Method and system for fast acquisition of time-domain model of passive photonic devices

Abstract

The application discloses a method for quickly obtaining a time-domain model of a passive photonic device. The method is aimed at the fundamental frequency equivalent scattering parameter of the passive photonic device, and an initial pole is obtained by using a fundamental frequency LM (Loewner Matrix) algorithm. Then, the obtained initial pole is iterated by using a complex vector fitting (CVF) algorithm, and finally, the pole residue model obtained can accurately represent the dynamic response of the system in the whole frequency range. Thus, the method for quickly obtaining the time-domain model of the passive photonic device ensures high efficiency, high accuracy and high practicability of the proposed model, and has important value for modeling and analysis of passive photonic integrated circuits.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of photonic integrated circuits, and particularly relates to a method and system for quickly obtaining a time-domain model of a passive photonic device. BACKGROUND

[0002] Optoelectronic chips exhibit great application potential in multiple fields, including high-speed data communication, quantum computing, all-optical machine learning, biosensing, laser radar, and gyroscope, etc. These applications not only promote the rapid development of optoelectronic technology, but also bring new opportunities to the fields of information communication, sensor technology, and new energy, while also posing unprecedented challenges.

[0003] In the design and application of optoelectronic chips, passive photonic devices play a crucial role. The input-output characteristics of these devices are usually characterized by scattering (S) parameters. Since S parameters cannot be directly applied to time-domain simulation, the current general method is to use the CVF algorithm to establish a pole-residue model, and to perform time-domain simulation by solving the corresponding state-space equation of the model. However, when using the CVF method to model passive photonic devices, the number of poles required for modeling cannot be directly determined from the S parameters. Therefore, when using the complex vector fitting algorithm, the number of poles needs to be gradually increased, and the initial poles are regenerated based on different numbers of poles and their positions are iterated. Therefore, the modeling can only be performed using nested loops. This modeling method is inefficient and time-consuming and labor-intensive when modeling devices with complex frequency-domain responses.

[0004] Therefore, there is an urgent need for a method for quickly obtaining a time-domain model of a passive photonic device that can balance accuracy and efficiency in the modeling and simulation of complex photonic integrated circuits. SUMMARY

[0005] The purpose of the present application is to provide a method and system for quickly obtaining a time-domain model of a passive photonic device.

[0006] To solve the above technical problems, the present application provides a method for quickly obtaining a time-domain model of a passive photonic device, comprising:

[0007] According to the base frequency equivalent scattering parameters of the passive photonic device, a Loewner matrix and a displacement Loewner matrix are constructed using the base frequency Loewner matrix algorithm, and the singular value decomposition method is used to determine the pole data required for the complex vector fitting method modeling;

[0008] The obtained pole data is used as the initial pole of the complex vector fitting algorithm, and the final pole-residue model is converted into a time-domain state-space model of the passive photonic device.

[0009] As a preferred mode of the present application, for the base frequency equivalent scattering parameters of the passive photonic device, the Loewner Matrix algorithm at the base frequency is used to construct the Loewner and displacement Loewner matrices based on the equivalent scattering parameters, and the singular value decomposition or random singular value decomposition is used to quickly and accurately determine the number and positions of the poles required for modeling, including:

[0010] The baseband equivalent frequency domain response of the passive photonic device is interpolated and approximated using the base frequency LM modeling method, the pole information of the passive photonic device model is preliminarily calculated, and the number and positions of the poles required for modeling are determined.

[0011] As a preferred mode of the present application, the obtained pole data is used as the initial poles of the CVF algorithm, which quickly converges to the optimal position, and the final pole-residue model can accurately represent the rational model of the passive photonic device, including:

[0012] The initial pole generation algorithm in the CVF algorithm is removed, and the iteration pole number algorithm in the nested loop of iteration pole number and optimization pole position is removed. The number of poles of the CVF algorithm is directly determined as the number of initial poles, and the poles generated by the base frequency LM method are used as the initial poles, which are quickly converged to the optimal position through the iteration of the zero and pole, and the baseband equivalent scattering parameters of the passive photonic device are reconstructed based on the finally obtained model. The imaginary parts of the known parts of the reconstructed spectrum and the original spectrum are compared, and the accuracy of the reconstructed spectrum is measured by the absolute error. If the absolute error is greater than -50dB, the threshold value of the base frequency LM algorithm is increased to generate more accurate initial poles for the CVF method and regenerate the model until the absolute error is less than -50dB.

[0013] As a preferred mode of the present application, the base frequency equivalent scattering parameters of the passive photonic device include:

[0014] For the passive photonic device, the base frequency equivalent scattering parameters are:

[0015] (f,S(f))→(f-f c ,S(f-f c ))

[0016] Where f is the frequency point, f c is the carrier frequency of the device, and S(f) is the frequency domain response at the corresponding frequency point; the subsequent algorithm is performed in the Laplace domain, i.e. (s,S(s)), where s=j2πf is the Laplace operator and j represents the imaginary unit.

[0017] As a preferred mode of the present application, when the Loewner Matrix algorithm at the base frequency is used to construct the Loewner and displacement Loewner matrices, the method includes the following steps:

[0018] The base frequency equivalent scattering parameters {(s n ,S(s n )),n=1,2,…,N} are divided into two disjoint subsets (α i ,S(α i )) contains the data corresponding to the odd position frequency points of (s,S(s)), (s1=α1,s3=α2,s5=ɑ3,…), and (β j ,S(β j )) contains the data corresponding to the even position frequency points of (s,S(s)), (s2=β1,s4=β2,s6=β3,…).

[0019] The Loewner matrix is constructed according to the two subsets:

[0020]

[0021] Where L i and R j are left and right tangents respectively, each of which is a unit diagonal matrix.

[0022] The displacement Loewner matrix is constructed according to the two subsets:

[0023]

[0024] As a preferred mode of the present application, in determining the pole data, the method comprises the following steps:

[0025] The number of poles and their positions required for the complex vector fitting method modeling are determined by using the singular value decomposition method or the random singular value decomposition method:

[0026]

[0027] Where Y,Σ,X are left singular value vector, singular value and right singular value vector respectively, and x is a value randomly selected from the frequency points s1,s2,…,s N .

[0028] As a preferred mode of the present application, for the Loewner matrix and the displacement Loewner matrix generated by the tangent matrix in the form of a matrix, the dimension is Ip*Jp, where p is the number of ports of the device, corresponding to the dimension of the S parameter matrix.

[0029] For the Loewner matrix and displacement Loewner matrix generated by the tangent matrix in vector form, the dimension is I*J, and considering that singular value decomposition of a matrix with too large dimension will seriously affect the efficiency, therefore, for the matrix with dimension greater than 350*350, the randomized singular value decomposition (Randomized-SVD) is applied:

[0030]

[0031] wherein k is the number of poles, the randomized singular value decomposition firstly compresses the dimension of the matrix to 350*350, then performs singular value decomposition on the compressed matrix, and restores the singular value vector.

[0032] As a preferred mode of the present application, the specific process of the randomized singular value decomposition is as follows:

[0033] generate a random Gaussian matrix

[0034] preprocess the matrix before compression:

[0035] perform QR decomposition on the matrix U: Q = qr(U);

[0036] compress the matrix wherein Q H is the Hermitian conjugate of Q;

[0037] perform singular value decomposition on the compressed matrix F:

[0038] restore the left singular value vector: Y = Q*Y

[0039] determine the number of poles according to the singular value, arrange the singular values in Σ from large to small, and determine the number of singular values meeting the condition according to the following requirements: wherein σ1 is the largest singular value in Σ, and k is the number of poles preliminarily determined;

[0040] according to the number of poles k, truncate the left and right singular value vectors Y and X:

[0041] Y k = Y(:,1:k)

[0042] X k = X(:,1:k)

[0043] wherein (:,1:k) represents taking all rows and the first k columns of data of the matrix;

[0044] descriptor state space parameters It can be calculated using the following formula:

[0045]

[0046] In this context, the superscript H represents complex conjugation;

[0047] The location of the pole in the complex frequency domain is Generalized eigenvalues:

[0048]

[0049] As a preferred embodiment of this application, when converting the final pole-residue model into a time-domain state-space model, the method includes the following steps:

[0050] The frequency domain response can be approximated using the complex vector fitting algorithm with the following formula:

[0051]

[0052] Where s is the Laplace operator, s = j2πf, f is the frequency point, and p i It is the model pole, r i d is the model residue, and d is the state-space model parameter.

[0053] As a preferred embodiment of this application, the specific process of the complex vector fitting algorithm is as follows:

[0054] Before the complex vector fitting algorithm begins its iterations, p 0 As the initial pole, an unknown auxiliary function σ(s) is introduced:

[0055]

[0056] Among them, σ(s) and σ(s)S(s) have the same initial poles. It is the residual, which contains the residue of the auxiliary function σ(s);

[0057] Solving the linear problem yields the zeros of σ(s):

[0058]

[0059] The new poles of S(s) are equivalent to the zeros of σ(s), which can be obtained by calculating the eigenvalues ​​of the matrix: H = A - bc T Where A is a region containing the initial pole p. 0 A diagonal matrix, b is a column vector of 1s, c T It includes residuals The row vectors; this process is carried out iteratively, with new poles replacing the poles of the previous iteration;

[0060] Solve the above linear problem using the given conditions of the poles and σ(s) = 1 to calculate the remaining unknown quantity r. i And d, thus obtaining the frequency domain model S(s), comparing S(s) with the fundamental frequency equivalent S-parameters and calculating the error. If it does not reach -50dB, it means that the number of poles does not meet the requirements and the model needs to be recalculated.

[0061] The final frequency domain model is then converted into a time-domain state-space model:

[0062]

[0063] Where u(t) and y(t) are the incident and reflected waves, x(t) is the state vector, and C and D are constant state-space parameters to accurately represent the input-output behavior.

[0064] As a preferred embodiment of this application, the method further includes the following steps when recalculating the model:

[0065] Increase the number of poles k;

[0066] Recalculate the initial pole p 0 ;

[0067] The new S(s) is calculated using a complex vector fitting algorithm, and the error is also calculated.

[0068] Repeat the above steps, iteratively increasing the number of poles until the model meets the error requirements.

[0069] This application also provides a system for rapidly obtaining a time-domain model of a passive photonic device using the method described above, comprising:

[0070] The pole data module is used to construct the Loewner matrix and displacement Loewner matrix using the fundamental frequency equivalent scattering parameters of passive photonic devices, and to determine the pole data required for modeling by the complex vector fitting method using the singular value decomposition method.

[0071] The model conversion module is used to take the obtained pole data as the initial poles of the complex vector fitting algorithm, converge to the optimal position, and convert the final pole-residue model into the time-domain state-space model of the passive photonic device.

[0072] The technical solution described in this application has the following advantages over the prior art:

[0073] Based on the fundamental frequency equivalent S-parameters of passive photonic devices, the Loewner matrix and displacement Loewner matrix are calculated. The poles of the device model are obtained through singular value decomposition (SVD), and these poles are then used as the initial poles for the CVF algorithm. Finally, the time-domain response of the passive photonic device is calculated by solving the time-domain state-space model. Compared with the independent fundamental frequency LM algorithm and CVF algorithm, this method achieves a fully automated modeling process, requiring only the setting of a singular value threshold. Furthermore, this method eliminates the need for initial pole selection and consideration of the properties of the initial poles in the CVF method. Since the initial poles obtained through the fundamental frequency LM algorithm are close to the final poles of the complex vector fitting algorithm, the convergence speed of the pole relocation process is very fast. Because the initial poles are relocated through the CVF algorithm, the high accuracy advantage of the CVF algorithm is retained in the final model. When the constructed model fails to meet the requirements of passivity or stability, the passivity and stability enforcement algorithms of the CVF method can be directly used to ensure that the constructed model possesses passivity or stability. This method demonstrates significant performance advantages in the modeling of passive photonic integrated circuits, particularly in terms of modeling efficiency, accuracy, automation, and stability. This technical solution is particularly suitable for scenarios requiring optimization of design parameters based on the frequency domain response of passive photonic integrated circuits, thereby significantly reducing modeling time and improving design efficiency. Furthermore, this solution minimizes human intervention in the modeling process, essentially achieving fully automated modeling, making it the preferred method for modeling circuit-level PICs. Attached Figure Description

[0074] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0075] Figure 1 This is a flowchart illustrating a method for obtaining the initial poles of a complex vector fitting algorithm, as provided in an embodiment of this application.

[0076] Figure 2 This is a flowchart illustrating the sub-dataset partitioning matrix method provided in an embodiment of this application.

[0077] Figure 3 This is a flowchart illustrating the random singular value decomposition method provided in an embodiment of this application.

[0078] Figure 4 This is a schematic flowchart of the model recalculation method provided in the embodiments of this application.

[0079] Figure 5A schematic diagram of the geometric structure of a series track ring resonator provided in an embodiment of this application.

[0080] Figure 6 The errors between the baseband scattering parameters of the series track ring resonator provided in the embodiments of this application and the proposed model and the independent CVF model are respectively.

[0081] Figure 7 This is a diagram showing the system module connections for rapidly acquiring the time-domain model of a passive photonic device, as provided in the embodiments of this application. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all embodiments. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention. 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.

[0083] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0084] It should be noted that the terms "first, second, and third" used in the embodiments of the present invention are only used to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first, second, and third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of the present invention described herein can be implemented in an order other than that illustrated or described herein.

[0085] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which these embodiments of the invention pertain. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0086] The development of optoelectronic chips has driven the evolution of optoelectronic technology from discrete devices to highly integrated systems, enabling optical signal processing and transmission to achieve higher efficiency and broader application potential. Early optoelectronic systems relied on the interconnection of multiple independent devices, while today, photonic integrated circuits (PICs) integrate multiple photonic devices onto a single chip through monolithic integration, significantly improving the compactness and reliability of the system.

[0087] Among these technologies, silicon-on-insulator (SOI) provides an ideal platform for optoelectronic integration. This technology not only supports high-density integration but also remains compatible with existing semiconductor manufacturing processes, enabling optoelectronic chips to be mass-produced using mature CMOS processes, reducing manufacturing costs and accelerating commercialization. Compared to traditional electrical signal transmission, optical signals offer faster transmission rates, longer propagation distances, lower power consumption, and stronger anti-interference capabilities. Therefore, optoelectronic chips are playing an increasingly important role in high-speed data communication, data center interconnects, and precision sensing.

[0088] Within optoelectronic chips, passive photonic devices play a crucial role in signal modulation and routing. These devices are diverse, including multimode interferometers (MMIs), Mach-Zehnder interferometers (MZIs), grating couplers, directional couplers, ring resonators, and arrayed waveguide gratings (AWGs). They can split, combine, modulate, filter, and couple optical signals to achieve complex photonic functions. The design and optimization of passive photonic devices are essential for improving the performance of optoelectronic chips. With the continuous evolution of optoelectronic technology, these devices are developing towards lower loss, higher precision, and stronger functional integration, laying a solid foundation for further breakthroughs in photonic integrated circuits.

[0089] Current state-space modeling algorithms for passive photonic devices primarily employ the Complex Vector Fitting (CVF) method, an extension of the Vector Fitting (VF) method proposed by Bjorn Gustavsen et al. The CVF method first converts the frequency domain response of the passive photonic device into baseband equivalent data. Specifically, it shifts the scattering matrix down the frequency axis by a distance equal to the carrier frequency, effectively removing the carrier component. This process generates a complex-valued non-physical system operating at the baseband frequency. Since the original VF method was only applicable to simulating real-valued physical systems, key steps were modified to adapt to the new baseband equivalent system, ultimately leading to the CVF method. In some cases, the CVF method remains efficient, providing compact models for passive photonic integrated circuits. However, a crucial iterative step in the CVF method, modified from the Sanathanan-Koerner (SK) iteration, requires generating initial poles in a specific manner and repositioning them through continuous iteration until they converge to their optimal locations. This process can be very time-consuming if the initial pole estimates differ significantly from their optimal locations. Furthermore, when modeling a wide frequency range or highly complex frequency response, a large number of poles may be required, making it difficult to determine the minimum model order to meet the modeling requirements. It's important to note that iterating the number of poles and zeros and optimizing their locations requires nested loops. In contrast, the previously mentioned digital infinite or finite impulse response models constructed based on scattering parameters are discrete in time, and their applications are relatively limited compared to continuous-time CVF models. Moreover, performing optoelectronic co-simulation using discrete-time models in SPICE or Verilog-A is also a challenge.

[0090] Therefore, in the field of passive optoelectronics, accurately converting band-limited scattering parameters into causal time-domain models remains a significant challenge.

[0091] This technique starts with the scattering parameters of the passive photonic device under study. Using a rational function model, it constructs a baseband equivalent state-space model in the form of pole residues, shifting the optical carrier to the fundamental frequency. Compared with the vector fitting (VF) method, the CVF method significantly reduces modeling time and simulation complexity without affecting accuracy. Although the CVF modeling method for passive photonic devices has advantages such as wide applicability and strong robustness, its modeling principle is to use a transfer function based on poles and residues to fit the S-parameters of the optoelectronic device (the transfer function based on "pole residues" is a variation of the transfer function based on "zero poles," which will be used as "zero poles" in the following text for ease of explanation). The modeling algorithm improves the fitting accuracy by continuously increasing the number of zero poles and optimizing the position of zero poles in the complex plane. Iterating the number of zero poles and optimizing the position of zero poles requires nested loops. Because the CVF modeling method cannot directly infer the number of zeros and poles required for modeling from the S-parameters, it requires a large number of iterations to determine the number of zeros and poles, resulting in a long processing time. Efficiency can only be improved through manual experience. Furthermore, the CVF modeling algorithm needs to generate initial poles in a specific way; a key step in pole iteration is the reconstructed SK (Sanathanan–Koerner) iteration method. If the initial poles are located far from the optimal convergence point, this process will also be very time-consuming.

[0092] In photonic circuit design, a core challenge lies in accurately converting S-parameters within a limited bandwidth into a causal time-domain model. This conversion process is crucial for ensuring that complex photonic integrated circuits maintain both high accuracy and high efficiency in time-domain simulations. Therefore, researchers are constantly exploring innovative algorithms and computational techniques to achieve the optimal balance between the two.

[0093] Currently, optoelectronic integrated circuits are still in the early stages of rapid development, and the academic and industrial communities have not yet reached a broad consensus on simulation algorithms and model standards. Therefore, modeling methods for passive photonic devices need to meet the following requirements to adapt to the automation needs of large-scale optoelectronic integrated design: First, the model should have broad applicability, covering various passive photonic devices; second, the model should possess high accuracy and compactness to improve simulation efficiency; furthermore, the model must have sufficient robustness to automatically handle multiple devices without human intervention; simultaneously, the constructed model must adhere to the basic physical properties of linear time-invariant systems, such as stability and causality, to ensure that the time-domain simulation results are both accurate and converge stably; finally, these models should be compatible with existing circuit simulation platforms to achieve optoelectronic co-simulation, providing strong support for the overall optimization of complex systems.

[0094] refer to Figure 1 As shown, Figure 1This is a flowchart illustrating a method for rapidly obtaining a time-domain model of a passive photonic device according to an embodiment of the present invention. The method includes at least the following steps:

[0095] Step S110: Use the baseband LM algorithm to extract the initial number and location of poles in the passive photonic device model.

[0096] Here, the B-LM algorithm is used to solve for the initial poles of the model's S-parameters at the fundamental frequency. A stochastic singular value decomposition (SVSFD) algorithm is utilized to optimize the time required for SVSFD on large-scale matrices, ensuring improved algorithm efficiency in accurately estimating model poles. It should be noted that due to limitations in experimental measurements and simulations, the S-parameters of passive photonic devices and systems are often only obtained within specific frequency bandwidths, such as [1.5, 1.6] μm (micrometers) or [187, 200] THz (terahertz). This presents two significant problems: firstly, time-domain simulations in this frequency band require sub-african second time steps, resulting in extremely low simulation efficiency. To address this issue, this invention models the fundamental frequency equivalent S-parameters of passive photonic devices, thereby improving simulation efficiency.

[0097] This invention utilizes the Black-Like (B-LM) algorithm to solve for the initial poles of the S-parameters at the fundamental frequency, then iterates these initial poles to their optimal positions using the CVF algorithm. Finally, the obtained pole-residue model is converted into a time-domain state-space model to characterize passive photonic devices, achieving robust and accurate modeling. Almost no external parameters are required during modeling, simplifying the initial data preparation work, as model construction relies solely on obtaining the equivalent S-parameters of the passive photonic device at the fundamental frequency.

[0098] Step S120: Use the initial poles obtained by the CVF algorithm iteration to establish a pole-residue model and convert it into a state-space model.

[0099] Here, since the B-LM algorithm provides the initial poles, the CVF algorithm does not need to iterate through the poles, thus improving modeling efficiency. Furthermore, because the initial poles are located very close to the poles in the final iteration of the CVF algorithm, the number of iterations is also reduced.

[0100] Therefore, this invention uses the CVF method to model the fundamental frequency equivalent S-parameters of passive photonic devices. To ensure that the model accurately reflects the system's response characteristics within the frequency range, this invention achieves this by constructing state-space equations. State-space equations are differential-algebraic equations, and only the input signal needs to be specified during time-domain simulation. The high accuracy and practicality of the model proposed in this invention are of significant value for the design and analysis of passive photonic integrated circuits.

[0101] In some possible embodiments, the Loewner and displacement Loewner matrices are constructed based on equivalent S-parameters using the fundamental frequency LM (Loewner Matrix) algorithm, with reference to... Figure 2 As shown, it specifically includes:

[0102] Calculate the Loewner matrix and the displacement Loewner matrix based on the baseband equivalent S-parameters (s, S(s)).

[0103]

[0104] In some possible embodiments, the step of rapidly and accurately determining the number and location of poles required for CVF method modeling using singular value decomposition or stochastic singular value decomposition includes:

[0105]

[0106] Where Y, Σ, and X are the left singular value vector, singular value, and right singular value vector, respectively. x represents the frequency points s1, s2, ..., s. N A value is randomly selected from the given values. This is assuming the selected x is not... One of the eigenvalues ​​is such that the result of equation (2-4a) will not be affected.

[0107] For the Loewner and displacement Loewner matrices generated from the matrix form of the tangential matrix, the dimension is Ip*Jp, where p is the number of ports of the device, which also corresponds to the dimension of the S-parameter matrix. For the Loewner and displacement Loewner matrices generated from the vector form of the tangential matrix, the dimension is I*J. Considering that performing singular value decomposition on matrices with excessively large dimensions would severely impact efficiency, randomized singular value decomposition (Randomized-SVD) is applied to matrices with dimensions greater than 350*350.

[0108]

[0109] Where k is the number of poles. Random singular value decomposition first divides the matrix... The dimension is compressed to 350*350, then singular value decomposition is performed on the compressed matrix, and the singular value vectors are restored. (Reference) Figure 3 As shown, the process of random singular value decomposition is as follows:

[0110] Step S160: Generate a random Gaussian matrix

[0111] Step S161: For the matrix Pre-processing before compression:

[0112]

[0113] Step S162: Perform QR decomposition on matrix U:

[0114] Q = qr(U) (2-5a);

[0115] Step S163: Compression Matrix

[0116]

[0117] Among them, Q H It is the Hermitian conjugate of Q;

[0118] Step S164: Perform singular value decomposition on the compressed matrix F:

[0119]

[0120] Step S165: Restore the left singular value vector:

[0121] Y = Q * Y (2-8a);

[0122] Step S166: Determine the number of poles based on singular values. Arrange the singular values ​​in Σ from largest to smallest, and roughly determine the number of singular values ​​that satisfy the following requirements.

[0123]

[0124] Here, σ1 is the largest singular value in Σ. k is the number of poles initially determined.

[0125] Step S167: Truncate the left and right singular value vectors Y and X according to the number of poles k.

[0126] Y k =Y(:,1:k) (2-10a);

[0127] X k =X(:,1:k) (2-10b);

[0128] Step S168: Descriptor state space parameters It can be calculated using the following formula:

[0129]

[0130] Step S169: The location of the pole in the complex frequency domain is... Generalized eigenvalues:

[0131]

[0132] In some possible embodiments, the step of using the CVF algorithm to establish a pole-residue model based on the poles calculated by B-LM and converting it into a state-space model includes:

[0133] The frequency domain response can be approximated using the complex vector fitting algorithm with the following formula:

[0134]

[0135] Where s is the Laplace operator, s = j2πf, f is the frequency point, and p i It is the model pole, r i is the model residue. D is the state-space model parameter.

[0136] The complex vector fitting algorithm can be divided into two steps. The first step is pole iteration, which converges the poles to the optimal position. The second step is to use the iterated poles to determine the residue.

[0137] Before the complex vector fitting algorithm begins its iterations, p 0 As the initial pole, an unknown auxiliary function σ(s) is introduced:

[0138]

[0139] Among them, σ(s) and σ(s)S(s) have the same initial poles. It is the residual, which contains the residue of the auxiliary function σ(s).

[0140] Multiplying f(s) of equation (2-13a) by σ(s) of equation (2-14a) yields the following linear problem:

[0141]

[0142] Solving equation (2-15a) yields the zeros of σ(s). The new poles of S(s) are equivalent to the zeros of σ(s), and can also be obtained by calculating the eigenvalues ​​of the matrix.

[0143] H = A - bc T (2-16a);

[0144] Where A is the region containing the initial pole p. 0 A diagonal matrix, b is a column vector of 1s, c T It includes residuals The row vectors are processed iteratively, with new poles replacing the poles of the previous iteration. After several iterations, the process converges.

[0145] Finally, by solving (2-15a) using the given conditions of the poles and σ(s) = 1, the remaining unknown quantity r can be calculated. iAnd d, thus obtaining the frequency domain model S(s) of formula (2-13a), comparing S(s) with the fundamental frequency equivalent S-parameters and calculating the error, if it does not reach -50dB, it indicates that the number of poles does not meet the requirement, refer to Figure 4 As shown, the device model needs to be recalculated step by step:

[0146] Increase the number of poles k according to the singular values;

[0147] Extract the corresponding singular value vector;

[0148] Calculate the state space parameters of the descriptor;

[0149] Perform eigenvalue decomposition to solve for the initial pole p 0 ;

[0150] The new S(s) is calculated using a complex vector fitting algorithm;

[0151] Repeat the above steps, iteratively increasing the number of poles until the model meets the error requirements.

[0152] The final frequency domain model can be easily converted into a time domain state-space model:

[0153]

[0154] Where u(t) and y(t) are the incident and reflected waves, respectively. x(t) is the state vector, and C and D are constant state-space parameters. This approach can accurately represent the input-output behavior of the system.

[0155] The method for rapidly obtaining the time-domain model of a passive photonic device is described below with reference to a specific embodiment. However, it is worth noting that this specific embodiment is only for better illustrating the present invention and does not constitute an improper limitation of the present invention.

[0156] This specific embodiment will demonstrate the practical effect of the invention by modeling the fundamental frequency equivalent S-parameters of a series-connected track ring resonator. The geometry of the series-connected track ring filter is as follows: Figure 2 As shown, Figure 2 The circuit consists of two cascaded ring resonators and two straight waveguides, forming a series filter. The gap between the waveguides and the rings is 230 nm, while the gap between the two rings is 410 nm. Their power coupling coefficients are κ1 = 0.015, κ2 = 0.00005, and κ3 = 0.015, respectively. The radii are R1 = 4.225 μm and R2 = 6.545 μm. The coupling length L is... c=15μm. The S-parameters of the series track ring resonator were obtained from IPKISS simulation. 2001 equidistant frequency samples were collected within the frequency range of [187.37, 199.86] THz, corresponding to wavelengths of [1.5, 1.6] μm. Then, using a preset carrier frequency f... c =191.83THz moved to baseband.

[0157] This invention first applies the baseband LM algorithm to the fundamental frequency equivalent S-parameters of a series track ring resonator, dividing it into left and right subsets. Then, Loewner and displacement Loewner matrices are constructed according to (2-1a) to (2-1b). Next, (2-3a) is calculated using the random singular value decomposition steps (2-4a) to (2-8b), obtaining the left and right singular value vectors and singular values ​​of the entire matrix. These are truncated according to a preset threshold to obtain left and right singular value vectors and singular values ​​containing more information, and the model poles are initially determined according to (2-12a). Subsequently, these poles are used as the initial poles for the CVF method, and the pole positions are iterated. After iteration, the model residues are solved, and the error between the proposed model and the fundamental frequency equivalent S-parameters is calculated. The fundamental frequency equivalent S-parameters of the series track ring resonator are shown in [the diagram]. Figure 7 As can be seen, the maximum absolute error between the model proposed in this invention and the fundamental frequency equivalent S-parameters is -68.26 dB. For comparison, an independent CVF method was used to model the baseband equivalent S-parameters of the device. Table 1 lists the simulation accuracy and efficiency of the two methods. All modeling and simulation were implemented in MATLAB, using a computer configured with an Intel Core i7 processor and 16GB of memory.

[0158] Table 1 compares the accuracy and efficiency of the proposed method with CVF in modeling cascaded filters.

[0159] Modeling method The method of the invention CVF Model maximum absolute error -68.26 dB -68.25 dB Modeling time 0.38s 1.92s Number of algorithm iterations 4 48

[0160] As can be seen from Table 1, compared with the existing CVF model, the model proposed by the method of this invention can be simulated more efficiently thanks to the significantly reduced number of algorithm iterations. At the same time, due to the use of the extreme point iteration algorithm of the CVF method, the modeling accuracy can also be maintained.

[0161] This invention offers significant performance advantages, providing an efficient and accurate method for modeling photonic integrated circuits (PICs). First, this method requires fewer parameters during modeling, simplifying initial data preparation as model building relies solely on obtaining the fundamental frequency equivalent S-parameters. This is particularly valuable for researchers and engineers seeking to quickly evaluate the performance of photonic devices. Second, since the poles generated by the baseband LM method closely approximate the final solution given by the CVF method, the pole relocation convergence process is very fast. Furthermore, because the initial poles are relocated using the CVF method, the high accuracy of the CVF technique is preserved in the final model. This efficiency makes it particularly suitable for scenarios requiring extensive simulations to optimize design parameters, significantly shortening the design cycle and improving work efficiency. Given that the proposed method is directly applied to the scattering matrix, it can model the S-parameters of various passive photonic devices while considering circuit non-ideals such as higher-order dispersion and wavelength-dependent losses. Moreover, the robustness and broad applicability of this method help minimize the need for manual intervention during modeling, making it a preferred solution among system-level PIC simulation tools.

[0162] The motivation for this invention stems from two aspects: 1) the urgent need for system-level PIC modeling driven by the rapid increase in the integration scale and complexity of photonic integrated circuits (PICs); and 2) the inefficiency of current complex vector fitting methods for modeling passive photonic devices, which cannot meet commercial requirements. Therefore, this invention proposes a method for obtaining the initial poles of the CVF algorithm. It has the following advantages:

[0163] This method is widely applicable to various integrated optical circuits (PICs), and its robust and automated modeling process makes it the optimal solution for design automation scenarios. It requires only the baseband equivalent S-parameters of passive photonic devices, efficiently obtaining the initial poles of complex vector fitting methods, avoiding nested loops in solving the device model, and significantly improving modeling efficiency. This method can capture dispersion, backscattering, and wavelength-dependent effects, which are crucial in many applications but often overlooked by other modeling techniques. Because the model proposed in this invention is stable and causal during construction and accurate and reliable in both the frequency and time domains, it can be used for simulations in both the frequency and time domains.

[0164] refer to Figure 7 As shown. In some embodiments of this application, this application also relates to a system for rapidly obtaining a time-domain model of a passive photonic device using the above-described method, comprising:

[0165] The pole data module is used to construct the Loewner matrix and displacement Loewner matrix using the fundamental frequency equivalent scattering parameters of passive photonic devices, and to determine the pole data required for modeling by the complex vector fitting method using the singular value decomposition method.

[0166] The model conversion module is used to take the obtained pole data as the initial poles of the complex vector fitting algorithm, converge to the optimal position, and convert the final pole-residue model into the time-domain state-space model of the passive photonic device.

[0167] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of the invention. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of the invention, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the invention. The sequence numbers of the above-described embodiments of the invention are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0168] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0169] In the several embodiments provided by this invention, it should be understood that the disclosed devices and methods can be implemented in other ways.

[0170] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined to obtain new method embodiments without conflict. The features disclosed in the several method or device embodiments provided by this invention can be arbitrarily combined to obtain new method or device embodiments without conflict.

[0171] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for rapidly obtaining a time-domain model of a passive photonic device, characterized in that, Includes the following steps: Based on the fundamental frequency equivalent scattering parameters of passive photonic devices, the Loewner matrix and displacement Loewner matrix are constructed using the fundamental frequency Loewner matrix algorithm, and the pole data required for modeling by the complex vector fitting method are determined using the singular value decomposition method. The obtained pole data is used as the initial poles of the complex vector fitting algorithm, which converges to the optimal position and the final pole-residue model is converted into the time-domain state-space model of the passive photonic device. When constructing the Loewner matrix and the shifted Loewner matrix using the fundamental frequency Loewner Matrix algorithm, the method includes the following steps: The fundamental frequency equivalent scattering parameters Divide into two disjoint subsets , , Include Data corresponding to odd-numbered frequency points , Include Data corresponding to even-numbered frequency points ; Construct the Loewner matrix based on the two subsets of data: in, and These are the left and right tangents, and each left and right tangent is a unit diagonal matrix; Construct the displacement Loewner matrix based on the two subsets of data: ； When determining pole data, the method includes the following steps: Using singular value decomposition (SVD) or stochastic singular value decomposition (SSVD), determine the number and location of poles required for complex vector fitting modeling: in, These are the left singular value vector, the singular value vector, and the right singular value vector, respectively. From frequency point A value is randomly selected from the data, as long as... no The eigenvalues ​​of the singular value decomposition will not be affected by the results of the singular value decomposition. The Loewner matrix and the displacement Loewner matrix generated from the tangential matrix in matrix form have the following dimensions: ,in, This represents the number of ports of the device, corresponding to the dimension of the S-parameter matrix; The Loewner matrix and the displacement Loewner matrix generated from the tangential matrix in vector form have the following dimensions: Considering that singular value decomposition on matrices with excessively large dimensions would severely impact efficiency, random singular value decomposition is applied to matrices with dimensions greater than 350×350. in, To determine the number of poles, random singular value decomposition first divides the matrix... The dimension is compressed to 350×350, then the compressed matrix is ​​subjected to singular value decomposition, and the singular value vector is restored. The specific process of performing random singular value decomposition is as follows: Generate random Gaussian matrices ; For matrix Pre-processing before compression: ; For matrix Perform QR decomposition: ; Compression matrix : ,in, yes Hermitian conjugate; For the compressed matrix Perform singular value decomposition: ; Restore the left singular value vector: Determine the number of poles based on singular values. Given a set of singular values ​​arranged from largest to smallest, determine the number of singular values ​​that satisfy the following condition: ,in, yes The largest singular value in, This represents the initial number of poles; Based on the number of poles , the left and right singular value vectors and Truncation: in, This means retrieving all rows and the first k columns of the matrix; Descriptor state space parameters It can be calculated using the following formula: Among them, superscript H Represents complex conjugation; The location of the pole in the complex frequency domain is Generalized eigenvalues: 。 2. The method for rapidly obtaining a time-domain model of a passive photonic device according to claim 1, characterized in that, The fundamental frequency equivalent scattering parameters of the passive photonic device include: For passive photonic devices, the fundamental frequency equivalent scattering parameter is: in, For frequency points, The carrier frequency of the device. This represents the frequency domain response at the corresponding frequency point; subsequent algorithms are performed in the Laplace domain, i.e. ,in It is the Laplace operator. It represents the imaginary unit.

3. The method for rapidly obtaining a time-domain model of a passive photonic device according to claim 1, characterized in that, When converting the final pole-residue model into a time-domain state-space model, the method includes the following steps: The frequency domain response is approximated using the complex vector fitting algorithm with the following formula: in, It is the Laplace operator, and has , These are model poles. It is the model residue. These are the parameters of the state-space model.

4. The method for rapidly obtaining a time-domain model of a passive photonic device according to claim 3, characterized in that, The specific process of the complex vector fitting algorithm is as follows: Before the complex vector fitting algorithm begins its iterations, As the initial pole, an unknown auxiliary function is introduced. : in, and Having the same initial poles, It is a residual, containing auxiliary functions. The residue; Solving the linear problem yields Zero point: The new pole is equivalent to The zeros are obtained by calculating the eigenvalues ​​of the matrix: Where A is the region containing the initial poles. The diagonal matrix , b is a column vector of 1s. It includes residuals The row vectors; this process is carried out iteratively, with new poles replacing the poles of the previous iteration; Given the poles and Solve the above linear problem under two conditions to calculate the remaining unknowns. and Thus, the frequency domain model is obtained. ,Will Compare with the equivalent S-parameters of the fundamental frequency and calculate the error. If it does not reach -50dB, it means that the number of poles does not meet the requirements and the model needs to be recalculated. The final frequency domain model is then converted into a time-domain state-space model: in, and It consists of incident wave and reflected wave. It is a state vector. These are constant state-space parameters used to accurately represent input-output behavior.

5. The method for rapidly obtaining a time-domain model of a passive photonic device according to claim 4, characterized in that, When recalculating the model, the method further includes the following steps: Increase the number of poles ; Recalculate the initial poles ; Calculate the new using the complex vector fitting algorithm. And calculate the error; Repeat the above steps, iteratively increasing the number of poles until the model meets the error requirements.

6. A system for rapidly acquiring a time-domain model of a passive photonic device using the method described in any one of claims 1-5, characterized in that, include: The pole data module is used to construct the Loewner matrix and displacement Loewner matrix using the fundamental frequency equivalent scattering parameters of passive photonic devices, and to determine the pole data required for modeling by the complex vector fitting method using the singular value decomposition method. The model conversion module is used to take the obtained pole data as the initial poles of the complex vector fitting algorithm, converge to the optimal position, and convert the final pole-residue model into the time-domain state-space model of the passive photonic device.

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