Photonic crystal resonant cavity, laser and resonant frequency tuning method

Abstract

The invention belongs to the technical field of photonic crystals, and discloses a photonic crystal resonant cavity, a laser and a resonant frequency tuning method. A Dirac photonic crystal is inserted into a domain wall of a spin-Hall topological cavity to obtain a photonic crystal resonant cavity, the photonic crystal resonant cavity composed of a region A, a region B and a region C is obtained, and a photonic crystal laser can be further manufactured; wherein the region B is a Dirac photonic crystal, and the region A and the region C are a topological non-trivialness photonic crystal and a topological trivialness photonic crystal respectively; primitive cell energy band structures of the photonic crystals in the region A and the region C are aligned; the resonant frequency of the photonic crystal resonant cavity and the number of primitive cells in the region B are linearly changed; the invention provides a simple and effective strategy which is used for finely regulating and controlling the resonant frequency of the photonic crystal resonant cavity and also can realize linear tuning frequency, so that a potential application prospect is provided for a dense wavelength division multiplexing technology of a multi-channel optical filter and a high-performance semiconductor laser array.

Description

Technical Field

[0001] The present invention belongs to the technical field of photonic crystals, and more specifically, relates to a photonic crystal resonant cavity, a laser, and a resonance frequency tuning method. Background Art

[0002] Dense multi-wavelength resonant cavity arrays have important applications in multi-channel optical communications, signal processing, photonic computing, and sensing. An ideal dense multi-wavelength resonant cavity array is one in which the frequency or wavelength of each cavity is determined during the design phase. Multiple cavities generate a dense, equally spaced spectrum covering a specific spectral range with small frequency spacing (e.g., 100 GHz). This densely distributed multi-wavelength resonant cavity array can be fabricated in one go through micro-nanofabrication. Current resonant cavity frequency tuning faces the following challenges: 1) Due to limitations in fabrication precision, precisely controlling the inherent resonant frequency by adjusting the cavity's geometric parameters is challenging in practice, especially in the short wavelength range. 2) While frequency tuning based on varying the cavity size is feasible, the so-called size-effect method exhibits nonlinear frequency tuning and a relatively limited tuning range. Consequently, precise frequency (or wavelength) control of photonic resonant cavity arrays is difficult, often requiring compensation for frequency drift through heating or current changes, which significantly increases the size and design complexity of the resonant cavity array. Topological photonics is a cutting-edge research field focused on exploring various physical mechanisms and optical phenomena in topological photonic structures, laying the foundation for innovative applications of optical materials and photonic devices. One of the most important applications in this field is the design of on-chip optical resonators. By leveraging the unique properties of topologically protected optical modes, it is possible to achieve specialized control of the resonant characteristics of optical cavities, solving problems that are difficult to overcome using conventional photonic device design principles. However, there is no prior research on how to use topological photonics to adjust the frequency (or wavelength) of photonic resonant cavity arrays. Therefore, expanding the application of topological photonics to frequency (or wavelength) adjustment of photonic resonant cavity arrays has great research value. Summary of the Invention

[0003] The present invention solves the problem in the prior art that the resonant mode frequency in the photonic crystal cavity cannot be accurately and linearly tuned by providing a photonic crystal resonant cavity, a laser and a resonant frequency tuning method.

[0004] In a first aspect, the present invention provides a method for tuning the resonant frequency of a photonic crystal resonant cavity. A Dirac photonic crystal is inserted into the domain wall of a spin-Hall topological cavity to obtain a photonic crystal resonant cavity. The resonant frequency of the photonic crystal resonant cavity is adjusted by adjusting the number of Dirac photonic crystals.

[0005] Preferably, the method of inserting a Dirac photonic crystal into the domain wall of a spin-Hall topological cavity to obtain a photonic crystal resonant cavity comprises the following steps: According to the different distribution of primitive structures in the original cell, the photonic crystal resonant cavity is divided into three areas: A, B, and C from the inside to the outside; The lattice constant of the primitive cell is determined according to the working wavelength of the photonic crystal resonant cavity, and a number of elementary structures are distributed in each primitive cell; Designing the primitive cell of region B, setting the duty cycle, determining the size of the elementary structure within the primitive cell of region B by the duty cycle, and adjusting the position of the elementary structure within the primitive cell to make region B a Dirac photonic crystal; The primitive cells of regions A and C are designed by adjusting the center of gravity of the primitive structure based on the primitive cell of region B to form primitive cells of regions A and C, respectively. Regions A and C are topologically nontrivial photonic crystals and topologically trivial photonic crystals, respectively. Determine whether there is resonance of dipole mode and quadrupole mode in regions A and C. If not, reset the duty cycle to design the primitive cells of regions A, B, and C.

[0006] Preferably, the unit cell types include triangular lattice, tetragonal lattice, hexagonal lattice, honeycomb lattice, and cage lattice.

[0007] Preferably, the primitive structure within the protocell is a dielectric column or air hole having a refractive index lower than that of the matrix material.

[0008] Preferably, the shape of the protocellular intracellular motif structure is circular, triangular, trapezoidal or crescent-shaped.

[0009] Preferably, in the primitive cell design of region B, when the Dirac cone dispersion curve cannot be obtained by adjusting the position of the primitive structure within the primitive cell, the Dirac cone dispersion curve is obtained by changing the duty cycle and then readjusting the position of the primitive structure. The condition for obtaining the Dirac cone dispersion curve is that the coupling strength between primitive cells is equal to the coupling strength within the primitive cell.

[0010] Preferably, during the design of the unit cells of regions A and C, the unit cells of regions A and C are obtained by translating the primitive structure close to and away from the center of the unit cell, respectively, and the band structures of the unit cells of the photonic crystals of regions A and C are aligned.

[0011] Preferably, after determining the primitive cell design of regions A and C, the optimal adjustment range of the Dirac point is determined by the band gap width of regions A and C, and the optimal adjustment range of the primitive structure size is determined by the optimal adjustment range of the Dirac point.

[0012] In a second aspect, the present invention provides a frequency-tunable photonic crystal resonant cavity, which is designed using the above-mentioned resonant frequency tuning method. During the design process, the resonant frequency of the photonic crystal resonant cavity is adjusted by adjusting the number of unit cells of the Dirac photonic crystal in region B.

[0013] In a third aspect, the present invention provides a frequency-tunable photonic crystal laser, wherein the photonic crystal laser has the above-mentioned frequency-tunable photonic crystal cavity.

[0014] One or more technical solutions provided in the present invention have at least the following technical effects or advantages: This invention provides a method for tuning the frequency by adjusting the Dirac photonic crystal domain within a topological laser cavity. Specifically, after inserting a Dirac photonic crystal (Dirac PC) into the domain wall of a spin-Hall topological cavity, the resonant frequencies of the dipole and quadrupole modes exhibit a linear relationship with the number of unit cells of the Dirac PC, rather than nonlinear frequency scaling due to size effects. This phenomenon is attributed to the uniform expansion of modes in a linear dispersion medium. The effectiveness of this mechanism was further verified through systematic numerical simulations and tight-binding calculations of a nontrivial-Dirac-trivial cavity. The results show that by adjusting the frequency of the Dirac point relative to the photonic crystal band gap, the frequency tuning coefficient can be effectively controlled. Furthermore, the linear frequency scaling principle was verified in a slab of an actual suspended photonic crystal cavity, and the tuning mechanism has minimal impact on the far-field radiation spot. This mechanism can be directly applied to adjust the operating frequency of on-chip topological cavities, topological lasers, or other resonant devices by simply varying the domain wall size (i.e., the number of unit cells) of the Dirac PC, significantly reducing the complexity of experimental fabrication. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0016] Figure 1 The figure is a flow chart of the resonant frequency tuning method of the photonic crystal resonant cavity of the present invention.

[0017] Figure 2 Schematic diagram of the photonic crystal resonant cavity structure in an embodiment of the present invention, which consists of A (topologically non-trivial), B (Dirac) and C (topologically trivial) domains.

[0018] Figure 3 Schematic diagram of a detailed portion of the A-Dirac-C topological cavity. The inter- and intra-primitive-cell coupling strengths are denoted as t1 and t2 (domain A), t3 (domain B), and t4 and t5 (domain C), respectively.

[0019] Figure 4 Schematic diagram of Dirac photonic crystal unit cell with different triangular air hole sizes; Figure 5 For A-Dirac-C: The band diagram of the unit cell in the topological cavity, where Figure 5 (d) in the figure is the energy band diagram of the Dirac photonic crystal unit cell; Figure 5 (e) is the energy band diagram of the topological trivial photonic crystal unit cell; Figure 5 (f) in the figure is the band diagram of the topological nontrivial photonic crystal unit cell.

[0020] Figure 6 (a) is the superimposed band diagram of three different photonic crystal domains, and the Dirac cone dispersion curve is represented by a gray dashed line; Figure 6 (b) shows the relationship between the frequency scaling of quadrupole and dipole modes and the number of inserted primitive cells of Dirac photonic crystal and topological nontrivial A photonic crystal; Figure 6 (c) in the figure is the electric field intensity of the quadrupole and dipole modes in the AC topological cavity ( )distributed; Figure 6 (d) A-Dirac-C: The electric field strength of the quadrupole and dipole modes in the topological cavity ( ) distribution, there are 180 Dirac primitive cells between the A / C domains; Figure 6 (e) in Figure 6 (c) The normalized electric field intensity of the quadrupole mode along the white dashed line ( ) distribution. Domains A, B, and C are represented by different colors; Figure 6 (f) in Figure 6 (c) The normalized electric field intensity of the dipole mode along the white dashed line ( ) distribution. Domains A, B, and C are represented by different colors; Figure 6 (g) in Figure 6 (d) The normalized electric field intensity of the quadrupole mode along the white dashed line ( ) distribution. Domains A, B, and C are represented by different colors; Figure 6 The (h) in Figure 6 (d) The normalized electric field intensity of the dipole mode along the white dashed line ( ) distribution. Domains A, B, and C are represented by different colors; Figure 7 (a) is the superposition band diagram of different photonic crystal domains. The size of the triangular air hole in the Dirac photonic crystal ( - ) causes the Dirac point to move; Figure 7 (b) in the figure shows different triangular air hole sizes ( - ) The relationship between the number of primitive cells of the Dirac photonic crystal and the frequency scaling of the quadrupole and dipole resonance modes; Figure 7 (c) is the theoretical prediction of the frequency scaling law of quadrupole and dipole resonance modes based on tight binding calculations; Figure 7 (d) in the equation is A-Dirac-C: - (N=414) The electric field strength of the dipole mode in the topological cavity ( )distributed; Figure 7 (e) in Figure 7 The corresponding normalized electric field intensity along the white dashed line in (d) is )distributed; Figure 7 Where (f) is A-Dirac-C: - The electric field strength of the quadrupole mode in the (N=414) topological cavity ( )distributed; Figure 7 (g) in Figure 7 The corresponding normalized electric field intensity along the white dashed line in (e) is ) distribution. Domains A, B, and C are marked with different colors.

[0021] Figure 8 (a) shows the number of primitive cells of Dirac photonic crystals and topological nontrivial photonic crystals inserted into the three-dimensional PC cavity as a function of the frequency scaling of the dipole and quadrupole resonance modes; Figure 8 (b) is the far-field distribution of the dipole mode in the AC topological cavity; Figure 8 (c) in the equation is AC: A (N=414) Far-field distribution of dipole modes in a topological cavity; Figure 8 (d) in the equation is A-Dirac-C: (N=414) Far-field distribution of dipole modes in a topological cavity; Figure 8 (e) in the figure is the far-field distribution of the quadrupole mode in the AC topological cavity; Figure 8 Where (f) is AC: A (N=414) Far-field distribution of quadrupole modes in a topological cavity; Figure 8 Where (g) is A-Dirac-C: (N=414) Far-field distribution of quadrupole modes in a topological cavity; Figure 8 The (h) in Figure 8 (b) to Figure 8 (d) Normalized far-field intensity distribution corresponding to the far-field distribution of the dipole mode in the topological cavity; Figure 8 The (i) in Figure 8 (e) to Figure 8 (g) Normalized far-field intensity distribution corresponding to the far-field distribution of the quadrupole mode in the topological cavity. DETAILED DESCRIPTION

[0022] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0023] In the description of the present invention, it should be noted that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "back," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer" and the like, indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0024] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "connected" and "connection" should be understood in a broad sense. For example, they can refer to fixed connection, detachable connection, or integral connection; mechanical connection, electrical connection; direct connection, or indirect connection through an intermediary. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0025] Example 1: Example 1 provides a method for tuning the resonant frequency of a photonic crystal resonant cavity, wherein a Dirac photonic crystal is inserted into a domain wall of a spin-Hall topological cavity to obtain a photonic crystal resonant cavity; and then the resonant frequency of the photonic crystal resonant cavity is adjusted by adjusting the number of Dirac photonic crystals. The method specifically includes the following steps: S100, dividing the photonic crystal resonant cavity into three regions A, B, and C from the inside to the outside according to the different distribution of the primitive structures in the original cell; S200, determining a lattice constant of a primitive cell according to an operating wavelength of the photonic crystal resonant cavity, wherein a plurality of elementary structures are distributed in each primitive cell; S300, designing a primitive cell in region B, setting a duty cycle, determining the size of the primitive structure in the primitive cell in region B by the duty cycle, and adjusting the position of the primitive structure in the primitive cell to make region B a Dirac photonic crystal; S400, design of primitive cells in regions A and C. Based on the primitive cell in region B, the center of gravity of the elementary structure is adjusted to form primitive cells in regions A and C, respectively. Regions A and C are non-topologically trivial photonic crystals and topologically trivial photonic crystals, respectively, and have the same band gap frequency range. S400, determining whether there are dipole modes and quadrupole modes in regions A and C. If not, resetting the duty cycle to perform primitive cell design in regions A, B, and C; S500 , adjusting the resonant frequency of the photonic crystal resonant cavity by adjusting the number of unit cells of the Dirac photonic crystal in region B.

[0026] After inserting the Dirac photonic crystal into the domain wall of the spin-Hall topological cavity, the present invention unexpectedly discovered that the resonant frequencies of the dipole and quadrupole modes show a linear relationship with the number of unit cells of the Dirac photonic crystal. Therefore, by adjusting the number of unit cells of the Dirac photonic crystal, the resonant frequency of the photonic crystal resonant cavity can be accurately and simply adjusted to meet the frequency tuning requirements of using it as a photonic crystal laser.

[0027] It should be noted that the unit cell of the present invention can be designed in any photonic crystal material, the unit cell matrix material can be a high refractive index material commonly used in the prior art, such as silicon, gallium arsenide, and silicon nitride, and the elementary structure material can be a low refractive index material commonly used in the prior art, such as air, silicon dioxide, polymer, and aluminum oxide. The specific details of the present invention will not be elaborated.

[0028] The unit cell types include triangular lattice, tetragonal lattice, hexagonal lattice, honeycomb lattice, and cage lattice; the shape of the unit cell structure is circular, triangular, trapezoidal, or crescent-shaped.

[0029] In step S300, when the position of the primitive structure in the primitive cell cannot be adjusted to obtain the Dirac cone dispersion curve, the position of the primitive structure is readjusted after changing the duty cycle to obtain the Dirac cone dispersion curve. The condition for obtaining the Dirac cone dispersion curve is that the coupling strength between primitive cells is equal to the coupling strength within the primitive cell.

[0030] In step S400, the primitive cells of region A and region C are obtained by translating the primitive structure close to and away from the center of the primitive cell, respectively. The band structures of the primitive cells of the photonic crystals in region A and region C are aligned. After the band structures of the primitive cells of the photonic crystals in region A and region C are aligned, impedance matching occurs between region A and region C, so that the mode field of the photonic crystal resonant cavity can be effectively confined to the center of the cavity; at the same time, based on the primitive cell of region B, the primitive cells of region A and region C are obtained by translating inward and outward, which can also ensure that the Dirac point in the band structure of the primitive cell of region B (Dirac photonic crystal) is located at the center of the photonic band gap between region A and region C.

[0031] It should be noted that, for the photonic crystal types of region A and region C, region A can be a topological non-trivial photonic crystal and region C can be a topological trivial photonic crystal, or region A can be a topological trivial photonic crystal and region C can be a topological non-trivial photonic crystal, as long as the band structures of region A and region C are aligned.

[0032] The present invention will be described below by taking silicon as the matrix material and six triangular air holes in the honeycomb lattice as the elementary structure as an example.

[0033] See also Figure 2 First, a topological laser cavity consisting of three different photonic crystal regions is constructed. The three different photonic crystal regions are arranged in an array according to the same lattice period (the lattice period of the photonic crystals in the three regions is set to a) and are divided into region A, region B and region C; the region B is located in the middle layer of the topological laser cavity and is a Dirac photonic crystal. Its inter-cell coupling strength is equal to its intra-cell coupling strength. The region A is a topological non-trivial photonic crystal. Its inter-cell coupling strength is greater than its intra-cell coupling strength. The region C is a topological trivial photonic crystal. Its inter-cell coupling strength is less than its intra-cell coupling strength.

[0034] The topological laser cavity is named A-Dirac-C topological cavity. The cavity presents a hexagonal photonic crystal (PC) structure, such as Figure 2 shown.

[0035] According to the working wavelength of the photonic crystal resonator The lattice constant of the primitive cell is determined by the material type of the primitive cell (which determines the refractive index difference between the primitive cell and the primitive structure) , and determine that the lattice type of the primitive cell is a hexagonal lattice, the primitive cells are composed of high refractive index medium plates (such as silicon), and the basic unit structure type is determined to be triangular air holes, which are arranged in the form of hexamer in the primitive cell; Figure 3 shown.

[0036] Unit cell design for region B: Duty cycle of given triangular air holes , the side length of a single triangular air hole is calculated by the duty cycle: ; Adjust the distance between the triangular air hole and the center of the cell , so that the coupling strength between the unit cells is equal to the coupling strength within the unit cell, and the coupling strength is t3, forming a Dirac photonic crystal; for example, the distance between the triangular air hole and the center of the unit cell is ; Brillouin zone center There are two degenerate Dirac cones at the point, such as Figure 5 (d), and each linear dispersion curve reflects the hybrid characteristics of the dipole mode and the quadrupole mode. If the Dirac cone dispersion curve cannot be obtained, it means that the given duty cycle does not match the unit cell design. The duty cycle needs to be re-given until the Dirac cone dispersion curve can be obtained. For example, the duty cycle of the given triangular air hole is , lattice constant , calculated , set the distance between the triangular air hole and the center of the unit cell to By drawing the energy band diagram, it is found that there is a Dirac point, that is, the area B of this design parameter is a Dirac photonic crystal; and under this design parameter, the center of the Brillouin zone There are two degenerate Dirac cones at the point, and each linear dispersion curve reflects the hybrid characteristics of the dipole mode and the quadrupole mode, such as Figure 5 (d) shows the Dirac frequency =123 THz.

[0037] Design of primitive cells in regions A and C: Based on the primitive cell in region B, the center of gravity of the primitive structure is adjusted to form primitive cells in regions A and C, where regions A and C are topologically nontrivial photonic crystals and topologically trivial photonic crystals, respectively. For example, the air holes in the unit cell of region B are moved outward. When the triangular air holes in the unit cell are moved inward (domain C) and outward (domain A) to reduce the structural symmetry, the degeneration of the Γ point can be achieved. The imbalance of the coupling strength within the unit cell and between the units further triggers different topological phase transitions. When the inter-unit cell coupling strength (t4) is less than the intra-unit cell coupling strength (t5), region C exhibits mediocre topological phase characteristics. Specifically, the band edge modes of the two energy bands surrounding the band gap correspond to degenerate dipole modes and quadrupole modes, respectively. On the contrary, when the inter-unit cell coupling strength (t1) is greater than the intra-unit cell coupling strength (t2), the center of the Brillouin zone of the innermost structure region A The band inversion phenomenon will occur at the point, thus inducing a non-trivial topological phase. The distance between the triangular air hole and the center of the unit cell is calculated as follows: , K is the center of gravity movement coefficient of the triangular air hole.

[0038] For example, the distance between the triangular air hole and the center of the unit cell is set to: , we can get the cell parameters of region C, and the energy band diagram is as follows Figure 5 As shown in (e), after translating the triangular air hole, the band gap in the band diagram opens, and the Dirac point in region B is guaranteed to be located in the middle of the band gap in region C.

[0039] By setting the distance between the triangular air hole and the center of the unit cell to: , we can get the unit cell parameters of region A, and the energy band diagram is as follows Figure 5 As shown in (f), after translating the triangular air hole, the band gap in the band diagram opens, and the Dirac point in region B is guaranteed to be located in the middle of the band gap in region A. Figure 5 (f), the center of the Brillouin zone At the same time, through the above parameter design, the energy band structure heights of region A and region C are aligned.

[0040] After determining the primitive cell design for regions A and C, the optimal adjustment range of the Dirac point is determined by the band gap width of regions A and C. This optimal adjustment range of the Dirac point also determines the optimal adjustment range of the primitive structure size. It is important to emphasize that the Dirac point needs to avoid alignment with the mode frequencies of regions A and C.

[0041] The present invention further studies the resonant frequency scaling characteristics of the above-mentioned A-Dirac-C topological cavity, where the size of the triangular air hole in the Dirac photonic crystal (PC) is set to ;like Figure 6 (a) shows the energy band diagram of three different photonic crystal regions. Since the energy band of the unit cell in region A is The energy band inversion occurs near the point, the quadrupole mode is at the lower energy band edge of the band gap, and the dipole mode is at the upper energy band edge of the band gap, which is consistent with the C region unit cell at The band-edge modes of the upper and lower bands of the band gap near a point are reversed. Based on this property, the present invention constructs an AC topological cavity consisting of nine layers of topologically nontrivial region A photonic crystals and ten layers of topologically trivial region C photonic crystals (i.e., region A has nine layers of unit cells from the inside out, and region C has ten layers of unit cells from the inside out). The impedance mismatch at the topological interface of the AC topological cavity effectively confines the two band-edge modes of region A (quadrupole and dipole modes) to the innermost layer. Based on this cavity structure, the present invention proposes a design scheme that embeds a Dirac photonic crystal (PC) with a specified number of unit cells (forming region B) along the A / C topological interface, namely, an A-Dirac-C topological cavity.

[0042] During the development of this invention, the focus was on the fundamental mode properties near the upper and lower band edges of the infinite topological non-trivial structure photonic crystal (region A). Since the linear dispersion curve exhibits hybrid characteristics of dipole and quadrupole modes, the optical mode field can be extended to the Dirac photonic crystal region. Specifically, the dipole and quadrupole fundamental modes exhibit excellent spatial localization performance in the structure and maintain the highest quality factor in all states. In addition, the Dirac photonic crystal does not need to surround region A with an integer multiple of the Dirac photonic crystal layer. The number of Dirac photonic crystal units can be flexibly adjusted without significantly affecting the above-mentioned mode characteristics. This characteristic can be attributed to the robustness of the topological structure.

[0043] The frequencies of both dipole and quadrupole modes can be linearly scaled by the number of Dirac photonic crystal units, i.e., the domain size of the Dirac photonic crystal. To more clearly describe the changes in the cavity structure, the present invention adds a topologically nontrivial photonic crystal unit cell at the A / C topological interface of the AC topological cavity. This topological cavity is named AC: A Type topological cavity; AC: A The type cavity is compared with the A-Dirac-C topological cavity, such as Figure 6 As shown in (b), Figure 6 (b) shows the dependence of the number of inserted topological nontrivial photonic crystal and Dirac photonic crystal units on the frequency of quadrupole and dipole modes, respectively. As more topological nontrivial photonic crystal units are added at the A / C topological interface, AC: A The frequency of the dipole (quadrupole) mode in the A-Dirac-C topological cavity changes nonlinearly, shifting downward (upward) due to the size effect. When the Dirac photonic crystal unit cell is inserted along the A / C topological interface, the frequency of the dipole (quadrupole) mode also shifts downward (upward), showing an abnormal linear scaling relationship. In A-Dirac-C: The size of the triangular air hole in the topological cavity (A-Dirac-C topological cavity) is set to ), the resonant frequencies of the dipole and quadrupole modes can be linearly scaled with the increase of the number of unit cells. This linear scaling law greatly simplifies the difficulty of frequency tuning and improves the accuracy of frequency tuning.

[0044] Although the introduction of the Dirac photonic crystal does not change the characteristics of the band-edge mode resonances in the topological cavity, it affects the electric field strength of these modes ( ) distribution. Figure 6 As shown in (c) and (d), in the AC topology cavity and A-Dirac-C: (N=180 cells in region B) In the topological cavity, the field distribution of the dipole and quadrupole modes is mainly concentrated in region A. However, for A-Dirac-C: In the topological cavity, the electric field extends to the surrounding Dirac photonic crystal (region B), and the field intensity changes ( Figure 6 (d)). More intuitive results are as follows Figure 6 (e)- Figure 6 (h) shows the normalized electric field strength of different modes ( )along Figure 6 The white dashed lines in (c) and (d) are extracted. Compared with the initial AC topology cavity, A-Dirac-C: The normalized field distribution of the topological cavity shows electric field intensity distribution in the Dirac photonic crystal region for both quadrupole and dipole modes.

[0045] In addition, the present invention further discovered during the research process that the resonance frequency tuning coefficient of the topological band edge mode is significantly affected by the position of the Dirac cone frequency point relative to the photonic band gap in region A / C, and this relative position is determined by the size of the triangular air hole in the Dirac photonic crystal. While ensuring that the design parameters of the unit cell in regions A and C remain unchanged and the lattice period in region B remains unchanged, the size of the triangular air hole is continuously scaled, and the scaling process is carried out with As the center, increase or decrease several points, and get 、 、 、 、 、 Design the size of the triangular air hole and draw the energy band diagram, such as Figure 7 As shown in (a); it can be seen that the Dirac point gradually moves from 128.55 THz to 116.84 THz, spanning the entire band gap of the photonic crystal in region A. Figure 7 (b) shows the number of Dirac photonic crystal unit cells A-Dirac-C: The influence of the frequencies of the quadrupole and dipole resonance modes in a topological cavity. A-Dirac-C: Topological cavities also have Figure 6 (b) shows the linear frequency scaling law, but the tuning coefficient of the dipole mode decreases, while the tuning coefficient of the quadrupole mode increases. When the size of the triangular air hole is ( ), the Dirac point is exactly aligned with the dipole (quadrupole) mode frequency in the original AC topological cavity. This causes the resonant frequency of the dipole (quadrupole) mode to remain almost constant. However, if the Dirac point is moved above (below) the dipole (quadrupole) mode band edge by adjusting the size of the triangular air hole, then in A-Dirac-C: ( ) topological cavity, the dipole (quadrupole) mode frequencies will shift upward (downward) in the opposite direction and be nonlinearly tuned with the insertion of the Dirac photonic crystal unit cell. Figure 7 (c) shows the number of Dirac photonic crystal units A-Dirac-C calculated using the tight binding model: - The influence of the frequency of the quadrupole and dipole resonance modes in the topological cavity, the changing rules and Figure 7 (b) shows the same change pattern. Therefore, the optimal adjustment range of the unit structure size is ~ , and does not include the two endpoints.

[0046] Figure 7 (d) shows the A-Dirac-C 、 、 (Number of unit cells in region B is N=414) Electric field strength of the dipole mode of the topological cavity distributed. Figure 7 (e) shows the corresponding normalization along the white dashed line As the Dirac point moves downward, the frequency of the dipole mode decreases and its electric field pattern expands outward. Similarly, A-Dirac-C: - Electric field strength of quadrupole modes in a (N=414) topological cavity Distribution and normalization along the white dashed line The distribution is as follows Figure 7 As shown in (f) and (g), as the Dirac point moves upward from below the lower band edge, the frequency of the quadrupole mode gradually increases, and its electric field mode expands outward. The expansion of the mode into the Dirac photonic crystal is due to the phase matching condition between the two internal photonic crystal domains. For A-Dirac-C: (N=414) topological cavity, a significant part of the field is coupled to region C, which may be due to the The significant bending of the energy band dispersion at the point is caused by Figure 7 (a). Therefore, the better range of size is ~ (including the end points), that is, the size of the triangular air hole is ~ When the frequency is adjusted, it has a better frequency tuning coefficient, or the frequency adjustment is more precise and sensitive.

[0047] For the application of linear frequency scaling laws in photonic devices such as topological photonic crystal lasers, it is necessary to consider the actual photonic structure and the impact of frequency tuning on other emission properties. Figure 8 (a) Shows the frequency variation of the dipole and quadrupole modes as the number of Dirac photonic crystal and topologically nontrivial photonic crystal units (corresponding to the AC topological cavity and A-Dirac-C topological cavity, respectively) is increased in a three-dimensional topological cavity with a photonic crystal slab structure. As the number of Dirac units increases from 0 to 414, the frequency of the dipole (quadrupole) mode decreases (increases) monotonically, similar to the two-dimensional A-Dirac-C: The situation of topological cavity is similar (see Figure 6 (b)). This verifies the applicability of linear frequency scaling law in precise and fine laser frequency tuning. The present invention also studies AC topological cavity, AC: A Topological cavity (N=414) and A-Dirac-C: Far-field emission of dipole and quadrupole modes in a (N=414) topological cavity. Figure 8 (b)–(d) show the Fourier transformed far-field distribution of the dipole mode, where the AC topological cavity and A-Dirac-C: (N = 414) topological cavities have similar single-lobe intensity distributions. In A-Dirac-C: In the (N=414) topological cavity, the divergence angle of the dipole mode is small, which is mainly due to the large size of the resonant cavity. In contrast, the far-field intensity distribution of the quadrupole mode forms a ring-shaped contour with a divergence angle of less than 5°. This is a typical emission feature of bound states in the continuum (BIC). Figure 8 As shown in (e)-(g), for AC topological cavity and A-Dirac-C: (N=414) topological cavity, there are side rings with weaker field strength, and for AC: A The beam quality of the topological cavity (N=414) is slightly reduced, and the side ring intensity is stronger. These results indicate that inserting a Dirac cell at the A / C topological interface can maintain the far-field emission mode and slightly reduce the divergence angle.

[0048] Example 2: The present invention also protects a photonic crystal resonant cavity, such as Figure 2 As shown, the topological laser cavity includes three regions A, B, and C from the inside to the outside, which are composed of different photonic crystals. The photonic crystals in the three regions A, B, and C have the same period, wherein region B is a Dirac photonic crystal, region A is a topological non-trivial photonic crystal, and region C is a topological trivial photonic crystal, or region A is a topological trivial photonic crystal, and region C is a topological non-trivial photonic crystal; the photonic band gaps of region A and region C are aligned.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for tuning the resonance frequency of a photonic crystal resonant cavity, characterized in that: A photonic crystal resonant cavity is obtained by inserting a Dirac photonic crystal into the domain wall of a spin-Hall topological cavity. The resonant frequency of the photonic crystal resonant cavity can be adjusted by adjusting the number of primitive cells of the Dirac photonic crystal.

2. The method for tuning the resonance frequency of a photonic crystal resonant cavity according to claim 1, wherein: The method for obtaining a photonic crystal resonant cavity by inserting a Dirac photonic crystal into a domain wall of a spin-Hall topological cavity comprises the following steps: According to the different distribution of primitive structures in the original cell, the photonic crystal resonant cavity is divided into three areas: A, B, and C from the inside to the outside; The lattice constant of the primitive cell is determined according to the working wavelength of the photonic crystal resonant cavity, and a number of elementary structures are distributed in each primitive cell; Designing the primitive cell of region B, setting the duty cycle, determining the size of the elementary structure within the primitive cell of region B by the duty cycle, and adjusting the position of the elementary structure within the primitive cell to make region B a Dirac photonic crystal; The primitive cells of regions A and C are designed by adjusting the center of gravity of the primitive structure based on the primitive cell of region B to form primitive cells of regions A and C, respectively. Regions A and C are topologically nontrivial photonic crystals and topologically trivial photonic crystals, respectively. Determine whether there is resonance of dipole mode and quadrupole mode in regions A and C. If not, reset the duty cycle to design the primitive cells in regions A, B, and C.

3. The method for tuning the resonance frequency of a photonic crystal resonant cavity according to claim 2, wherein: The unit cell types include triangular lattice, tetragonal lattice, hexagonal lattice, honeycomb lattice, and cage lattice.

4. The method for tuning the resonance frequency of a photonic crystal resonant cavity according to claim 2, wherein: The primitive structure within the original cell is a dielectric column or air hole with a refractive index lower than that of the matrix material.

5. The method for tuning the resonance frequency of a photonic crystal resonant cavity according to claim 2, wherein: The shape of the primitive structure within the protocell is circular, triangular, trapezoidal or crescent.

6. The method for tuning the resonance frequency of a photonic crystal resonant cavity according to claim 2, wherein: In the primitive cell design of region B, when the Dirac cone dispersion curve cannot be obtained by adjusting the position of the primitive structure within the primitive cell, the Dirac cone dispersion curve can be obtained by changing the duty cycle and then readjusting the position of the primitive structure. The condition for obtaining the Dirac cone dispersion curve is that the coupling strength between primitive cells is equal to the coupling strength within the primitive cell.

7. The method for tuning the resonance frequency of a photonic crystal resonant cavity according to claim 2, wherein: During the design process of the primitive cells of regions A and C, the primitive cells of regions A and C are obtained by translating the primitive structure close to and away from the center of the primitive cell, respectively, and the band structures of the primitive cells of the photonic crystals in regions A and C are aligned.

8. The method for tuning the resonance frequency of a photonic crystal resonant cavity according to claim 2, wherein: After determining the primitive cell designs of regions A and C, the optimal adjustment range of the Dirac point is determined by the band gap widths of regions A and C, and the optimal adjustment range of the primitive structure size of region B is determined by the optimal adjustment range of the Dirac point.

9. A frequency-tunable photonic crystal resonant cavity, characterized in that: The resonant frequency tuning method according to any one of claims 1 to 8 is used for designing. During the design process, the resonant frequency of the photonic crystal resonant cavity is adjusted by adjusting the number of primitive cells of the Dirac photonic crystal in region B.

10. A frequency tunable photonic crystal laser, characterized in that: The photonic crystal laser has the frequency-tunable photonic crystal resonant cavity as claimed in claim 9 .

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