Design method of topological photon flat band

Abstract

The invention discloses a design method of a topological photonic flat band, and relates to the technical field of optical information, and the method comprises the following steps: arranging a plurality of dielectric cylinders with C6 rotational symmetry on a topological photonic crystal primitive cell lattice; part of the dielectric cylinders are shrunk inwards along the center of the crystal lattice to form a common area; extending the rest dielectric cylinders outwards along the center of the crystal lattice to form a non-trivialness area; and combining the trivialness region and the non-trivialness region to form a supercell crystal, and obtaining a topological photon flat band under optical excitation. A topological boundary state photon flat band which covers a full Brillouin region and has extremely low group velocity is realized, and the topological boundary state photon flat band is protected by the topology of a wide band gap, so that the development of a novel topological slow light device is facilitated.

Description

Technical Field

[0001] This application relates to the field of optical information technology, and particularly to a design method for topological photonic flat bands. Background Art

[0002] Topological photonics is a newly emerging branch of photonics research in recent years. Derived from condensed matter, it can robustly manipulate the propagation and localization of light. With the development of nanomanufacturing technology and new materials, topological photonics has been widely applied in many fields such as directional waveguides, power splitters, filters, lasers, etc. Summary of the Invention

[0003] This application provides a design method for topological photonic flat bands to provide a photonic flat band.

[0004] In a first aspect, this application provides a design method for topological photonic flat bands, including the following steps:

[0005] Open a plurality of dielectric columns with C6 rotational symmetry on the lattice of the primitive cell of the topological photonic crystal;

[0006] Shrink some of the dielectric columns inward along the lattice center to form a trivial region;

[0007] Extend the remaining dielectric columns outward along the lattice center to form a non-trivial region;

[0008] Combine the trivial region and the non-trivial region to form a supercell crystal, and obtain topological photonic flat bands under optical excitation.

[0009] This application divides the topological photonic crystal into a trivial region and a non-trivial region by opening a plurality of dielectric columns on the lattice of a single primitive cell of the topological photonic crystal, with the dielectric columns distributed with rotational symmetry. The dielectric columns in the trivial region are shrunk inward along the lattice center, and the dielectric columns in the non-trivial region are extended outward along the lattice center to form a supercell structure, and topological photonic flat bands are calculated. This application realizes a topological boundary state photonic flat band that covers the entire Brillouin zone and has an extremely low group velocity, and is topologically protected by a wide bandgap, which helps to develop new types of topological slow light devices.

[0010] In some embodiments, among the multiple dielectric columns with C6 rotational symmetry opened on the primitive cell lattice of the topological photonic crystal, the number of dielectric columns on a single primitive cell lattice of the topological photonic crystal is 12. Generally, for a typical topological photonic crystal based on the quantum spin Hall effect (QSHE), its unit cell lattice contains six dielectric cylinders in an air background. In the Transverse-Magnetic (TM) polarization mode, each dielectric column is regarded as the fusion of two dielectric columns and separated, forming a symmetric unit cell structure containing 12 cylinders. The number of dielectric columns on a single primitive cell lattice of the topological photonic crystal being 12 ensures the C6 rotational symmetry of the unit cell structure and ensures its topological protection based on the quantum spin Hall effect.

[0011] In some embodiments, in the step of extending the remaining part of the dielectric columns outward along the lattice center to form a non-trivial region:

[0012] The degree of outward extension is S 1 , 410nm ≤ S 1 ≤ 470nm. The degree of outward extension affects the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. The value of the degree of outward extension within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions.

[0013] In some embodiments,

[0014]

[0015] where: x 1 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction during outward extension to the lattice center, 160nm ≤ x 1 ≤ 200nm; The value of x 1 affects the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. The value of x 1 within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions.

[0016] l 1 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction during outward extension to the lattice center, 390nm ≤ l 1 ≤ 410nm. The value of l 1 affects the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. The value of l 1 within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions.

[0017] In some embodiments, when part of the dielectric pillars are contracted inward along the lattice center to form an ordinary region, the degree of inward contraction is S 2 , 195 nm ≤ S 2 ≤ 225 nm. The degree of inward contraction changes the topological properties of the unit cell structure. When the value of the degree of inward contraction is within this range, the ordinary characteristics of the unit cell structure can be ensured, and topological phase transitions can be avoided.

[0018] In some embodiments,

[0019]

[0020] where: x 2 is the horizontal distance from the dielectric pillar farthest from the lattice center in the vertical direction during inward contraction to the lattice center, 50 nm ≤ x 2 ≤ 70 nm; The value of x 2 affects the topological properties of the lattice. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. When the value of x 2 is within this range, topological phase transitions can be avoided.

[0021] l 2 is the vertical distance from the dielectric pillar farthest from the lattice center in the vertical direction to the lattice center, 190 nm ≤ l 2 ≤ 210 nm. The value of l 2 affects the topological properties of the lattice. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. When the value of l 2 is within this range, topological phase transitions can be avoided.

[0022] In some embodiments, the ratio of the diameter of the dielectric pillars on the primitive cell lattice of the photonic crystal to the lattice constant of the photonic crystal satisfies: 0.1 ≤ D / α ≤ 0.25;

[0023] where α is the lattice constant of the photonic crystal;

[0024] D is the diameter of the dielectric pillar.

[0025] The ratio of the diameter of the dielectric pillar to the lattice constant of the photonic crystal, that is, the lattice filling ratio, affects the effective refractive index of the lattice. When the value of the ratio of the diameter of the dielectric pillar to the lattice constant of the photonic crystal is within this range, it helps to enhance the topologically protected edge states and also avoids excessive influence on the photonic bandgap.

[0026] In some embodiments, 900 nm ≤ a ≤ 1100 nm. The lattice constant of the photonic crystal affects the frequency of the band mode. When the value of the lattice constant of the photonic crystal is within this range, a better optical bandgap can be achieved while taking into account the manufacturability of the structure; and / or,

[0027] 90 nm ≤ D ≤ 275 nm. The diameter of the dielectric pillar affects the distribution and flatness of the energy band. When the value of the diameter of the dielectric pillar is within this range, a better optical bandgap can be achieved while taking into account the manufacturability of the structure.

[0028] In some embodiments, the supercell crystal includes a first region and a second region arranged in sequence, where:

[0029] The first region includes a plurality of trivial unit cell lattices arranged in sequence along a first direction;

[0030] The second region includes a plurality of non-trivial unit cell lattices arranged in sequence along the first direction.

[0031] For the supercell crystal formed by a plurality of trivial unit cell lattices arranged in sequence along the first direction and a plurality of non-trivial unit cell lattices arranged in sequence along the first direction, the distribution range and flat characteristics of the boundary state energy band protected by topology can be determined through the calculation of the energy band structure.

[0032] In some embodiments, the number of trivial unit cell lattices in the first region is greater than or equal to 5. The number of trivial unit cell lattices being greater than or equal to 5 can ensure sufficient structural complexity, avoid inaccurate calculation results, and not increase excessive calculation burden; and / or,

[0033] The number of non-trivial unit cell lattices in the second region is greater than or equal to 5. The number of non-trivial unit cell lattices being greater than or equal to 5 can ensure sufficient structural complexity, avoid inaccurate calculation results, and not increase excessive calculation burden. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] To more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0035] Figure 1 It is a flowchart of the design method of the topological photonic flat band according to an embodiment of the present application.

[0036] Figure 2 It is a schematic diagram of the typical topological photonic crystal unit cell structure and energy band of the design method of the topological photonic flat band according to an embodiment of the present application.

[0037] Figure 3 It is a schematic diagram of the supercell structure, electric field distribution, Poynting vector diagram and energy band diagram of the design method of the topological photonic flat band according to an embodiment of the present application.

[0038] Figure 4Schematic diagram of the flatness change of the flat band in the design method of the topological photonic flat band according to an embodiment of the present application. Detailed implementation manners

[0039] To make the objectives, technical solutions, and advantages of the present application clearer, the technical solutions of the present application will be clearly and completely described below in conjunction with the embodiments of the present application. Apparently, the described embodiments are some, rather than all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the scope of protection of the present application.

[0040] Topological photonics is a newly emerging branch of photonics research in recent years. Derived from condensed matter, it can robustly manipulate the propagation and localization of light. With the development of nanofabrication technology and new materials, topological photonics has been widely applied in many fields such as directional waveguides, power splitters, filters, lasers, etc.

[0041] The slow light effect can enhance the nonlinear interaction between light and matter, thereby designing photon devices such as efficient optical storage devices and tunable time-delay devices. Topological photonic crystals have the advantages of low loss, robustness, and one-way propagation, providing an ideal platform for manipulating the propagation of light. By structural design in topological photonic crystals, different band dispersion curves can be obtained to achieve an optical flat band covering the entire Brillouin zone, which can effectively control the propagation speed of light and provide a new solution for the development of advanced topological micro-nano photonic devices.

[0042] In view of this, the present application provides a design method for a topological photonic flat band to provide a photonic flat band.

[0043] In a first aspect, as Figure 1 shown, the present application provides a design method for a topological photonic flat band, including the following steps:

[0044] S100. Open a plurality of dielectric columns with C6 rotational symmetry on the primitive cell lattice of the topological photonic crystal;

[0045] S200. Shrink some of the dielectric columns inward along the lattice center to form a trivial region;

[0046] S300. Extend the remaining dielectric columns outward along the lattice center to form a non-trivial region;

[0047] S400. Combine the trivial region and the non-trivial region to form a supercell crystal, and obtain a topological photonic flat band under light excitation.

[0048] In this application, multiple dielectric columns are opened on a single topological photonic crystal primitive cell lattice. The distribution of the dielectric columns has rotational symmetry. The topological photonic crystal is divided into a trivial region and a non-trivial region. The dielectric columns in the trivial region are contracted inward along the lattice center, and the dielectric columns in the non-trivial region are extended outward along the lattice center to form a supercell structure, and a topological photonic flat band is calculated. This application realizes a topological boundary state photonic flat band that covers the entire Brillouin zone and has an extremely low group velocity, and is topologically protected by a wide bandgap, which helps to develop new types of topological slow light devices.

[0049] It should be noted that C 6 Rotational symmetry refers to the property that the geometric structure of an object or molecule remains unchanged when rotated by 60 degrees around its center. The inward contraction of some dielectric columns along the lattice center means that x 1 and l 1 decrease simultaneously, and the outward extension of some dielectric columns along the lattice center means that x 2 and l 2 increase simultaneously. The trivial region refers to the region in the unit cell structure where the intra-cell hopping of energy is greater than the inter-cell hopping, and its topological property is trivial. The non-trivial region refers to the region in the unit cell structure where the intra-cell hopping of energy is less than the inter-cell hopping, and its topological property is non-trivial, and the inversion of the band quadrupole state and dipole state occurs. The topological photonic flat band refers to a band in the band structure of a topological photonic crystal that is protected by topological properties and has good flat characteristics. The Brillouin zone refers to a region in the reciprocal space that represents the wave vector distribution of photons in a crystal. The first Brillouin zone is the most basic unit in the Brillouin zone, usually the most symmetric and smallest region in the wave vector space, used to describe all possible photon states. The group velocity refers to the derivative of the frequency of each band in the band diagram with respect to the Brillouin zone wave vector k, representing the propagation speed of light waves or particles in a crystal. A slow light device refers to a device that, by designing a special structure of a topological photonic crystal, significantly reduces the propagation speed of light in certain frequency ranges, thereby achieving the "slowing down" of light and enabling stable and adjustable light speed control. These devices have the advantage of topological protection and have important application prospects in the fields of optical storage, quantum communication, optical signal processing, etc.

[0050] In combination with the first aspect, in some embodiments provided by the present application, among the multiple dielectric cylinders with C6 rotational symmetry opened on the topological photonic crystal primitive cell lattice, the number of dielectric cylinders on a single topological photonic crystal primitive cell lattice is 12. Generally, for a typical topological photonic crystal based on the quantum spin Hall effect (QSHE), its unit cell lattice contains six dielectric cylinders in an air background. In the Transverse-Magnetic (TM) polarization mode, each dielectric cylinder is regarded as the fusion of two dielectric cylinders and separated, forming a symmetric unit cell structure containing 12 cylinders. The number of dielectric cylinders on a single topological photonic crystal primitive cell lattice being 12 can ensure the C6 rotational symmetry of the unit cell structure and ensure its topological protection based on the quantum spin Hall effect.

[0051] In combination with the first aspect, in some embodiments provided by the present application, in the step of extending the remaining part of the dielectric cylinders outward along the lattice center to form a non-trivial region:

[0052] The degree of outward extension is S 1 , 410 nm ≤ S 1 ≤ 470 nm. The degree of outward extension affects the topological properties of the lattice. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. The value of the degree of outward extension within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions. The value of S 1 includes but is not limited to 410 nm, 415 nm, 420 nm, 425 nm, 430 nm, 435 nm, 440 nm, 445 nm, 450 nm, 455 nm, 460 nm, 465 nm or 470 nm.

[0053] In combination with the first aspect, in some embodiments provided by the present application,

[0054]

[0055] where: x 1 is the horizontal distance from the dielectric cylinder farthest from the lattice center in the vertical direction during outward extension to the lattice center, 160 nm ≤ x 1 ≤ 200 nm; The value of x 1 affects the topological properties of the unit cell structure. When unit cell lattices with different topological characteristics form a supercell, they have different band characteristics. The value of x 1 within this range can ensure the non-trivial characteristics of the unit cell structure and avoid topological phase transitions. The value of x 1 includes but is not limited to 160 nm, 165 nm, 170 nm, 175 nm, 180 nm, 185 nm, 190 nm, 195 nm or 200 nm.

[0056] l 1 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction when extending outward to the lattice center, 390 nm ≤ l 1 ≤ 410 nm. The value of l 1 affects the topological properties of the unit cell structure. When unit cells with different topological characteristics form a supercell, they have different band characteristics. 1 The value of l includes but is not limited to 390 nm, 385 nm, 390 nm, 395 nm, 400 nm, 405 nm, 410 nm, 415 nm or 410 nm.

[0057] Combined with the first aspect, in some embodiments provided by the present application, when partially contracting the dielectric columns along the lattice center to form a trivial region: the degree of inward contraction is S 2 , 195 nm ≤ S 2 ≤ 225 nm. The degree of inward contraction affects the topological properties of the lattice. When unit cells with different topological characteristics form a supercell, they have different band characteristics. When the value of the degree of inward contraction is within this range, the trivial characteristics of the unit cell structure can be ensured and topological phase transition can be avoided. 2 The value of S includes but is not limited to 195 nm, 200 nm, 205 nm, 210 nm, 215 nm, 220 nm or 225 nm.

[0058] Combined with the first aspect, in some embodiments provided by the present application,

[0059]

[0060] where: x 2 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction when contracting inward to the lattice center, 50 nm ≤ x 2 ≤ 70 nm; the value of x 2 affects the topological properties of the lattice. When unit cells with different topological characteristics form a supercell, they have different band characteristics. When the value of x 2 is within this range, topological phase transition can be avoided. 2 The value of x includes but is not limited to 50 nm, 52 nm, 55 nm, 58 nm, 60 nm, 62 nm, 65 nm, 68 nm or 70 nm.

[0061] l 2 is the vertical distance from the dielectric column farthest from the lattice center in the vertical direction when contracting inward to the lattice center, 190 nm ≤ l 2 ≤ 210 nm. The value of l 2 affects the topological properties of the lattice. When unit cells with different topological characteristics form a supercell, they have different band characteristics. 2When the value of [] is within this range, topological phase transitions can be avoided. l 2 The value of [] includes but is not limited to 190nm, 192nm, 195nm, 198nm, 200nm, 202nm, 205nm, 207nm or 210nm.

[0062] Combined with the first aspect, in some embodiments provided by the present application, the ratio of the diameter of the dielectric column on the primitive cell lattice of the photonic crystal to the lattice constant of the photonic crystal satisfies: 0.1 ≤ D / α ≤ 0.25;

[0063] where α is the lattice constant of the photonic crystal;

[0064] D is the diameter of the dielectric column.

[0065] The ratio of the diameter of the dielectric column to the lattice constant of the photonic crystal is the lattice filling ratio, which affects the effective refractive index of the lattice. When the value of the ratio of the diameter of the dielectric column to the lattice constant of the photonic crystal is within this range, it helps to enhance the topologically protected edge states and at the same time avoid excessive influence on the photonic bandgap.

[0066] Combined with the first aspect, in some embodiments provided by the present application, 900nm ≤ a ≤ 1100nm. The lattice constant of the photonic crystal affects the frequency of the energy band mode. When the value of the lattice constant of the photonic crystal is within this range, a better optical bandgap can be achieved and the manufacturability of the structure can be taken into account.

[0067] Combined with the first aspect, in some embodiments provided by the present application, 90nm ≤ D ≤ 275nm. The diameter of the dielectric column affects the distribution and flatness of the energy bands. When the value of the diameter of the dielectric column is within this range, a better optical bandgap can be achieved and the manufacturability of the structure can be taken into account.

[0068] Combined with the first aspect, in some embodiments provided by the present application, the supercell crystal includes a first region and a second region arranged in sequence, where:

[0069] The first region includes a plurality of trivial unit cells arranged in sequence along a first direction;

[0070] The second region includes a plurality of non-trivial unit cells arranged in sequence along the first direction.

[0071] The supercell crystal formed by a plurality of trivial unit cells arranged in sequence along the first direction and a plurality of non-trivial unit cells arranged in sequence along the first direction can determine the distribution interval and flat characteristics of the energy bands of the topologically protected edge states through the calculation of the energy band structure.

[0072] In combination with the first aspect, in some embodiments provided by the present application, the number of trivial unit cells in the first region is greater than or equal to 5. The number of trivial unit cells being greater than or equal to 5 can ensure sufficient structural complexity, avoid inaccurate calculation results, and not increase excessive computational burden.

[0073] In combination with the first aspect, in some embodiments provided by the present application, the number of non-trivial unit cells in the second region is greater than or equal to 5. The number of non-trivial unit cells being greater than or equal to 5 can ensure sufficient structural complexity, avoid inaccurate calculation results, and not increase excessive computational burden.

[0074] It should be noted that the material of the dielectric pillar includes any one of silicon, germanium, and quantum well. The quantum well material includes but is not limited to at least one of InGaAsP, InGaAs, and AlGaAs. The lattice arrangement type of the photonic crystal includes but is not limited to triangular lattice, square lattice, or honeycomb lattice.

[0075] The technical solution provided by the present application will be described in detail below in combination with embodiments.

[0076] Embodiment 1

[0077] Embodiment 1 of the present application provides a method for realizing topological photonic flat bands, including the following steps:

[0078] A typical topological photonic crystal based on the Quantum Spin Hall Effect (QSHE), as Figure 2 shown in (a), its unit cell lattice contains six dielectric cylinders in an air background, and the polarization mode of the photonic crystal is the Transverse-Magnetic (TM) mode. Figure 2 (b), Figure 2 (c) shows that each dielectric pillar is regarded as two dielectric pillars fused together and separated to form a symmetric unit cell structure containing 12 cylinders. In the new photonic crystal lattice structure, the lattice constant a = 1 μm, the cylinder diameter D = 180 nm, and the refractive indices of the dielectric pillar and the air background are 3.27 and 1 respectively;

[0079] The degree of lattice deformation is determined by x and l. Figure 2 (d) and Figure 2 (e) are the energy band distribution diagrams of the two-dimensional photonic crystal, and its optical bandgap is opened. Figure 2 (d) shows that as x and l decrease, 12 cylinders merge to form a petal-like structure, and the size of its optical bandgap Δω is 0.135c / a, where c is the speed of light in air, and the red and blue energy bands represent the dipole state and the quadrupole state respectively. Figure 2(e) When x and l increase, two previously separated cylinders recombine and are segmented by the hexagonal boundary of the unit cell lattice, with an optical bandgap size of 0.172c / a. The inversion between the dipole state (d) and the quadrupole state (p) indicates a topological phase transition. By adjusting the degree of cylinder deformation, the transition energies inside and outside the unit cell are changed. As the dielectric cylinder extends outward, the effective transition energy inside the cell decreases, while the transition energy outside the cell increases. Therefore, the quadrupole state and the dipole state are inverted in the energy band diagram, forming a topologically non-trivial bandgap, and vice versa, a topologically trivial bandgap is formed.

[0080] When two topological photonic crystal unit cells with topologically distinct bandgaps are in contact, there are topologically protected topological boundary states at their interface. The topological photonic crystal waveguide constructed in this way supports spin-momentum locked boundary states. Figure 3 (a) is composed of Figure 2 (d) and Figure 2 (e) The schematic diagram of the supercell structure composed of the unit cell structures, with 10 trivial unit cells and 10 non-trivial unit cells in the vertical direction (the first direction). Figure 3 (b) is Figure 3 The energy band diagram of the structure in (a). Figure 3 (c) shows the electric field distribution and the Poynting vector diagrams at points A, B, C, D ( Figure 3 the points shown in yellow in (b)). Points A / B show non-zero forward / backward electromagnetic energy fluxes in the pseudo-spin down / up states, clearly indicating the backward propagation at the interface related to different pseudo-spin characteristics, which is a signature of the QSHE boundary state. In the typical supercell energy band diagram based on QSHE, two boundary state energy bands intersect at the high-symmetry point (=0) of the Brillouin zone. It can be found that the two boundary state energy bands are opened from the intersection point, with a relatively large bandgap of 0.047c / a.

[0081] In addition, Figure 3 The upper boundary state energy band in (b) shows a very flat characteristic throughout the Brillouin zone, with the difference between the highest frequency point and the lowest frequency point being 0.00117c / a. As can be seen from Figure 3 (c), compared with the lower boundary state energy band with obvious pseudo-spin characteristics, in the upper boundary state energy band with flat band characteristics, the electric field distribution at points C(D) is more localized and the energy is more concentrated than that at points A(B) at the same wave vector. In addition, the frequency range of the upper boundary state energy band is significantly deviated from the vicinity of the bulk mode energy band (the gray marked area), resulting in a bandgap of 0.063c / a between the upper boundary state energy band and the bulk mode energy band. Figure 3(d) Schematic diagram of the group velocity distribution of the upper boundary state energy band. The figure contains two sets of closed curves because the energy band evolves from two intersecting boundary state energy bands with pseudospin characteristics. However, due to the nature of its flat band, the group velocity within the entire Brillouin zone is in a very low range (absolute value less than 0.005 and with little variation), which is crucial for topological slow light applications.

[0082] While maintaining the topological properties unchanged, by scanning the structural parameters, the flatness of the upper boundary state energy band can be finely adjusted within a certain parameter space range. The l values of the unit cell structures on both sides of the interface are adjusted, where l 1 and l 2 correspond to the non-trivial and trivial unit cell structures respectively. The flatness p of the energy band is defined as:

[0083]

[0084] where, f max is the highest frequency of the upper boundary state energy band, fmin is the lowest frequency of the upper boundary state energy band, and f avg is the average frequency of the modes along the entire energy band. When calculating, 50 topological boundary state modes uniformly distributed along the wave vector direction of the momentum space are considered. A smaller p value means better flatness performance of the topological boundary state energy band. Figure 4 (a) Distribution diagram of p with respect to the parameter changes of l 1 and l 2 . The value range of l 1 is 390 - 410 nm, and the value range of l 2 is 180 - 220 nm. It can be seen that the order of magnitude of p is in 10 -3 , having good flat characteristics. In actual situations, it is also necessary to simultaneously consider that the band gap size between the upper boundary state energy band and the bulk mode energy band region as well as the lower boundary state energy band is in a relatively optimal value. Figure 3 (b) Schematic diagram for selecting a set of parameters, l 1 = 400 nm, l 2 = 200 nm. Correspondingly, x 1 = 180 nm and x 2 = 60 nm are selected. Under this set of parameters, p is 0.0023.

[0085] To further study the variation trend of the energy band flatness performance, fixing all other parameters, the energy band distribution diagram when only l 2 changes is calculated and shown in Figure 4 (b). As l 2With the change of , the relative position between the lower boundary state energy band and the lower body mode energy band region basically does not change within a large confidence interval. At the same time, the large bandgap between the two boundary state energy bands still exists, so this part of the region is not shown in the figure. On the premise that the topological phase transition does not occur, l 2 changes from 250 nm to 200 nm in steps of 10 nm. As l 2 decreases, the boundary of the upper body mode energy band region gradually moves upward, while the moving amplitude of the upper boundary state energy band with flat band characteristics is relatively small. This forms a significantly increased bandgap. The upper boundary state energy band is shown in the Figure 4 magnified inset of (b), indicating an upward moving trend similar to that of the upper body mode energy band region. At the same time, the upper boundary state energy band also gradually becomes flatter, and the minimum p value appears at l 2 = 200 nm. For cases less than 200 nm, a change in the flatness of the energy band can be clearly observed in Figure 4 (a), and the p value becomes larger.

[0086] By adjusting l 1 and l 2 , a topological flat band covering the entire Brillouin zone in the photonic crystal is generated. The proposed trivial and non-trivial unit cell structures in this application have a four-dimensional adjustable parameter space (l 1 , l 2 , x 1 , x 2 ), which provides unprecedented degrees of freedom for adjusting the energy band dispersion characteristics of topological boundary states. It can be achieved through some optimization algorithms such as annealing, genetic algorithms, or combined with neural networks, and has a compact energy distribution. This topological photonic boundary state flat band with a large bandgap and flexible adjustment characteristics provides convenience for the optical mode manipulation of on-chip micro-nano systems and has important application prospects.

[0087] In summary, by opening multiple dielectric cylinders on the lattice of a single topological photonic crystal primitive cell, the dielectric cylinder distribution has rotational symmetry, dividing the topological photonic crystal into trivial regions and non-trivial regions. The dielectric cylinders in the trivial regions are contracted inward along the lattice center, and the dielectric cylinders in the non-trivial regions are extended outward along the lattice center to form a supercell structure, and the topological photonic flat band is calculated. This application realizes a topological boundary state photonic flat band covering the entire Brillouin zone with an extremely low group velocity and is topologically protected by a wide bandgap, which helps to develop new topological slow light devices.

[0088] In the description of this specification, the descriptions with reference to terms such as "one embodiment / way", "some embodiments / ways", "example", "specific example" or "some examples" etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment / way or example are included in at least one embodiment / way or example of this application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment / way or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments / ways or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments / ways or examples described in this specification and the features of different embodiments / ways or examples.

[0089] It should be noted that in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the said element. In this application, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0090] The above are only the specific embodiments of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features claimed herein.

Claims

1. A design method for a topological photonic flat band, characterized in that: The following steps are involved: A plurality of dielectric columns with C6 rotational symmetry are opened on the topological photonic crystal primitive cell lattice; Shrink some dielectric columns inward along the center of the lattice to form a mediocre region; Extend the remaining dielectric columns outward along the center of the lattice to form a non-trivial region; The trivial regions and non-trivial regions are combined to form a supercell crystal, and a topological photonic flat band is obtained under optical excitation.

2. The design method of the topological photonic flat band according to claim 1, characterized in that: In the method of providing a plurality of dielectric columns with C6 rotational symmetry on the topological photonic crystal primitive cell lattice, the number of dielectric columns on a single topological photonic crystal primitive cell lattice is 12.

3. The design method of the topological photonic flat band according to claim 1, characterized in that: Step 1: Extend the remaining dielectric columns outward along the center of the lattice to form a non-trivial region: The degree of outward extension is S1, 410nm≤S1≤470nm.

4. The design method of the topological photonic flat band according to claim 3, characterized in that: Where: x1 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when extending outward, 160nm≤x1≤200nm; l1 is the vertical distance from the dielectric column farthest from the center of the lattice in the vertical direction to the center of the lattice when extending outward, 390nm≤l1≤410nm.

5. The design method of the topological photonic flat band according to claim 1, characterized in that: The dielectric columns are partially contracted inward along the center of the lattice to form a mediocre region: The degree of inward contraction is S2, 195nm≤S2≤225nm.

6. The design method of the topological photonic flat band according to claim 5, characterized in that: Where: x2 is the horizontal distance from the dielectric column farthest from the lattice center in the vertical direction to the lattice center when shrinking inward, 50nm≤x2≤70nm; l2 is the vertical distance from the dielectric column farthest from the center of the lattice to the center of the lattice in the vertical direction, 190nm≤l2≤210nm.

7. The design method of the topological photonic flat band according to claim 1, characterized in that: The ratio of the diameter of the dielectric column on the photonic crystal primitive cell lattice to the lattice constant of the photonic crystal satisfies: 0.1≤D / α≤0.25; Where α is the lattice constant of the photonic crystal; D is the diameter of the medium column.

8. The method for designing a topological photonic flat band according to claim 7, characterized in that: 900nm≤a≤1100nm; and / or, 90nm≤D≤275nm.

9. The design method of the topological photonic flat band according to claim 1, characterized in that: The supercell crystal comprises a first region and a second region arranged in sequence, wherein: The first region includes a plurality of mediocre unit cell lattices arranged in sequence along a first direction; The second region includes a plurality of non-trivial unit cell lattices arranged sequentially along a first direction.

10. The method for designing a topological photonic flat band according to claim 9, characterized in that: The number of trivial unit cells of the first region is the same as the number of non-trivial unit cells of the second region.

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