Topology angular state regulation and control method based on flat-band two-dimensional micro-ring lattice

Abstract

The invention discloses a topology angular state regulation and control method based on a flat-band two-dimensional micro-ring lattice, and belongs to the technical field of topology angular state regulation and control, and the method comprises the following steps: S1, constructing the flat-band two-dimensional micro-ring lattice; s2, dynamically regulating and controlling a topological angular state based on the constructed flat-band two-dimensional micro-ring crystal lattice; according to the invention, through the design of the hexagonal honeycomb type micro-ring resonant cavity and the combination of the dynamic phase regulation and control technology, flexible regulation of the photon standard potential and a compact local mode in which the angular state of the topological state has robustness are realized, and the core problems of inflexible regulation and control of the photon standard potential, insufficient locality of the topological state, poor manufacturing fault tolerance and the like in the prior art are solved; and a high-performance and high-reliability design normal form is provided for the on-chip integrated photonic device.

Description

Technical Field

[0001] The present invention belongs to the technical field of topological angle state regulation, and specifically relates to a topological angle state regulation method based on a flat-band two-dimensional micro-ring lattice. Background Art

[0002] As semiconductor technology gradually approaches physical limits, optical communication technology has become an important way to meet the needs of high-speed and large-capacity information transmission.

[0003] As an information carrier, photons have the advantages of high-speed transmission, resistance to electromagnetic interference, large bandwidth and high energy efficiency, making them an ideal choice for high-speed and large-capacity information transmission in the future. However, their practical application faces two major challenges: one is how to achieve flexible control of light, and the other is how to efficiently and stably integrate micro-optical components into photonic devices.

[0004] At present, the photon gauge potential is constructed through spatiotemporal regulation, nonlinear effects, tilted geometric design, etc. to realize phenomena such as the photon Aharonov-Bohm effect, Bloch oscillation, negative refraction and dynamic localization. However, its regulation relies on complex structural design and fixed parameters, and cannot flexibly adjust the phase and coupling strength, which limits the dynamic localization and diffusion control of photons and makes it difficult to adapt to the needs of multiple scenarios.

[0005] Currently, topological photonics in the field of integrated photonic circuits suppresses the effects of defects and disorders on light transmission by constructing robust boundary modes, but existing topological structures such as one-dimensional or simple two-dimensional lattices make it difficult to achieve highly localized topological states such as topological corner states in compact sizes.

[0006] At present, on-chip integrated photonic devices have extremely high requirements for manufacturing precision. Traditional topological structures are prone to band distortion when there are process errors, affecting the robustness of the topological state.

[0007] In view of this, a topological corner state regulation method based on flat-band two-dimensional microring lattice is designed to solve the above problems. Summary of the invention

[0008] To solve the problems raised in the above background technology, the present invention provides a method for controlling topological corner states based on a flat-band two-dimensional micro-ring lattice, which has the characteristics of solving the core problems of the prior art, such as the inflexible control of photon gauge potential, insufficient localization of topological states, and poor manufacturing fault tolerance.

[0009] To achieve the above object, the present invention provides the following technical solution: a method for controlling topological corner states based on a flat-band two-dimensional microring lattice, comprising the following steps:

[0010] S1: Construction of a flat-band two-dimensional microring lattice;

[0011] S2: Dynamically control topological corner states based on the constructed flat-band two-dimensional microring lattice.

[0012] Furthermore, in the step S1, the constructed flat-band two-dimensional micro-ring lattice includes a number of unit cells of the array, and the unit cells include six hexagonal honeycomb main rings, and the six hexagonal honeycomb main rings are positively coupled or negatively coupled through rectangular connecting rings, wherein the rectangular connecting rings are designed with an additional path length to meet the anti-resonance relationship and introduce negative coupling so as to flexibly adjust the coupling phase and amplitude, and the rectangular connecting rings move in the vertical direction to generate a direction-related phase between the hexagonal honeycomb main rings, and the input and output ports are distributed at different positions of the lattice.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] The present invention realizes flexible regulation of the photon gauge potential and a compact localized mode with robustness of the angular state of the topological state through the design of a hexagonal honeycomb microring resonator combined with dynamic phase control technology, thereby solving the core problems of the prior art such as inflexible regulation of the photon gauge potential, insufficient localization of the topological state, and poor manufacturing fault tolerance, and provides a high-performance and high-reliability design paradigm for on-chip integrated photonic devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of the structure of the two-dimensional photon AB trapping lattice;

[0016] Figure 2 The energy band structure diagram of the lattice under the periodic boundary conditions of the present invention;

[0017] Figure 3 It is the energy band structure diagram under the fully open boundary condition of the present invention;

[0018] Figure 4 is a schematic diagram of the three-dimensional structure of the two-dimensional micro-ring lattice of the present invention;

[0019] Figure 5 It is a local pattern diagram of the topological state of the present invention;

[0020] Figure 6 It is the energy band structure diagram under the open boundary condition of the present invention;

[0021] Figure 7 It is the Wannier band under the periodic boundary conditions of the present invention. DETAILED DESCRIPTION

[0022] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0023] The two-dimensional photon AB trapping lattice has two degrees of freedom in two directions. Its band structure is more complex than that of one-dimensional and can support a variety of topological states, such as Figure 1 As shown, the dotted box represents the unit cell, the thick solid line represents the positive coupling (t), and the thin solid line represents the negative coupling (-t). It can be seen from the figure that the lattice structure is composed of multiple interlaced hexagonal honeycomb cells, each of which contains six lattice points. There are two coupling modes in the lattice, namely positive coupling t and negative coupling -t. Through this unique design, each rhombus structure can achieve an equivalent π-photon gauge potential;

[0024] Specifically, some rhombus structures contain three positive couplings and one negative coupling, while the rest contain one positive coupling and three negative couplings. No matter which combination, it can be equivalent to a magnetic flux of π, thereby achieving a uniform distribution of the photon gauge potential in the lattice. This design not only simplifies the complexity of the structure, but also provides a flexible platform for the regulation of topological states.

[0025] Since this unique diamond structure design can regulate the photon gauge potential in each unit cell, the band structure under different photon gauge potentials is further studied;

[0026] Under the periodic boundary condition (PBC), only the nearest neighbor coupling of the two-dimensional model is considered, and the next nearest neighbor coupling is ignored. The band structure of the two-dimensional model is as follows: Figure 2 As shown:

[0027] When the photon gauge potential φ in the unit cell is 0, the band structure is as follows Figure 2 As shown in (a), it can be seen that the energy band is not completely degenerate at this time. The upper and lower dispersion spaces each contain two energy bands, which are close to each other to form a dispersion band, while the zero energy band with energy E = 0 shows a flat band characteristic, and the group velocity is zero;

[0028] When the photon gauge potential φ = π, the band structure is as follows Figure 2 As shown in (b), it can be seen that the energy band degenerates and degenerates into three completely flat energy bands. At this time, the model as a whole presents flat band characteristics and no dispersion occurs, which proves that the two-dimensional photon AB trapping lattice is successfully constructed;

[0029] Based on the above results, it can be predicted that under open boundary conditions (OBC), the model will have robust topological boundary states and the mode field distribution will show a compact localized mode. This feature provides an important basis for the design and application of topological photonic devices.

[0030] The corresponding band structure is drawn under completely open boundary conditions (OBC), such as Figure 3 As shown:

[0031] In order to ensure the completeness of the band structure, the two-dimensional lattice is truncated along the x and y axes, and the number of lattice points of the finite lattice is guaranteed to be an integer multiple of the unit cell to avoid inaccurate calculation of the gap state due to excess or missing lattice points. Specifically, the lattice contains three unit cell units in the x direction and two unit cell units in the y direction, for a total of 36 lattice points, such as Figure 3 (a)

[0032] There are three different intra-gap states in the energy gap between the upper and lower energy bands, namely, square points represent the boundary states of the upper and lower boundaries, regular pentagon points represent the boundary states of the left and right boundaries, and five-pointed stars represent the corner states, such as Figure 3 (b)

[0033] It is worth noting that under completely open boundary conditions, isolated zero-dimensional corner states will appear at the junction of the two boundaries of the two-dimensional photon AB trapping lattice. Similar to the boundary states, the zero-dimensional corner states also exhibit flat band characteristics, but their mode field distribution and energy size are different from those of the boundary states. The energy of the corner states is lower, and the energy gap between them and the bulk state is larger, which indicates that the corner states may have stronger robustness.

[0034] The structure of the two-dimensional photon AB trapping lattice is relatively complex. Each lattice point is coupled with multiple adjacent lattice points, and the influence of the next nearest neighbor coupling needs to be ignored. In addition, in order to achieve the localization and diffusion of light, it is necessary to introduce a controllable magnetic flux into the unit cell. Based on the design of the micro-ring resonator array, complex coupling terms can be constructed in the structure, and the photon gauge potential can be flexibly controlled.

[0035] To this end, it is redesigned, as shown in the attached Figure 4 As shown, specifically:

[0036] The present invention provides the following technical solution: a method for regulating topological corner states based on a flat-band two-dimensional microring lattice, comprising the following steps:

[0037] S1: Construction of a flat-band two-dimensional microring lattice;

[0038] The constructed flat-band two-dimensional micro-ring lattice includes several unit cells of the array, and the unit cell includes six hexagonal honeycomb main rings, and the six hexagonal honeycomb main rings are connected by positive coupling or negative coupling through rectangular connecting rings, wherein the rectangular connecting rings are designed with an additional path length to meet the anti-resonance relationship and introduce negative coupling so as to flexibly adjust the coupling phase and amplitude, and the rectangular connecting rings move in the vertical direction to generate a phase related to the direction between the hexagonal honeycomb main rings, and input and output ports are evenly distributed at different positions of the lattice;

[0039] S2: Dynamically control topological corner states based on the constructed flat-band two-dimensional microring lattice.

[0040] The finite element method is used to perform full-wave simulation to simulate the excitation process of the lattice. The corresponding mode field distribution is shown in Figure 5 As shown:

[0041] Figure 5 (a) represents the topological corner state, Figure 5 (b) represents the topological boundary states at the upper and lower boundaries, Figure 5 (c) represents the topological boundary states at the left and right boundaries. It can be seen that the mode field presents a compact localized mode, and the energy is only distributed in the five lattice points near the input port. There is no exponential decay from the edge to the middle of the lattice. In particular, the topological corner state located in the corner has a more compact mode field distribution than the topological boundary state, and the energy is highly concentrated in the main resonant ring near the input port, without any signs of diffusion. This feature further verifies the advantages of the topological corner state in terms of locality and robustness.

[0042] The topological edge states and topological corner states of the lattice exhibit compact localized modes, that is, the energy does not decay exponentially from the edge to the middle of the structure, but is confined within the range of a single unit cell.

[0043] Since the flat-band localization characteristics of the two-dimensional photon AB trapping lattice originate from the destructive interference effect of light, the topological edge states and topological corner states are subject to enhanced topological protection and show strong robustness to disorder, and this robustness is independent of the model size;

[0044] The structure of the two-dimensional photon AB trapping lattice is relatively complex. Each lattice point is coupled with up to six adjacent lattice points, and the positive and negative coupling terms are arranged alternately. In addition, the realization of the two-dimensional AB trapping effect depends on the generation of the gauge potential π in each unit cell to achieve interference cancellation of light. At the same time, there are common errors in the manufacturing process of on-chip nanophotonic devices, which brings great challenges to the practical application of the lattice. Despite this, the strong robustness of topological boundary states and topological corner states makes their tolerance to magnetic field disorder a key issue worthy of in-depth study. In order to explore this issue, the band structure of the two-dimensional photon AB trapping lattice under open boundary conditions is plotted as the trend of the photon gauge potential φ, as shown in the figure. Figure 5 As shown:

[0045] The variation law of the intrinsic energy of the lattice with the gauge potential φ is as follows Figure 6 As shown in (a), it can be seen that as the gauge potential φ changes, the energy of the state also changes. When φ = π, the energy band degenerates and collapses into a complete flat band model with a fixed energy value.

[0046] enlarge Figure 6 (a) The square area, such as Figure 6 As shown in (b), the circle represents the body state, the five-pointed star represents the boundary state at the upper and lower boundaries, the square represents the boundary state at the left and right boundaries, and the pentagon represents the corner state. It can be seen that the phase transition points of the topological boundary state and the topological corner state are not the same;

[0047] The robustness of the topological state is judged by the phase transition of the energy band. That is, if the energy of a certain mode is confused with other modes, it can be judged that it has lost its robustness. This analysis method provides an intuitive basis for evaluating the stability of the topological state, and also points out the direction for optimizing the lattice design to improve the robustness.

[0048] Topological non-trivial phases refer to phases with non-zero topological invariants. These phases exhibit unique topological properties, such as the quantum Hall effect and topological insulators. These properties are extremely robust to small changes in external conditions, that is, they can resist external perturbations within a certain range and maintain the topological state unchanged. This robustness makes topological non-trivial phases have important application potential in fields such as quantum information and low-power electronic devices.

[0049] In contrast, the topological invariant of a topological trivial phase is zero, and its properties are relatively ordinary, lacking the uniqueness and robustness of a non-trivial phase. However, since it may be the starting point for the transition to a topological non-trivial phase, or has other special physical properties, the topological trivial phase is still of great significance in materials science.

[0050] Prove the existence of bulk topological index characterizing higher-order topological insulators (HOTIs):

[0051] In the one-dimensional model, the polarization px along the x-axis is the bulk topological index, which is protected by the mirror symmetry along the x-direction. This concept is extended to higher dimensions, and when calculating the boundary topological phase transition of higher-order topological insulators, the calculation method of boundary polarization and Wilson loop is introduced to analyze the contribution of each lattice point to the polarization.

[0052] The bulk polarization characterizes the displacement of the average position of the Wannier state relative to the center of the unit cell;

[0053] In general, a zero bulk polarization indicates that the mode is fixed at the center and there is no localized state at the boundary. However, in the case of topological nontrivial, a non-zero bulk polarization will induce localized modes at the boundary, forming topological edge states and corner states, such as Figure 7 As shown:

[0054] Figure 7 (a) and 7(b) respectively represent the polarization intensity distribution when the photon gauge potential φ = π. It can be seen that the polarization intensities px and py obtained by integration are 0.2128 and 0.0089, respectively, indicating that the model is in a topological non-trivial phase;

[0055] Figure 7 (c) and 7(d) respectively represent the polarization intensity distribution when the photon gauge potential φ = 0. It can be seen that the polarization intensities px and py are both 0, and the surface model exhibits a topological trivial phase;

[0056] This result clearly reveals the difference between topological non-trivial phases and trivial phases, and provides a theoretical basis for the design and regulation of topological states.

[0057] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for controlling topological angle states based on a flat-band two-dimensional microring lattice, characterized in that: The following steps are involved: S1: Construction of a flat-band two-dimensional microring lattice; S2: Dynamically control topological corner states based on the constructed flat-band two-dimensional microring lattice.

2. The method for controlling topological angle states based on a flat-band two-dimensional microring lattice according to claim 1, characterized in that: In the step S1, the constructed flat-band two-dimensional micro-ring lattice includes a number of unit cells of the array, and the unit cell includes six hexagonal honeycomb main rings, and the six hexagonal honeycomb main rings are connected by positive coupling or negative coupling through rectangular connecting rings, wherein the rectangular connecting rings are designed with an additional path length to meet the anti-resonance relationship and introduce negative coupling so as to flexibly adjust the coupling phase and amplitude, and the rectangular connecting rings move in the vertical direction to generate a direction-related phase between the hexagonal honeycomb main rings, and input and output ports are distributed at different positions of the lattice.

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