A method for controlling topological corner states based on flat-band two-dimensional micro-ring lattice

Abstract

The application discloses a kind of based on flat band two-dimensional micro-ring lattice Topological Corner State Regulation Method, belong to topological corner state regulation technical field, including the following steps: S1: construct flat band two-dimensional micro-ring lattice;S2: based on the dynamic regulation topological corner state of constructed flat band two-dimensional micro-ring lattice;The application is designed by hexagonal honeycomb micro-ring resonator, combined with dynamic phase regulation technology, realize the flexible adjustment of photonic gauge potential and the compact local mode of robustness of topological state angular state, solve the core problems such as photonic gauge potential regulation inflexibility, topological state local deficiency and poor fault tolerance in prior art, provide high performance and high reliability design paradigm for on-chip integrated photonic devices.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of topological corner state regulation, and particularly relates to a topological corner state regulation method based on a flat-band two-dimensional micro-ring lattice. BACKGROUND

[0002] With the semiconductor process gradually approaching the physical limit, optical communication technology becomes an important way to solve the demand for high-speed and large-capacity information transmission.

[0003] As an information carrier, photons have the advantages of high-speed transmission, anti-electromagnetic interference, large bandwidth and high energy consumption ratio, and become an ideal choice for future high-speed and large-capacity information transmission. However, there are two major challenges in its practical application: one is how to realize flexible manipulation of light, and the other is how to efficiently and stably integrate micro-optical elements into photonic devices.

[0004] At present, photonic gauge potential is constructed through space-time modulation, nonlinear effect, tilted geometric design and other ways to realize photonic Aharonov-Bohm effect, Bloch oscillation, negative refraction and dynamic localization, but its regulation depends on complex structure design and fixed parameters, which cannot flexibly adjust the phase and coupling strength, limits the dynamic localization and diffusion control of photons, and is difficult to adapt to multi-scenario requirements.

[0005] At present, the topological photonics in the field of integrated photonic circuits suppresses the influence of defects and disorder on light transmission by constructing robust boundary modes, but the existing one-dimensional or simple two-dimensional lattice topological structure is difficult to realize highly localized topological states such as topological corner states in a compact size.

[0006] At present, the on-chip integrated photonic device has very high manufacturing precision requirements, and the traditional topological structure is easy to cause energy band distortion when there is process error, which affects the robustness of the topological state.

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

[0008] To solve the problems raised in the background art, the application provides a topological corner state regulation method based on a flat-band two-dimensional micro-ring lattice, which has the characteristics of solving the core problems of non-flexible photonic gauge potential regulation, insufficient localization of topological states and poor manufacturing fault tolerance in the prior art.

[0009] To achieve the above purpose, the application provides the following technical scheme: a topological corner state regulation method based on a flat-band two-dimensional micro-ring lattice, comprising the following steps:

[0010] S1: constructing a flat-band two-dimensional micro-ring lattice;

[0011] S2: dynamically regulating the topological corner state based on the constructed flat-band two-dimensional micro-ring lattice.

[0012] Further, in the step S1, the constructed flat-band two-dimensional micro-ring lattice includes an array of several unit cells, the unit cell includes six hexagonal honeycomb main rings, the six hexagonal honeycomb main rings are connected through rectangular connection rings in positive coupling or negative coupling, wherein the rectangular connection ring is designed with an additional path length, which meets the anti-resonance relationship to introduce negative coupling while flexibly adjusting the coupling phase and amplitude, the rectangular connection ring is moved along the vertical direction to make the hexagonal honeycomb main rings produce a direction-related phase, and the input and output ports are distributed at different positions of the lattice.

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

[0014] The present application realizes flexible adjustment of photonic gauge potential and compact local mode of robust topological corner state of the angle state through the design of hexagonal honeycomb micro-ring resonant cavity combined with dynamic phase regulation technology, solves the core problems of inflexible photonic gauge potential regulation, insufficient localizability of topological state and poor fault tolerance in the prior art, and provides a high-performance and high-reliability design paradigm for on-chip integrated photonic devices. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 It is a structural schematic diagram of a two-dimensional photonic AB trapped lattice.

[0016] Figure 2 It is a band structure diagram of the lattice under periodic boundary conditions of the present application.

[0017] Figure 3 It is a band structure diagram under completely open boundary conditions of the present application.

[0018] Figure 4 It is a three-dimensional structural schematic diagram of a two-dimensional micro-ring lattice of the present application.

[0019] Figure 5 It is a local mode diagram of a topological state of the present application.

[0020] Figure 6 It is a band structure diagram under open boundary conditions of the present application.

[0021] Figure 7 It is a van Hove band under periodic boundary conditions of the present application. DETAILED DESCRIPTION

[0022] With reference to the drawings and embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

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

[0024] Specifically, part of the rhombus structure contains three positive couplings and one negative coupling, and the remaining rhombus structure contains one positive coupling and three negative couplings. Regardless of which combination, it can be equivalent to π magnetic flux, so as to realize 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 rhombus structure design can regulate the photon gauge potential in each unit cell, further research is conducted on the energy band structure under different photon gauge potentials;

[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 energy band structure of the two-dimensional model is as shown in Figure 2

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

[0028] When the photon gauge potential φ is π, the energy band structure is as shown in Figure 2 (b). As can be seen, the energy band is degenerate, and degenerates into three completely flat energy bands. At this time, the model as a whole exhibits a flat-band characteristic, and no dispersion occurs. Thus, it can be proved that a two-dimensional photonic AB trapped lattice is successfully constructed;

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

[0030] The corresponding band structure under the completely open boundary condition (OBC) is shown in FIG. Figure 3

[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 ensured to be an integer multiple of the unit cell, so as to avoid inaccurate calculation of the in-gap state due to excess or lack of lattice points, specifically, the lattice contains three unit cell units in the x direction and two unit cell units in the y direction, a total of 36 lattice points, as shown in FIG. Figure 3

[0032] Three different in-gap states appear in the energy gap of the upper and lower bands, namely the square points represent the boundary states of the upper and lower boundaries, the pentagonal points represent the boundary states of the left and right boundaries, and the pentagram represents the corner state, as shown in FIG. Figure 3

[0033] It is worth noting that under the completely open boundary condition, isolated zero-dimensional corner states appear at the intersection of the two boundaries of the two-dimensional photonic AB trapping lattice, similar to the boundary state, the zero-dimensional corner state also shows the flat band characteristic, but its mode field distribution and energy size are different from the boundary state, the energy of the corner state is lower, and the energy gap between the corner state and the bulk state is higher, which indicates that the corner state may have stronger robustness;

[0034] The structure of the two-dimensional photonic 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 realize the localization and diffusion of light, a controllable magnetic flux needs to be introduced into the unit cell, based on the design of the micro-ring resonant cavity array, a complex coupling term can be constructed in the structure, and the photon gauge potential can be flexibly controlled.

[0035] Therefore, it is redesigned, as shown in the accompanying Figure 4 , specifically as follows:

[0036] The present application provides the following technical scheme: a topological corner state regulation method based on a flat-band two-dimensional micro-ring lattice, comprising the following steps:

[0037] S1: constructing a flat-band two-dimensional micro-ring lattice;

[0038] ​​​The constructed flat-band two-dimensional microring lattice includes several unit cells of the array, each of which consists of six hexagonal honeycomb main rings. The six hexagonal honeycomb main rings are connected by rectangular connecting rings with positive or negative coupling. The rectangular connecting rings are designed with additional path length to meet the antiresonance relationship, introduce negative coupling, and flexibly adjust the coupling phase and amplitude. The rectangular connecting rings move in the vertical direction, generating a direction-dependent phase between the hexagonal honeycomb main rings. Input and output ports are distributed at different positions in 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 as follows: 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. The energy is highly concentrated in the main resonant ring near the input port, and there is no sign of diffusion. This feature further verifies the advantages of the topological corner state in terms of localization and robustness.

[0042] The topological edge states and topological corner states of this 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 to 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 exhibit 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 staggered. 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 huge challenges to the practical application of this 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 a function 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 topological states is determined by energy band phase transitions. If the energy of a certain mode is confused with other modes, it can be judged to have lost its robustness. This analytical method provides an intuitive basis for evaluating the stability of topological states and also points the way to optimize lattice design to improve robustness.

[0048] Topologically nontrivial phases are those 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 while maintaining their topological state. This robustness gives topologically nontrivial phases significant potential for applications 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, because it may be the starting point for the transition to a topological non-trivial phase or possess other special physical properties, the topological trivial phase still has important significance in materials science.

[0050] Prove the existence of bulk topological indices that characterize 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. 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, when the bulk polarization is zero, the mode is fixed at the center and there is no localized state at the boundary. However, in the case of topological nontrivial, when the bulk polarization is nonzero, localized modes are induced at the boundary, forming topological edge states and corner states, such asFigure 7 are shown in FIG. 7(a) and 7(b), respectively. It can be seen that the integrated polarized intensity pxand pyare 0.2128 and 0.0089, respectively, indicating that the model is in the topologically nontrivial phase;

[0054] Figure 7 (c) and 7(d) represent the polarized intensity distribution when the photon gauge potential φ = 0, respectively. It can be seen that the polarized intensity pxand pyare both 0, indicating that the surface model is in the topologically trivial phase;

[0055] Figure 7 (c) and 7(d) represent the polarized intensity distribution when the photon gauge potential φ = 0, respectively. It can be seen that the polarized intensity pxand pyare both 0, indicating that the surface model is in the topologically trivial phase;

[0056] This result clearly reveals the difference between the topologically nontrivial phase and the trivial phase, providing a theoretical basis for the design and control of topological states.

[0057] Although embodiments of the present application have been shown and described, it is to be understood that various modifications, substitutions, replacements and changes can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for controlling topological corner 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; The constructed flat-band two-dimensional microring lattice includes several unit cells of the array, each of which consists of six hexagonal honeycomb main rings. The six hexagonal honeycomb main rings are connected by rectangular connecting rings with positive or negative coupling. The rectangular connecting rings are designed with additional path length to meet the antiresonance relationship, introduce negative coupling, and flexibly adjust the coupling phase and amplitude. The rectangular connecting rings move in the vertical direction, generating a direction-dependent phase between the hexagonal honeycomb main rings. Input and output ports are distributed at different positions in the lattice. S2: Dynamically control topological corner states based on the constructed flat-band two-dimensional microring lattice.

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