VCSEL chip-oriented multi-dimensional performance parameter simulation analysis system

Abstract

The application discloses a multi-dimension performance parameter simulation analysis system for a VCSEL chip, a modulation bandwidth is obtained through frequency response function fitting, the modulation bandwidth corresponds to a frequency point when the amplitude of the frequency response function decreases to a preset proportion of the low frequency amplitude, the module also analyzes the damping envelope of transient relaxation oscillation, extracts the damping ratio and the resonance frequency, a bandwidth prediction function is constructed based on the damping resonance model, the bandwidth prediction function represents the modulation bandwidth as a functional relationship of the resonance frequency and the damping ratio, the modulation bandwidth is proportional to the resonance frequency and is nonlinearly restricted by the damping ratio, the scanning module supports multi-dimension scanning of injection current, temperature and structure parameters, and outputs current-voltage characteristic curves, optical power-current characteristic curves, modulation response curves and eye diagrams. The application realizes accurate prediction and visual evaluation of the high-speed performance of the laser.

Description

Technical Field

[0001] This invention belongs to the field of optoelectronic device simulation technology, and relates to a multi-dimensional performance parameter simulation and analysis system for VCSEL chips. Background Technology

[0002] Vertical-cavity surface-emitting lasers (VCSELs) are key devices in optical communication and optical sensing. With the development of integrated photonics, higher demands are placed on the accuracy and efficiency of device performance simulation. Existing simulation methods often employ general-purpose numerical solvers to handle the coupling equations between carriers and photons. These methods often suffer from low computational efficiency when dealing with strongly nonlinear systems, especially during transient response simulations. Fixed-step-size algorithms are prone to numerical oscillations in rigid regions, making it difficult for simulation results to accurately reflect the true physical characteristics of the device. Furthermore, traditional models lack sufficient description of the feedback mechanism of stimulated emission processes, failing to accurately establish the dynamic correlation between carrier consumption and photon generation. The lack of effective modeling methods for multimode competition effects in current technologies leads to significant deviations in predicting high-speed modulation bandwidths. These problems severely restrict the design and optimization process of laser chips.

[0003] Therefore, there is an urgent need to develop a simulation analysis system that can balance computational efficiency and physical accuracy. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention proposes a multi-dimensional performance parameter simulation and analysis system for VCSEL chips.

[0005] The first aspect of this application provides a multi-dimensional performance parameter simulation and analysis system for VCSEL chips, including: a modeling module, a solving module, a prediction module, and a scanning module;

[0006] The modeling module is used to construct a coupled model of the carrier continuity equation and the multimode photon rate equation. The coupled model establishes a nonlinear feedback mechanism between carrier concentration and photon density by introducing a photon density-dependent net recombination rate expression, so as to simulate the strong nonlinear coupling characteristics in the process of generating light output by electrical injection.

[0007] The solution module is used to solve the coupled model by employing an implicit Runge-Kutta algorithm combined with a local truncation error control strategy, dynamically adjusting the time step according to the local truncation error in the calculation process, so as to suppress numerical calculation divergence.

[0008] The prediction module is used to extract the relaxation oscillation frequency and damping factor based on the transient response simulation results, construct the frequency response function and calculate the modulation bandwidth.

[0009] The scanning module is used to support multi-dimensional scanning of injected current, temperature and structural parameters, and outputs performance index curves.

[0010] Optionally, when constructing the coupled model, the modeling module is configured to solve the balance relationship between the time change rate of carrier concentration and the injection current density, net recombination rate, and carrier diffusion term, as well as the balance relationship between the time change rate of photon density and the optical field confinement factor, group velocity, gain coefficient, total loss, and spontaneous emission rate; the net recombination rate expression integrates a stimulated emission extraction term, which is used to characterize the real-time modulation effect of photon density on the carrier consumption rate.

[0011] Optionally, the modeling module configures the net recombination rate expression as an algebraic sum of radiative recombination terms, non-radiative recombination terms, and stimulated emission extraction terms; wherein the stimulated emission extraction terms are set as a product of group velocity, gain coefficient, and photon density to achieve self-consistent feedback between photon generation and carrier consumption during the numerical solution process.

[0012] Optionally, the solution module adopts the Radau IIA-type implicit Runge-Kutta method, which is internally configured with a third-order precision scheme and a fifth-order precision scheme, and calls the Newton-Raphson iteration method to linearize and solve the nonlinear equation system.

[0013] Optionally, the solver module is configured to perform the following operations when executing the local truncation error control strategy:

[0014] The magnitude of the difference between the solution vector of the fifth-order precision scheme and the solution vector of the third-order precision scheme is calculated as an estimate of the local truncation error.

[0015] When the estimated value of the local truncation error is greater than the preset tolerance, it is determined that the numerical solution at the current time step does not meet the stability requirements, and a backoff calculation is performed and the time step is reduced.

[0016] When the estimated value of the local truncation error is less than or equal to the preset tolerance, the numerical solution is determined to be converged, the current solution is accepted, and the time step is increased.

[0017] Optionally, the prediction module is configured to apply a small-signal sinusoidal perturbation current to the laser, solve for the transient response time series of the optical output power, and convert the transient response time series into a frequency response function through Fourier transform.

[0018] Optionally, the prediction module obtains the modulation bandwidth by fitting the frequency response function, and the modulation bandwidth corresponds to the frequency point where the amplitude of the frequency response function drops to a preset proportion of the low-frequency amplitude.

[0019] Optionally, the prediction module is also used to analyze the decay envelope of transient relaxation oscillations, extract the damping ratio and resonant frequency, and construct a bandwidth prediction function based on the damped resonance model.

[0020] Optionally, the bandwidth prediction function expresses the modulation bandwidth as a function of the resonant frequency and the damping ratio, wherein the modulation bandwidth is proportional to the resonant frequency and is subject to the nonlinearity of the damping ratio.

[0021] Optionally, the performance index curves output by the scanning module include current-voltage characteristic curves, optical power-current characteristic curves, modulation response curves, and eye diagrams.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] This invention discloses a multi-dimensional performance parameter simulation and analysis system for VCSEL chips, which significantly improves the numerical stability and computational efficiency of the simulation process. By constructing a coupled model including a photon density-dependent net recombination rate expression, a nonlinear feedback mechanism between carrier concentration and photon density is effectively established, enabling a more realistic simulation of the strong nonlinear coupling characteristics in the process of optical output generation by electrical injection. This invention employs an implicit Runge-Kutta algorithm combined with a local truncation error control strategy, which can dynamically adjust the time step based on the local truncation error during the calculation process, effectively suppressing divergence phenomena in the numerical calculation. This invention utilizes Radau IIA-type implicit Runge-Kutta methods combined with the Newton-Raphson iteration method to efficiently solve rigid equation systems, significantly improving the convergence speed under strong nonlinear coupling conditions. This invention uses the difference magnitude of solution vectors with different precision formats as an estimate of the local truncation error, and implements step back and adjustment accordingly, forming a closed-loop error control mechanism to ensure the accuracy of the simulation results. This invention extracts the relaxation oscillation frequency and damping factor based on transient response simulation results, which can accurately construct the frequency response function and calculate the modulation bandwidth. Through the scanning module, it supports multi-dimensional scanning of injection current, temperature and structural parameters, and can output comprehensive performance index curves, providing reliable data support for the optimized design of vertical cavity surface-emitting laser chips. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of a multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to an embodiment of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] In one embodiment, such as Figure 1As shown, a multi-dimensional performance parameter simulation and analysis system for VCSEL chips is provided. This system includes a modeling module, a solution module, a prediction module, and a scanning module. Detailed descriptions of each functional module are as follows:

[0027] The modeling module constructs a coupled model of the carrier continuity equation and the multimode photon rate equation. This coupled model establishes a nonlinear feedback mechanism between carrier concentration and photon density by introducing a photon density-dependent net recombination rate expression, simulating the strong nonlinear coupling characteristics in the process of light output generation via electrical injection. The solution module uses an implicit Runge-Kutta algorithm combined with a local truncation error control strategy to dynamically adjust the time step based on the local truncation error during calculation, thus suppressing numerical calculation divergence. The prediction module extracts the relaxation oscillation frequency and damping factor based on the transient response simulation results, constructs the frequency response function, and calculates the modulation bandwidth. The scanning module supports multi-dimensional scanning of injection current, temperature, and structural parameters, outputting performance index curves.

[0028] In one embodiment, the modeling module is used to construct a coupled model of the carrier continuity equation and the multimode photon rate equation. The coupled model establishes a nonlinear feedback mechanism between carrier concentration and photon density by introducing a photon density-dependent net recombination rate expression, so as to simulate the strong nonlinear coupling characteristics in the process of generating light output by electrical injection.

[0029] Specifically, the modeling module is used to construct a coupled model that realistically reflects the internal physical mechanisms of a vertical-cavity surface-emitting laser (VCSEL). The modeling module first establishes a carrier continuity equation to describe the change in carrier concentration over time within the active region. This rate of change is determined by the injection current density, net recombination rate, and carrier diffusion term. The injection current provides energy to the system, driving electrons to transition from the valence band to the conduction band. The net recombination rate comprehensively reflects the overall effects of radiative recombination, non-radiative recombination, and stimulated emission extraction. To introduce a photon density dependency, the coupled model explicitly integrates a stimulated emission extraction term into the net recombination rate expression. This stimulated emission extraction term is set as the product of the group velocity, gain coefficient, and photon density. This mathematical configuration physically characterizes the real-time modulation effect of photon density on the carrier consumption rate. When the intracavity photon density increases, the stimulated emission process intensifies, leading to a faster carrier consumption rate. Conversely, when the photon density decreases, the carrier consumption rate slows down. Through this mechanism, the coupled model establishes a self-consistent feedback between photon generation and carrier consumption. In the construction of the multimode photon rate equation, the time-varying rate of photon density is jointly determined by the optical field confinement factor, group velocity, gain coefficient, total loss, and spontaneous emission rate. The gain coefficient itself has a nonlinear relationship with the carrier concentration. Due to the presence of the stimulated emission extraction term, the change in photon density, in turn, affects the rate of change of carrier concentration. This bidirectional interaction forms a strongly nonlinear coupled system.

[0030] For example, the system initializes with a specific injection current density and initial carrier concentration. After the simulation begins, the modeling module calculates the photon density in real time for each mode. As the photon density accumulates, the value of the stimulated emission extraction term increases, thereby deducting more carrier consumption from the net recombination rate. This process dynamically adjusts the carrier lifetime, enabling the simulation results to accurately simulate the transient nonlinear behavior during the light output process generated by electrical injection.

[0031] This invention realizes a nonlinear feedback mechanism between carrier concentration and photon density. Compared with traditional linear models or models that neglect stimulated emission feedback, this invention can more accurately capture the dynamic characteristics of lasers under high-speed modulation or large-signal driving. This invention effectively solves the problem of insufficient simulation accuracy caused by the simplification of physical models in existing technologies.

[0032] Furthermore, when constructing the coupled model, the modeling module is configured to solve the balance relationship between the time change rate of carrier concentration and the injection current density, net recombination rate, and carrier diffusion term, as well as the balance relationship between the time change rate of photon density and the optical field confinement factor, group velocity, gain coefficient, total loss, and spontaneous emission rate; the net recombination rate expression integrates a stimulated emission extraction term, which is used to characterize the real-time modulation effect of photon density on the carrier consumption rate.

[0033] Specifically, the modeling module implements the following steps when constructing the coupled model: First, for the carrier continuity equation, the module is configured to solve for the rate of change of carrier concentration over time. This rate of change is determined by the injection current density, net recombination rate, and carrier diffusion term. The injection current density provides new carriers to the active region through electrode injection. The net recombination rate describes the rate at which carriers disappear due to radiative and non-radiative processes. The carrier diffusion term reflects the migration behavior of carriers in space. These three factors together constitute the balance between carrier generation and consumption. Second, for the multimode photon rate equation, the module is configured to solve for the rate of change of photon density over time. This rate of change has a direct balance relationship with the optical field confinement factor, group velocity, gain coefficient, total loss, and spontaneous emission rate. The optical field confinement factor describes the degree of overlap of the optical field within the active region. The group velocity determines the propagation characteristics of photons within the cavity. The gain coefficient, determined by the carrier concentration, provides the mechanism for optical amplification. Total loss includes cavity mirror loss and material absorption loss. Spontaneous emission rate exists as both a noise source and an initial photon source. These parameters collectively determine the photon accumulation and decay process. Crucially, the net recombination rate expression is not a simple constant or solely a function of carrier concentration, but rather explicitly integrates a stimulated emission extraction term. This stimulated emission extraction term is mathematically defined as the product of group velocity, gain coefficient, and photon density. This configuration physically characterizes the real-time modulation effect of photon density on the carrier consumption rate. When the photon density of a mode increases, the stimulated emission process is enhanced, leading to faster carrier consumption. This change in consumption rate, in turn, affects the gain coefficient, and consequently, the photon growth rate of that mode or other modes.

[0034] For example, when the injected current density suddenly increases, the carrier concentration rises rapidly. According to conventional models, the net recombination rate increases only slowly with the carrier concentration. However, in the coupling model of this invention, as the carrier concentration increases, the gain coefficient reaches a threshold, and the photon density of a specific mode begins to increase exponentially. This increase in photon density instantaneously increases the net recombination rate through stimulated emission extraction terms. This leads to the suppression of the increasing trend of carrier concentration, and the system quickly reaches a new dynamic equilibrium point.

[0035] This invention achieves strong bidirectional coupling between charge carriers and photons. Compared to models that neglect stimulated emission extraction terms, this invention can more accurately simulate multimode competition effects. During multimode competition, the increase in photon density of one mode suppresses the gain of other modes through stimulated emission extraction terms, thus realistically reflecting the suppression and competition behavior between modes. This technical solution effectively overcomes the defects in the simulation of multimode dynamic characteristics caused by the simplification of physical models in existing technologies.

[0036] Furthermore, the modeling module configures the net recombination rate expression as an algebraic sum of radiative recombination terms, non-radiative recombination terms, and stimulated emission extraction terms; wherein, the stimulated emission extraction terms are set as a product of group velocity, gain coefficient, and photon density, so as to achieve self-consistent feedback between photon generation and carrier consumption during the numerical solution process.

[0037] Specifically, the modeling module, when constructing the coupled model, is configured to achieve a bidirectional dynamic equilibrium between the carrier system and the photon system. In solving the carrier continuity equation, the module first establishes a conservation relationship between the time-varying rate of carrier concentration and the injected current density, net recombination rate, and carrier diffusion term. The injected current density, as an external excitation source, continuously injects new carriers into the active region. The net recombination rate comprehensively characterizes the total rate at which carriers disappear due to radiative recombination, non-radiative recombination, and stimulated emission. The carrier diffusion term describes the diffusion motion of carriers when they are spatially non-uniformly distributed. These three factors collectively determine the transient evolution of carrier concentration. In solving the multimode photon rate equation, the module establishes a gain-loss balance relationship between the time-varying rate of photon density and the optical field confinement factor, group velocity, gain coefficient, total loss, and spontaneous emission rate. The optical field confinement factor reflects the confinement effect of the optical field within the active region. The group velocity is related to the photon propagation characteristics and the refractive index distribution of the medium. The gain coefficient, determined by the current carrier concentration, provides the driving force for optical amplification. Total losses include the transmission loss of the cavity mirror and the absorption loss of the material. The spontaneous emission rate, acting as a background source, provides initial seed photons for laser oscillation. These parameters collectively determine the establishment and maintenance of photon densities for each longitudinal mode. To achieve strong nonlinear coupling, a stimulated emission extraction term is integrated into the net recombination rate expression. This stimulated emission extraction term is specifically configured in numerical calculations as a product of group velocity, gain coefficient, and photon density. This mathematical configuration has a clear physical mechanism, characterizing the real-time modulation effect of photon density on the carrier consumption rate. When the photon density of a specific mode increases, the stimulated emission process corresponding to that mode intensifies, leading to faster carrier consumption. This increase in consumption rate immediately feeds back to the carrier continuity equation, causing a decrease in carrier concentration. The decrease in carrier concentration, in turn, reduces the gain coefficient, thus affecting the photon growth rate of that mode and other competing modes. For example, the system simulates the dynamic process under a step injection current. Initially, the injected current density surges above the threshold, causing a rapid accumulation of carrier concentration. As the carrier concentration increases, the gain exceeds the loss, and the photon density of the dominant mode begins to grow exponentially. At this point, the value of the stimulated emission extraction term increases sharply with the photon density, instantaneously increasing the net recombination rate. This rapidly suppresses the increasing trend of carrier concentration, and the system reaches dynamic equilibrium in a very short time. Without this stimulated emission extraction term, the carrier concentration would continue to rise to a high steady-state value, making it impossible to simulate the actual clamping effect.

[0038] The technical solution of this invention effectively overcomes the defects of decoupling or weak coupling in the physical model of the prior art. It realizes real-time bidirectional feedback between charge carriers and photons, and can accurately simulate complex physical phenomena such as multimode competition, spatial hole burning, and transient chirping. This modeling method significantly improves the physical realism of the simulation results, and provides a high-fidelity analytical basis for the performance prediction of vertical-cavity surface-emitting laser chips.

[0039] In one embodiment, the solution module is used to solve the coupled model by employing an implicit Runge-Kutta algorithm combined with a local truncation error control strategy, dynamically adjusting the time step according to the local truncation error during the calculation process, so as to suppress numerical calculation divergence.

[0040] Specifically, the core of the solution module lies in addressing the rigidity problem inherent in the coupled model. The physical processes of a vertical-cavity surface-emitting laser involve the coexistence of fast and slow timescales. The recombination lifetime of charge carriers differs significantly from that of photons. This results in the differential equations describing the system exhibiting strong rigidity. Traditional explicit algorithms, in solving such problems, must employ extremely small time steps to ensure numerical stability. This severely reduces computational efficiency. Even with inappropriate step sizes, the calculation results may exhibit severe oscillations or divergence. To overcome this technical challenge, the solution module is configured to employ an implicit Runge-Kutta algorithm. This algorithm determines the state variables for the next time step by solving a system of nonlinear equations. The stability region of the implicit algorithm is much larger than that of the explicit algorithm. It allows for the use of larger time steps to capture slowly varying processes. Simultaneously, it can still accurately describe rapidly changing physical transients. To further ensure computational accuracy and suppress numerical divergence, the module incorporates a local truncation error control strategy. In each iteration, the module estimates the local truncation error at the current step size. This error reflects the deviation between the numerical solution and the true solution. The module compares the estimated error with a preset tolerance limit. If the error exceeds the tolerance, the current step size is deemed too large. The module automatically triggers a step size adjustment mechanism, backsliding and reducing the time step. If the error is less than the tolerance, the current step size is deemed appropriate. The module accepts the calculation result for this step size and appropriately increases the step size of the next time step to improve efficiency. For example, when simulating the turn-on process of a laser, the carrier concentration and photon density change drastically within nanoseconds. At this time, the local truncation error increases instantaneously. After detecting this increase in error, the solution module immediately and automatically reduces the integration step size from the picosecond level to the femtosecond level. This fine step size can accurately capture the peaks and troughs of relaxation oscillations. As the system enters steady-state oscillation, the changes in physical quantities tend to level off. The local truncation error decreases. The module then automatically increases the time step size. Thus, while ensuring accuracy, the total number of calculation steps is greatly reduced.

[0041] By combining this implicit Runge-Kutta algorithm with a local truncation error control strategy, this invention achieves dynamic adjustment of the time step. This adaptive mechanism effectively balances the trade-off between computational efficiency and numerical stability, avoiding numerical oscillations caused by improper fixed step size settings. It also ensures convergence of the solution under strongly nonlinear coupling conditions. This technical solution addresses the problems of simulation divergence or excessive computation time in existing technologies, providing a reliable guarantee for long-term simulation of complex dynamic characteristics.

[0042] Furthermore, when executing the local truncation error control strategy, the solution module is configured to perform the following operations: calculate the magnitude of the difference between the solution vector in the fifth-order precision scheme and the solution vector in the third-order precision scheme as the local truncation error estimate; when the local truncation error estimate is greater than a preset tolerance, determine that the numerical solution at the current time step does not meet the stability requirements, perform backtracking calculation and reduce the time step; when the local truncation error estimate is less than or equal to the preset tolerance, determine that the numerical solution has converged, accept the current solution and increase the time step.

[0043] Specifically, the solution module implements the local truncation error control strategy as follows: The module integrates an embedded Runge-Kutta method, which includes computational flows for both fifth-order and third-order precision schemes. During each time step, the module simultaneously calculates two solution vectors of different orders. The fifth-order precision scheme provides a high-precision reference solution. The third-order precision scheme provides a lower-precision predicted solution. To obtain a local truncation error estimate, the module calculates the magnitude of the difference between these two solution vectors. This magnitude mathematically reflects the truncation error of the numerical solution at the current step size. The module compares this error estimate with a preset tolerance limit in real time. The preset tolerance includes absolute and relative tolerances, used to define the acceptable range of the numerical solution. When the local truncation error estimate exceeds the preset tolerance, the module determines that the current time step is too large. This means that the oscillation amplitude of the numerical solution exceeds the stability region and cannot meet the convergence requirements. The module immediately triggers a backoff calculation mechanism, canceling the calculation results of the current step. Simultaneously, the module automatically reduces the time step according to the error ratio. The reduced step size is used for recalculation to ensure the solution falls within the stable region. When the estimated local truncation error is less than or equal to the preset tolerance, the module determines that the current numerical solution has converged. This means that the accuracy of the calculation result is within the allowable range. The module accepts the current solution vector as a valid result and stores it in the historical data queue. To improve computational efficiency, the module appropriately increases the time step size in the next time step to adapt to the range of gradual changes in physical quantities. For example, when simulating the transient response of a laser, the system state variables undergo a sudden change. At this time, the magnitude of the difference between the fifth-order solution and the third-order solution increases instantaneously, exceeding the preset tolerance. After detecting this out-of-tolerance signal, the solution module determines that the numerical solution is unstable. The module automatically reverts to the previous stable moment and reduces the time step size by an order of magnitude. This fine step size can effectively suppress numerical divergence and capture sharp physical peaks. Through this error estimation and step size control mechanism based on the magnitude of the difference, the present invention achieves intelligent adaptive solution process. This technical solution maximizes integration efficiency while ensuring computational accuracy. It effectively avoids the numerical oscillation and divergence phenomena commonly found in the solution of rigid systems, and provides a high-fidelity and high-efficiency numerical analysis method for long-term dynamic simulation of vertical cavity surface-emitting lasers.

[0044] In one embodiment, the prediction module is used to extract the relaxation oscillation frequency and damping factor based on the transient response simulation results, construct the frequency response function, and calculate the modulation bandwidth.

[0045] Specifically, the prediction module is a unit that enables rapid evaluation of high-speed performance. The prediction module's workflow begins with receiving and processing the transient response simulation results. The prediction module obtains the optical power output waveform of the laser under step current excitation from the solution module. The optical power output waveform completely records the dynamic process of photon density changing over time, containing rich information about system dynamics.

[0046] Upon receiving the transient response simulation results, the prediction module first performs feature extraction to obtain the relaxation oscillation frequency and damping factor. The relaxation oscillation frequency is a key parameter characterizing the rate of interaction between charge carriers and photons within the laser. The prediction module converts the signal from the time domain to the frequency domain by performing a Fast Fourier Transform on the time-domain waveform. In the resulting spectrum, the frequency corresponding to the peak with the largest amplitude is the relaxation oscillation frequency. The damping factor reflects the rate of energy dissipation in the system and determines the rate of oscillation decay. The prediction module accurately extracts the damping factor by analyzing the decay trend of the time-domain waveform envelope and calculating the ratio of the amplitudes of adjacent peaks.

[0047] After successfully extracting the relaxation oscillation frequency and damping factor, the prediction module constructs a frequency response function using these two key parameters. This function is a mathematical model of a second-order linear system, capable of accurately describing the laser's response to modulation signals of different frequencies. The prediction module substitutes the relaxation oscillation frequency and damping factor as core variables into the transfer function expression, thereby establishing a frequency domain model that reflects the physical essence of the device. This method avoids the tedious frequency scanning required in traditional methods, greatly simplifying the calculation process.

[0048] Based on the constructed frequency response function, the prediction module ultimately calculates the modulation bandwidth. Modulation bandwidth is a crucial indicator of a laser's high-speed performance. The prediction module searches the amplitude-frequency characteristic curve of the frequency response function for the frequency point where the gain drops to a specific proportion of its low-frequency value. This frequency point is the modulation bandwidth. Through this physical model-based fitting and calculation method, the prediction module can quickly and accurately provide predictions of the laser's high-speed performance.

[0049] For example, when a step current is applied to a laser, its optical power output exhibits a distinct damped oscillation characteristic. The prediction module captures this transient waveform, quickly identifies the oscillation period, and calculates the relaxation oscillation frequency accordingly. Simultaneously, the prediction module analyzes the decay rate of the oscillation amplitude to obtain the damping factor. Using these two parameters, the prediction module constructs an accurate frequency response model and predicts the modulation bandwidth based on it.

[0050] Through this post-processing analysis based on transient response simulation results, this technical solution achieves a seamless transition from time-domain dynamics to frequency-domain performance. This method is not only computationally efficient but also has clear physical meaning. It can accurately predict the high-speed modulation capability of lasers, providing a direct and reliable theoretical basis for optimizing device structure and improving communication rates, effectively avoiding the high R&D costs and long development cycles associated with traditional trial-and-error methods.

[0051] Furthermore, the prediction module is configured to apply a small-signal sinusoidal perturbation current to the laser, solve for the transient response time series of the optical output power, and convert the transient response time series into a frequency response function through Fourier transform.

[0052] Specifically, the prediction module's workflow begins with applying a small-signal sinusoidal perturbation current to the laser. The prediction module first superimposes a small-amplitude sinusoidal AC signal onto the DC bias current. The amplitude of this sinusoidal AC signal is much smaller than the DC bias current. This ensures that the laser operates in the quasi-linear region. The prediction module then uses the superimposed total current as the input excitation source for the modeling module.

[0053] Under the influence of the input excitation, the prediction module calls the solution module to solve for the transient response time series of the optical output power. This time series records the complete dynamic process of the optical power changing with time. Due to the superimposed sinusoidal perturbation, the transient response of the optical output power contains an oscillating component corresponding to the perturbation frequency. The prediction module captures this subtle dynamic change through high-precision numerical integration.

[0054] After obtaining the transient response time series, the prediction module converts it into a frequency response function using a Fourier transform. The Fourier transform decomposes the time-domain signal into sinusoidal components of different frequencies. The module extracts the amplitude of the component in the optical power signal that coincides with the disturbance frequency. Simultaneously, the prediction module records the phase difference between this component and the input current signal.

[0055] The prediction module iterates through a preset frequency range, sequentially applying small-signal sinusoidal perturbation currents of different frequencies. For each frequency point, the module repeats the above solution and transformation process. Finally, the module combines the amplitude ratios and phase differences of all frequency points to construct a complete frequency response function. This function comprehensively describes the gain and phase delay characteristics of the laser at different frequencies.

[0056] For example, the prediction module sets the scanning frequency range from low to high frequencies. At each frequency, a small current perturbation is applied and the transient waveform of the optical power is recorded. Using a fast Fourier transform algorithm, the prediction module extracts the fundamental component from the time-domain waveform and then calculates the normalized response amplitude at that frequency.

[0057] This invention, based on small-signal sinusoidal perturbation and Fourier transform, can accurately simulate the frequency domain characteristics of lasers. It avoids the difficulty of directly solving complex frequency domain equations. By deriving the frequency domain response using time-domain simulation results, the physical accuracy of the calculations is ensured, providing reliable data support for evaluating the high-speed modulation performance of lasers.

[0058] Furthermore, the prediction module obtains the modulation bandwidth by fitting the frequency response function, and the modulation bandwidth corresponds to the frequency point where the amplitude of the frequency response function drops to a preset proportion of the low-frequency amplitude.

[0059] Specifically, after obtaining the frequency response function, the prediction module further performs fitting and calculation of the modulation bandwidth. This module first normalizes the frequency response function. The module extracts the amplitude of the frequency response function in the low-frequency band as a reference. This low-frequency amplitude typically corresponds to the optical power response intensity under DC or near-DC conditions.

[0060] The prediction module sets a preset ratio as the threshold for bandwidth determination. In the fields of optics and electronics, this preset ratio is typically set to 0.707, a value corresponding to a physical state where power is halved. The prediction module searches for the frequency point on the amplitude-frequency characteristic curve of the frequency response function where the amplitude equals the low-frequency amplitude multiplied by the preset ratio.

[0061] To accurately determine the frequency point, the prediction module employs a numerical interpolation algorithm. Since the frequency response function obtained from simulation calculations consists of discrete data points, the actual cutoff frequency may lie between two calculated points. The prediction module uses linear interpolation or spline interpolation methods to fit between adjacent data points. This allows for the precise calculation of the specific frequency value at which the amplitude crosses the threshold. This frequency value is the modulation bandwidth.

[0062] The prediction module can also generate a Bode plot based on the fitting results. The Bode plot visually displays the decreasing trend of the amplitude-frequency response curve. The prediction module marks the cutoff frequency points on the plot at preset percentages, providing designers with an intuitive visual reference.

[0063] For example, the prediction module acquires the frequency response data of the laser under a specific bias current. The low-frequency amplitude is normalized to 1. The prediction module sets a preset ratio of 0.707, and by scanning the frequency response function, it finds that the amplitude crosses the threshold near a specific frequency. Using an interpolation algorithm, the prediction module accurately calculates the specific value of the modulation bandwidth.

[0064] By employing this fitting method based on the amplitude decrease ratio of the frequency response function, this invention can accurately define the high-speed performance limit of lasers. This technical solution conforms to internationally accepted bandwidth definition standards. It allows simulation results to be directly compared with experimental test data, providing clear quantitative indicators for optimizing laser structure to improve transmission rates.

[0065] Furthermore, the prediction module is also used to analyze the decay envelope of transient relaxation oscillations, extract the damping ratio and resonant frequency, and construct a bandwidth prediction function based on the damped resonance model.

[0066] Specifically, when analyzing transient characteristics, the prediction module first focuses on the decay envelope of transient relaxation oscillations. When a laser is excited by a step current, its optical output power exhibits damped oscillation characteristics. The prediction module processes the time-domain waveform using the Hilbert transform algorithm to extract the instantaneous amplitude of the oscillation signal. The curve formed by connecting these instantaneous amplitudes is the decay envelope. This envelope reflects the rate of energy dissipation of the system.

[0067] Based on the extracted attenuation envelope, the prediction module extracts the damping ratio and resonant frequency. The damping ratio is a dimensionless parameter that measures the degree of attenuation of system oscillations. The prediction module calculates the damping ratio using the logarithmic reduction method by calculating the ratio of adjacent peaks on the envelope. The resonant frequency corresponds to the natural frequency of the oscillation waveform. The module calculates the oscillation period by measuring the time interval between the zero-crossing points of the envelope, and thus obtains the resonant frequency.

[0068] After obtaining the damping ratio and resonant frequency, the prediction module constructs a bandwidth prediction function based on the damped resonance model. This prediction module treats the laser as a second-order linear system. The prediction module substitutes the extracted damping ratio and resonant frequency as system parameters into the second-order transfer function. This second-order transfer function describes the system's response characteristics to signals of different frequencies.

[0069] The bandwidth prediction function establishes a mathematical relationship between the resonant frequency, damping ratio, and modulation bandwidth. The prediction module uses this function to directly calculate the system's cutoff frequency. Compared to directly performing a Fourier transform on the time-domain signal, this method utilizes the system's inherent physical characteristics and can effectively filter out high-frequency noise interference.

[0070] For example, the prediction module captures the relaxation oscillation waveform at the instant the laser is turned on. By fitting the envelope of the waveform, the prediction module identifies that the system is in an underdamped state, and the calculated damping ratio indicates that the oscillation will continue for several cycles. The resonant frequency indicates the upper limit of the system's response speed. The bandwidth prediction function constructed based on these two parameters accurately predicts the frequency response range of the laser under high-speed modulation.

[0071] By employing this modeling method based on time-domain envelope analysis, this invention achieves a precise mapping from transient characteristics to frequency-domain performance. This technical solution fully utilizes the physical information contained in relaxation oscillations, avoids computational redundancy caused by complex frequency-domain scanning, significantly improves the efficiency and accuracy of bandwidth prediction, and provides a powerful analytical tool for evaluating the dynamic performance of lasers.

[0072] Furthermore, the bandwidth prediction function expresses the modulation bandwidth as a function of the resonant frequency and the damping ratio, wherein the modulation bandwidth is proportional to the resonant frequency and is subject to the nonlinear constraint of the damping ratio.

[0073] Specifically, the bandwidth prediction function mathematically establishes a mapping relationship between the modulation bandwidth and the inherent parameters of the system. This prediction module explicitly sets the modulation bandwidth as the dependent variable between the resonant frequency and the damping ratio. Physically, the resonant frequency reflects the rate of interaction between photons and charge carriers within the laser. A higher resonant frequency means the system can respond to signal changes more quickly. Therefore, in the bandwidth prediction function, the modulation bandwidth is directly proportional to the resonant frequency. As the resonant frequency increases, the modulation bandwidth broadens linearly.

[0074] However, the system's response speed is not solely determined by the resonant frequency; it is also influenced by the energy dissipation mechanism. This influence is manifested through the damping ratio. In the bandwidth prediction function, the damping ratio imposes a nonlinear constraint on the modulation bandwidth. The damping ratio characterizes the rate at which the system oscillations decay; when the damping ratio changes, the modulation bandwidth does not change linearly but follows a complex nonlinear curve.

[0075] For example, when the damping ratio is in a relatively small range, the system exhibits underdamped characteristics. In this case, the bandwidth prediction function shows that the modulation bandwidth is quite sensitive to changes in the damping ratio. As the damping ratio increases, the bandwidth prediction function calculates that the modulation bandwidth gradually increases. This is because appropriate damping can suppress high-frequency resonance peaks, making the amplitude-frequency response curve flatter, thereby expanding the effective bandwidth.

[0076] When the damping ratio continues to increase and exceeds a certain critical value, the system enters an overdamped state. At this point, the bandwidth prediction function shows that the growth trend of the modulation bandwidth slows down or even decreases. This is because excessive damping causes the system response to become sluggish, similar to the cutoff frequency of a low-pass filter shifting to lower frequencies. This nonlinear constraint accurately reflects the trade-off between speed and stability in the physical world.

[0077] By constructing this functional relationship, this invention can accurately quantify the impact of structural parameters on high-speed performance. This technical solution not only considers the upper limit of response speed but also takes into account the constraints of system stability, avoiding design deviations caused by simply pursuing high resonant frequencies while neglecting damping effects. It provides precise theoretical guidance for optimizing the high-speed modulation performance of vertical-cavity surface-emitting lasers.

[0078] In one embodiment, the scanning module is used to support multi-dimensional scanning of injected current, temperature, and structural parameters, and output performance index curves.

[0079] Specifically, the scanning module is a key interactive unit connecting user configuration and the core simulation engine. The scanning module is configured to receive multi-dimensional scanning commands set by the user. These dimensions cover electrical excitation, environmental conditions, and device physical structure. Specifically, the scanning module supports scanning the injected current. Users can set the starting value, ending value, and step increment of the current through the scanning module, enabling the system to simulate the complete turn-on process of a laser from spontaneous emission to stimulated emission.

[0080] In addition to electrical parameters, the scanning module also supports temperature parameter scanning. Temperature is a key environmental factor affecting the performance of semiconductor devices. Through the scanning module, users can set a series of discrete or continuous temperature points. During simulation, the system automatically calls temperature-related material parameter models to reflect thermal effects such as bandgap contraction, carrier mobility changes, and gain spectrum drift.

[0081] Regarding structural parameters, the scanning module allows for variable settings of device geometry or material composition. For example, users can set the active region thickness, the number of mirror layers, or the doping concentration as scanning variables. The scanning module maps these structural parameters into the equations of the modeling module, thereby enabling batch evaluation of different device designs.

[0082] After parameter settings are completed, the scanning module controls the simulation engine to sequentially calculate each parameter point. For each parameter point, the system generates corresponding transient or steady-state response data. The scanning module then aggregates and organizes these scattered data points. Finally, the scanning module outputs performance index curves. These curves visually demonstrate the trends of modulation bandwidth, threshold current, or slope efficiency as a function of the scanning variables.

[0083] For example, the user uses the scanning module to set up a dual scan of injection current and temperature. The scanning module controls the simulator to first scan the current at a low temperature, recording changes in optical power and bandwidth. Subsequently, the scanning module automatically adjusts the temperature setting and repeats the current scanning process. Finally, the scanning module outputs a set of graphs containing multiple curves, each curve corresponding to a specific temperature condition.

[0084] Through this multi-dimensional scanning mechanism, the present invention achieves comprehensive characterization of laser performance, avoiding tedious manual parameter modification and repetitive simulation operations, greatly improving the efficiency of design optimization, enabling designers to quickly identify the sensitivity of device performance to environmental changes or structural deviations, and providing strong data support for improving product yield and reliability.

[0085] Furthermore, the performance indicator curves output by the scanning module include current-voltage characteristic curves, optical power-current characteristic curves, modulation response curves, and eye diagrams.

[0086] Specifically, the performance index curves output by the scanning module provide a comprehensive quantitative representation of the laser's electro-optic characteristics and high-speed transmission quality. These curves cover three key dimensions: DC characteristics, frequency domain response, and time domain signal integrity.

[0087] First, the performance index curves include the current-voltage characteristic curve. This curve describes the functional relationship between the voltage across the laser and the injected current. The turn-on voltage and series resistance characteristics of the laser can be visually observed through this curve. When the current is below a threshold, the voltage increases exponentially with the current. When the current exceeds the threshold, the voltage increases linearly with the current. The slope of this curve directly reflects the ohmic contact quality and internal losses of the device.

[0088] Secondly, the performance index curves include the optical power-current characteristic curve. This is the core graph for evaluating the energy conversion efficiency of the laser. The performance index curve shows the trend of output optical power changing with the injection current. The performance index curve allows for the precise definition of the laser's threshold current point. Above the threshold, optical power and current exhibit a good linear relationship. The slope of the performance index curve is the slope efficiency, characterizing the device's ability to convert electrical energy into optical energy.

[0089] Secondly, the performance index curves include the modulation response curve. The performance index curve reflects the frequency response capability of the laser under high-speed modulation. The horizontal axis represents the modulation frequency, and the vertical axis represents the normalized optical power response amplitude. The position and height of the relaxation oscillation peak can be clearly seen through the performance index curve. The performance index curve intuitively demonstrates the process of signal amplitude attenuation as the frequency increases, and is a direct basis for determining the modulation bandwidth.

[0090] Finally, the performance metric curves include the eye diagram. An eye diagram is a comprehensive graphical representation of the quality of high-speed digital signal transmission, superimposing all possible transition waveforms of the digital signal. The open area in the center of the eye diagram is called the eye aperture. The height of the eye aperture reflects the noise margin, and the width of the eye aperture reflects the timing jitter margin. By observing the degree of eye opening, the location of crossover points, and the thickness of the lines in the eye diagram, the bit error rate performance of the signal in high-speed transmission can be qualitatively and quantitatively determined.

[0091] For example, after completing a full-temperature scan, the scanning module automatically generates a set of comprehensive reports. The reports display the current-voltage characteristic curves and the optical power-current characteristic curves at different temperatures side-by-side. Designers, through comparison, discovered that the threshold current drifts as the temperature increases. Simultaneously, the scanning module also outputs an eye diagram at the corresponding operating point, showing that the eye height is compressed at high temperatures due to increased noise.

[0092] By outputting these multi-dimensional performance index curves, this invention achieves visualized full inspection of laser performance, transforming complex simulation data into intuitive engineering design charts. This enables designers to evaluate the static operating point and dynamic transmission quality of devices in a one-stop manner, greatly simplifying the device characterization process and providing complete data support for the research and development and verification of high-performance optoelectronic devices.

[0093] The modules in the aforementioned multi-dimensional performance parameter simulation and analysis system for VCSEL chips can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of a computer device in hardware form or independent of it, or stored in the memory of the computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0094] Those skilled in the art will understand that all or part of the processes in the systems described in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the system can be divided into different functional units or modules to complete all or part of the functions described above.

[0095] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-dimensional performance parameter simulation and analysis system for VCSEL chips, characterized in that, include: Modeling module, solving module, prediction module, and scanning module; The modeling module is used to construct a coupled model of the carrier continuity equation and the multimode photon rate equation. The coupled model establishes a nonlinear feedback mechanism between carrier concentration and photon density by introducing a photon density-dependent net recombination rate expression, so as to simulate the strong nonlinear coupling characteristics in the process of generating light output by electrical injection. The solution module is used to solve the coupled model by employing an implicit Runge-Kutta algorithm combined with a local truncation error control strategy, dynamically adjusting the time step according to the local truncation error during the calculation process, so as to suppress numerical calculation divergence; wherein, the solution module adopts the Radau IIA-type implicit Runge-Kutta method, internally configured with a third-order precision scheme and a fifth-order precision scheme, and calls the Newton-Raphson iteration method to linearize and solve the nonlinear equation system; When executing the local truncation error control strategy, the solution module is configured to perform the following operations: The magnitude of the difference between the solution vector of the fifth-order precision scheme and the solution vector of the third-order precision scheme is calculated as an estimate of the local truncation error. When the estimated value of the local truncation error is greater than the preset tolerance, it is determined that the numerical solution at the current time step does not meet the stability requirements, and a backoff calculation is performed and the time step is reduced. When the estimated value of the local truncation error is less than or equal to the preset tolerance, the numerical solution is determined to be converged, the current solution is accepted, and the time step is increased. The prediction module is used to extract the relaxation oscillation frequency and damping factor based on the transient response simulation results, construct the frequency response function and calculate the modulation bandwidth. The scanning module is used to support multi-dimensional scanning of injected current, temperature and structural parameters, and output performance index curves.

2. The multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to claim 1, characterized in that, When constructing the coupled model, the modeling module is configured to solve the balance between the time-varying rate of carrier concentration and the injection current density, net recombination rate, and carrier diffusion term, as well as the balance between the time-varying rate of photon density and the optical field confinement factor, group velocity, gain coefficient, total loss, and spontaneous emission rate. The net recombination rate expression integrates a stimulated emission extraction term, which is used to characterize the real-time modulation effect of photon density on the carrier consumption rate.

3. The multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to claim 2, characterized in that, The modeling module configures the net recombination rate expression as an algebraic sum of radiative recombination, non-radiative recombination, and stimulated emission extraction terms; wherein the stimulated emission extraction term is set as a product of group velocity, gain coefficient, and photon density to achieve self-consistent feedback between photon generation and carrier consumption during the numerical solution process.

4. The multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to claim 1, characterized in that, The prediction module is configured to apply a small-signal sinusoidal perturbation current to the laser, solve for the transient response time series of the optical output power, and convert the transient response time series into a frequency response function through Fourier transform.

5. The multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to claim 4, characterized in that, The prediction module obtains the modulation bandwidth by fitting the frequency response function, and the modulation bandwidth corresponds to the frequency point when the amplitude of the frequency response function drops to a preset proportion of the low-frequency amplitude.

6. The multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to claim 4, characterized in that, The prediction module is also used to analyze the decay envelope of transient relaxation oscillations, extract the damping ratio and resonant frequency, and construct a bandwidth prediction function based on the damped resonance model.

7. The multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to claim 6, characterized in that, The bandwidth prediction function expresses the modulation bandwidth as a function of the resonant frequency and the damping ratio, wherein the modulation bandwidth is proportional to the resonant frequency and is subject to the nonlinear constraint of the damping ratio.

8. The multi-dimensional performance parameter simulation and analysis system for VCSEL chips according to claim 1, characterized in that, The performance index curves output by the scanning module include current-voltage characteristic curves, optical power-current characteristic curves, modulation response curves, and eye diagrams.

Images