Photonic crystal resonator, laser and method for tuning resonance frequency

Abstract

The application belongs to the technical field of photonic crystals, and discloses a photonic crystal resonant cavity, a laser and a resonant frequency tuning method. The photonic crystal resonant cavity is obtained by inserting a Dirac photonic crystal into a domain wall of a spin-Hall topological cavity, and the photonic crystal resonant cavity is composed of a region A, a region B and a region C. Further, a photonic crystal laser can be manufactured. The region B is a Dirac photonic crystal, and the regions A and C are a topological non-trivial photonic crystal and a topological trivial photonic crystal, respectively. The primitive cell band structure of the photonic crystals in the regions A and C is aligned. The resonant frequency of the photonic crystal resonant cavity linearly changes with the number of primitive cells of the region B. A simple and effective strategy is provided for fine regulation of the resonant frequency of the photonic crystal resonant cavity, and linear tuning of the frequency can also be realized. This provides potential application prospects for multi-channel optical filters and dense wavelength division multiplexing technology of high-performance semiconductor laser arrays.

Description

Technical Field

[0001] This invention belongs to the field of photonic crystal technology, and more specifically, relates to a photonic crystal resonant cavity, a laser, and a method for tuning the resonant frequency. Background Technology

[0002] Dense multi-wavelength resonant cavity arrays have important applications in multi-channel optical communication, signal processing, photonic computing, and sensing. An ideal dense multi-wavelength resonant cavity array refers to an array where the frequency or wavelength of each resonator is determined during the design phase. Multiple resonators generate densely spaced, equally spaced spectra covering a certain spectral range with small frequency intervals (e.g., 100 GHz). This array is fabricated in a single step using micro- and nano-fabrication techniques to create a densely distributed, equally spaced multi-wavelength resonant cavity array. Currently, resonant cavity frequency tuning faces the following challenges: 1) Due to limitations in manufacturing precision, accurately controlling the inherent resonant frequency by adjusting the resonant cavity's geometric parameters presents significant challenges in practical operation, especially in the short wavelength range. 2) While the so-called size effect method, which adjusts the frequency by changing the cavity size, is feasible, its frequency tuning exhibits nonlinear characteristics and has a relatively limited tuning range. Therefore, precise frequency (or wavelength) control of photonic resonant cavity arrays is very difficult, often requiring compensation for frequency drift through heating or changing current, which greatly increases the size and design complexity of the resonant cavity array. Topological photonics is a cutting-edge research field that focuses on exploring various physical mechanisms and optical phenomena in topological photonic structures, laying the foundation for innovative applications of optical materials and photonic devices. Among these, on-chip optical resonator design is one of the most important applications. By utilizing the unique properties of topologically protected optical modes, special modulation of the resonant characteristics of optical cavities can be achieved, solving problems that are difficult to overcome in conventional photonic device design principles. However, how to use topological photonics to adjust the frequency (or wavelength) of photonic resonator arrays is not currently studied. Therefore, expanding the application of topological photonics to frequency (or wavelength) adjustment of photonic resonator arrays has significant research value. Summary of the Invention

[0003] This invention provides a photonic crystal resonator, a laser, and a resonant frequency tuning method, thereby solving the problem in the prior art that the resonant mode frequency in a photonic crystal cavity cannot be precisely and linearly tuned.

[0004] In a first aspect, the present invention provides a method for tuning the resonant frequency of a photonic crystal resonator, wherein a photonic crystal resonator is obtained by inserting a Dirac photonic crystal into the domain wall of a spin-Hall topological cavity, and the resonant frequency of the photonic crystal resonator is adjusted by adjusting the number of Dirac photonic crystals.

[0005] Preferably, the method for obtaining a photonic crystal resonator by inserting a Dirac photonic crystal into the domain wall of a spin-Hall topological cavity includes the following steps:

[0006] Based on the different distribution of the primitive unit structures within the original cell, the photonic crystal resonator is divided into three regions, A, B, and C, from the inside out.

[0007] The lattice constant of the unit cell is determined based on the operating wavelength of the photonic crystal resonator, and several basic structures are distributed within each unit cell;

[0008] The unit cell design of region B is carried out by setting the duty cycle, determining the size of the basic structure within the unit cell of region B by the duty cycle, and adjusting the position of the basic structure within the unit cell to make region B a Dirac photonic crystal.

[0009] The unit cell design for regions A and C is based on the unit cell of region B, by adjusting the position of the centroid of the basic structure to form unit cells for regions A and C respectively, where regions A and C are topological nontrivial photonic crystal and topological trivial photonic crystal respectively;

[0010] Determine whether dipole and quadrupole modes resonate in regions A and C. If not, reset the duty cycle and design the unit cells for regions A, B, and C.

[0011] Preferably, the unit cell type includes triangular lattice, tetragonal lattice, hexagonal lattice, honeycomb lattice, and kabuki lattice.

[0012] Preferably, the intracellular basic structure is a dielectric pillar or air pore with a refractive index lower than that of the matrix material.

[0013] Preferably, the shape of the intracellular primitive structure is circular, triangular, trapezoidal, or crescent-shaped.

[0014] Preferably, in the unit cell design of region B, if adjusting the position of the unit cell structure cannot obtain the Dirac cone dispersion curve, the duty cycle is changed and the position of the unit cell structure is readjusted to obtain the Dirac cone dispersion curve. The condition for obtaining the Dirac cone dispersion curve is that the coupling strength between unit cells is equal to the coupling strength within the unit cell.

[0015] Preferably, in the design process of the unit cells of regions A and C, the unit cells of regions A and C are obtained by translating the basic structures closer to the unit cell center and further away from the unit cell center, respectively, and the unit cell band structures of the photonic crystals of regions A and C are aligned.

[0016] Preferably, after determining the unit 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 unit structure size is determined by the optimal adjustment range of the Dirac point.

[0017] Secondly, the present invention provides a frequency-tunable photonic crystal resonator, which is designed using the above-mentioned resonant frequency tuning method. In the design process, the resonant frequency of the photonic crystal resonator is adjusted by adjusting the number of unit cells of the Dirac photonic crystal in region B.

[0018] Thirdly, the present invention provides a frequency-tunable photonic crystal laser having the aforementioned frequency-tunable photonic crystal cavity.

[0019] One or more technical solutions provided in this invention have at least the following technical effects or advantages:

[0020] This invention provides a method for tuning frequencies by adjusting the Dirac photonic crystal domain in a topological laser cavity. Specifically, after inserting a Dirac photonic crystal (Dirac PC) into the domain walls of a spin-Hall topological cavity, the resonant frequencies of dipole and quadrupole modes exhibit a linear relationship with the number of unit cells in the Dirac photonic crystal, rather than a nonlinear frequency scaling caused by size effects. This phenomenon is attributed to the uniform spread of modes in a linearly dispersed medium. The effectiveness of this mechanism is further verified through systematic numerical simulations and tight-binding calculations on a nontrivial-Dirac-trivial cavity. The results show that the frequency tuning coefficient can be further effectively controlled by adjusting the frequency of the Dirac point relative to the bandgap of the photonic crystal. Furthermore, the linear frequency scaling law was also verified in a practical slab suspended photonic crystal cavity, and the tuning mechanism has a negligible 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 changing the domain wall size (i.e., the number of unit cells) of the Dirac photonic crystal, thus significantly reducing the complexity of experimental fabrication. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 This is a flowchart of the resonant frequency tuning method for the photonic crystal resonator of the present invention.

[0023] Figure 2 This is a schematic diagram of the photonic crystal resonator structure in an embodiment of the present invention, which consists of A (topological nontrivial), B (Dirac) and C (topological trivial) domains.

[0024] Figure 3This is a detailed schematic diagram of a local A-Dirac-C topological cavity. The inter- and intra-unit coupling strengths are represented as t1 and t2 (A domain), t3 (B domain), and t4 and t5 (C domain), respectively.

[0025] Figure 4 A schematic diagram of a Dirac photonic crystal unit cell with different triangular air hole sizes;

[0026] Figure 5 For A-Dirac-C: The band structure of a unit cell in a topological cavity, where, Figure 5 (d) in the diagram represents the band structure of a Dirac photonic crystal unit cell. Figure 5 (e) in the diagram is the band structure of a topologically trivial photonic crystal unit cell; Figure 5 (f) in the diagram is the band diagram of the unit cell of a topologically nontrivial photonic crystal.

[0027] Figure 6 (a) in the figure is the superposition band diagram of three different photonic crystal domains, and the Dirac cone dispersion curve is represented by a gray dashed line;

[0028] Figure 6 (b) shows the relationship between the frequency scaling of the quadrupole and dipole modes and the number of unit cells of the inserted Dirac photonic crystal and the topologically nontrivial A-photonic crystal;

[0029] Figure 6 In the diagram, (c) represents the electric field intensity in the quadrupole and dipole modes of the AC topological cavity. )distributed;

[0030] Figure 6 (d) A-Dirac-C: Electric field intensity in quadrupole and dipole modes in a topological cavity ( The distribution is such that there are 180 Dirac units between the A and C domains;

[0031] Figure 6 (e) in the middle is Figure 6 (c) Normalized electric field intensity along the white dashed line in quadrupole mode ( Distribution. Fields A, B, and C are represented by different colors;

[0032] Figure 6 (f) in the middle is Figure 6 (c) Normalized electric field intensity along the white dashed line in dipole mode ( Distribution. Fields A, B, and C are represented by different colors;

[0033] Figure 6 (g) in Figure 6(d) Normalized electric field intensity along the white dashed line in quadrupole mode ( Distribution. Fields A, B, and C are represented by different colors;

[0034] Figure 6 (h) in Figure 6 (d) Normalized electric field intensity along the white dashed line in dipole mode ( Distribution. Fields A, B, and C are represented by different colors;

[0035] Figure 7 (a) shows the superposition band structure of different photonic crystal domains, and the size of the triangular air hole in the Dirac photonic crystal. - The change in ) causes the Dirac point to move;

[0036] Figure 7 (b) represents different triangular air hole sizes. - The relationship between the number of unit cells in a Dirac photonic crystal and the frequency scaling of the quadrupole and dipole resonance modes;

[0037] Figure 7 (c) in the figure represents the theoretical prediction of the frequency scaling law of the quadrupole and dipole resonance modes based on tight-binding calculations;

[0038] Figure 7 (d) in the text represents A-Dirac-C: - (N=414) Electric field intensity in dipole mode in topological cavity ( )distributed;

[0039] Figure 7 (e) in the middle is Figure 7 (d) The corresponding normalized electric field strength along the white dashed line ( )distributed;

[0040] Figure 7 (f) in the equation represents A-Dirac-C: - (N=414) Electric field intensity in quadrupole mode in the topological cavity ( )distributed;

[0041] Figure 7 (g) in Figure 7 (e) The corresponding normalized electric field strength along the white dashed line ( Distribution. Domains A, B, and C are marked with different colors.

[0042] Figure 8In the example, (a) represents the number of unit cells in the three-dimensional PC cavity where Dirac photonic crystals and topologically nontrivial photonic crystals are inserted, as a function of frequency scaling for dipole and quadrupole resonant modes;

[0043] Figure 8 (b) in the figure represents the far-field distribution of the dipole mode in the AC topological cavity;

[0044] Figure 8 (c) in the equation represents AC: A (N=414) Far-field distribution of dipole modes in a topological cavity;

[0045] Figure 8 (d) in the text represents A-Dirac-C: (N=414) Far-field distribution of dipole modes in a topological cavity;

[0046] Figure 8 In the figure, (e) represents the far-field distribution of the quadrupole mode in the AC topological cavity;

[0047] Figure 8 (f) in the equation represents AC: A (N=414) Far-field distribution of quadrupole modes in a topological cavity;

[0048] Figure 8 (g) in the formula is A-Dirac-C: (N=414) Far-field distribution of quadrupole modes in a topological cavity;

[0049] Figure 8 (h) in Figure 8 (b) to Figure 8 (d) Normalized far-field intensity distribution corresponding to the far-field distribution of dipole modes in the topological cavity;

[0050] Figure 8 (i) in the middle is 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 Implementation

[0051] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and should not be construed as limiting the scope of the invention.

[0052] In the description of this invention, it should be noted that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0053] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0054] Example 1:

[0055] Example 1 provides a method for tuning the resonant frequency of a photonic crystal resonator. The method involves inserting Dirac photonic crystals into the domain walls of a spin-Hall topological cavity to obtain the photonic crystal resonator. The resonant frequency of the photonic crystal resonator is then adjusted by changing the number of Dirac photonic crystals. The method specifically includes the following steps:

[0056] S100. Based on the different distribution of the basic unit structure within the original cell, the photonic crystal resonator is divided into three regions, A, B, and C, from the inside out.

[0057] S200. The lattice constant of the unit cell is determined according to the working wavelength of the photonic crystal resonator. Several basic structures are distributed in each unit cell.

[0058] S300, the unit cell design of region B, setting the duty cycle, determining the size of the basic structure in the unit cell of region B by the duty cycle, and adjusting the position of the basic structure in the unit cell to make region B a Dirac photonic crystal.

[0059] The S400 unit cell design for regions A and C is based on the unit cell of region B. The position of the centroid of the basic structure is adjusted to form the unit cells of regions A and C respectively. Regions A and C are non-topologically trivial photonic crystals and topologically trivial photonic crystals respectively, and their bandgap frequency ranges are consistent.

[0060] S400. Determine whether dipole mode and quadrupole mode exist in regions A and C. If not, reset the duty cycle and perform unit cell design for regions A, B, and C.

[0061] S500: Adjust the resonant frequency of the photonic crystal resonator by adjusting the number of unit cells in region B of the Dirac photonic crystal.

[0062] This invention, after inserting a Dirac photonic crystal into the domain wall of a spin-Hall topological cavity, unexpectedly discovered that the resonant frequencies of the dipole and quadrupole modes exhibit a linear relationship with the number of unit cells in the Dirac photonic crystal. Therefore, by adjusting the number of unit cells in the Dirac photonic crystal, the resonant frequency of the photonic crystal resonant cavity can be precisely and easily adjusted to meet the frequency tuning requirements for using it as a photonic crystal laser.

[0063] 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. The basic structure material can be a low refractive index material commonly used in the prior art, such as air, silicon dioxide, polymer, and alumina. The specific details will not be elaborated further in this invention.

[0064] The unit cell types include triangular lattices, tetragonal lattices, hexagonal lattices, honeycomb lattices, and kabuki lattices; the shapes of the unit structures are circular, triangular, trapezoidal, or crescent-shaped.

[0065] In step S300, if adjusting the position of the primitive structure within the primitive cell fails to obtain the Dirac cone dispersion curve, the duty cycle is changed and the position of the primitive structure is readjusted to obtain the Dirac cone dispersion curve. The condition for obtaining the Dirac cone dispersion curve is that the inter-cell coupling strength is equal to the intra-cell coupling strength.

[0066] In step S400, the unit cells of regions A and C are obtained by translating the unit cell structure closer to and further away from the unit cell center, respectively. The unit cell band structures of the photonic crystals in regions A and C are aligned. After the unit cell band structures of the photonic crystals in regions A and C are aligned, there is impedance matching between regions A and C, so that the mode field of the photonic crystal resonator can be effectively confined to the center of the cavity. At the same time, the unit cells of regions A and C are obtained by translating the unit cell of region B inward and outward, which also ensures that the Dirac point in the unit cell band structure of region B (Dirac photonic crystal) is located at the center of the photonic band gap of regions A and C.

[0067] It should be noted that for the photonic crystal types of regions A and C, region A can be a topologically nontrivial photonic crystal and region C can be a topologically trivial photonic crystal, or region A can be a topologically trivial photonic crystal and region C can be a topologically nontrivial photonic crystal, as long as the band structure of regions A and C is aligned.

[0068] The present invention will be further explained below using silicon as the matrix material and six triangular air holes in the honeycomb lattice as the basic structure.

[0069] See Figure 2 First, a topological laser cavity composed of three different photonic crystal regions is constructed. The three different photonic crystal regions are arranged in an array with the same lattice period (the lattice period of the photonic crystals in the three regions is set to a) and divided into regions A, B and C. Region B is located in the middle layer of this topological laser cavity and is a Dirac photonic crystal, whose inter-cell coupling strength is equal to its intra-cell coupling strength. Region A is a topologically nontrivial photonic crystal, whose inter-cell coupling strength is greater than its intra-cell coupling strength. Region C is a topologically trivial photonic crystal, whose inter-cell coupling strength is less than its intra-cell coupling strength.

[0070] The topological laser cavity is named an A-Dirac-C topological cavity. This cavity exhibits a hexagonal photonic crystal (PC) structure, such as... Figure 2 As shown.

[0071] Based on the operating wavelength of the photonic crystal resonator The lattice constant of the unit cell is determined by the material type of the unit cell (which determines the refractive index difference between the unit cell and the basic structure). Furthermore, the lattice type of the unit cell was determined to be hexagonal, and all unit cells were composed of high-refractive-index dielectric plates (such as silicon). The basic structure type was determined to be triangular air holes, arranged in hexamethylene form within the unit cell; such as Figure 3 As shown.

[0072] Unit cell design for region B: Given the duty cycle of the triangular air holes The side length of a single triangular air hole is calculated using the duty cycle. ;

[0073] Adjust the distance between the triangular air pore and the center of the unit cell This ensures that the coupling strength between unit cells is equal to the coupling strength within the unit cell, both being t3, thus forming a Dirac photonic crystal; for example, the distance between the triangular air hole and the center of the unit cell... Brillouin District Center At point A, there exist two degenerate Dirac cones, such as... Figure 5 As shown in (d), each linear dispersion curve reflects the hybridization characteristics of the dipole mode and the quadrupole mode.

[0074] If the Dirac cone dispersion curve cannot be obtained, it indicates that the given duty cycle does not match the unit cell design. The duty cycle needs to be redefined until the Dirac cone dispersion curve can be obtained. For example, given the duty cycle of a triangular air hole... lattice constant After calculation, The distance between the triangular air pore and the center of the unit cell is set to By plotting the band structure, a Dirac point was found, meaning that region B under these design parameters is a Dirac photonic crystal; and under these design parameters, the Brillouin zone center... At the point, there are two degenerate Dirac cones, and each linear dispersion curve reflects the hybridization characteristics of the dipole and quadrupole modes, such as... Figure 5 As shown in (d); Dirac frequency =123 THz.

[0075] Unit cell design for regions A and C: Based on the unit cell of region B, the centroid position of the basic structure is adjusted to form unit cells for regions A and C respectively, where regions A and C are topological nontrivial photonic crystals and topological trivial photonic crystals respectively;

[0076] For example, moving the air holes in the unit cell of region B outwards can achieve degeneracy at the Γ point by reducing structural symmetry through moving the triangular air holes inwards (domain C) and outwards (domain A) within the unit cell. The imbalance between intracellular and intercellular coupling strengths further induces different topological phase transitions. When the intercellular coupling strength (t4) is less than the intracellular coupling strength (t5), region C exhibits trivial topological phase characteristics. Specifically, the band-edge modes of the two bands surrounding the band gap correspond to degenerate dipole and quadrupole modes, respectively. Conversely, when the intercellular coupling strength (t1) is greater than the intracellular coupling strength (t2), the center of the Brillouin zone in the innermost structural region A... At this point, band reversal will occur, inducing a nontrivial topological phase. The formula for calculating the distance between the triangular air hole and the unit cell center is: K is the centrifugal displacement coefficient of the triangular air hole.

[0077] For example, the distance between the triangular air pore and the center of the unit cell is set as follows: The unit cell parameters of region C can be obtained, and the band structure diagram is shown below. 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 located in the middle of the band gap in region C.

[0078] By setting the distance between the triangular air pore and the center of the unit cell as: The unit cell parameters of region A can be obtained, and the band structure diagram is shown below. Figure 5 As shown in (f), after translating the triangular air hole, the band gap in the band structure opens, and the Dirac point in region B is ensured to be located in the middle of the band gap in region A. Figure 5 (f) Brillouin District Center A band reversal phenomenon occurs near the point; at the same time, through the above parameter design, the band structures of region A and region C are highly aligned.

[0079] After determining the unit cell design for regions A and C, the optimal adjustment range of the Dirac point is determined by the bandgap 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. It is important to emphasize that the Dirac point needs to avoid alignment with the mode frequencies of regions A and C.

[0080] This invention further investigates the resonant frequency scaling characteristics of the aforementioned A-Dirac-C topological cavity, wherein the size of the triangular air hole in the Dirac photonic crystal (PC) is set to... ;like Figure 6 (a) shows the band structure of three superimposed photonic crystal regions. Since the band structure of the unit cell in region A is... Band reversal occurred near the point, with the quadrupole mode at the lower band edge of the band gap and the dipole mode at the upper band edge. This is consistent with the situation in the unit cell of the C region. The band-edge modes of the upper and lower bands near the band gap are reversed. Based on this characteristic, this invention constructs an AC topological cavity consisting of 9 layers of topologically nontrivial region A photonic crystals and 10 layers of topologically trivial region C photonic crystals (i.e., region A has 9 unit cells from the inside out, and region C has 10 unit cells from the inside out). The impedance mismatch at the topological interface of the AC topological cavity allows the two band-edge modes (quadrupole and dipole modes) of region A to be effectively confined to the innermost layer. Based on this cavity structure, this invention proposes a design scheme for embedding 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.

[0081] In the development of this invention, the focus was on the fundamental mode characteristics near the upper and lower band edges of the infinite topological nontrivial photonic crystal (region A). Due to the hybridization of dipole and quadrupole modes exhibited by the linear dispersion curve, the optical mode field can extend into 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 across all bulk states. Furthermore, the Dirac photonic crystal does not need to surround region A in integer multiples of the Dirac photonic crystal layers. The number of Dirac photonic crystal units can be flexibly adjusted without significantly affecting the aforementioned mode characteristics. This characteristic can be attributed to the robustness of the topological structure.

[0082] The frequencies of both dipole and quadrupole modes can be linearly scaled by the number of Dirac photonic crystal unit cells, i.e., the domain size of the Dirac photonic crystal. To more clearly describe the changes in the cavity structure, this 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-type topological cavity; AC: AA comparison is made between the type-3 cavity and 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 topologically nontrivial photonic crystal units and Dirac photonic crystal units on the quadrupole and dipole mode frequencies, respectively. With the addition of more topologically nontrivial photonic crystal units at the A / C topological interface, AC: A In the A-Dirac-C: topological cavity, the frequency of the dipole (quadrupole) mode undergoes a nonlinear shift, moving downwards (upwards) due to size effects. When a Dirac photonic crystal unit cell is inserted along the A / C topological interface, the frequency of the dipole (quadrupole) mode also shifts downwards (upwards), exhibiting an anomalous linear scaling relationship. The dimensions of the triangular air holes in the topological cavity (A-Dirac-C topological cavity) are set as follows: In this model, the resonant frequencies of dipole and quadrupole modes can scale linearly with the increase of the number of unit cells. This linear scaling law greatly simplifies the frequency tuning difficulty and improves the frequency tuning accuracy.

[0083] Although the introduction of Dirac photonic crystals did not change the characteristics of band-edge mode resonance in the topological cavity, it affected the electric field intensity of these modes. Distribution. For example... Figure 6 As shown in (c) and (d), in the AC topological cavity and A-Dirac-C: (In the topological cavity where the number of unit cells in region B is N=180), the field distributions of dipole and quadrupole modes are mainly concentrated in region A. However, for A-Dirac-C: In a topological cavity, the electric field extends to the surrounding Dirac photonic crystal (region B), and the field strength changes. Figure 6 (d)). A more intuitive result is as follows: Figure 6 (e)- Figure 6 As shown in (h), the normalized electric field strength for different modes ( )along Figure 6 Extraction of the white dashed lines in (c) and (d). A-Dirac-C compared to the initial AC topology cavity: The normalized field distribution of the topological cavity exhibits an electric field intensity distribution for both quadrupole and dipole modes within the Dirac photonic crystal region.

[0084] Furthermore, during the research process, this invention further discovered that the resonant frequency tuning coefficient of the topological band-edge mode is significantly affected by the Dirac cone frequency point relative to the photonic bandgap position of region A / C, and this relative position is determined by the size of the triangular air hole in the Dirac photonic crystal. While keeping the unit cell design parameters of regions A and C unchanged, and the lattice period of region B unchanged, the size of the triangular air hole is continuously scaled, with the scaling process using… Using a central point as the center, increase or decrease the number of points taken to obtain a series of points from largest to smallest. , , , , , Design the triangular air vents to the required dimensions, and draw the band structure 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 bandgap of the photonic crystal in region A. Figure 7 (b) Shows the number of unit cells in a Dirac photonic crystal in relation to A-Dirac-C: The influence of quadrupole and dipole resonant mode frequencies in a topological cavity. A-Dirac-C: Topological cavities also have, for example, Figure 6 (b) shows a 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... ( At this point, the Dirac point is precisely aligned with the dipole (quadrupole) mode frequency in the original AC topology cavity. This results in the resonant frequency of the dipole (quadrupole) mode remaining 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: ( In the topological cavity, the dipole (quadrupole) mode frequency will shift upward (downward) in the opposite direction and will be nonlinearly tuned as the Dirac photonic crystal unit cell is inserted. Figure 7 (c) Shows the number of Dirac photonic crystal unit cells calculated using the tight-binding model for A-Dirac-C: - The influence and variation law of quadrupole and dipole resonance mode frequencies in a topological cavity. Figure 7 (b) The observed patterns of change are consistent. Therefore, the optimal adjustment range for the basic structural dimensions is... ~ And does not include the two endpoints.

[0085] Figure 7 (d) Shows the A-Dirac-C respectively , , (Number of unit cells in region B N=414) Electric field intensity of dipole mode in topological cavity distributed. Figure 7 (e) gives the corresponding normalization along the white dashed line. Distribution. As the Dirac point moves downwards, the frequency of the dipole mode gradually decreases, and its electric field mode expands outwards. Similarly, A-Dirac-C: - (N=414) Electric field intensity in quadrupole mode in the topological cavity Distribution and normalization along the white dashed line The distributions are 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. This expansion of modes 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, significant portion of the field is coupled to region C, which may be due to non- This is caused by band dispersion with significant bending at the point, such as... Figure 7 As shown in (a). Therefore, the optimal size range is ~ (Including the endpoints), that is, the size of the triangular air hole is... ~ At that time, it has a better frequency tuning coefficient, or in other words, the frequency adjustment is more precise and sensitive.

[0086] When applying the linear frequency scaling law to 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 characteristics. Figure 8 (a) illustrates the relationship between the number of unit cells (corresponding to AC and A-Dirac-C topological cavities, respectively) inserted into a Dirac photonic crystal and a topologically nontrivial photonic crystal in a three-dimensional topological cavity with a photonic crystal planar structure and the frequency variations of dipole and quadrupole modes. As the number of inserted Dirac unit cells changes from 0 to 414, the frequency of the dipole (quadrupole) mode monotonically decreases (increases), compared to the two-dimensional A-Dirac-C: The case for topological cavities is similar (see Figure 6(b)). This verifies the applicability of the linear frequency scaling law in precise and fine laser frequency tuning. This invention also investigates AC topological cavities, AC: A Topological cavity (N=414) and A-Dirac-C: (N=414) Far-field emission of dipole and quadrupole modes in the topological cavity. Figure 8Figures (b)–(d) show the Fourier transform far-field distributions of the dipole modes, where the AC topological cavity and A-Dirac-C: (N = 414) The topological cavities have similar single-lobe intensity distributions. However, in A-Dirac-C: In the (N=414) topological cavity, the dipole mode exhibits a small divergence angle, primarily due to the larger cavity size. In contrast, the quadrupole mode displays a far-field intensity distribution with a ring-shaped profile and a divergence angle less than 5°. This is a typical emission characteristic of bound states (BICs) in a continuum. Figure 8 As shown in (e)-(g), for AC topological cavities and A-Dirac-C: (N=414) Topological cavity, with a side ring of relatively weak electric field, while for AC: A The beam quality of the topological cavity (N=414) decreased, while the side ring intensity was stronger. These results indicate that inserting a Dirac unit cell at the A / C topological interface can maintain the far-field emission mode and slightly reduce the divergence angle.

[0087] Example 2: This invention also protects a photonic crystal resonator, such as... Figure 2 As shown, a topological laser cavity is composed of three regions, A, B, and C, which are composed of different photonic crystals from the inside out. The photonic crystals in regions A, B, and C have the same period. Region B is a Dirac photonic crystal, region A is a topologically nontrivial photonic crystal, and region C is a topologically trivial photonic crystal, or region A is a topologically trivial photonic crystal and region C is a topologically nontrivial photonic crystal. The photonic band gaps of regions A and C are aligned.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of tuning the resonance frequency of a photonic crystal resonator, comprising: The method comprises the following steps: According to the distribution of the unit structures in the unit cell, the photonic crystal resonant cavity is divided into three regions A, B and C from inside to outside; The lattice constant of the unit cell is determined according to the operating wavelength of the photonic crystal resonant cavity, and a plurality of unit structures are distributed in each unit cell; In the design of the unit cell in region B, the duty cycle is set, the size of the unit structure in the unit cell in region B is determined through the duty cycle, and the unit structure in the unit cell in region B is adjusted to form the Dirac photonic crystal in region B; In the design of the unit cell in regions A and C, the center of gravity of the unit structure is adjusted on the basis of the unit cell in region B to form the unit cell in regions A and C, wherein regions A and C are topologically trivial photonic crystals and topologically nontrivial photonic crystals, respectively; If the resonances of the dipole mode and the quadrupole mode do not exist in regions A and C, the duty cycle is reset to design the unit cells in regions A, B and C.

2. The method of claim 1, wherein the resonant frequency of the photonic crystal cavity is tuned by changing the refractive index of the material of the photonic crystal cavity. The unit cell types include triangular lattices, square lattices, hexagonal lattices, honeycomb lattices and cage lattices.

3. The method of claim 1, wherein the resonant frequency of the photonic crystal cavity is tuned by changing the refractive index of the material of the photonic crystal cavity. The unit structure in the unit cell is a dielectric column or an air hole with a refractive index less than that of the matrix material.

4. The method of claim 1, wherein the resonant frequency of the photonic crystal cavity is tuned by changing the refractive index of the material of the photonic crystal cavity. The shape of the unit structure in the unit cell is circular, triangular, trapezoidal or crescent-shaped.

5. The method of claim 1, wherein the resonant frequency of the photonic crystal cavity is tuned by changing the refractive index of the material of the photonic crystal cavity. In the design of the unit cell in region B, if the Dirac cone dispersion curve cannot be obtained by adjusting the position of the unit structure in the unit cell, the duty cycle is changed, the position of the unit structure is adjusted again to obtain the Dirac cone dispersion curve, and the condition for obtaining the Dirac cone dispersion curve is that the inter-unit cell coupling strength is equal to the intra-unit cell coupling strength.

6. The method of claim 1, wherein the resonant frequency of the photonic crystal cavity is tuned by changing the refractive index of the material of the photonic crystal cavity. In the design of the unit cell in regions A and C, the unit cell in region A and region C is obtained by translating the unit structure close to and away from the center of the unit cell, and the band structure of the photonic crystal in regions A and C is aligned.

7. The method of claim 1, wherein the resonant frequency of the photonic crystal cavity is tuned by changing the refractive index of the material of the photonic crystal cavity. After the design of the unit cell in regions A and C is determined, the optimal adjustment range of the Dirac point is determined through the bandgap width of regions A and C, and the optimal adjustment range of the size of the unit structure in region B is determined through the optimal adjustment range of the Dirac point.

8. A frequency tunable photonic crystal resonator, characterized by The photonic crystal laser has the frequency-tunable photonic crystal resonant cavity according to claim 8.

9. A frequency tunable photonic crystal laser, characterized by The photonic crystal laser has the frequency-tunable photonic crystal resonant cavity according to claim 8.

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