Topological flatband control method and system based on non-hermitian micro-ring resonator array

Abstract

This invention relates to a method and system for topological flat-band manipulation based on a non-Hermitian microring resonator array. The method includes: periodically arranging multiple microring resonator arrays into a one-dimensional rhombic structure; controlling the positions and relative gain magnitudes of the gain and loss rings in the microring resonator arrays to achieve a topological phase transition, constructing topologically trivial and topologically non-trivial cell structures; placing a point light source at the center of the multiple microring resonator arrays to excite bulk band modes, achieving a non-Hermitian AB cage effect; and placing the point light source at the edges of the multiple microring resonator arrays to achieve energy-gain topological boundary states or topologically trivial local states induced by interference. The microring resonator array configuration provided by this invention has flexible and controllable characteristics, enriching the means of generating topological states in flat bands.

Description

Technical Field

[0001] This invention belongs to the field of topological photonics technology, specifically relating to a topological flat-band modulation method and system based on a non-Hermitian microring resonator array. Background Technology

[0002] Precise control of photon transport is crucial for realizing next-generation photonic integration, and the development of topological photonics provides new methods for this. Optical topological insulators are an optical analogue to electron transport in a crystal lattice. Based on topological degrees of freedom, constructing topologically protected optical and integrated photonic devices enables disturbance-resistant photon transport and solves problems such as device crosstalk and disordered scattering. However, due to the complexity of fabricating materials with magnetic responses, recent research in topological photonics has shifted towards constructing topologically protected systems by controlling the optical properties of artificial micro / nano structures. Microring resonators are important components in photonic integration and have attracted much attention. They are widely used in designing functional devices such as low-threshold lasers, filters, and phase delayers, and have entered fields such as nonlinear optics, topology, and sensing. Due to their relatively mature fabrication process and ease of realizing photonic gauge potentials, they are used to study topological band structures and topological optical effects. By rationally designing the structural characteristics of microring resonant cavity arrays, different types of artificial lattices can be realized in optical systems, Hamiltonians can be constructed and their on-situ energy, coupling strength and gauge potential can be precisely controlled, and different band structures can be realized. Topological states such as optical topological insulators and optical topological half-metals can be realized, and the topological properties of light waves during transmission can be controlled to realize classical physical phenomena such as the quantum Hall effect.

[0003] In optical systems, gain and loss are ubiquitous and easily manipulated, and their non-Hermitian properties have attracted widespread attention. Non-Hermitian systems are a class of systems with material refractive index gain / loss or open boundaries, and their eigenvalues ​​are generally complex numbers, with their imaginary parts representing energy gain or loss during the evolution of the optical field. Furthermore, non-Hermitian systems possess topological properties not found in Hermitian systems; for example, eigenmodes do not satisfy orthogonality and normalization, and even at some special locations called singularities, eigenvalues ​​and eigenmodes are completely degenerate. Recently, researchers have verified the topological theory of non-Hermitian systems based on microring resonator systems: the number of turns, a topological invariant of non-Hermitian systems, was defined using complex energy spectra, and the volume-edge correspondence and evolution of topological boundary states in Hermitian systems were generalized non-Hermitianly. This research provides new ideas for photon manipulation and a new platform for expanding the topological properties of photons.

[0004] Flat band structures are a special type of dispersion-free band structure. In real space, the corresponding optical field exhibits compact localization characteristics, which is applied in applications such as diffraction-free image transmission, optical localization, and flat band mode lasers. Flat band structures can be realized by designing special lattices to induce destructive interference of light waves, such as Kagome, Dice, and Lieb lattices. In recent years, the organic integration of flat band localization and topology concepts with optical microstructures has led to extremely rapid development in the research of flat band photonics systems, giving rise to a series of novel photophysical phenomena and potential applications. Microring resonators provide a tunable platform for studying flat band physics and topological effects. Research results show novel flat band optical localization and real-space topological phenomena, such as the photonic AB cage effect, localization effect, and Landau-Ziner tunneling. Furthermore, researchers have introduced gain-loss modulation to control the topological phase transition of the system in microring arrays, demonstrating topological boundary modes induced by non-Hermitian flat band localization effects and realizing non-Hermitian AB cage effects. The study of non-Hermitian flat-band photonic microstructures provides a new perspective for understanding and recognizing the topological origin of flat bands, and has broad application prospects in fields such as optical information processing and optical sensing. Summary of the Invention

[0005] To enrich the topological states of flat bands and their tunable characteristics, a method for topological flat band manipulation based on a non-Hermitian microring resonator array is provided in a first aspect of the present invention. The method includes: periodically arranging multiple microring resonator arrays into a one-dimensional rhombic structure; controlling the positions and relative gain magnitudes of the gain and loss rings in the microring resonator arrays to achieve a topological phase transition and construct topologically trivial and topologically nontrivial cell structures; placing point light sources at the center positions of the multiple microring resonator arrays to excite bulk band modes and achieve a non-Hermitian AB cage effect; and placing point light sources at the edge positions of the multiple microring resonator arrays to achieve energy-gain type topological boundary states or topologically trivial local states induced by interference.

[0006] In some embodiments of the present invention, the coupling coefficient within each topological nontrivial cell is set as t, and the coupling coefficient between cells is set as it and -it; the coupling coefficient within each topological trivial cell is set as t and it, and the coupling coefficient between cells is set as t and -it; where t is a real number and i is an imaginary unit.

[0007] Furthermore, each topologically nontrivial unit cell includes eight rhomboidally arranged microring resonators, wherein: four main microring resonators are located at the lattice points of the unit cell, and four connecting microring resonators are used for connection between adjacent main microring resonators; the four main microring resonators, in a clockwise direction, are ordinary dielectric, gain dielectric, ordinary dielectric, and loss dielectric, and each main microring resonator is resonant; the four connecting microring resonators, in a clockwise direction, are ordinary dielectric, gain dielectric, ordinary dielectric, and loss dielectric, and the connecting ring of each ordinary dielectric is non-resonant, while the connecting ring of each gain-loss dielectric is resonant.

[0008] Furthermore, each topologically trivial unit cell includes eight rhomboidally arranged microring resonators, wherein: four main microring resonators are located at the lattice points of the unit cell, and four connecting microring resonators are used for connection between adjacent main microring resonators; the four main microring resonators, in a clockwise direction, are respectively a gain medium, a loss medium, a loss medium, and a gain medium, and each main microring resonator is resonant; the four connecting microring resonators, in a clockwise direction, are respectively a normal medium, a gain medium, a normal medium, and a loss medium; and the connecting ring of each normal medium is non-resonant, while the connecting ring of each gain-loss medium is resonant.

[0009] Preferably, the lateral and longitudinal lengths of all main microring resonators are less than or equal to 8 μm; the lateral and longitudinal lengths of each resonant connecting microring resonator are 8 μm, and the lateral and longitudinal lengths of each non-resonant connecting microring resonator are 8.175 μm and 8 μm, respectively.

[0010] In the above embodiments, the thickness and bending radius of each microring resonator are 0.27 μm and 3 μm, respectively; the spacing between two microring resonators is 0.34 μm.

[0011] A second aspect of the present invention provides a topological flat-band control system based on a non-Hermitian microring resonator array, comprising: an arrangement module for periodically arranging multiple microring resonator arrays into a one-dimensional rhombic structure; a control module for controlling the positions and relative gain magnitudes of gain loops and loss loops in the microring resonator arrays to achieve a topological phase transition and construct topologically trivial and topologically nontrivial cell structures; a setting module for placing point light sources at the center positions of the multiple microring resonator arrays to excite bulk band modes and achieve a non-Hermitian AB cage effect; and placing point light sources at the edge positions of the multiple microring resonator arrays to achieve energy-gain type topological boundary states or topologically trivial local states caused by interference.

[0012] The beneficial effects of this invention are:

[0013] This invention combines non-Hermitian effects with flat-band topological physics, proposing a topological flat-band manipulation method based on a non-Hermitian microring resonator array. By introducing a photonic gauge potential into the closed loop of the unit cell of the one-dimensional microring resonator array, the system exhibits flat-band characteristics. Furthermore, by introducing gain and loss coefficients into the loops and adjusting the positions of the gain and loss loops and their relative magnitudes, a topological phase transition can be achieved, constructing flat-band states with both topological nontriviality and topological triviality. This configuration offers flexibility and tunability, enriching the means of generating topological states. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the basic process of the topology flat-band modulation method based on non-Hermitian microring resonator array in some embodiments of the present invention.

[0015] Figure 2 This is a schematic diagram of a topological nontrivial model in some embodiments of the present invention;

[0016] Figure 3 These are schematic diagrams illustrating simulation results of topological nontrivial models in some embodiments of the present invention;

[0017] Figure 4 This describes the light field distribution within a topologically nontrivial model lattice in some embodiments of the present invention.

[0018] Figure 5 This is a schematic diagram of a topological trivial model in some embodiments of the present invention;

[0019] Figure 6 These are schematic diagrams illustrating simulation results of the topological triviality model in some embodiments of the present invention;

[0020] Figure 7 This is the light field distribution within a topologically trivial model lattice in some embodiments of the present invention. Detailed Implementation

[0021] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0022] refer to Figure 1 and Figure 2In a first aspect of the present invention, a method for topological flat-band modulation based on a non-Hermitian microring resonator array is provided, comprising: S100. periodically arranging multiple microring resonator arrays into a one-dimensional rhombic structure; S200. controlling the positions and relative gain magnitudes of the gain loops and loss loops in the microring resonator arrays to achieve a topological phase transition and construct topologically trivial and topologically nontrivial cell structures; S300. placing point light sources at the center positions of the multiple microring resonator arrays to excite bulk band modes and achieve a non-Hermitian AB cage effect; and placing point light sources at the edge positions of the multiple microring resonator arrays to achieve energy-gain type topological boundary states or topologically trivial local states caused by interference.

[0023] For ease of description, a micro-ring resonator (MRR) is simply referred to as a micro-ring. It typically consists of a straight waveguide and a ring waveguide; this type of micro-ring structure is also known as an all-pass type. When the input light in the straight waveguide passes through the intermediate coupling region, part of the light is coupled into the ring waveguide, while the rest remains in the straight waveguide. The light coupled into the ring waveguide, after propagating along one circumference, returns to the coupling region, where again part of the light is coupled into the straight waveguide, and the rest remains in the ring waveguide. Optical field localization refers to the lateral distribution of the optical field being concentrated in a specific region of space, where the light intensity is zero. The laterally localized optical field is called a localized state, which is also the eigenstate of the equation describing the optical field.

[0024] In step S200 of some embodiments of the present invention, the coupling coefficient within each topological non-trivial cell is set as t, the coupling coefficient between cells is set as it and -it, and the coupling coefficient between cells is set as it; the coupling coefficient within each topological trivial cell is set as t and it, and the coupling coefficient between cells is set as t and -it; where t is a real number and i is an imaginary unit.

[0025] Specifically, refer to Figure 2 The non-trivial eigenmode occupies three distinct lattice points in the flat-band lattice. The intralattice coupling coefficient is a real number t, and the interlattice coupling coefficient is an imaginary number ±it. A beam of light passing through the leftmost lattice point of the unit cell splits into two beams. One beam propagates upwards with a cumulative phase of π / 2, and the other beam propagates downwards with a cumulative phase of -π / 2. They then refocus upon passing through the next unit cell. Consequently, a magnetic flux of π accumulates throughout the entire lattice.

[0026] It is understandable that arranging a multi-period microring resonator array into a one-dimensional rhombus structure, and adjusting the positions of the gain and loss loops and their relative magnitudes, such that the coupling coefficients between each cell lattice point are t, t, it, and -it respectively, with a closed-loop magnetic flux of π, results in a one-dimensional rhombus array whose energy spectrum is flat throughout the Brillouin zone, and each point on the spectrum is a third-order EP degeneracy point. Setting the intra-cell coupling coefficient to t and the inter-cell coupling coefficients to ±it, the system is topologically non-trivial, supporting topologically protected boundary states on the boundaries of the one-dimensional rhombus array. Setting the intra-cell coupling coefficients to t and it and the inter-cell coupling coefficients to t and -it, the system is topologically trivial, in which case no topological boundary states appear.

[0027] Furthermore, each topologically nontrivial unit cell includes eight rhomboidally arranged microring resonators, wherein: four main microring resonators are located at the lattice points of the unit cell, and four connecting microring resonators are used for connection between adjacent main microring resonators; the four main microring resonators, in a clockwise direction, are ordinary dielectric, gain dielectric, ordinary dielectric, and loss dielectric, and each main microring resonator is resonant; the four connecting microring resonators, in a clockwise direction, are ordinary dielectric, gain dielectric, ordinary dielectric, and loss dielectric, and the connecting ring of each ordinary dielectric is non-resonant, while the connecting ring of each gain-loss dielectric is resonant.

[0028] It can be understood that ordinary medium, gain medium, and loss medium respectively represent that the medium has no gain effect on the light intensity under the illumination of incident light, has a gain effect, and has a loss effect, with corresponding gain coefficients of zero, positive, and negative, respectively.

[0029] Furthermore, each topologically trivial unit cell includes eight rhomboidally arranged microring resonators, wherein: four main microring resonators are located at the lattice points of the unit cell, and four connecting microring resonators are used for connection between adjacent main microring resonators; the four main microring resonators, in a clockwise direction, are respectively a gain medium, a loss medium, a loss medium, and a gain medium, and each main microring resonator is resonant; the four connecting microring resonators, in a clockwise direction, are respectively a normal medium, a gain medium, a normal medium, and a loss medium; and the connecting ring of each normal medium is non-resonant, while the connecting ring of each gain-loss medium is resonant.

[0030] Preferably, the lateral and longitudinal lengths of all main microring resonators are less than or equal to 8 μm; the lateral and longitudinal lengths of each resonant connecting microring resonator are 8 μm, and the lateral and longitudinal lengths of each non-resonant connecting microring resonator are preferably 8.175 μm and 8 μm, respectively.

[0031] Specifically, the microring resonator is preferably made of silicon, the thickness of the microrings is preferably 0.27 μm, the spacing between the microrings is preferably 0.34 μm, the bending radius of the microrings is preferably 3 μm, the transverse and longitudinal lengths of the main ring are preferably 8 μm, the transverse and longitudinal lengths of the resonant connecting ring are preferably 8 μm, and the transverse and longitudinal lengths of the non-resonant connecting ring are preferably 8.175 μm and 8 μm, respectively. The refractive index of the gain dielectric main ring is expressed as n = 3 - iρ1, the refractive index of the loss dielectric main ring is expressed as n = 3 + iρ1, the refractive index of the gain dielectric connecting ring is expressed as n = 3 - iρ2, and the refractive index of the loss dielectric main ring is expressed as n = 3 + iρ2. Wherein, ρ1 = 2.25 × 10⁻¹⁰. －4 ρ2 = 0.0152 are the loss (or gain) coefficients in the main loop and the connecting loop, respectively.

[0032] In this embodiment, based on a topologically nontrivial structure, the band structure is calculated using Comsol software based on the finite element method. Due to the introduction of non-Hermitian modulation, the energy spectrum is complex, such as... Figure 3 As shown in (a) and 3(b), the eigenstates of the real and imaginary energy spectra are mainly concentrated on the flat band, with four isolated boundary states distributed on both sides of the flat band. The boundary states on the left and right sides correspond to... and The real and imaginary energy spectra under its periodic boundary are as follows: Figure 3 (c) and Figure 3 As shown in (d), it can be observed that eight additional patterns separate from the left and right sides of the body posture, which is consistent with... Figure 3 The results in (a) and 3(b) do not match. This is because the ring structure contains a pair of degenerate modes, causing the number of boundary states to increase. Figure 3 Four of (a) and 3(b) evolved into eight.

[0033] From the perspective of topological photonics, topological invariants can be used to describe the topological properties of a system. There are two ways to measure topological invariants: one is by calculating the number of coils and the Zak phase, and the other is by measuring the topological boundary states. However, for the multi-level degenerate system in this embodiment, due to the presence of the EP point, the number of coils and the Zak phase cannot be directly calculated, and probing the boundary states is also very difficult. According to the Majorana theory proposed by E. Majorana for describing multi-degenerate systems, the eigenstates of the system can be mapped onto Majorana stars on Bloch spheres. Under open boundary conditions, the Hamiltonian of the system can be expressed as...

[0034]

[0035] in For the Bloch momentum of the Bloch wave packet, we obtain the eigenvalues ​​E of H. 1,2,3=0 indicates that the system is third-order EP degenerate, and the corresponding eigenstate is The eigenstate Ψ 1,2,3 Mapped onto the Bloch sphere, the corresponding spherical coordinate system is (l, θ, φ), and its relationship with the spherical coordinate angle is:

[0036]

[0037] Where C l It is the spherical coordinate form of the eigenstate Ψ, which can be solved. x 1,2,3 Represented as x m =tan(θ) m / 2)exp(iφ m ), where m = 1, 2, 3, the number of windings can be calculated using the following formula.

[0038]

[0039] here When x ranges from 0 to 4π, all values ​​represent the complete Majorana star trajectory, and any point on the trajectory can be traced back to the origin via the trajectory curve. For example... Figure 2 As shown in (e), the Majorana star trajectory forms a closed curve perpendicular to the x-axis on the Bloch sphere. According to formula (3), the number of wraps is calculated to be 2, and the number of boundary states is exactly equal to the number of wraps, that is, the number of topological boundary states is also 2. Figure 2 (a) and Figure 2 (b) shows 8 topological boundary states, which contradicts the previous statement. This is because our instance uses periodic boundary conditions; considering the left and right boundaries, the number of boundary states becomes 4. Furthermore, the ring structure contains a pair of degenerate modes, increasing the number of boundary states from 4 to 8.

[0040] The topological properties of an optical system can also be expressed by the square of the Hamiltonian H. 2 The topological properties of the system are analyzed by examining its corresponding eigenvalues ​​and eigenstates. The squared Hamiltonian H of this example system... 2 for

[0041]

[0042] Similarly, H can be calculated. 2 The eigenvalue is E = ±2t 2 It has the same eigenstate Ψ as H. 1，2，3 For non-zero eigenstates Ψ 2，3 Perform a rotational transformation to obtain a new form Ψ 2，3 =(cos(θ / 2), achievable And φ = π / 2. The eigenstates Ψ of the entire Brillouin zone are characterized using spherical coordinates. 2，3 The evolution, such as Figure 3 As shown in (f), its trajectory is also a closed curve around the x-axis with a number of turns of 2, which is consistent with the previous theory.

[0043] Due to the symmetry of the lattice chains, beams with the same path in the lattice will undergo destructive interference at a certain main ring lattice point, resulting in the localization of the optical field at certain specific lattice points and producing a non-Hermitian AB cage effect. Then, by using point sources to excite the beams at different locations in the micro-ring array, such as... Figure 4 As shown, excitation from the S1 microring position will excite real boundary states, with the light field perfectly localized within the three adjacent bottom main rings, and the intensity relationship within the lattice is 2:1:1. Excitation from the S2 microring position will localize the light field within the seven main rings near the incident position. Excitation from the S3 microring position will excite imaginary boundary states. After a dynamic evolution process within the lattice, the amplification mode will dominate, with the light field localized within the three adjacent top main rings, and the intensity relationship within the lattice is 1:1:2.

[0044] In another embodiment, a trivial eigenmode occupies three distinct lattice points in a flat-band lattice, with intralattice coupling coefficients of real numbers t and it, and interlattice coupling coefficients of t and -it. A beam passing through the leftmost lattice point of the unit cell splits into two beams. One beam propagates upwards with an accumulated phase of -π / 2, and the other beam propagates downwards with an accumulated phase of π / 2, and then refocuses upon passing through the next unit cell. Consequently, a magnetic flux of π accumulates throughout the entire lattice.

[0045] like Figure 5 As shown in (b), the second embodiment of the present invention includes a micro-ring resonant cavity array containing five periods arranged in a rhombus. Each unit cell consists of eight micro-ring resonant cavities arranged in a rhombus. Four main rings are located at the lattice points of the unit cell, and four connecting rings are used for connecting adjacent main rings. The four main rings, in a clockwise direction, are a gain medium, a loss medium, a loss medium, and a gain medium, respectively. The four connecting rings, in a clockwise direction, are a normal medium, a gain medium, a normal medium, and a loss medium, respectively. All the main rings are resonant, the connecting rings of the normal medium are non-resonant, and the connecting rings of the gain and loss media are resonant.

[0046] like Figure 4As shown in (c), the intra-lattice coupling coefficients are real numbers t and it, and the inter-lattice coupling coefficients are t and -it. A configuration of two main rings and one connecting ring is used to flexibly adjust the coupling coefficients. Without introducing gain or loss modulation within the rings, a real coupling coefficient t can be achieved, the value of which is related to the coupling distance between the rings. If gain modulation is introduced within the two main rings and loss modulation is introduced within the connecting ring, a virtual coupling coefficient it can be achieved. Conversely, if loss modulation is introduced within the two main rings and gain modulation is introduced within the connecting ring, virtual coupling absorption -it can be achieved. In the real coupling case, the two main rings are resonant, and the connecting ring in the middle is non-resonant, while in the virtual coupling case, both the main rings and the connecting ring are resonant.

[0047] To achieve efficient excitation of the microring array, the thickness of the microrings in the described topologically trivial structure is chosen to be 0.27 μm, the spacing between microrings to be 0.34 μm, the bending radius of the microrings to be 3 μm, the lateral and longitudinal lengths of all main rings to be 8 μm, the lateral and longitudinal lengths of the gain dielectric / loss dielectric connecting rings to be 8 μm, and the lateral and longitudinal lengths of the ordinary dielectric connecting rings to be 8.175 μm and 8 μm, respectively. The refractive index of the gain dielectric main ring is expressed as n = 3 - iρ1, the refractive index of the loss dielectric main ring is expressed as n = 3 + iρ1, the refractive index of the gain dielectric connecting ring is expressed as n = 3 - iρ2, and the refractive index of the loss dielectric main ring is expressed as n = 3 + iρ2. Where ρ1 = 2.25 × 10⁻¹⁰. －4 ρ2 = 0.0152 are the loss (or gain) coefficients in the main loop and the connecting loop, respectively.

[0048] It is understood that in the above embodiments, the coupling coefficients within the unit cell are t and it, and the coupling coefficients between unit cells are t and -it. In this case, the system is topologically trivial, meaning that no boundary states appear in the system's energy spectrum, such as... Figure 6 As shown in (a) and 6(b), the band structure was calculated using Comsol software, as follows: Figure 6 As shown in (c) and 6(d), the energy spectrum of the system is a flat band, with no isolated boundary states appearing. In this case, the Hamiltonian of the system under open boundary conditions is...

[0049]

[0050] Based on the above formula, the eigenvalue E can be calculated. 1，2，3 =0, corresponding eigenstate Ψ 1，2，3 = (0, 1, i) T / 2. The eigenstate Ψ 1，2，3 Mapping onto the Bloch sphere and substituting into formula (3), we can solve for... Corresponding to Figure 6 (e) shows two Majorana stars on the Bloch sphere. The Hamiltonian H... trivial After squaring, we get

[0051]

[0052] Similarly, With H trivial Having the same eigenvalues ​​and eigenstates, the eigenstates are represented in spherical coordinates, corresponding to... Figure 6 (f) shows a Majorana star on the Bloch sphere. In this example, the trajectory is a fixed point in both topological representation methods, so the number of turns in the system is 0.

[0053] Next, excitation was achieved by using point light sources at different locations on the micro-ring array, such as... Figure 7 As shown, when excited from the S1 microring, the light field is perfectly localized within the three lowest adjacent main rings, with an intensity ratio of 1:1:2 within the grid. When excited from the S2 microring, the light field is localized within the five main rings near the incident position. When excited from the S3 microring, the light field is localized within the three highest adjacent main rings, with an intensity ratio of 1:1:2 within the grid. It is noteworthy that the localization effect in the topologically trivial configuration is caused by destructive interference, rather than by excited topological boundary state modes. This is the biggest difference between topologically trivial and topologically non-trivial configurations.

[0054] Example 2

[0055] A second aspect of the present invention provides a topological flat-band control system based on a non-Hermitian microring resonator array, comprising: an arrangement module for periodically arranging multiple microring resonator arrays into a one-dimensional rhombic structure; a control module for controlling the positions and relative gain magnitudes of gain loops and loss loops in the microring resonator arrays to achieve a topological phase transition and construct topologically trivial and topologically nontrivial cell structures; a setting module for placing point light sources at the center positions of the multiple microring resonator arrays to excite bulk band modes and achieve a non-Hermitian AB cage effect; and placing point light sources at the edge positions of the multiple microring resonator arrays to achieve energy-gain type topological boundary states or topologically trivial local states caused by interference.

[0056] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0057] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for topological flat-band control based on a non-Hermite micro-ring resonator array, characterized in that, include: Multiple micro-ring resonant cavity arrays are periodically arranged into a one-dimensional rhombic structure; By adjusting the positions and relative gain magnitudes of the gain and loss rings in the microring resonator array, a topological phase transition is achieved, and a topologically nontrivial cell structure is constructed. The coupling coefficient within each topologically nontrivial cell is denoted as t, and the coupling coefficients between cells are denoted as it and -it, where t is a real number and i is the imaginary unit. Point light sources are placed at the center of multiple micro-ring resonant cavity arrays to excite bulk band modes and achieve the non-Hermitian ABcage effect; Point light sources are placed at the edges of multiple micro-ring resonant cavity arrays to achieve energy-gain type topological boundary states; or, By adjusting the positions and relative gain of the gain ring and loss ring in the microring resonator array, a topological phase transition is achieved, and a topologically trivial cell structure is constructed. The coupling coefficients within each topologically trivial cell are denoted as t and it, and the coupling coefficients between cells are denoted as t and -it, where t is a real number and i is the imaginary unit. Point light sources are placed at the edges of multiple micro-ring resonator arrays to achieve topologically trivial local states caused by interference.

2. The method of topological band regulation based on a non-Hermite micro-ring resonator cavity array according to claim 1, wherein, Each topologically nontrivial unit cell includes eight rhomboidally arranged microring resonators, of which: four main microring resonators are located at the lattice points of the unit cell, and four connecting microring resonators are used for the connection between adjacent main microring resonators. The four main micro-ring resonators are arranged clockwise as ordinary dielectric, gain dielectric, ordinary dielectric, and loss dielectric, and each main micro-ring resonator is in resonance. The four connected micro-ring resonant cavities are, in clockwise order, a normal dielectric, a gain dielectric, a normal dielectric, and a loss dielectric; and the connecting ring of each normal dielectric is non-resonant, while the connecting ring of each gain-loss dielectric is resonant.

3. The method of claim 1, wherein the non-Hermite micro-ring resonator array is a photonic crystal ring resonator array. Each topologically trivial unit cell includes eight rhomboidally arranged microring resonators, of which: four main microring resonators are located at the lattice points of the unit cell, and four connecting microring resonators are used for the connection between adjacent main microring resonators. The four main micro-ring resonators are arranged clockwise as gain medium, loss medium, loss medium and gain medium, and each main micro-ring resonator is in resonance. The four connected micro-ring resonant cavities are, in clockwise order, a normal dielectric, a gain dielectric, a normal dielectric, and a loss dielectric; and the connecting ring of each normal dielectric is non-resonant, while the connecting ring of each gain-loss dielectric is resonant.

4. The topological flat-band modulation method based on a non-Hermitian microring resonator array according to claim 2 or 3, characterized in that, The lateral and longitudinal lengths of all main microring resonators are less than or equal to 8 μm; the lateral and longitudinal lengths of each resonant connecting microring resonator are 8 μm, and the lateral and longitudinal lengths of each non-resonant connecting microring resonator are 8.175 μm and 8 μm, respectively.

5. The method of topological band regulation based on a non-Hermitian array of microring resonators according to any one of claims 1 to 3, wherein, The thickness and bending radius of each microring resonator are 0.27 μm and 3 μm, respectively; the spacing between two microring resonators is 0.34 μm.

6. A topology flatband control system based on non-Hermite micro-ring resonator array, characterized in that, include: The arrangement module is used to periodically arrange multiple micro-ring resonant cavity arrays into a one-dimensional rhombic structure; The control module controls the position and relative gain of the gain ring and loss ring in the micro-ring resonator array to achieve a topological phase transition and construct a topologically nontrivial cell structure. The coupling coefficient within each topologically nontrivial cell is set as t, and the coupling coefficients between cells are set as it and -it, where t is a real number and i is the imaginary unit. Alternatively, by adjusting the positions and relative gain of the gain ring and loss ring in the microring resonator array, a topological phase transition can be achieved, constructing a topologically trivial unit cell structure; the coupling coefficients within each topologically trivial unit cell are set as t and it, and the coupling coefficients between units are set as t and -it; where t is a real number and i is the imaginary unit; The setup module is used to place the point light source at the center of multiple micro-ring resonant cavity arrays to excite the bulk band mode and realize the non-Hermitian AB cage effect. Point light sources are placed at the edges of multiple micro-ring resonant cavity arrays to achieve energy-gain type topological boundary states; Alternatively, point light sources can be placed at the edges of multiple micro-ring resonator arrays to achieve topologically trivial local states caused by interference.

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