Photon link fast frequency domain calculation method based on multi-mode coupling and sub-network growth

Abstract

The application belongs to the technical field of photonic link, and particularly relates to a photonic link fast frequency domain calculation method based on multimode coupling and sub-network growth, which comprises the following steps: S1, constructing a multimode scattering model of an optical device; S2, constructing a sub-network multimode scattering matrix; and S3, sub-network merging and optimization. The method is suitable for a photonic network containing any interconnected multi-port elements, can accurately characterize multimode propagation and coupling phenomena by using scattering parameters, can support any number of modes in a waveguide element and mode coupling effects, and can realize efficient calculation of photonic link frequency domain response through step-by-step solution of the multimode scattering matrix.

Description

Technical Field

[0001] This application belongs to the field of photonic link technology, specifically relating to a fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth. Background Technology

[0002] Efficient photonic link simulation is a powerful support for the automated design of photonic integrated circuits (PICs). For complex devices and links, iterative adjustments to the structure and parameters are necessary to evaluate circuit performance and post-manufacturing yield under process variations. Photonic links contain dozens to hundreds of devices with numerous adjustable parameters. Especially in Monte Carlo analysis, the system needs to perform tens of thousands of simulations, which can be computationally expensive and time-consuming. Currently, there are several commercial photonic link simulation software programs, such as Lumerical Interconnect, VPI Photonics, and Max-Optics, which are excellent circuit simulation tools for specific scenarios. However, as the number of parameters or components in the circuit grows to a large scale, many of these tools quickly become cumbersome, and their computational speed needs to be improved to meet the demands of large-scale link simulation. Therefore, developing efficient photonic link calculation methods is of great significance for improving PIC design efficiency.

[0003] In high-frequency network analysis and design, scattering parameters (S-parameters) can unify the characterization of lumped and distributed components into a multi-port equivalent model, described by normalized wave variables, and their data are easily measurable, making them an important tool for system-level performance analysis. These parameters are arranged in matrix form and are related to the transmitted and reflected waves at the input and output ports. Circuit analysis programs typically calculate the overall characteristics of the circuit based on the system model and component parameters. A typical system model is a network of interconnected multi-port components, described by scattering matrices; for example, modeling a communication system composed of subsystems typically characterized by single-mode scattering matrices.

[0004] In photonic links, physical effects such as multimode transmission, polarization state evolution, and mode coupling require the coordinated processing of multiple electromagnetic modes. However, existing reports mostly focus on system modeling based on single-mode scattering matrices. These frequency domain solutions, such as the advantageous subnetwork growth method, are only applicable to single-mode propagation and struggle to handle multimode transmission and coupling, thus exhibiting significant limitations in multimode scenarios such as photonic integrated circuits. Therefore, there is an urgent need to develop novel and efficient frequency domain calculation methods for multimode photonic links to support rapid simulation and design of photonic links. Summary of the Invention

[0005] To address the need for efficiency improvements in photonic link frequency domain simulation and the limitation of existing algorithms that only support single-mode systems, this invention proposes a fast frequency domain calculation method for photonic links based on the subnetwork growth concept. The technical solution is as follows:

[0006] A fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth includes the following steps:

[0007] S1. Construct a multimode scattering model for optical devices: Each port has M independent propagation modes, and each mode supports bidirectional transmission. Each transmission direction is represented in the complex form of the optical signal.

[0008] S2. Constructing the multimode scattering matrix of the sub-network: A multi-port photonic network consists of multiple sub-networks. The process is to calculate the combined circuit of two sub-networks at a time until all sub-networks are connected.

[0009] S3. Subnetwork merging and optimization: Connect two subnetworks each time to make the combined network formed after the connection have the fewest external ports.

[0010] Preferably, in the optical port, a signal may contain multiple modes, each mode corresponding to the Fourier transform of the time-varying complex envelope of a specific optical mode, and characterized in the form of normalized wave variables. A generalized scattering matrix (GSM) is introduced to characterize the linear coupling relationship between modes: for an optical device with N ports, and each port supporting M modes, its multimode-generalized scattering matrix (MSM) is described in the following form:

[0011] ;

[0012] element Indicates the first physical port j v Each incident pattern, to the physical port u The k Generalized transmission coefficients of each emission mode; multimode scattering matrix This study comprehensively characterized the bidirectional transmission and multimode coupling electromagnetic properties of photonic devices.

[0013] Preferably, a multi-port photonic network consists of multiple sub-networks, and its multimode scattering equation can be written as:

[0014] ;

[0015] in, and These are the output and input mode variables of the external port e. and These are the output and input mode variables of internal port c. The constraint relationships generated by the connections between internal interconnect ports c are expressed as follows:

[0016] ;

[0017] in To describe the multimode connection matrix of the network topology, the elements corresponding to the connection ports are 1, and the rest are 0. Combining equations (2) and (3), we obtain the scattering matrix of the entire network. for:

[0018] ;

[0019] For the generalized transmission coefficients between e-mode variables of the subnet external ports, The generalized transmission coefficients of the mode variable from internal port c to external port e of the subnet. For the generalized transmission coefficient from external port e to internal port c of the subnet, This represents the generalized transmission coefficient between ports within the subnetwork.

[0020] Preferably, the two sub-networks A and B are connected, and the external ports and internal ports are divided into two groups, e1 and e2 representing the external ports of sub-networks A and B, respectively. q and r Representing the internal ports respectively, the overall uncoupled scattering matrix of the two components is given by formula (2). Represented as:

[0021] (5);

[0022] external port e1 Multimode scattering parameters between; external port e2 Multimode scattering parameters between; For internal ports q to external port e1 Multimode scattering parameters; For internal ports q Multimode scattering parameters between; external port e1 to internal port q Multimode scattering parameters; external port e2 to internal port r Multimode scattering parameters; internal port r to external port e2 Multimode scattering parameters; internal port r Multimode scattering parameters between them.

[0023] Preferably, when interconnecting ports, considering that multiple modes transmit independently on the transmission line, coupling is only performed within the photonic device. For both TE and TM polarization modes, any pair of interconnected internal ports... k , jMust meet:

[0024] (7);

[0025] For the output TE polarization mode at port k;

[0026] For the output TM polarization mode at port k;

[0027] For the output TE polarization mode of port j;

[0028] For the output TM polarization mode of port j;

[0029] For the incident TE polarization mode at port k;

[0030] For the incident TM polarization mode at port k;

[0031] For the incident TE polarization mode at port j;

[0032] For the incident TM polarization mode at port j;

[0033] Therefore, the multimode connection matrix of the two networks can be obtained in the following form:

[0034] ;

[0035] in, for An identity matrix of order 1, where c is the number of internal connection ports between subnetworks, and M is the number of modes transmitted per port.

[0036] Preferably, the matrix that needs to be inverted ( ) is represented as:

[0037] ;

[0038] The overall scattering matrix of the two subnetworks can then be expressed as:

[0039] (10);

[0040] (11);

[0041] (12).

[0042] Preferably, the number of arithmetic operations required to calculate the scattering matrix of a given topology circuit depends on the order in which the subnetworks are connected. To minimize computation time, a suboptimal sorting algorithm is used to determine the optimal connection order of the subnetworks.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] (1) High computational efficiency: By adopting a merging strategy of step-by-step growth and optimization of subnetworks, the computational load of large-scale matrix inversion is significantly reduced. Case studies show that its computational speed can reach more than twice that of existing commercial simulation software, and its advantages are more obvious in large-scale networks;

[0045] (2) Multimode support: For the first time, a multimode scattering matrix is ​​introduced into the subnetwork growth method, which can accurately simulate complex physical effects such as multimode transmission and polarization coupling in photonic links, filling the gap of existing methods in multimode scenarios;

[0046] (3) Guarantee of computational accuracy: The calculation results of this method are highly consistent with those of the commercial simulation software (LumericalInterconnect), with an error of less than 1×10⁻¹. 0 This ensures the reliability of the simulation results;

[0047] (4) Good versatility and integration: It can be widely used in the design of photonic links containing complex components such as polarization rotators, beam splitters, and waveguides, and supports integration with existing commercial simulation tools. Attached Figure Description

[0048] Figure 1 Schematic diagram of a multimode transmission model for a two-port optical device;

[0049] Figure 2 : A schematic diagram of multimode transmission connecting two sub-networks;

[0050] Figure 3 Schematic diagram of the subnetwork merging process: (a) Photonic link consisting of 6 subnetworks; (b) Topology changes during the merging process;

[0051] Figure 4 : Photonic link structure diagram of Case 1 (passive demultiplexer);

[0052] Figure 5 Comparison results and error analysis of the multimode frequency domain response in Case 1;

[0053] Figure 6 Optical architecture diagram of Case 2 (MZI cascade structure);

[0054] Figure 7 Comparison results and error analysis of multimode frequency domain response in Case 2. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] To address the need for efficiency improvements in the frequency domain simulation of photonic links and the limitation of existing algorithms that only support single-mode systems, this invention proposes a fast frequency domain calculation method for photonic links based on the subnetwork growth concept. This method is applicable to photonic networks containing arbitrarily interconnected multi-port elements, accurately characterizes multimode propagation and coupling phenomena using scattering parameters, supports any number of modes in waveguide elements and intermode coupling effects, and achieves efficient calculation of the frequency domain response of photonic links through step-by-step solution of the multimode scattering matrix.

[0057] The effectiveness and superiority of this method are verified through two case studies. The error between the calculation results of this method and the simulation results of Lumerical Interconnect is less than 1×10⁻⁶. -10 The computation speed is more than twice that of existing commercial simulation software such as Lumerical Interconnect, VPI Photonics, and Max-Optics, making it highly valuable for engineering applications. Since the network's scattering matrix is ​​determined by the S-matrices of each sub-network (element), it can be integrated with any commercial photonic link simulation software, making it a user-friendly, efficient, and practical frequency domain solution technique.

[0058] A fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth includes the following steps:

[0059] S1. Multimode scattering model of optical devices:

[0060] In an optical port, a signal can contain multiple modes, each corresponding to the Fourier transform of the time-varying complex envelope of a specific optical mode, and characterized in the form of normalized wave variables. This invention constructs a multimode and bidirectional transmission model for an optical device, where each transmission direction is represented in complex form of the optical signal:

[0061] .

[0062] like Figure 1 As shown in the diagram, each port has M independent propagation modes, and each mode supports bidirectional transmission. The arrows in the diagram indicate the directions of the incident (blue) and outgoing (red) modes, respectively.

[0063] ;

[0064] Among them, elements Indicates from physical port j The v Each incident pattern, to the physical port u The k Generalized transmission coefficients of each output mode. Multimode scattering matrix. This study comprehensively characterized the bidirectional transmission and multimode coupling electromagnetic properties of photonic devices.

[0065] S2. Multimodal network growth method:

[0066] 2.1 Sub-network multimode scattering matrix:

[0067] A multi-port photonic network consists of multiple sub-networks (elements), and its multimode scattering equation can be written as:

[0068] (2);

[0069] in, and These are the output and input mode variables of the external port e. and These are the output and input mode variables of the internal port c. The constraint relationships arising from the connections between the internal interconnect ports c are expressed as follows:

[0070] (3);

[0071] in The multimode connection matrix describes the network topology, with elements corresponding to connection ports set to 1 and all others to zero. Combining equations (2) and (3), the scattering matrix of the entire network is obtained. for:

[0072] (4);

[0073] By calculating the combined circuit of only two sub-networks at a time until all sub-networks are connected, the computational complexity of matrix inversion can be significantly reduced. The schematic diagram of a multimode transmission circuit connecting two sub-networks A and B is shown below. Figure 2 As shown, the external and internal ports are divided into two groups, e1 and e2 representing the external ports of A and B respectively, and q and r representing the internal ports respectively. From formula (2), the overall uncoupled scattering matrix of the two components is... Represented as:

[0074] (5).

[0075] For the two polarization modes TE and TM, according to formula (5). Figure 2The global uncoupled multimode scattering matrix equations for the two subnetworks A and B are as follows:

[0076] (6).

[0077] When interconnecting ports, considering that multiple modes can be transmitted independently on the transmission line, coupling is only performed within the photonic device. Figure 2 For both TE and TM polarization modes, any pair of interconnect ports k , j Must meet:

[0078] (7);

[0079] Therefore, the multimode connection matrix of the two networks can be obtained in the following form:

[0080] (8);

[0081] in, for The identity matrix is ​​of order , c is the number of internal connection ports between sub-networks, and M is the number of modes transmitted per port. At this point, the matrix that needs to be inverted in equation (4) is ( ) is represented as:

[0082] (9);

[0083] The overall scattering matrix of the two subnetworks can then be expressed as:

[0084] (10);

[0085] (11);

[0086] (12);

[0087] Now we only need to consider the two orders. The matrix is ​​inverted, and the order of the matrices involved in the multiplication operation is reduced accordingly. Using formula (10) (N-1) times, the multimode scattering matrix of the entire network can be calculated efficiently, that is, the multimode coupling scattering parameters TE-TE, TE-TM, TM-TE, and TM-TM of the photonic network can be obtained simultaneously.

[0088] S3. Subnetwork merging optimization method:

[0089] The number of arithmetic operations required to compute the scattering matrix of a given topology circuit depends on the order in which the subnetworks are connected. To minimize computation time, a suboptimal sorting algorithm is used to determine the optimal connection order of the subnetworks. The core principle of this method is to connect two subnetworks at a time such that the resulting combined network has the fewest external ports. Regardless of the circuit topology, this connection order always means that the number of algebraic operations is very close to the minimum. The network connection process analyzed using the subnetwork growth method is as follows: Figure 3 As shown, Figure 3 (a) is a link structure consisting of 6 components. Figure 3 (b) The topology changes during the merging process are shown step by step, with a total of 5 mergings, resulting in a three-port network.

[0090] 4. Case Study:

[0091] 4.1 Case 1: Passive Demultiplexer:

[0092] The photonic link structure of a passive demultiplexer is as follows Figure 4 As shown, the model consists of an edge coupler, a polarization beam splitter (PSR) composite model, and two symmetrical sub-links. Each sub-link includes a waveguide, a loaded micro-ring MZI composite model, and a mirror element. The link contains a total of 42 devices and 88 physical ports.

[0093] To verify the accuracy of our MSG calculations, we compared the MSG calculation results with the simulation results from Lumerical Interconnect. Figure 5 (a) The multimode frequency domain response results of the photonic circuit in case 1 at port 1 and port 2 are given. Comparative analysis shows that the maximum error between the two methods is less than 4.9109 × 10⁻⁶. -11 %,like Figure 5 As shown in (b).

[0094] 4.2 Case 2: MZI Cascade Structure

[0095] Linear computational optical architectures for optical neural networks, such as Figure 6 As shown, the optical architecture is constructed by cascading basic MZI units arranged in a topological order. Linear computation of optical signals is achieved through this unit cascading. Each MZI unit consists of two directional couplers and two phase shifters. This optical architecture contains a total of 138 devices and 408 physical ports.

[0096] In case 2, the multimode frequency domain response of the photonic circuit at ports 1 to 6 is as follows: Figure 7 As shown in (a), the comparative analysis indicates that the maximum error between MSG and Lumerical Interconnect is less than 3.2765 × 10⁻⁶.-12 %,like Figure 7 As shown in (b).

[0097] 4.3 Analysis and Discussion:

[0098] Table 1 compares the computation time of the proposed method with that of the solvers in the simulation software Lumerical Interconnect, VPI Photonics and Max-Optics.

[0099] Table 1 Comparison of Calculation Time

[0100] .

[0101] As shown in Table 1, for case 1, the minimum computation time of the commercial solver is 1.4142 s, while the method proposed in this paper only takes 0.6619 s, making it 2.14 times faster than the simulation software. For case 2, the minimum simulation time of the commercial solver is 3.1325 s, while the method proposed in this paper only takes 1.4403 s, making it 2.17 times faster than the simulation software. It can be seen that the computation speed increases with the scale of the link topology; the larger and more complex the network, the more significant the computational speed advantage of the proposed method becomes.

Claims

1. A fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth, characterized in that, Includes the following steps: S1. Constructing a multimode scattering model for optical devices: Each port has M independent propagation modes, and each mode supports bidirectional transmission. Each transmission direction is represented in complex form of the optical signal. A generalized scattering matrix (GSM) is introduced to characterize the linear coupling relationship between modes. For an optical device with N ports, a multimode scattering matrix is ​​constructed. ; S2. Constructing the multimode scattering matrix of the sub-network: A multi-port photonic network consists of multiple sub-networks. The process is to calculate the combined circuit of two sub-networks at a time until all sub-networks are connected. A multi-port photonic network consists of multiple subnetworks, and its multimode scattering equation can be written as: ； in, and These are the output and input mode variables of the external port e. and These are the output and input mode variables of internal port c. The constraint relationships generated by the connections between internal interconnect ports c are expressed as follows: ； in To describe the multimode connection matrix of the network topology, the elements corresponding to the connection ports are 1, and the rest are 0. Combining equations (2) and (3), we obtain the scattering matrix of the entire network. for: ； For the generalized transmission coefficients between e-mode variables of the subnet external ports, For subnet internal ports c to external port e The generalized transfer coefficients of the pattern variables, external port of subnet e to internal port c Generalized transmission coefficient, For the generalized transmission coefficient between ports within the subnetwork; Two subnets, A and B, are connected, dividing the external ports into two groups: internal ports and external ports. e1 and e2 represent the external ports of subnets A and B, respectively. q and r Representing the internal ports respectively, the overall uncoupled scattering matrix of the two components is given by formula (2). Represented as: ； external port e1 Multimode scattering parameters between; external port e2 Multimode scattering parameters between; For internal ports q to external port e1 Multimode scattering parameters; For internal ports q Multimode scattering parameters between; external port e1 to internal port q Multimode scattering parameters; external port e2 to internal port r Multimode scattering parameters; internal port r to external port e2 Multimode scattering parameters; internal port r Multimode scattering parameters between; S3. Subnetwork merging and optimization: Connect two subnetworks each time to make the combined network formed after the connection have the fewest external ports.

2. The fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth according to claim 1, characterized in that, In an optical port, a signal can contain multiple modes, each corresponding to the Fourier transform of the time-varying complex envelope of a specific optical mode, and characterized in the form of normalized wave variables. The multimode-generalized scattering matrix (MSM) is described in the following form: ； element Indicates the first physical port j v Each incident pattern, to the physical port i The u Generalized transmission coefficients of each emission mode; multimode scattering matrix This study comprehensively characterized the bidirectional transmission and multimode coupling electromagnetic properties of photonic devices.

3. The fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth according to claim 1, characterized in that, When interconnecting ports, considering that multiple modes transmit independently on the transmission line and are coupled only within the photonic device, for both TE and TM polarization modes, any pair of interconnected internal ports... k , j Must meet: ； For the output TE polarization mode at port k; For the output TM polarization mode at port k; For the output TE polarization mode of port j; For the output TM polarization mode of port j; For the incident TE polarization mode at port k; For the incident TM polarization mode at port k; For the incident TE polarization mode at port j; For the incident TM polarization mode at port j; Therefore, the multimode connection matrix of the two networks can be obtained in the following form: ； in, for An identity matrix of order 1. M represents the number of internal connection ports between subnets, and M represents the number of modes transmitted per port.

4. The fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth according to claim 1, characterized in that, The matrix that needs to be inverted ( ) is represented as: ； The overall scattering matrix of the two subnetworks can then be expressed as: ； ； ； for identity matrix of order 1 This represents the number of internal connection ports between subnets.

5. The fast frequency domain calculation method for photonic links based on multimode coupling and subnetwork growth according to claim 1, characterized in that, The number of arithmetic operations required to calculate the scattering matrix of a given topology depends on the order in which the subnetworks are connected. To minimize computation time, a suboptimal sorting algorithm is used to determine the optimal connection order of the subnetworks.

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