A method for obtaining causal impulse response of passive photonic integrated circuits

Abstract

The present invention proposes a method for obtaining the causal pulse response of a passive photonic integrated circuit. The method first shifts the band-limited scattering parameters (S parameters) of the passive photonic device down to the fundamental frequency according to a preset carrier frequency, and further extrapolates the obtained band-limited fundamental frequency spectrum. These S parameters are used to describe the input and output characteristics of the passive photonic device. In order to ensure that the model can accurately map the physical behavior of the system within the measurement frequency range, the method achieves this goal by constructing a set of matrix equations based on the Hilbert transform integral in the Z domain. The parameters of the extrapolated spectrum are optimized by minimizing the frequency domain extrapolation error, thereby ensuring the causality of the system. This invention ensures the high accuracy and practicality of the proposed model, and is of great value for the design and analysis of passive photonic integrated circuits.

Description

Technical Field

[0001] The present invention relates to the field of photonic integrated circuits, and in particular to, but not limited to, a method for obtaining a causal pulse response of a passive photonic integrated circuit. Background Art

[0002] Optoelectronic chips have broad application prospects in high-speed data communication, quantum computing, all-optical machine learning, biosensing, lidar, gyroscopes, etc. This trend not only promotes the development of optoelectronic technology, but also brings new opportunities and challenges to the progress of information communication, sensor technology and new energy fields.

[0003] Passive photonic devices play an important role in the development and application of optoelectronic chips. The input and output characteristics of these devices are usually described by S parameters. Due to its simplicity and accuracy, the S parameter model is a widely used distributed model in the circuit-level simulation of photonic integrated circuits. However, S parameters belong to the frequency domain information of the device and cannot be directly used for time domain simulation. The frequency domain S parameter information can be directly converted into a time domain pulse response through IFFT (Inverse Fast Fourier Transform), and then the input signal is convolved with the obtained time domain pulse response to achieve time domain simulation. Its modeling process is simple but there are multiple problems. First, the S parameters of photonic devices are bandwidth-limited. For example, the S parameter matrix of the device at a series of discrete points in the band of 1.5μm to 1.6μm (micrometers) is obtained through FDTD (finite-difference time-domain) full-wave simulation, but there is no device information in the bands below 1.5μm and above 1.6μm. Directly performing IFFT on the bandwidth-limited S parameters to obtain the pulse response will seriously damage the basic physical property of causality. Although the damage to causality can be alleviated by preprocessing such as adding window functions to the S parameters, the accuracy of the pulse response and its corresponding frequency response is reduced. Secondly, the selection of the time step size in the process of obtaining the discrete-time pulse response will affect the accuracy of the pulse response and convolution as well as the simulation efficiency.

[0004] Therefore, in the field of system-level simulation of photonic integrated circuits, accurately converting bandwidth-limited S-parameters into causal time-domain models remains a major challenge. Researchers must continue to explore novel methods and computational techniques to address this challenge and strive to achieve a delicate balance between accuracy and efficiency in time-domain simulation of complex photonic integrated circuits. Summary of the invention

[0005] In view of this, an embodiment of the present invention provides a method for obtaining a causal impulse response of a passive photonic integrated circuit.

[0006] The technical solution of the embodiment of the present invention is achieved as follows:

[0007] An embodiment of the present invention provides a method for obtaining a causal pulse response of a passive photonic integrated circuit, the method comprising:

[0008] The S parameters of a passive photonic device are shifted to a base frequency according to a preset carrier frequency for modeling; wherein the S parameters are used to characterize the input and output characteristics of the passive photonic device; by minimizing the frequency domain extrapolation error, the parameters of the extrapolated spectrum are optimized to achieve extrapolation of the S parameters of the passive photonic device outside a limited bandwidth; and the causal pulse effect of the passive photonic device after extrapolation is calculated by an inverse fast Fourier transform.

[0009] In some possible embodiments, the parameters of the extrapolated spectrum are optimized by minimizing the frequency domain extrapolation error to achieve extrapolation of the S parameters of the passive photonic device outside the limited bandwidth, including: dividing the full spectrum into a negative half-spectrum unknown part, a negative half-spectrum known part, a positive half-spectrum known part and a positive half-spectrum unknown part, and solving the negative half-spectrum unknown part and the positive half-spectrum unknown part; comparing the imaginary part of the known spectrum part in the reconstructed spectrum with the imaginary part of the known part in the original spectrum, and using the absolute error to measure the accuracy of the reconstructed spectrum. If the absolute error is greater than -50dB, the value of the discrete Fourier coefficient w(0) in the discrete time series w(n) will be replaced, and the iteration is performed until the absolute error is less than -50dB.

[0010] In some possible embodiments, the S parameters of the passive photonic device are adjusted at a specific frequency f c Move to the fundamental frequency for modeling, including:

[0011] Determine the real part Y(k) and imaginary part X(k) of a discrete time series w(n) uniformly sampled with N samples:

[0012]

[0013]

[0014]

[0015] Where W(k) is the Fourier coefficient of w(n); Equations (2-1a) and (2-1b) are expressed in matrices as follows:

[0016]

[0017]

[0018] in, The coefficients of the matrix C k,l Written as:

[0019]

[0020] Among them, variables k, l∈(0, N-1), and N is the total number of samples.

[0021] In some possible embodiments, solving the unknown negative half-spectrum part and the unknown positive half-spectrum part includes:

[0022] Convert equation (2-2a) and equation (2-2b) into the following block matrix forms:

[0023]

[0024]

[0025]

[0026]

[0027] Among them, N1, N0, P0, P1 represent the number of sample points of the unknown part of the negative half spectrum, the known part of the negative half spectrum, the known part of the positive half spectrum and the unknown part of the positive half spectrum respectively; (2-4a) and (2-4b) represent the negative half spectrum, (2-5a) and (2-5b) represent the positive half spectrum; considering that the Hilbert transform of the constant is zero, equations (2-4a) and (2-5a) are rewritten as:

[0028]

[0029]

[0030] Merge the bottom rows of equations (2-4b) and (2-6), (2-5b) and (2-7), and the matrices of the positive and negative half frequencies can be written as follows:

[0031]

[0032]

[0033] in, and Represents the identity matrix.

[0034] By and Subtract a guess about w(0) from the original to get and , and then substitute the value of into (2-8a) and (2-8b) to calculate and And calculate the full spectrum S according to formula (2-9) E (f i ):

[0035]

[0036] in, represents the discrete Hilbert transform,

[0037] The main steps and beneficial effects of the technical solution provided by the embodiment of the present invention include at least:

[0038] In an embodiment of the present invention, the S parameters of the passive photonic device are first moved to the base frequency for modeling according to a preset carrier frequency, and then the parameters of the extrapolated spectrum are optimized by minimizing the frequency domain extrapolation error to achieve the extrapolation of the S parameters of the passive photonic device outside the limited bandwidth, and finally the causal pulse response of the passive photonic device after extrapolation is calculated by IFFT. This modeling method simplifies the preliminary data preparation work because the model construction only depends on the acquisition of the S parameters. Moreover, by reducing the extrapolation error and adjusting the parameters of the extrapolation function using an optimization algorithm, the accuracy of the constructed model is guaranteed, and the time domain model is ensured to have causality and stability. The results show significant performance advantages in the field of modeling and simulation of photonic integrated circuits (PICs), especially in terms of stability, causality verification, and simulation efficiency. The high efficiency of this technical solution is particularly suitable for scenarios where a large number of simulations are required to optimize the design parameters of passive photonic integrated circuits, thereby significantly shortening the design cycle and improving work efficiency. Its robustness and wide applicability enable this technical solution to minimize human intervention in the modeling and simulation process, making it a preferred method for line-level PICs modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0040] Figure 1 A schematic diagram of the relationship between the model accuracy based on FIR (Finite Impulse Response) and the number of cascaded photonic devices provided in the related art;

[0041] Figure 2 A schematic flow chart of a method for obtaining a causal pulse response of a passive photonic integrated circuit provided by an embodiment of the present invention;

[0042] Figure 3 A schematic diagram of a process of directly performing IFFT on the band-limited S parameters of a passive photonic integrated circuit provided by an embodiment of the present invention;

[0043] Figure 4A schematic diagram of the geometric structure of the MZI cascade filter provided in an embodiment of the present invention;

[0044] Figure 5 The baseband scattering parameter S of the MZI cascade filter provided in the embodiment of the present invention is 17 The errors between the model provided by the embodiment of the present invention and the CVF model respectively;

[0045] Figure 6 The cascade filter provided in the embodiment of the present invention is S after frequency extrapolation. 17 The impulse response and the un-extrapolated S 17 Schematic diagram of the comparison between the impulse responses of

[0046] Figure 7 A schematic diagram comparing the time domain simulation results of the modeling method provided in an embodiment of the present invention and using the CVF model. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0048] In the following description, reference is made to “some embodiments”, which describe a subset of all possible embodiments, but it will be 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.

[0049] It should be pointed out that the terms "first\second\third" involved in the embodiments of the present invention are only used to distinguish similar objects and do not represent a specific ordering of the objects. It can be understood that "first\second\third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of the present invention described here can be implemented in an order other than that illustrated or described here.

[0050] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the field to which the embodiments of the present invention belong. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with those in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined as here.

[0051] The research and development of optoelectronic chips represents an important transformation in the field of optoelectronic technology. From traditional discrete devices to today's integrated chips, optoelectronic chips have made great progress in cost, volume, power consumption, performance and integration. The use of optoelectronic integration technology based on the silicon-on-insulator (SOI) material platform enables a variety of optoelectronic devices to be integrated on a single chip. This technology allows the integration of a large number of optoelectronic devices in a tiny size and is compatible with CMOS processes, providing a low-cost solution for the large-scale manufacturing and commercialization of optoelectronic integrated chips. In addition, compared with traditional electrical signal transmission, optical signal transmission has the advantages of higher transmission rate, longer transmission distance, smaller signal loss and lower interference. As the core device of photoelectric conversion, optoelectronic chips play a vital role in achieving high-speed, efficient and stable signal transmission.

[0052] In optoelectronic chips, passive photonic devices can be used as key components for optical transmission and optical signal processing. There are various passive devices such as MMI (multi-mode interferometer), MZI (Mach-Zehnder interferometer), grating coupler, directional coupler, resonant ring, AWG (arrayed waveguide) and various photonic filters, which are used to manipulate and control the flow in optical networks.

[0053] Currently, there are three main models of passive photonic devices used in system-level simulation: 1) analytical model; 2) FIR-based behavioral model; 3) CVF (Complex Vector Fitting)-based state-space model.

[0054] The analytical model is based on the working principle of the device and derives the relationship between its input and output in an analytical way. This type of modeling method is only applicable to photonic devices with simple working principles, and the modeling process is often difficult to accurately simulate the non-ideal characteristics of the device, such as dispersion; therefore, the analytical model can be regarded as a simplified model of the photonic device, which is generally used in situations where the system simulation accuracy is not required. The latter two models are both behavioral models. Their modeling process is based on the S parameter matrix of the passive photonic device, which only describes the input-output relationship of the device and generally does not reflect the actual working principle of the device. Due to the high degree of abstraction, this type of model is relatively compact and suitable for system-level simulations with high timeliness requirements.

[0055] The second model is proposed by Sergei Mingaleev et al. in 2015. The method of building a time domain model by designing an FIR filter to make its frequency response close to the S parameters of the photonic device is used. However, the accuracy of this modeling method is easily affected by the FIR filter design method adopted, and large errors will occur at the edge of the modeling frequency range. In addition, when the FIR models of multiple photonic devices are cascaded, the accuracy of the entire model will drop rapidly with the increase of photonic devices, such as Figure 1 As shown, the left part shows the relationship between the absolute error of the frequency response of the FIR model and the actual S parameters and the number of cascaded devices, and the right part shows that the accurate bandwidth range of the FIR model narrows rapidly as the number of cascaded devices increases. The accuracy of the FIR model is also easily affected by the minimum group delay of the device. When the time step of the FIR model is much smaller than the minimum group delay, the model accuracy is high. Otherwise, the model accuracy will deteriorate rapidly. In response to this problem, Sergei Mingaleev proposed a "time-frequency domain" solution, that is, after obtaining the S parameters of the entire cascaded passive photonic circuit module in the frequency domain simulation, it is converted into a time domain FIR model, thereby avoiding the reduction of accuracy caused by cascading FIR models in the time domain. However, this method regards the entire passive module as a "black box". Although the output signal of the entire module can be obtained during the simulation process, the specific information inside the module cannot be accessed. At present, some commercial companies have adopted this modeling method to develop and apply related products.

[0056] The third model is the CVF (Complex Vector Fitting) modeling method. Starting from the scattering parameters of the passive photonic device under study, this technology constructs a baseband equivalent state space model in the form of pole residues, and moves the scattering parameters to the base frequency according to the preset carrier frequency, which significantly reduces the modeling time and simulation complexity without affecting the accuracy. Although the CVF modeling method of passive photonic devices has the advantages of wide application range, high modeling accuracy, strong robustness, and compact model, its modeling principle is to use a transfer function based on poles and residues to fit the S parameters of optoelectronic devices (the transfer function based on "pole residues" is a deformation of the transfer function based on "zero poles", and "zero poles" will be used in the following text for the convenience of explaining the problem). 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, which leads to some photonic devices using the CVF modeling method. The model will be too large and complex. In addition, the CVF model is still a mathematical model and cannot be directly used for optoelectronic joint simulation.

[0057] Therefore, in the field of photonic integrated circuit design, accurately converting bandwidth-limited S parameters into causal time-domain models remains a major challenge. Researchers must continue to explore novel methods and computational techniques to address this challenge and strive to achieve a delicate balance between accuracy and efficiency in the time-domain simulation of complex photonic integrated circuits. At present, since optoelectronic integrated circuits are still in their early stages of development, there is no widely recognized simulation algorithm and model standard in academia and industry. The following requirements are put forward for the passive photonic device modeling method to meet the needs of large-scale optoelectronic integrated design automation: 1) Widely applicable to a variety of passive photonic devices; 2) High modeling accuracy; 3) Compact model and high simulation efficiency; 4) Strong robustness, able to model a variety of passive devices without human intervention to adapt to the application scenarios of optoelectronic design automation; 5) The constructed model must meet the inherent physical properties of linear time-invariant systems such as stability and causality to ensure that the time-domain simulation results are accurate and convergent; 6) The model has the potential to be compatible with the circuit simulation platform to achieve electro-optical co-simulation.

[0058] Figure 2 A flow chart of a method for obtaining a causal pulse response of a passive photonic integrated circuit provided by an embodiment of the present invention is shown as follows: Figure 2 As shown, the method comprises at least the following steps:

[0059] Step S210, the S parameters of the passive photonic device are shifted to the base frequency according to the preset carrier frequency for modeling.

[0060] Here, the passive photonic devices include filters, optical fibers, optical waveguide devices, gratings, photodiodes, etc. These devices mainly achieve their functions through the transmission, modulation and detection of light without external energy input. The S parameters are band-limited scattering parameters of passive photonic devices, which are used to characterize the input and output characteristics of passive photonic devices. The S parameters contain a lot of information, which describes the reflection and transmission behavior of photonic devices at different frequencies, that is, how to respond to light signals of different frequencies. Specifically, the S parameters can provide detailed information about how the device converts the incident wave into reflected waves and transmitted waves, including the amplification or attenuation of the signal by the device, the phase change, and the interference and coupling degree between the signals. Through these parameters, the transmission characteristics and network behavior of photonic devices can be fully understood, providing a basis for the design, analysis and optimization of devices. In implementation, we implement this process by constructing a set of equations based on the matrix expression of the Hilbert transform integral in the Z domain.

[0061] The present invention uses an optimization algorithm to extrapolate the S parameters at the base frequency to ensure their causality, and then converts the extrapolated causal and stable spectrum into a time domain pulse signal through IFFT to characterize the passive photonic device and achieve robust and accurate modeling. Fewer parameters are required for modeling, which simplifies the initial data preparation work because the model construction only depends on the acquisition of the S parameters of the passive photonic device.

[0062] Step S220 , optimizing the parameters of the extrapolated spectrum by minimizing the frequency domain extrapolation error, so as to implement extrapolation of the S parameters of the passive photonic device outside the limited bandwidth.

[0063] Here, the method of minimizing the frequency domain extrapolation error includes using the Hilbert transform to enforce the causality of the extrapolation function, and using optimization algorithms such as particle swarm optimization, Newton iteration method, etc. to optimize the parameters of the extrapolation function (w(0) in formula (2-9)) to ensure accurate reflection of the physical behavior of the system in the entire frequency range and improve the accuracy of restoring the full frequency response.

[0064] The model developed by optimizing the parameters of the polynomial function extrapolation is not only stable and accurate, but also causal. The causality of this model can be directly detected by IFFT, ensuring the physical credibility of the model in time domain simulation. This is crucial for the design of high-performance photonic integrated circuits that need to accurately reflect the propagation and interaction of electromagnetic waves.

[0065] Step S230, calculating the causal pulse effect of the passive photonic device after extrapolation by inverse fast Fourier transform.

[0066] It should be noted that due to the limitations of experimental measurement and simulation, the S parameters of passive photonic devices and systems are often only obtained within a specific frequency bandwidth, such as [1.5, 1.6] μm (micrometers) or [187, 200] THz (terahertz). This will bring two significant problems. First, time domain simulation in this frequency band must use sub-second time steps, which will cause extremely low simulation efficiency. To solve this problem, the present invention presets the S parameters of passive photonic devices at the carrier frequency f c Simulation efficiency can be improved by moving to fundamental frequency modeling.

[0067] At the same time, this band-limited spectrum has another tricky problem for time domain simulation. When IFFT is directly applied to convert frequency domain data into time domain impulse response, since IFFT assumes that the input signal is known over the entire frequency range, the incomplete frequency information caused by the band-limited S parameters may produce non-physical impulse responses that violate causality, such as Figure 3 shown.

[0068] To alleviate this problem, researchers and engineers have adopted a variety of windowing operations. These windowing operations reduce the edge effects produced when band-limited S parameters are directly converted by applying specific window functions in the frequency domain, thereby restoring the physical rationality of the causal pulse response to a certain extent. However, these strategies often sacrifice the accuracy of the S parameters, because the application of window functions may suppress certain characteristics in the frequency domain data, resulting in a deviation between the final time domain model and the actual physical system. Therefore, ensuring that the pulse response obtained from the band-limited S parameters satisfies causality is the key to high-precision photonic integrated circuit design and simulation.

[0069] The key to solving this challenge is to recover a full frequency response that satisfies the bandwidth restrictions and is causal from the existing band-limited S parameters. This usually involves extrapolating the S parameters outside the limited bandwidth to supplement the lost information before the IFFT. The choice of the extrapolation method is very critical, it must accurately reflect the physical behavior of the system over the entire frequency range while maintaining mathematical rigor and physical feasibility.

[0070] Therefore, the present invention shifts the S parameters of the passive photonic device down to the base frequency according to the predetermined carrier frequency for modeling, and further extrapolates the unknown part of the spectrum. In order to ensure that the model can accurately map the physical performance of the system in the entire frequency range, the present invention achieves this goal by constructing a series of equations. These equations are based on the matrix expression of the Hilbert transform integral in the Z domain, and the parameters of the extrapolation function are optimized by minimizing the frequency domain extrapolation error, and finally an accurate causal time domain model is obtained through IFFT. Thereby ensuring the causality of the system and improving the accuracy of restoring the full frequency response, the high precision and practicality of the model proposed by the method of the present invention are of great value for the design and analysis of passive photonic integrated circuits.

[0071] In some possible embodiments, in order to ensure that the model can accurately map the physical behavior of the system within the measurement frequency range, the method achieves this goal by constructing a set of matrix equations based on the Hilbert transform integral in the Z domain. c Move to the fundamental frequency for modeling, including:

[0072] Determine the real part Yg(k) and imaginary part X(k) of a discrete time series w(n) uniformly sampled with N samples:

[0073]

[0074]

[0075]

[0076] Where W(k) is the Fourier coefficient of w(n); Equations (2-1a) and (2-1b) are expressed in matrices as follows:

[0077]

[0078]

[0079] in, The coefficients of the matrix C k,l Written as:

[0080]

[0081] Among them, variables k, l∈(0, N-1), and N is the total number of samples.

[0082] In some possible embodiments, the parameters of the extrapolated spectrum are optimized by minimizing the frequency domain extrapolation error to achieve extrapolation of the S parameters of the passive photonic device outside the limited bandwidth, including: dividing the full spectrum into a negative half-spectrum unknown part, a negative half-spectrum known part, a positive half-spectrum known part and a positive half-spectrum unknown part, and solving the negative half-spectrum unknown part and the positive half-spectrum unknown part; comparing the imaginary part of the known spectrum part in the reconstructed spectrum with the imaginary part of the known part in the original spectrum, and using the absolute error to measure the accuracy of the reconstructed spectrum. If the absolute error is greater than -50dB, the value of the discrete Fourier coefficient w(0) in the discrete time series w(n) will be replaced, and the iteration is performed until the absolute error is less than -50dB.

[0083] Here, the S parameters of the passive photonic device are first adjusted to a specific frequency f before modeling. c Moved to the fundamental frequency, the spectrum is not symmetrical, e.g. Figure 3 As shown, the spectrum is divided into four parts: the negative half spectrum unknown part, the negative half spectrum known part, the positive half spectrum known part and the positive half spectrum unknown part. The number of sample points in these four parts are represented by N1, N0, P0 and P1 respectively.

[0084] In some possible embodiments, solving the unknown negative half-spectrum part and the unknown positive half-spectrum part includes:

[0085] Convert equation (2-2a) and equation (2-2b) into the following block matrix forms:

[0086]

[0087]

[0088]

[0089]

[0090] Among them, N1, N0, P0, P1 represent the number of sample points of the unknown part of the negative half spectrum, the known part of the negative half spectrum, the known part of the positive half spectrum and the unknown part of the positive half spectrum respectively; (2-4a) and (2-4b) represent the negative half spectrum, (2-5a) and (2-5b) represent the positive half spectrum; considering that the Hilbert transform of the constant is zero, equations (2-4a) and (2-5a) are rewritten as:

[0091]

[0092]

[0093] The bottom rows of equations (2-4b) and (2-6), (2-5b) and (2-7) are combined, because the extrapolation method used uses two forced equations, in which the real and imaginary parts of the unknown spectrum must be operated through square matrices. Here, only the bottom rows of equations (2-4b) and (2-6), (2-5b) and (2-7) meet this condition, and the matrices of the positive and negative half frequencies after the combination can be written as:

[0094]

[0095]

[0096] in, and represents the identity matrix. It can be seen that solving the unknown spectrum requires inverting the square matrix that depends only on N1 and P1. This allows the lengths of the known spectra N0 and P0 and the unknown spectra N1 and P1 to be independently selected. In implementation, it is more advantageous to reasonably select the lengths of N0, P0, N1, and P1.

[0097] It is important to note that solving equation (2-8) requires knowing the value of w(0) in advance, which is impossible for an extrapolation process. and Subtract a guess about w(0) from the original to get and , and then substitute the value of into (2-8a) and (2-8b) to calculate and And calculate the full spectrum S according to formula (2-9) E (f i ):

[0098]

[0099] in, represents the discrete Hilbert transform, This allows the causality of the spectrum to be preserved.

[0100] Then, the reconstructed spectrum S E (f i ) The imaginary part of the known spectrum is compared with the imaginary part of the known part of the original spectrum, and the absolute error is used to measure the accuracy of the reconstructed spectrum. If the absolute error is greater than -50dB, it means that this error is unacceptable, and the value of w(0) will be replaced again. This iteration is repeated until the absolute error is less than -50dB. It should be noted that the value of w(0) can be predicted using any optimization algorithm, such as using a particle swarm optimization algorithm to predict the value of w(0).

[0101] The method for obtaining the causal pulse response of a passive photonic integrated circuit provided by an embodiment of the present invention is widely applicable to various PICs, and the modeling process is robust and automatable, which makes it the best solution in the design automation scenario. The method can capture dispersion, backscattering and wavelength-related effects, which are very important in many applications but are often ignored by some other modeling and simulation techniques. The model proposed in the present invention is stable and causal when constructed, and is accurate and reliable in both the frequency domain and the time domain. Therefore, it can be used for simulation in the frequency domain and the time domain. Compared with the existing CVF model, the proposed model can be simulated more efficiently.

[0102] The method for obtaining the causal pulse response of a passive photonic integrated circuit is described below in conjunction with a specific embodiment. However, it should be noted that this specific embodiment is only for better illustrating the present invention and does not constitute an improper limitation to the present invention.

[0103] This specific embodiment will demonstrate the practical effect of the present invention by modeling the S parameters of an MZI cascade filter. The geometric structure of the MZI cascade filter is as follows: Figure 4 As shown in the figure, there are three cascaded Mach-Zehnder interferometers (MZIs) that form a cascade filter. Each MZI contains five directional couplers, and their power coupling coefficients are 0.5, 0.13, 0.12, 0.5, and 0.25 respectively. Figure 4 As shown, ΔL1 = 11.18 μm, ΔL2 = 5.6 μm, and ΔL3 = 5.68 μm. All SOI-based waveguides in the cascade filter have an effective refractive index of 2.30 at 1.55 μm and a group refractive index of 4.18. The scattering parameter S of the cascade filter 17 The simulation was performed in IPKISS with a frequency range of [189.96, 193.84] THz, with a total of 151 equally spaced points. Then, the signal was moved to the baseband using a preset carrier frequency of fc = 191.83 THz.

[0104] The present invention applies the proposed extrapolation algorithm to the baseband S parameters S of the cascaded filters. 17 The optimization algorithm used in this invention is the particle swarm algorithm. First, w(0) is given an initial value and then brought into (2-8a) and (2-8b) to calculate and And calculate the full spectrum S according to formula (2-9) E (f i ), then, the reconstructed spectrum S E (f i ) compares the imaginary part of the known spectrum with the imaginary part of the known part of the original spectrum, and uses the absolute error to measure the accuracy of the reconstructed spectrum. By continuously optimizing the value of w(0) to reduce the absolute error, if the absolute error is less than -50dB, the causal complete extrapolated spectrum is obtained. 17 The amplitude (Magnitude) and phase (Phase) and the complete spectrum (Frequency) are displayed in Figure 5 It can be seen that the proposed model of this invention is similar to S 17 The maximum absolute error (Deviation) is -56.52dB. At the same time, for comparison, the CVF method is also used to calculate S 17 Modeling, modeling consumes 30 poles, and the CVF model (CVF model) and S 17 The maximum absolute error is -46.80dB.

[0105] In order to check the causality of the calculated complete spectrum, the MZI cascade filter S is calculated by IFFT. 17 The time domain impulse response of Figure 6 As shown, the dotted line drawn represents the cascade filter S calculated after extrapolation. 17 The time domain impulse response (h(t) from the proposed model) is shown in Figure 2. The solid line represents the time domain impulse response directly from S without extrapolation. 17 The calculated impulse response (h(t)of S17without extrapolation) is provided for comparison. Considering that the impulse response of the baseband system is complex-valued, Figure 6 The absolute value of the impulse response is shown.

[0106] Once the causal pulse response is obtained, a time domain simulation can be performed by linear convolution. When a narrow pulse with a width of 1ps is given to port P1, the response of output port P7 is as follows: Figure 7 In order to verify the accuracy and efficiency of the proposed method in time domain simulation, the same time domain simulation is performed using the CVF model. Figure 7In addition, Table 1 lists the simulation accuracy and efficiency of the cascade filter modeling. All modeling and simulation are implemented in MATLAB, and the computer is equipped with an Intel Core i7 processor and 16 GB memory.

[0107] Table 1 Comparison of the accuracy and efficiency of the proposed method and CVF for modeling cascade filters

[0108]

[0109] It can be seen from Table 1 that, compared with the existing CVF model, the model proposed by the method of the present invention can perform simulation more effectively.

[0110] The present invention has significant performance advantages, and provides an efficient and accurate method for modeling and simulating PICs. First, this method requires fewer parameters when modeling, which simplifies the preliminary data preparation work, because the model construction only relies on the acquisition of S parameters. This is particularly valuable for researchers and engineers who want to quickly evaluate the performance of photonic devices. Secondly, the model developed by extrapolation of the optimization algorithm is not only stable and accurate, but also causal. The causality of this model can be directly detected by IFFT, ensuring the physical credibility of the model in time domain simulation. This is crucial for the design of high-performance photonic integrated circuits that need to accurately reflect the propagation and interaction of electromagnetic waves. Furthermore, the proposed method shows high efficiency in the simulation process, and the simulation results can be easily obtained by directly applying linear convolution. The efficiency of this method makes it particularly suitable for scenarios where a large number of simulations are required to optimize design parameters, thereby greatly shortening the design cycle and improving work efficiency. Since the proposed method is directly applied to the scattering matrix, it is able to model the S parameters of various passive photonic devices while considering the non-idealities of the circuit (such as high-order dispersion and wavelength-dependent losses). The robustness and wide applicability of this method help it to minimize the need for human intervention in the modeling process, making it a preferred solution among system-level PICs simulation tools.

[0111] The motivation for the present invention is twofold: 1) the urgent need for system-level PICs simulation driven by the rapid growth in integration scale and complexity of PICs; and 2) the lack of robust and accurate modeling of passive photonic devices in current commercial circuit simulation tools. Therefore, the present invention proposes a robust method for obtaining the causal impulse response of passive photonic devices. It has the following advantages:

[0112] The method is widely applicable to various PICs, and the modeling process is robust and automatable, which makes it the best solution in design automation scenarios. The method is able to capture dispersion, backscattering and wavelength-dependent effects, which are very important in many applications but are often overlooked by some other modeling and simulation techniques. Since the model proposed by the method is stable and causal when constructed, and is accurate and reliable in both frequency and time domains, it can be used for simulation in both frequency and time domains.

[0113] It should be understood that "one embodiment" or "an embodiment" mentioned throughout the specification means that specific features, structures or characteristics related to the embodiment are included in at least one embodiment of the present invention. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. In addition, these specific features, structures or characteristics can be combined in one or more embodiments in any suitable manner. It should be understood that in various embodiments of the present invention, the size of the serial number of the above-mentioned processes does not mean the 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 embodiment of the present invention. The serial numbers of the above-mentioned embodiments of the present invention are only for description and do not represent the advantages and disadvantages of the embodiments.

[0114] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0115] In several embodiments provided by the present invention, it should be understood that the disclosed devices and methods can be implemented in other ways.

[0116] The methods disclosed in several method embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments. The features disclosed in several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments or device embodiments.

[0117] The above is only an embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for obtaining a causal impulse response of a passive photonic integrated circuit, characterized in that: The method comprises: The S parameters of passive photonic devices are adjusted to a specific frequency. Moving to the fundamental frequency for modeling; wherein the S parameters are used to characterize the input and output characteristics of the passive photonic device; By minimizing the frequency domain extrapolation error, the parameters of the extrapolated spectrum are optimized to achieve extrapolation of the S parameters of the passive photonic device outside the limited bandwidth; Calculate the causal impulse response of the passive photonic device after extrapolation by inverse fast Fourier transform; The S parameters of the passive photonic device are calculated at a specific frequency. Move to the fundamental frequency for modeling, including: Determine a discrete time series with N samples uniformly sampled The real part of and the imaginary part : (2-1a)； (2-1b)； (2-1c)； in yes Fourier coefficients; Formula (2-1a) and (2-1b) are expressed as matrices: (2-2a)； (2-2b)； in, , the coefficients of the matrix Written as: (2-3)； Among them, the variable , N is the total number of samples.

2. The method according to claim 1, characterized in that The method of minimizing the frequency domain extrapolation error and optimizing the parameters of the extrapolation spectrum to achieve extrapolation of the S parameters of the passive photonic device outside the limited bandwidth includes: Divide the full spectrum into a negative half spectrum unknown part, a negative half spectrum known part, a positive half spectrum known part and a positive half spectrum unknown part, and solve the negative half spectrum unknown part and the positive half spectrum unknown part; Compare the imaginary part of the known spectrum in the reconstructed spectrum with the imaginary part of the known spectrum in the original spectrum, and use the absolute error to measure the accuracy of the reconstructed spectrum. If the absolute error is greater than -50dB, the discrete time series will be replaced again. Discrete Fourier coefficients The value is adjusted, and the iteration is continued until the absolute error is less than -50dB.

3. The method according to claim 2, characterized in that The step of solving the unknown part of the negative half spectrum and the unknown part of the positive half spectrum comprises: Convert equation (2-2a) and equation (2-2b) into the following block matrix forms: (2-4a)； (2-4b)； (2-5a)； (2-5b)； in, , , , Respectively represent the number of sample points of the unknown part of the negative half spectrum, the known part of the negative half spectrum, the known part of the positive half spectrum and the unknown part of the positive half spectrum; (2-4a) and (2-4b) represent the negative half spectrum, (2-5a) and (2-5b) represent the positive half spectrum; considering that the Hilbert transform of the constant is zero, rewrite equations (2-4a) and (2-5a) as follows: (2-6)； (2-7)； Merge the bottom rows of equations (2-4b) and (2-6), (2-5b) and (2-7), and the matrices of the positive and negative half frequencies can be written as follows: (2-8a)； (2-8b)； in, and represents the identity matrix; By and Subtract one pair from The guess is to estimate and , and then substitute the value of into (2-8a) and (2-8b) to calculate and , and calculate the full spectrum according to formula (2-9) : (2-9) in, represents the discrete Hilbert transform, .

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