° or θ=48° has a double Dirac cone; The photonic crystal structure PC5 that meets the condition 12°<θ<48° has topologically trivial properties; The photonic crystal structure PC6 that meets the conditions 0°<θ<12° and 48°<θ<60° has topological non-trivial properties; The optical waveguide is composed of a photonic crystal structure PC5 with topological non-trivial properties and a photonic crystal structure PC6 with topological trivial properties, and there is an interface between the two; r1=r2=0.04a, The θ of the photonic crystal structure PC5 is 0°; the θ of the photonic crystal structure PC6 is 15°; the working bandwidth of the optical waveguide is 0.68 (2πc / a) to 0.70 (2πc / a).
4. The optical waveguide according to any one of claims 1 to 3, characterized in that: The first dielectric column and the second dielectric column are both made of silicon, and the lattice constant a=1000nm.