Integrated photon matrix vector multiplication calculator based on optical resonant cavity and method thereof

Abstract

The invention provides an integrated photon matrix vector multiplication calculator based on an optical resonant cavity and a method thereof. A continuum bound state is constructed on a chip by using an optical resonant cavity array, an output spectrum and a light field are analyzed through a coupled mode theory and a transmission matrix theory, amplitude of input light forms a one-dimensional input vector as a multiplier, a regulation and control matrix calculated by the coupled mode theory or a transmission matrix method is used as another multiplier, and the continuum bound state is obtained. An intelligent photon matrix vector multiplication calculator is constructed, construction of an on-chip large-scale compact continuum bound state BIC is realized, a non-Hermite control BIC system is introduced to generate space-time breaking, and single-mode output of a continuum bound state BIC mode is completed. And the calculation robustness and expandability of the intelligent photon matrix vector multiplication calculator based on the BIC configuration are further improved.

Description

Technical Field

[0001] The present invention relates to a photon multiplication calculator technology, and in particular to an integrated photon matrix vector multiplication calculator based on an optical resonant cavity and an implementation method thereof. Background Art

[0002] With the rapid development of information technology, artificial intelligence and large models have demonstrated remarkable performance and are widely used. This, in turn, has led to higher demands on computing platforms for both computational power and power consumption. Due to the ultra-high propagation speed, ultra-low power consumption, and high bandwidth of photons, optical computing using photons as information carriers holds unique potential for solving problems that are beyond the reach of traditional von Neumann architectures. Existing optical computing approaches primarily focus on three approaches: optical networks based on cascaded Mach-Zehnder interferometers, optical networks based on optical resonators and wavelength division multiplexing, and diffractive optical networks based on metasurfaces. However, these approaches are limited by manufacturing process precision, require extensive calibration for experiments and applications, and suffer from stability issues. Wavelength division multiplexing optical networks based on optical resonators have attracted widespread attention due to their high integration density and controllable flexibility. However, since their computational approach relies on the resonant states of outwardly radiated energy formed by each optical resonator in a continuous domain, this approach suffers from low stability. Although continuum bound states exist in the continuous domain, they do not radiate energy outward. Their implementation solutions are currently concentrated in metasurfaces and photonic crystals, and there is a lack of on-chip integrated implementation solutions. Their applications are currently concentrated in fields such as nonlinear lasers and filtering sensors, and there is a lack of application scenarios for intelligent optical computing. Summary of the Invention

[0003] In order to solve the problems existing in the above-mentioned prior art, the present invention proposes an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity and its implementation method, which can compactly realize continuum bound states on a chip and combine non-Hermitian control to construct a robust matrix-vector multiplication calculator.

[0004] An object of the present invention is to provide an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity.

[0005] The integrated photon matrix vector multiplication calculator based on an optical resonant cavity of the present invention comprises: a substrate and a plurality of optical resonant cavities; the plurality of optical resonant cavities are formed on the substrate; wherein the refractive index of the substrate is less than the refractive index of the optical resonant cavity; the shape of the optical resonant cavity is a circular ring with a thickness;

[0006] n×n optical resonant cavities are arranged in a two-dimensional array of n rows and n columns to form a basic unit, where n is an odd number ≥ 3. Two small optical resonant cavities and two straight waveguides are disposed within the central optical resonant cavity in the center of each basic unit. The diameter of the small optical resonant cavity is smaller than the radius of the optical resonant cavity, and the length of the straight waveguide allows it to be placed within the optical resonant cavity. A line connecting the centers of the two small optical resonant cavities passes through the center of the central optical resonant cavity, and the angle between the line and the row and column directions is 45°, thereby minimizing interference from adjacent optical resonant cavities to the small optical resonant cavity. The straight waveguide is located outside the small optical resonant cavity and is tangential to the small optical resonant cavity, and there is a distance between the straight waveguide and the small optical resonant cavity. The distance between the centers of adjacent optical resonant cavities is equal between rows and columns, i.e., the positions of the centers are periodically distributed in a two-dimensional manner. The waveguide width of each optical resonant cavity is independently adjustable, and the coupling distance between adjacent optical resonant cavities is adjusted by changing the waveguide width of the resonant cavity.

[0007] A photon matrix vector multiplication calculator is constructed by arranging M×K basic units in two dimensions, where M and K are natural numbers, and adjacent basic units share a row or column of optical resonant cavities. The coupling distance between two adjacent optical resonant cavities in each basic unit is independently adjustable. Calculations based on coupled-mode theory reveal that the photon matrix vector multiplication calculator exhibits a symmetric mode in one direction and an antisymmetric mode in the other, resulting in a continuum bound state. The calculation results exhibit strong anti-interference capabilities and robustness. Non-Hermitian control is achieved by introducing loss through doping in the optical resonant cavity, causing the two-dimensional photon matrix vector multiplication calculator to break parity-time (PT) symmetry, i.e., PT violation.

[0008] One end of each straight waveguide serves as an input port, and the other end as an output port; external input light is coupled into the input port, and the M×K×2 beams of input light are independent of each other. The amplitude of the input light contains input information, and the amplitudes of all input lights constitute a one-dimensional input vector as a multiplier; the distance between the straight waveguide and the small optical resonant cavity and the coupling distance between two adjacent optical resonant cavities determine the control matrix, which is calculated by coupled mode theory or transfer matrix method and serves as another multiplier; each output port is connected to a channel of a photodetector; the number of input ports and output ports is M×K×2, respectively, and the dimension of the control matrix is (M×K×2)×(M×K×2); the photon matrix-vector multiplication calculator multiplies the input vector with the control matrix to obtain the multiplied result output. The photon matrix-vector multiplication calculator has PT breaking, thereby achieving single-mode output and further improving the stability of the calculator.

[0009] Plot the output spectrum for each output port by varying the detuning in the diagonal terms of the Hamiltonian.

[0010] By doping phosphorus or boron in the optical resonant cavity, loss is introduced for non-Hermitian control: by shifting the loss-gain zero point, the contrast of different losses is considered to be the contrast of gain-loss. The doping concentration of phosphorus or boron is 1×10 15 ~1×10 18 cm-3.

[0011] One direction is in the direction of the connection between the two small optical resonant cavities, and the other direction is perpendicular to the direction of the connection between the two small optical resonant cavities. The photon matrix vector multiplication calculator has an antisymmetric mode in the direction of the connection between the two small optical resonant cavities and a symmetric mode in the orthogonal direction of this direction.

[0012] The material of the substrate is silicon dioxide; the material of the optical resonance cavity is silicon.

[0013] The diameter of the optical resonant cavity is 30 to 60 μm; the waveguide width is 0.45 to 0.50 μm. The distance between the edges of two adjacent optical resonant cavities is 200 to 300 nm. The length of the straight waveguide is 5 to 8 μm, and the waveguide width is 0.45 to 0.50 μm. The diameter of the small optical resonant cavity is 10 to 20 μm, and the waveguide width is 0.45 to 0.50 μm. The distance between the centers of two adjacent optical resonant cavities is 30.15 to 60.35 μm. The distance between the straight waveguide and the small optical resonant cavity is 0.15 to 0.35 μm; the thickness of the optical resonant cavity is 0.2 to 0.25 μm.

[0014] The range of M is 1 to 5; the range of K is 1 to 5.

[0015] Another object of the present invention is to provide a method for implementing an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity.

[0016] The method for implementing the integrated photon matrix-vector multiplication calculator based on an optical resonant cavity of the present invention comprises the following steps:

[0017] 1) Basic unit:

[0018] A circular ring with thickness is used as an optical resonant cavity;

[0019] Arrange n×n optical resonant cavities into a two-dimensional array of n rows and n columns to form a basic unit, where n is an odd number ≥3;

[0020] Two small optical resonant cavities and two straight waveguides are arranged in the central optical resonant cavity in the middle of the basic unit. The diameter of the small optical resonant cavity is smaller than the radius of the optical resonant cavity, and the length of the straight waveguide is sufficient to be placed in the optical resonant cavity. The line connecting the centers of the two small optical resonant cavities passes through the center of the central optical resonant cavity, and the angle between the line and the row direction and the column direction is 45 degrees, so that the interference of the small optical resonant cavity with the adjacent optical resonant cavity is minimized.

[0021] The straight waveguide is located outside the small optical resonant cavity and is tangent to the small optical resonant cavity, and there is a distance between the straight waveguide and the small optical resonant cavity;

[0022] The distances between the centers of adjacent optical resonant cavities are equal between rows and columns, i.e., the positions of the centers are periodically distributed in two dimensions. The waveguide width of each optical resonant cavity is independently adjustable, and the coupling distance between adjacent optical resonant cavities is adjusted by changing the waveguide width of the resonant cavity.

[0023] 2) Construct an integrated photon matrix-vector multiplication calculator:

[0024] Arrange M×K basic units in two dimensions, where M and K are natural numbers, and adjacent basic units share a row or column of optical resonant cavities, to form a photon matrix vector multiplication calculator;

[0025] In each basic unit, the coupling distance between two adjacent optical resonant cavities can be adjusted independently;

[0026] According to coupled mode theory, the photon matrix vector multiplication calculator is calculated to have a symmetric mode in one direction and an antisymmetric mode in the other direction, thus having a continuum bound state. The calculation results have strong anti-interference ability and are robust.

[0027] By introducing loss through doping in the optical resonant cavity for non-Hermitian control, the two-dimensional photon matrix vector multiplication calculator breaks the parity-time (PT) symmetry, i.e., PT violation occurs.

[0028] 3) Multiplication calculation:

[0029] One end of each straight waveguide serves as an input port, and the other end as an output port;

[0030] External input light is coupled into the input port. The M×K×2 beams of input light are independent of each other. Each output port is connected to a channel of the photodetector.

[0031] The amplitude of the input light contains the input information. All the input light amplitudes form a one-dimensional input vector as a multiplier. The distance between the straight waveguide and the small optical resonant cavity and the coupling distance between two adjacent optical resonants determine the control matrix. The control matrix is calculated using coupled mode theory or the transfer matrix method and serves as another multiplier.

[0032] The number of input ports and output ports is M×K×2 respectively, and the dimension of the control matrix is (M×K×2)×(M×K×2);

[0033] The photon matrix-vector multiplication calculator multiplies the input vector with the control matrix to obtain the multiplied result output. The photon matrix-vector multiplication calculator has PT breaking, thereby achieving single-mode output and further improving the stability of the calculator.

[0034] Furthermore, the output spectrum of each output port is plotted by changing the detuning amount in the diagonal terms of the Hamiltonian.

[0035] In step 3), according to the coupled mode theory, the Hamiltonian of the photon matrix-vector multiplication calculator is obtained, and the Green's function is calculated through the Hamiltonian. The corresponding small optical resonant cavity part is taken out from the matrix of the Green's function to obtain the control matrix of the photon matrix-vector multiplication calculator, which has a dimension of (M×K×2)×(M×K×2).

[0036] Another object of the present invention is to provide an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity for use in a neural network.

[0037] Advantages of the present invention:

[0038] The present invention constructs a continuum bound state on-chip using an optical resonant cavity array, analyzes its output spectrum and light field through coupled mode theory and transfer matrix theory, and cascades them to construct an intelligent photon matrix-vector multiplication calculator, thereby realizing the construction of large-scale compact continuum bound states on-chip. A non-Hermitian control BIC system is introduced to produce parity-time (PT) violation, completing the single-mode output of the continuum bound state BIC mode, further improving the computational robustness and scalability of the intelligent photon matrix-vector multiplication calculator based on the BIC configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The Hamiltonian eigenvector probability density distribution diagram of an embodiment of the integrated photon matrix-vector multiplication calculator based on an optical resonant cavity of the present invention is shown in FIG. (a) is the probability density distribution diagram of the Hamiltonian eigenvector after modulo square, (b) is the probability density distribution diagram of the eigenvector with added perturbation, and (c) is the probability density distribution diagram of the eigenvector with added transmission perturbation.

[0040] Figure 2 Schematic diagram of an embodiment of an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity of the present invention;

[0041] Figure 3 Output spectra of an embodiment of the integrated photon matrix-vector multiplication calculator based on an optical resonant cavity of the present invention, wherein (a) is the spectrum without adding non-Hermitian control, and (b) is the spectrum after adding non-Hermitian control and the system undergoes PT violation.

[0042] Figure 4 A graph showing a trend of the ratio of the output power of a basic unit of an embodiment of an integrated photonic matrix-vector multiplication calculator based on an optical resonant cavity of the present invention with non-Hermitian regulation introduced to the output power without non-Hermitian regulation versus gain loss, wherein (a) is a graph of the output of the control group without any non-Hermitian regulation, (b) is a graph of the power of the non-BIC mode in the spectrum after the non-Hermitian regulation is introduced, and (c) is a graph of the power of the BIC mode in the spectrum after the non-Hermitian regulation is introduced;

[0043] Figure 5 Output spectrum diagram of a BIC unit structure of an embodiment of an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity of the present invention under different gain-loss control, where (a)-(f) correspond to Figure 4 Output spectra of the six control parameter points in (b);

[0044] Figure 6 Figure 1 is a robustness analysis diagram of an embodiment of an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity of the present invention, wherein (a) is a comparison of the system output spectrum without non-Hermitian control and PT violation when the coupling perturbation introduced in the BIC optical computing configuration changes from small to large, (b) is a comparison of the system output spectrum without non-Hermitian control and PT violation in the non-BIC configuration, (c) is the change in the output spectrum center frequency with error based on the BIC optical computing configuration and the non-BIC configuration, and (d) is the linewidth of the output spectrum center mode based on the BIC optical computing configuration and the non-BIC configuration;

[0045] Figure 7 A schematic diagram of constructing a transmission matrix for the coupling process of an integrated photon matrix-vector multiplication calculator based on an optical resonant cavity according to an embodiment of the present invention;

[0046] Figure 8 A schematic diagram of constructing a transmission matrix for the propagation process of an embodiment of an integrated photonic matrix-vector multiplication calculator based on an optical resonant cavity of the present invention;

[0047] Figure 9A schematic diagram of constructing a transmission matrix for a BIC configuration of an integrated photonic matrix-vector multiplication calculator based on an optical resonant cavity according to an embodiment of the present invention;

[0048] Figure 10 This is a light field diagram of a single BIC structure drawn using the transfer matrix method for an embodiment of the integrated photon matrix-vector multiplication calculator based on an optical resonator of the present invention. (a) shows the light field diagram without adding non-Hermitian control, (b) shows the light field distribution diagram when adding loss to the optical resonator causes PT violation in the system, and (c) shows the light field distribution diagram when adding gain to the optical resonator causes PT violation in the system.

[0049] Figure 11 The training results of the neural network of an embodiment of the integrated photon matrix-vector multiplication calculator based on an optical resonant cavity of the present invention are shown, wherein (a) is a curve graph showing the decrease of the loss function with the number of training rounds during the training process, (b) is a target matrix graph, and (c) is a training result graph. DETAILED DESCRIPTION

[0050] The present invention will be further described below through specific embodiments in conjunction with the accompanying drawings.

[0051] Bound states in the continuum (BIC) are quasi-BICs based on symmetry protection. This involves introducing a structural symmetry that differs from the symmetry of the radiative state, leading to decoupling between the two. The unit cell of a BIC consists of a pair of optical resonators aligned along the x-axis and a pair of symmetric optical resonators aligned along the y-axis. The eigenstates of the two symmetric y-axis optical resonators exhibit a phase difference of π, resulting in odd symmetry. The continuous state along the x-axis exhibits even symmetry, leading to decoupling between the two discrete y-axis states and the continuous state, resulting in a BIC. Furthermore, the BIC in the continuous state persists under certain coupling and transmission perturbations.

[0052] The system's output spectrum contains BIC modes and other non-BIC interference modes. The presence of interference modes can negatively impact detection quality and accuracy, leading to inaccurate results in intelligent optical computations. Therefore, by utilizing non-Hermitian modulation to break parity-time (PT) symmetry, a single BIC mode can be manipulated within the system, while filtering out other interference modes, improving mode purity and, consequently, the accuracy of optical computations.

[0053] Multiple optical resonators create on-chip continuum bound states:

[0054] Taking the number of optical resonators N = 21 as an example, they are arranged in sequence along the x-axis, d represents the index of the d-th optical resonator, and the coupling coefficient between each optical resonator is k d, the intrinsic loss is γ d , which is called an optical resonant cavity. Two symmetrical optical resonant cavities are added to the 11th optical resonant cavity, that is, the optical resonant cavity at the center of the x-axis in the y-axis direction, and their coupling coefficients are κ 12 and κ 13 , the intrinsic losses are γ 12 and γ 13 , which is called a small optical resonant cavity. According to the coupled mode theory, the Hamiltonian of the system is written as H t =H0+H rand +H γ +H δ , where H0 is the coupling between the optical resonator and the optical resonator and the coupling between the optical resonator and the small optical resonator, expressed as

[0055]

[0056] H rand is the random coupling perturbation term, dκ is the perturbation of the coupling coefficient, H rand Expressed as

[0057]

[0058] H γ is the Hamiltonian corresponding to the intrinsic loss γ of the optical resonant cavity and the small optical resonant cavity, expressed as

[0059]

[0060] H δ is the Hamiltonian corresponding to the transmission disturbance term δ of the system, expressed as

[0061]

[0062] By calculating the Hamiltonian H of the system t The eigenvalues and eigenvectors of , it is found that its eigenvector v satisfies:

[0063] v(13,12)=-v(12,12)

[0064] That is, the eigenvectors of the 12th and 13th resonators have a phase difference of π, indicating that an antisymmetric mode is generated between the two small optical resonators, which are symmetrical about the y-axis, while a symmetric mode is generated about the x-axis. The probability density of the Hamiltonian's eigenvectors after taking the square modulus has three discrete bound states, located at the center and on either side of the entire continuous state. Figure 1(a) is the probability density distribution diagram after the Hamiltonian eigenvector is squared. It can be clearly seen that there are three discrete bound states. The first and last bound states exist on the 11th central resonant cavity. These two bound states are symmetrical, but because they are at the edge of the entire continuous state, they are not connected to the continuous band, thus forming ordinary bound states. The central bound state exists on the two resonant cavities symmetrical about the y-axis. It is in the continuous state, but because it is antisymmetric in the vertical direction, it is decoupled from the continuous state, thus forming a BIC. Adding a perturbation to the coupling perturbation term, we get Figure 1 (b) shows the probability density distribution of the eigenvectors. Adding transmission perturbations can obtain Figure 1 (c) shows the probability density distribution diagram of the eigenvectors. By comparison, it can be found that after adding the perturbation, the central BIC mode still exists, which illustrates the robustness of the BIC mode based on the on-chip optical resonant cavity proposed in this patent to perturbations.

[0065] Based on the above-mentioned method of constructing on-chip BIC using optical resonant cavity, a basic unit is obtained, where the x-axis direction and the y-axis direction are the row direction and the column direction respectively, as shown in Figure 2 As shown in Figure 2, 3×3 optical resonant cavities are arranged into a two-dimensional array of three rows and three columns to form a basic unit, as shown in Figure 2. Figure 2As shown in the dotted line frame in the figure; the thickness of the optical resonant cavity is 0.22 μm; two small optical resonant cavities and two straight waveguides are set in the optical resonant cavity in the middle of the basic unit. The diameter of the small optical resonant cavity is smaller than the radius of the optical resonant cavity, and the length of the straight waveguide is such that it can be placed in the optical resonant cavity; the line connecting the centers of the two small optical resonant cavities passes through the center of the central optical resonant cavity, and the angle between the line and the row direction and the column direction is 45°, so that the interference of the small optical resonant cavity with the adjacent optical resonant cavity is minimized; the straight waveguide is located in the small A linear waveguide is located outside the optical resonator and tangential to the small optical resonator. A distance exists between the linear waveguide and the small optical resonator. The distance between the centers of adjacent optical resonators is equal in both rows and columns, indicating a periodic two-dimensional distribution. The waveguide width of each optical resonator is independently adjustable, and the coupling distance between adjacent optical resonators is adjusted by varying the resonator waveguide width. A 3×3 basic unit cell is arranged two-dimensionally, with adjacent units sharing a row or column of optical resonators, to form a photon matrix vector multiplication calculator. The key feature of this structure is a symmetric mode in one direction and an antisymmetric mode in the other. This unit cell structure is simplified and expanded to form a photon matrix vector multiplication calculator. Two small optical resonators are each coupled to a straight waveguide for energy transfer with the outside world, resulting in two input ports and two output ports. This unit cell structure is cascaded into an array in the x and y directions, sharing adjacent optical resonators, to achieve an optical computing configuration with multiple input and output ports. Based on coupled-mode theory, the Hamiltonian of this array system is written, and the Green's function is calculated from the Hamiltonian. Taking the small optical resonator portion corresponding to the Green's function, we obtain the system's control matrix G. The system's output is obtained by multiplying the input vector by the control matrix, and the output spectrum of each port can be plotted by varying the detuning in the diagonal terms of the Hamiltonian.

[0066] To avoid interference from other non-BIC modes that could reduce the accuracy of intelligent optical computing results, it was proposed that the introduction of non-Hermitian modulation could break the PT symmetry, enabling manipulation of a single BIC mode in the system while filtering out other interference modes. To simplify the problem, the proposed BIC optical computing system was abstracted into a three-level system, where all optical resonators were summarized as one energy level, and the two small optical resonators were each one energy level. Gain or dissipation was added to these three energy levels, reflecting the opposite gain and dissipation in the imaginary part i of the diagonal element in the Hamiltonian. By adjusting the relationship between gain and dissipation, the eigenvalue of the Hamiltonian becomes a complex number, and its real part degenerates. This process of changing from real eigenvalues to complex eigenvalues corresponds to a PT phase transition, and the system after the complex eigenvalue appears is said to have broken PT symmetry.

[0067] Hamiltonian construction:

[0068] Assuming that the basic unit has M rows and K columns, there are (2M+1)(2K+1) optical resonators and 2MK small optical resonators, for a total of (2M+1)(2K+1)+2MK. The real part of the Hamiltonian represents the coupling between the optical resonators and the coupling coefficient between the optical resonators and the small optical resonators. The coupling between the small optical resonator and the external waveguide is achieved by adding an imaginary part to the diagonal terms of the small optical resonator. The size of the imaginary part is the loss of the small optical resonator coupled to the outside world. Finally, the loss added to the imaginary part of the overall diagonal terms of the Hamiltonian represents the intrinsic loss of the optical resonator and the small optical resonator. At this point, the Hamiltonian construction of the entire BIC configuration is completed.

[0069] Green's function calculation:

[0070] In order to study the response characteristics of the BIC system under external excitation, the Green's function matrix G is introduced, which is as follows:

[0071] G=I+2i1oss·H -1 , where I is the unit matrix, and its dimension is the total number of resonant cavities in the system (2M+1)(2K+1)+2MK, H is the Hamiltonian, which includes the coupling relationship and loss mechanism within the system, and loss represents the loss term introduced by the small optical resonant cavity and the external coupling. This formula is derived from the linear response theory, where H -1 describes the frequency response behavior of the system to external excitation, while the overall structure reflects the interaction between the coupled detection and the system. Since the final detection is the straight waveguide coupled from the small optical resonant cavity, the corresponding part G is extracted from the Green's function. s , which is the portion of the matrix after the (2M+1)(2K+1) rows and the (2M+1)(2K+1) columns. This completes the calculation of the system's Green's function, which can be used as the control matrix for subsequent optical calculations.

[0072] Construct an input excitation vector All elements are initialized to zero, that is, v in = 0, then, by transferring the transfer function matrix G s Acting on the input vector, we get the system’s output response vector: v out =G·v in , where G s Characterizes the response characteristics of the system, v out It reflects the response amplitude and phase information on each output waveguide of the system under the input condition.

[0073] Plot the output spectrum:

[0074] To plot the system's output characteristics at different frequencies, the system's response at different frequencies can be expressed by adding a detuning amount to the real part of the Hamiltonian's diagonal terms. The range of the detuning amount is the frequency range of the output spectrum. Its form is as follows: H' = H - ΔI, where I is the identity matrix with dimensions equal to the total number of resonant cavities in the system (2M+1)(2K+1)+2MN. Using H' with the added detuning amount to calculate the Green's function, the system's output spectrum can be discretely plotted by selecting the step size and range of Δ.

[0075] Non-Hermitian regulation:

[0076] Non-Hermitian control can be introduced by adding loss and gain to the imaginary part of the Hamiltonian diagonal term. A unit structure is selected as the research object, and a spectrum diagram is drawn comparing the addition of non-Hermitian control before and after. Figure 3 As shown, Figure 3 (a) is the spectrum before non-Hermitian modulation, Figure 3 (b) is the spectrum after non-Hermitian regulation. The resonance peak in the center is the BIC mode, and the resonance peaks on the left and right sides are other non-BIC modes. It can be clearly seen that after PT breaking, the output spectrum of the system only retains the BIC mode, and successfully filters out other non-BIC interference modes. In order to further explore the single-mode output effect of non-Hermitian on the spectrum, different gain losses are introduced into the optical resonant cavity, and no gain loss is introduced into the small optical resonant cavity, and its impact on the output spectrum is analyzed. Figure 4 As shown, the horizontal axis is the gain or loss introduced in the optical resonant cavity, positive numbers are gain, and negative numbers are loss. The vertical axis is the output power percentage before and after the addition of non-Hermitian control. Figure 4 (a) is the output of the control group without any non-Hermitian regulation, Figure 4 (b) is the power in non-BIC mode, Figure 4 (c) is the power of BIC mode. Figure 5 The six pictures (a) to (f) correspond to Figure 4 The output spectra under the six control parameters in (b) intuitively show the process of gradually completing the BIC single-mode output as the gain loss changes.

[0077] Robustness analysis:

[0078] Based on the BIC optical computing configuration and non-Hermitian control scheme proposed above, random coupling and perturbation can be added to the coupling term of the Hamiltonian. For the perturbation of the optical resonant cavity, a perturbation matrix of size (2M+1)(2N+1) is generated, where each element comes from a normal distribution with mean 0 and standard deviation err. Similarly, a small optical resonant cavity perturbation with a matrix size of 2MN can be generated. The Green's function and output spectrum are calculated step by step using the Hamiltonian with the added perturbation according to the above method. Figure 6 (a) shows the comparison of the system output spectrum without non-Hermitian control and PT breaking when the coupling perturbation introduced in the BIC system changes from small to large. It can be seen that the output is more stable after mode selection. Figure 6 (b) shows the comparison of the system output spectra without non-Hermitian control and after PT breaking in the non-BIC configuration. Combining these two results, it can be analyzed that the BIC configuration has the best effect with non-Hermitian control. Figure 6 (c) shows the change of the center frequency with the error. It can be clearly seen that the center frequency stability under the BIC configuration is significantly improved. Figure 6 (d) shows the linewidth of the central mode, which is narrower and more stable in the BIC configuration. In addition to using coupled-mode theory to construct the BIC and analyze the output spectrum, the theoretical verification and theoretical rendering of the optical field are performed using the transfer matrix.

[0079] For the first and second optical resonant cavities with the same mode, E1 and E1′ represent the input and output electric fields of the first optical resonant cavity, and E2 and E2′ represent the input and output electric fields of the second optical resonant cavity. Figure 7 As shown, the electric fields of the two satisfy a linear change relationship, which can be expressed by a matrix:

[0080]

[0081] Where t and κ are the transmittance and coupling efficiency. If light propagates independently for a certain distance in the first and second optical resonators, the phase changes are φ1 and φ2 respectively, as shown in Figure 8 As shown, the electric field change can be expressed by the matrix:

[0082]

[0083] For the configuration of the present invention, Figure 9 The part shown in the figure is used as an example to illustrate how to apply the transfer matrix method for theoretical calculation. For the configuration of M×K repeating units, the electric field of each section in all optical resonant cavities is arranged in sequence as a vector of length (2M+1)(2K+1)+2MK. The electric field of the optical resonant cavity before passing through the coupling region is E m , the electric field of the optical resonant cavity after the coupling region is E′ m , the small optical resonant cavity is arranged as a vector of length 2MK, and the electric field of the small optical resonant cavity before the coupling region is E s , the electric field of the small optical resonant cavity after the coupling region is E s ′, due to the nature of matrix operations, all couplings can be summarized as:

[0084]

[0085] Where H is a square matrix of order (2M+1)(2K+1)+4MK. All propagation in the optical resonant cavity can be summarized as:

[0086] E′ m =FE m

[0087] Where F is the total control matrix of the optical resonator, a matrix with an order of (2M+1)(2K+1)+2MK. In order to obtain E s ′ and E s , H is divided into four matrices, A is the control matrix of the optical resonant cavity passing through the coupling region, B is the matrix of the optical resonant cavity controlled by the small optical resonant cavity, C is the matrix of the small optical resonant cavity controlled by the optical resonant cavity, and D is the control matrix of the optical resonant cavity passing through the coupling region. The order of A is (2M+1)(2K+1)+2MK, and the order of D is 2MK:

[0088]

[0089] The solution is:

[0090] E m =(FA) -1 BE s

[0091] E s ′=GE s

[0092] in

[0093] G=C(FA) -1 B+D

[0094] The input and output electric fields of each coupled waveguide are E in and E out , according to E s and E s ′ in the same order as the phase φ on the small optical resonator s and φ s ′ are arranged into a diagonal matrix, φ s and P s are the phase of the small optical resonant cavity before passing through the coupling region and the diagonal matrix formed by the phases, and P is the total diagonal matrix. The coupling rate κ and transmittance t are also arranged in the same order into diagonal matrices K0 and T0, and the coupling is summarized as:

[0095]

[0096] Lianli Es ′=GE s The solution is:

[0097] E s =iK0(P-T0G) -1 P s 'E in

[0098] E out =QE in

[0099] in

[0100] Q=T0-K0G(P-T0G) -1 K0

[0101] Q is the transformation matrix calculated using the transfer matrix method, which is also used to calculate non-Hermitian control. The propagation phase is taken as a complex number. Then its imaginary part Represents the gain loss γ, and the corresponding relationship is:

[0102]

[0103] In addition, losses are introduced at the coupling location, which can be 2 +t 2 The coupling ratio and transmittance can be adjusted more freely within the limit of <1.

[0104] By changing the number of rings and designing the coupling ratio, phase and gain loss at each position, various linear light calculations can be performed, and the results can be obtained from the above formulas. For a configuration of size M×K, the input vector E in The maximum length of is 2MK, and the maximum size of matrix Q is 2MK×2MK. In addition, E in Directly calculate the electric field value of each part and draw the light field distribution diagram. Fill the corresponding position of the ring with grayscale to represent the electric field intensity of the light intensity. Figure 10 (a) shows the light field diagram of a single BIC structure drawn using the above-mentioned transfer matrix method. Figure 10 (b) The optical field distribution diagram is further drawn when the loss is added to the optical resonant cavity, causing the system to have PT violation. Figure 10 (c) is the light field distribution diagram when adding gain to the optical resonant cavity causes PT violation in the system.

[0105] Calculator application expansion:

[0106] The optical computing configuration proposed in this paper works near the resonant state of the system, mainly by changing the coupling rate and transmittance to change the transmission matrix and perform various calculations. The coupling matrix construction, phase matrix construction and photon multiplication calculation are implemented using the tensor type in PyTorch. The parameters involved are set as follows: in the resonant state, all phases φ are set to a fixed value of 0; coupling energy is conserved, and each coupling position has κ 2 +t 2 <1. Target matrix Q target It is a normalized matrix. The transformation matrix Q calculated by the transfer matrix method is also normalized to obtain the normalized matrix Q norm , define the loss function as the normalized matrix Q norm With the target matrix Q target The mean square error of the corresponding position matrix elements is trained using the Adam optimizer. After a certain number of training rounds, the optimal hyperparameters can be trained, and the coupling rate and transmittance can be calculated. Take the size M×K=2×1, give a 4×4 target matrix, and the learning rate lr=0.001. After 30,000 training, the loss function decreases during the training process. Figure 11 As shown in (a), the target matrix and the trained matrix are respectively Figure 11 (b) and (c) show that the present invention is a calculator capable of performing matrix-vector multiplication, and is further used to perform neural network tasks.

[0107] Finally, it should be noted that the purpose of disclosing the embodiments is to facilitate a further understanding of the present invention. However, those skilled in the art will appreciate that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the contents disclosed in the embodiments; the scope of protection claimed by the present invention shall be determined by the scope defined in the claims.

Claims

1. An integrated photon matrix-vector multiplication calculator based on an optical resonant cavity, characterized in that: The integrated photon matrix vector multiplication calculator comprises: a substrate and a plurality of optical resonant cavities; the plurality of optical resonant cavities are formed on the substrate; wherein the refractive index of the substrate is less than the refractive index of the optical resonant cavities; the optical resonant cavities are in the shape of a circular ring with a thickness; n×n optical resonant cavities are arranged in a two-dimensional array of n rows and n columns to form a basic unit, where n is an odd number ≥ 3. Two small optical resonant cavities and two straight waveguides are disposed within the central optical resonant cavity in the center of each basic unit. The diameter of the small optical resonant cavity is smaller than the radius of the optical resonant cavity, and the length of the straight waveguide allows it to be placed within the optical resonant cavity. A line connecting the centers of the two small optical resonant cavities passes through the center of the central optical resonant cavity, and the angle between the line and the row and column directions is 45°, thereby minimizing interference from adjacent optical resonant cavities to the small optical resonant cavity. The straight waveguide is located outside the small optical resonant cavity and is tangential to the small optical resonant cavity, and there is a distance between the straight waveguide and the small optical resonant cavity. The distance between the centers of adjacent optical resonant cavities is equal between rows and columns, i.e., the positions of the centers are periodically distributed in a two-dimensional manner. The waveguide width of each optical resonant cavity is independently adjustable, and the coupling distance between adjacent optical resonant cavities is adjusted by changing the waveguide width of the resonant cavity. A photon matrix vector multiplication calculator is constructed by arranging M×K basic units in two dimensions, where M and K are natural numbers, and adjacent basic units share a row or column of optical resonant cavities. The coupling distance between two adjacent optical resonant cavities in each basic unit is independently adjustable. Calculations based on coupled-mode theory reveal that the photon matrix vector multiplication calculator exhibits continuum bound states, and the calculation results exhibit strong anti-interference and robustness. Non-Hermitian control is achieved by introducing loss through doping into the optical resonant cavity, causing the two-dimensional photon matrix vector multiplication calculator to break parity-time PT symmetry, i.e., PT violation. One end of each straight waveguide serves as an input port, and the other end as an output port; external input light is coupled into the input port, and the M×K×2 beams of input light are independent of each other. The amplitude of the input light contains input information, and the amplitudes of all input lights constitute a one-dimensional input vector as a multiplier; the distance between the straight waveguide and the small optical resonant cavity and the coupling distance between two adjacent optical resonant cavities determine the control matrix, which is calculated by coupled mode theory or transfer matrix method and serves as another multiplier; each output port is connected to a channel of a photodetector; the number of input ports and output ports is M×K×2, respectively, and the dimension of the control matrix is (M×K×2)×(M×K×2); the photon matrix-vector multiplication calculator multiplies the input vector with the control matrix to obtain the multiplied result output. The photon matrix-vector multiplication calculator has PT breaking, thereby achieving single-mode output and further improving the stability of the calculator.

2. The integrated photonic matrix-vector multiplication calculator according to claim 1, wherein: The diameter of the optical resonance cavity is 30-60 μm; the width of the waveguide is 0.45-0.50 μm.

3. The integrated photonic matrix-vector multiplication calculator according to claim 1, wherein: The distance between the two adjacent optical resonant cavities is 200-300 nm.

4. The integrated photonic matrix-vector multiplication calculator according to claim 1, wherein: The length of the straight waveguide is 5 to 8 μm.

5. The integrated photonic matrix-vector multiplication calculator according to claim 1, wherein: The optical resonant cavity is doped with phosphorus or boron to introduce loss.

6. The integrated photonic matrix-vector multiplication calculator according to claim 1, wherein: The diameter of the small optical resonance cavity is 10-20 μm.

7. A method for implementing the integrated photon matrix-vector multiplication calculator based on an optical resonant cavity as claimed in claim 1, characterized in that: The implementation method comprises the following steps: 1) Basic unit: A circular ring with thickness is used as an optical resonant cavity; Arrange n×n optical resonant cavities into a two-dimensional array of n rows and n columns to form a basic unit, where n is an odd number ≥3; Two small optical resonant cavities and two straight waveguides are arranged in the central optical resonant cavity in the middle of the basic unit. The diameter of the small optical resonant cavity is smaller than the radius of the optical resonant cavity, and the length of the straight waveguide is such that it can be placed in the optical resonant cavity. The line connecting the centers of the two small optical resonant cavities passes through the center of the central optical resonant cavity, and the angle between the line and the row direction and the column direction is 45 degrees, so that the interference of the small optical resonant cavity with the adjacent optical resonant cavity is minimized. The straight waveguide is located outside the small optical resonant cavity and is tangent to the small optical resonant cavity. There is a distance between the straight waveguide and the small optical resonant cavity. The distances between the centers of adjacent optical resonant cavities are equal between rows and columns, i.e., the positions of the centers are periodically distributed in two dimensions. The waveguide width of each optical resonant cavity is independently adjustable, and the coupling distance between adjacent optical resonant cavities is adjusted by changing the waveguide width of the resonant cavity. 2) Construct an integrated photon matrix-vector multiplication calculator: Arrange M×K basic units in two dimensions, where M and K are natural numbers, and adjacent basic units share a row or column of optical resonant cavities, to form a photon matrix vector multiplication calculator; In each basic unit, the coupling distance between two adjacent optical resonant cavities can be adjusted independently; According to the coupled mode theory, the photon matrix vector multiplication calculator has a continuum bound state, and the calculation results have strong anti-interference ability and are robust. By introducing loss through doping in the optical resonant cavity for non-Hermitian control, the two-dimensional photon matrix vector multiplication calculator breaks the parity-time (PT) symmetry, i.e., PT violation occurs. 3) Multiplication calculation: One end of each straight waveguide serves as an input port, and the other end as an output port; External input light is coupled into the input port. The M×K×2 beams of input light are independent of each other. Each output port is connected to a channel of the photodetector. The amplitude of the input light contains the input information. All the input light amplitudes form a one-dimensional input vector as a multiplier. The distance between the straight waveguide and the small optical resonant cavity and the coupling distance between two adjacent optical resonants determine the control matrix. The control matrix is calculated using coupled mode theory or the transfer matrix method and serves as another multiplier. The number of input ports and output ports is M×K×2 respectively, and the dimension of the control matrix is (M×K×2)×(M×K×2); the photon matrix-vector multiplication calculator multiplies the input vector with the control matrix to obtain the multiplied result output. The photon matrix-vector multiplication calculator has PT breaking, thereby realizing single-mode output and further improving the stability of the calculator.

8. The implementation method according to claim 7, characterized in that: In step 3), based on the coupled mode theory, the Hamiltonian of the photon matrix-vector multiplication calculator is obtained, and the Green's function is calculated through the Hamiltonian. The corresponding small optical resonant cavity part is taken out from the matrix of the Green's function to obtain the control matrix of the photon matrix-vector multiplication calculator.

9. The implementation method according to claim 7, wherein: By varying the detuning in the diagonal terms of the Hamiltonian, the output spectrum of each output port is plotted.

10. Use of the integrated photon matrix-vector multiplication calculator based on an optical resonant cavity as claimed in claim 1 in a neural network.

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