Generation method of soliton comb state in Kerr cavity based on hierarchical cost dominated genetic algorithm

Abstract

The application discloses a Kerr cavity soliton comb state generation method based on a hierarchical cost dominated genetic algorithm, which is suitable for the technical field of optical frequency comb, and takes a fiber Kerr cavity as an example. A pre-classification improved multi-objective genetic algorithm model is constructed, the driving power and the detuning frequency of the soliton are taken as individual coding parameters to construct an initialization population, numerical evolution is performed on each parameter group through a Mifune mapping equation, corresponding cavity optical field solutions are obtained, the solutions are automatically classified and scored according to time-frequency characteristics, and then a hierarchical cost dominated genetic algorithm is used for target state searching and optimization, so that the efficiency and stability of the target soliton comb state generation in the fiber Kerr cavity are significantly improved. Compared with the traditional genetic algorithm, the method performs multi-objective optimization on multiple key performance indicators such as pulse peak power, pulse width, continuous background level and breath depth in the process of obtaining the target comb state, so that the generation efficiency, stability and comprehensive performance of the fiber Kerr cavity soliton comb state are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of optical frequency combs, and more specifically to a method for generating soliton comb states in a Kerr cavity based on a hierarchical cost-dominated genetic algorithm. Background Technology

[0002] A fiber optic Kerr cavity specifically refers to an optical resonator that uses optical fiber as the medium and has sufficiently high internal light intensity, allowing the Kerr effect of the fiber to play a dominant role in the evolution of the optical field. A soliton comb state is a special and stable optical frequency comb state generated by a fiber optic Kerr cavity under specific operating parameters (mainly pump drive power and dispersion management). The core is the dissipative Kerr soliton. Fiber optic Kerr soliton combs are an important technology in optical frequency combing, bringing revolutionary tools and application prospects to fields such as precision measurement science (time, frequency, distance, spectrum), optical communication, and fundamental physics research.

[0003] The generation and stability of soliton comb states in fiber Kerr cavities have long been a research challenge in the field of optics. In existing technologies, soliton comb states are often affected by a variety of factors, such as fluctuations in driving power, frequency detuning, and external interference, leading to system instability. The most common problems are soliton breathing and soliton annihilation.

[0004] Although optimization techniques such as genetic algorithms (GA) have been applied to mode locking in lasers and microcavities, existing algorithms have not been able to effectively handle multi-objective optimization problems in complex fiber Kerr cavities. In particular, when performing global optimization in high-dimensional parameter spaces, they are prone to getting trapped in local optima and cannot guarantee the accurate acquisition of the target state. Summary of the Invention

[0005] The purpose of this invention is to provide a method for generating soliton comb states in a Kerr cavity based on a hierarchical cost-dominated genetic algorithm. This method achieves accurate generation of soliton comb states in an optical fiber Kerr cavity through an improved genetic algorithm—the hierarchical cost-dominated genetic algorithm. This algorithm can effectively avoid the local optimum problem common in existing methods, and provides a solution suitable for multi-objective optimization. It controls the generation conditions and stability of solitons in an optical fiber Kerr cavity, and ensures the stability and reliability of soliton comb states under various perturbations.

[0006] The present invention achieves the above objectives through the following technical solutions:

[0007] A method for generating soliton comb states in Kerr cavity based on a hierarchical cost-dominated genetic algorithm includes:

[0008] S1. Randomly generate an initial population containing multiple individuals, each individual representing a set of control parameters for the fiber optic Kerr cavity, including drive power and detuning frequency;

[0009] S2. For each individual, the output solution of the fiber optic Kerr cavity is simulated by solving the Ikeda mapping equation;

[0010] S3. Sort the individuals based on the time-frequency characteristics of the output solution and the first evaluation strategy, select a number of elite individuals, and sort the remaining individuals based on the time-frequency characteristics of the output solution and the second evaluation strategy, select a number of individuals as winners and the rest as losers.

[0011] S4. Cross and mutate between the winning individuals and elite individuals, and cross and mutate between the losing individuals to update the population.

[0012] S5. Repeat S2-S4 until the preset number of iterations is reached, then output the individual with the best output solution in the population, which is used to control the generation of soliton comb states in the fiber Kerr cavity.

[0013] Furthermore, step S2 includes:

[0014] Establish the Ikeda mapping equation, which includes the intracavity propagation equation and the boundary coupling equation:

[0015] ;

[0016] ;

[0017] Where z is the spatial coordinate of the optical path propagating along the Kerr cavity, L is the length of the entire cavity, z=0 is the starting point of the Kerr cavity, and z=L is the ending point of the Kerr cavity. Let represent the pulse envelope of the optical field within the cavity in the nth cycle, and t be the fast time in the reference frame moving along the group velocity. This represents the envelope of the inner field of the nth Kerr cavity. The rate of change along the propagation direction z The second-order dispersion coefficient, Here, n is the non-linear coefficient, and n is the number of round-trip indices. The field amplitude transmission coefficient of the cavity; As the driving field, , δ is the driving power; δ is the phase detuning frequency per round trip caused by the angular frequency detuning between the pump and the Kerr cavity. = - , The driving laser frequency for pumping, This is the Kerr cavity resonant frequency; The coupling efficiency of the driving field;

[0018] The Ikeda mapping equation is iteratively solved under a given driving power and detuning to obtain the physical output solution of the individual.

[0019] Furthermore, the physical output solution for this individual is obtained, including:

[0020] The Ikeda mapping equation is iteratively solved under a given driving power and detuning, and the complex envelope function at the end of the Kerr cavity is obtained as the output solution.

[0021] Furthermore, the time-frequency characteristics of the output solution include the time-domain waveform, spectrum, radio spectrum, autocorrelation curve, and energy evolution curve obtained based on the complex envelope function.

[0022] Furthermore, in step S3, the individuals / remaining individuals are sorted, including:

[0023] Based on the time-frequency characteristics of the output solution, soliton cost information is obtained to characterize whether solitons exist, whether solitons are in a stable or breathing state, and the number of solitons. The soliton cost information is used as the criterion for determining the genetic individual.

[0024] The judgment index is mapped to a score. Based on the score and the first evaluation strategy, all individuals in the population are ranked, and the highest-ranked individuals are selected as elite individuals. After removing the elite individuals, the remaining individuals are ranked again according to the score and the second evaluation strategy. The top-ranked individuals are selected as winners, and the rest are losers.

[0025] Furthermore, individuals / remaining individuals are ranked based on scoring and evaluation strategies, including:

[0026] Define the cost function:

[0027] ;

[0028] in, Let be the soliton cost information of the i-th individual. Information content related to the cost of the target soliton;

[0029] The individuals are initially sorted from smallest to largest according to the cost function;

[0030] For individuals with the same amount of cost information, a Pareto strategy is used for further ranking based on time-frequency characteristics.

[0031] Furthermore, the Pareto strategy based on time-frequency characteristics is used for further sorting, including:

[0032] The time-frequency characteristics of individuals with the same soliton cost information are extracted as the dominant objective function, and the dominant objective functions among individuals are compared using the following formula:

[0033] ;

[0034] in, Here, m is the index of the time-frequency characteristic, and m is the total number of time-frequency characteristics. The dominant objective function;

[0035] Establish a Pareto trade-off framework, prioritizing individuals with the highest number of dominant objective functions;

[0036] If two individuals have the same number of dominant objective functions, a crowding distance strategy is used for supplementary sorting.

[0037] Furthermore, the supplementary sorting using the crowding distance strategy includes:

[0038] Establish a coordinate system based on the individual's driving power and detuning frequency. The sub-crowding distance for all individuals within a preset radius surrounding the i-th individual is determined using the following formula:

[0039] ;

[0040] in, For the first Individual, It is a preset radius range. For the first The coordinate system distance between individuals A constant used to control the degree of influence of congestion distance;

[0041] The number is determined based on the following formula. Crowding distance between individuals:

[0042] ;

[0043] Where N is the total number of individuals;

[0044] Individuals with large crowd distances are prioritized.

[0045] Furthermore, in the first evaluation strategy, before using the crowding distance strategy for supplementary ranking, it also includes: determining the ranking priority based on the degree of demand of the dominant objective function; if the degree of demand of the dominant objective function is the same, then the crowding distance strategy is used for supplementary ranking.

[0046] Furthermore, in the second evaluation strategy, after supplementing the ranking using the crowding distance strategy, if the crowding distances are the same, it also includes: determining the ranking priority based on the degree of demand of the dominant objective function.

[0047] The beneficial effects of this invention are as follows:

[0048] This invention constructs a pre-classification improved multi-objective genetic algorithm model. An initial population is built using the soliton's driving power and detuning frequency as individual encoding parameters. Numerical evolution of each parameter group is performed using the Ikeda mapping equation to obtain the corresponding intracavity optical field solution. The solution is automatically classified and scored based on time-frequency characteristics. Then, a hierarchical cost-dominated genetic algorithm is used for target state search and optimization, significantly improving the efficiency and stability of target soliton comb state generation in fiber Kerr cavities. Compared with traditional genetic algorithms, this method performs multi-objective optimization on several key performance indicators such as pulse peak power, pulse width, continuous background level, and breathing depth during the acquisition of target comb states, thereby significantly improving the generation efficiency, stability, and overall performance of soliton comb states in fiber Kerr cavities.

[0049] This invention introduces soliton cost information, cost function, and hierarchical cost domination strategy, directly embedding information such as "whether it is a soliton, soliton type, and number of solitons" into the screening process of the genetic algorithm. It can automatically eliminate non-target solutions such as continuous waves, Turing states, and chaotic states within a wide parameter space of driving power-detuning frequency. It can obtain different target soliton comb states such as single solitons, breathing solitons, and multiple solitons as needed with a limited number of computations / experiments, significantly improving the probability and reproducibility of target state acquisition.

[0050] This invention constructs a multidimensional dominant objective function by combining the time-domain waveform, spectrum, radio spectrum, autocorrelation curve, and energy evolution curve of the output solution. It adopts a multi-objective optimization framework that combines Pareto trade-offs, the degree of demand for the dominant objective, and crowding distance. While maintaining global search capability and population diversity, it performs synergistic optimization on key performance indicators such as pulse peak power, pulse width, continuous background level, and breathing depth. Compared with traditional genetic algorithms, it has a faster convergence speed and higher optimization efficiency.

[0051] The method of this invention is simple to implement. It only requires adjusting controllable parameters such as driving power and detuning frequency to complete the intelligent optimization and steady-state acquisition of soliton comb state, which is easy to extend to fiber optic Kerr cavities and related frequency comb systems with different structures.

[0052] This invention is applied to soliton comb state optimization in fiber optic Kerr cavities. Specifically, by adjusting the driving power and detuning frequency, the input parameters are optimized to achieve stable soliton comb state generation, providing stronger global convergence capability and optimization efficiency compared to conventional genetic algorithms. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the genetic algorithm for the cost control strategy of the present invention;

[0054] Figure 2 This is a flowchart of the algorithm of the present invention;

[0055] Figure 3This is a schematic diagram of a single soliton implementation of the present invention. Figure 1 ;

[0056] Figure 4 This is a schematic diagram of a single soliton implementation of the present invention. Figure 2 ;

[0057] Figure 5 This is a schematic diagram comparing the present invention with conventional genetic algorithms. Detailed Implementation

[0058] The present application will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present application and should not be construed as limiting the scope of protection of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application based on the above application content.

[0059] Example 1

[0060] like Figure 1-5 As shown, the method for generating soliton comb states in the Kerr cavity based on the hierarchical cost-dominated genetic algorithm includes the following steps:

[0061] S1: Randomly generate an initial population containing multiple individuals, each representing a set of control parameters for the fiber optic Kerr cavity, including drive power and detuning frequency;

[0062] Specifically, driving power refers to the optical power input from the external pump laser into the Kerr cavity, which is the energy source for maintaining soliton states. Solitons only exist within a specific power range. If the power is too low, the nonlinearity is insufficient to counteract the loss, and the soliton will annihilate. If the power is too high, it will cause higher-order solitons to split. The detuning frequency is the offset between the pump laser frequency and the Kerr cavity cold cavity mode frequency. A pump light frequency lower than the cold cavity frequency is a necessary condition for soliton formation.

[0063] S2. For each individual, the output solution of the fiber optic Kerr cavity is simulated by solving the Ikeda mapping equation;

[0064] The output solution can be transformed to obtain the time-frequency characteristics of the soliton, namely the frequency domain characteristics and time domain characteristics, such as RF spectrum, energy evolution curve and autocorrelation curve. By extracting the characteristics in the frequency domain characteristics and time domain characteristics, the state of the soliton and the number of stable solitons can be evaluated, which is used as the cost information of the soliton to characterize the soliton.

[0065] The initial population can be represented as:

[0066] ;

[0067] Furthermore, step S2 specifically includes:

[0068] S21: Establish the Ikeda mapping equation, which includes the cavity propagation equation and the boundary coupling equation. For a Kerr cavity with preset parameters, its output is mainly determined by two parameters: driving power. and detuning frequency (The frequency of phase detuning per round trip caused by the angular frequency detuning between the pump and the Kerr cavity). = - , Indicates the Kerr cavity resonance frequency. Indicates the driving laser frequency of the pump:

[0069] ;

[0070] ;

[0071] Where z is the spatial coordinate of the optical path propagating along the Kerr cavity, L is the length of the entire cavity, z=0 is the starting point of the Kerr cavity, and z=L is the ending point of the Kerr cavity. Let represent the pulse envelope of the optical field within the cavity in the nth cycle, and t be the fast time (on the order of picoseconds) in the reference frame moving along the group velocity. This represents the envelope of the inner field of the nth Kerr cavity. The rate of change along the propagation direction z The second-order dispersion coefficient, Here, n is the non-linear coefficient, and n is the number of round-trip indices. It is the second derivative with respect to t, corresponding to the group velocity dispersion (GVD) operator, and its effect is determined by the preceding coefficients. control, It is a Kerr third-order nonlinear (self-phase modulation, SPM) term. The field amplitude transmission coefficient of the cavity. As the driving field, , For driving power; The coupling efficiency of the driving field.

[0072] In this embodiment, the Ikeda mapping equation couples the continuous nonlinear evolution of the optical pulse with the periodic boundary reset through discrete iteration. The remaining energy after each pulse cycle is coupled with the new energy of the pump to form a new pulse. This process is repeated until it converges to a stable state.

[0073] S22: The Ikeda mapping equation is iteratively solved under a given driving power and detuning. The iteration is stopped after 500 pulse envelope cycles, and the complex envelope function at the end point of the Kerr cavity (z = L) is obtained. The complex envelope function is used as the physical output solution of the individual and is used in subsequent steps to extract time-frequency characteristic parameters such as time-domain waveform, spectrum, radio spectrum, autocorrelation curve and energy evolution curve through Fourier transform, autocorrelation operation and energy statistics, etc., to form the output parameter set characterizing the superiority or inferiority of the soliton corresponding to the individual.

[0074] In this embodiment, it can be understood that the intracavity propagation equation is solved using the step-by-step Fourier transform method, wherein the linear dispersion term... Solving in the frequency domain involves using a Fourier transform to convert the pulse to the frequency space, multiplying it by a dispersive phase factor, and then converting it back to the time domain. The Kerr nonlinear term is then addressed. The solution is obtained in the time domain based on the fourth-order Runge-Kutta method, which is a numerical integration method and is an existing technology, so it will not be described in detail in this invention.

[0075] This example provides a simulation parameter where cavity losses are concentrated in... In the middle, and Corresponding to the total power loss for each round trip, The proportion of the cavity field returning to the cavity after passing through the coupler is determined. The parameters used in the simulation are shown in the table below. In the simulation, the time window is set to 100 picoseconds, including 2... 10 One point.

[0076] ;

[0077] In the simulation parameters of this embodiment, SMF represents single-mode fiber, and Length represents the Kerr cavity length L. A negative dispersion coefficient (anomalous dispersion) favors soliton formation, and its magnitude determines the strength of dispersion. The intracavity pulse power loss after each cycle is: Specifically, it is 16%. Represents the external driving field Amplitude transmittance coupled into the cavity This means that the power coupling efficiency of the laser driver is 5%.

[0078] It should be noted that, It includes all losses, primarily those at the output of the coupler, but may also include other minor losses within the cavity such as absorption and scattering. It is the ratio of the driving power coupled into the Kerr cavity. It is the proportion of light coupling back to itself within the cavity.

[0079] In addition, during the specific implementation process, the soliton state and the number of stable solitons are obtained based on the time-frequency characteristics as soliton cost information.

[0080] Specifically, unlike continuous light (CW) or Turing modes caused by modulation instability, cavity solitons (CS) are stable local structures that correspond to the desired output solution of the system. CS solitons can be distinguished from non-CS solitons by examining the peak height of the radio frequency (RF) signal at the fundamental frequency fR. Non-CS solitons include continuous light, chaotic, or Turing modes. The RF spectrum can be obtained by performing a Fourier transform on the pulse sequence of a CS soliton. For a stable CS soliton, the RF spectrum has a clear single peak at the fundamental frequency fR and no sidebands. Typically, the CS soliton state will exhibit a strong RF signal.

[0081] Furthermore, the number of CS solitons can be inferred from the number of significant peaks on one side of the autocorrelation (AC) curve. The autocorrelation curve of solitons is a key technique for measuring the width of ultrashort optical pulses (especially on the femtosecond scale). It indirectly reflects the temporal intensity envelope of the pulse through the principle of nonlinear optical interference. Therefore, the specific number of CS solitons can be further categorized based on this. For m solitons, the number of significant peaks on one side of the autocorrelation curve is m-1. For example, for a two-soliton state, the corresponding autocorrelation curve will have one significant peak on one side, meaning that there are equidistant peaks on both sides of the central peak. Similarly, for a three-soliton state, the corresponding autocorrelation curve will have two significant peaks on one side.

[0082] In some cases, solitons are not in a steady state. Their characteristics (such as pulse duration, pulse peak power, and / or pulse energy) fluctuate periodically. This unique state is often called a "breathing cavity soliton" (BCS). The most intuitive way to determine the respiratory state is by judging whether there is a respiratory rate fb near fR. If there is, it is a respiratory soliton.

[0083] This involves a threshold used to determine whether fR exists. This threshold is defined as a, which represents the ratio of the intensity fR of the radio frequency spectrum RF at the fundamental frequency to the intensity f0 at the continuous light frequency. In this embodiment, a=0.01 is set.

[0084] Relying solely on RF sidebands for respiratory soliton identification leads to limited accuracy. To address this issue, the periodic changes in pulse energy during evolution are examined. Solitons with periodic pulse energy changes are identified as BCSs, while those with no periodic pulse energy changes are classified as chaotic states. To accurately distinguish between stable and unstable soliton solutions, the evolution of intracavitary pulse energy is observed over at least 100 rounds, and the difference between the maximum and minimum energies is defined as a threshold to differentiate between stable and unstable soliton solutions. In this embodiment, the threshold b = 0.05 is set.

[0085] The continuous light background in the time domain will produce a non-zero background on the autocorrelation curve, which may affect the statistics of the number of solitons. Therefore, in this embodiment, a threshold is set in the autocorrelation curve to determine the level of continuous light CW background. In this embodiment, the value is c=0.35.

[0086] This embodiment extracts soliton cost information from time-frequency characteristics using the above method, as shown in the following formula:

[0087] ;

[0088] Where y is a positive integer representing the number of solitons, which is entirely related to the value calculated from the one-sided peak of its autocorrelation AC. Thus, y=1 represents the stable mode-locked state of a single soliton, and y=n represents the stable mode-locked state of n solitons. According to the formula, Y can only take integer and half-integer values, where half-integers represent breathing solitons. For example, Y=1.5 represents the breathing state of a single soliton. However, solutions containing more than 10 solitons, as well as solutions with continuous light (CW), Turing modes, and chaos, will be classified as other solutions, and the corresponding Y(y) value will be set to 10. For each individual in the population, a Yi value is assigned as the soliton cost information based on its characteristics, i(i N) is the index of an individual in the population, and its value is a non-negative integer from 1 to 20.

[0089] This invention uses the RF spectrum, energy evolution curve, and autocorrelation curve obtained from the complex envelope function to perform multi-level judgment on the output solution: First, using the ratio of the RF fundamental frequency to the DC component and the pulse energy fluctuation threshold, continuous waves, Turing states, and chaotic states are screened out, retaining only stable or breathing soliton solutions; then, the number of solitons is determined based on the number of significant side peaks of the autocorrelation curve, and the "existence of solitons, whether the solitons are in a breathing state, and the number of solitons" are jointly encoded into soliton cost information, and a cost function is constructed accordingly to achieve hierarchical screening and ranking of individuals in the population, providing judgment indicators for subsequent hierarchical cost domination strategies.

[0090] S3: Sort the individuals based on the time-frequency characteristics of the output solution and the first evaluation strategy, select a number of elite individuals, and sort the remaining individuals based on the time-frequency characteristics of the output solution and the second evaluation strategy, select a number of individuals as winners, and the rest as losers.

[0091] The ranking order for the first evaluation strategy is: cost function ranking, Pareto advantage ranking, demand level ranking of the dominant objective function, and crowding distance ranking; the selection order for the second evaluation strategy is: cost function ranking, Pareto advantage ranking, crowding distance ranking, and demand level ranking of the dominant objective function.

[0092] The difference between the first and second evaluation strategies lies in the fact that the first evaluation strategy focuses on the degree of demand of the dominant objective function, while the second evaluation strategy focuses more on checking the crowding distance to avoid the crowding distance being too close to avoid duplication. Specifically, both ranking strategies extract features through time-frequency characteristics and use the above evaluation strategies to rank individuals / remaining individuals.

[0093] The evaluation strategies specifically include:

[0094] Cost function sorting: Defining the cost function:

[0095] ;

[0096] in, Let be the soliton cost information of the i-th individual. Information content related to the cost of the target soliton;

[0097] Individuals are initially sorted according to their cost function from smallest to largest; the smaller the cost function, the higher the priority of the individual.

[0098] The process of defining a cost function specifically includes:

[0099] Step 1: First, filter out non-soliton states, then distinguish the type and number of solitons:

[0100] Define the RF threshold 'a' as the threshold for determining whether a solution is a "soliton state". Perform a Fourier transform on the 100-cycle time-domain signal to obtain the RF spectrum, which is expressed as:

[0101] Cavity fundamental frequency (10GHz);

[0102] :exist Spectral line intensity at;

[0103] DC component;

[0104] Calculate the ratio: ;like (With an empirical threshold of a≈0.01), it is classified as CW / Turing / Chaos and directly categorized as "others," no longer considered as an orphan candidate.

[0105] Define an energy threshold b: use it to distinguish between stable and unstable soliton solutions, and calculate the energy variation range for the last 100 cycles. ,like (Empirical evidence b≈0.05), it is determined to be a stable solution; if This indicates strong energy fluctuations. To further determine whether it is a BCS or a chaotic state, if the energy evolution exhibits periodic oscillations, and the RF spectrum is in... Paired sidebands appear on both sides (respiratory rate) If the energy change has no obvious periodicity or the RF sideband has no clear structure, it is judged as a chaotic state and classified as "others".

[0106] CW / Turing / Chaotic / High-Density Multipulse are all classified as "others", while stable CS and BCS are further determined in the subsequent "soliton type and number" assessment.

[0107] Step 2: The entire process of determining the number of solitons (y):

[0108] Perform intensity autocorrelation on the output pulse to obtain the AC curve; select a certain time window on one side (e.g., the right side) of the AC curve and use a threshold... (≈0.35) Determine the "number of significant peaks". ;

[0109] Define the number of solitons: ;

[0110] Single Orphan: ;

[0111] Two orphans: ;

[0112] The Three Orphans: …;

[0113] like It is considered to be a high-density multi-pulse state, which does not belong to the target range, and is denoted as "others".

[0114] Step 3: Synthesize the "soliton cost information content" and use it as a judgment indicator:

[0115] For those that have been confirmed as CS / BCS and The solution provides the "soliton cost information content":

[0116] ;

[0117] It also encodes whether it is a soliton / whether it is breathing / the number of solitons; for the target state (e.g., single soliton SCS): Single respiror BCS: Define the cost function: .

[0118] Pareto dominance ranking: For individuals with the same amount of cost information, a Pareto strategy is used for further ranking based on time-frequency characteristics, specifically including:

[0119] Extracting the time-frequency characteristics of individuals with similar cost information as the dominant objective function, and comparing the dominant objective functions among individuals using the following formula:

[0120] ;

[0121] in, Here, m is the index of the time-frequency characteristic, and m is the total number of time-frequency characteristics. The dominant objective function;

[0122] A Pareto trade-off framework is established, prioritizing individuals with the highest number of dominant objective functions. If the number of dominant objective functions is the same, the next step of ranking is performed.

[0123] This embodiment presents an example where, for a single soliton with m=3, the Pareto advantage of each individual can be evaluated using the following three dominant objective functions:

[0124] ;

[0125] Where Ppeak represents the peak power of the pulse. Indicates pulse width. If the background level represents the continuous wave, then the single soliton solution with high peak power, narrow pulse width and low noise floor is most likely to be the optimal solution. This embodiment uses the Pareto dominance principle to balance the trade-offs between different objectives, which is very important for multi-objective optimization problems.

[0126] Demand Ranking of Dominant Objective Functions: The ranking priority is determined based on the degree of demand for the dominant objective functions. This degree of demand is determined according to actual needs, such as... Figure 3 , 4 In the example of the optimized single soliton shown, the peak power demand is higher. It is preferable to sort the individuals with higher peak power in the Pareto trade-off framework. If the demand of the dominant objective function is the same, then the next sorting step is performed.

[0127] Crowded Distance Sort: A crowded distance strategy is used for supplementary sorting, specifically including:

[0128] Establish a coordinate system based on the individual's driving power and detuning frequency. The sub-crowding distance for all individuals within a preset radius surrounding the i-th individual is determined using the following formula:

[0129] ;

[0130] in, For the first Individual, It is a preset radius range. For the first The coordinate system distance between individuals A constant used to control the degree of influence of congestion distance;

[0131] The number is determined based on the following formula. Crowding distance between individuals:

[0132] ;

[0133] Where N is the total number of individuals;

[0134] Individuals with large crowding distances are prioritized; if the crowding distances are the same, they are ranked according to the degree of demand of the dominant objective function in the second ranking strategy.

[0135] Based on the above sorting strategy, the individuals are sorted, and the resulting population is:

[0136] ;

[0137] Among them, the top E individuals are selected as elite individuals, and the remaining individuals are further sorted to obtain ND winners, and the rest are R losers.

[0138] Specifically, As the first-level sorting criterion, all non-target state / multiple solitons / non-soliton solutions are pre-excluded, and only individuals that are closer to the target soliton number and type are retained before proceeding to subsequent Pareto optimization (pulse width, peak power, CW background, etc.).

[0139] In the cost function Among similar candidates, the merits are distinguished by multi-objective factors, Pareto principle, and crowding distance, specifically including:

[0140] 1. Extract multi-dimensional time-frequency characteristic indicators for each individual to form the dominant objective function vector Fᵢ=(f1ᵢ,f2ᵢ,…,fmᵢ), such as: pulse width, peak power, CW background height, RFSNR, respiratory depth, etc.

[0141] 2. Compare Fᵢ using the Pareto strategy: If individual A is not inferior to individual B in all objectives, and is better than individual B in at least one objective, then individual A Pareto dominates individual B; count how many objectives each individual is dominated by / dominates how many objectives, and classify them into Pareto ranks (frontier 1, frontier 2, etc.). The higher the rank, the better the overall performance.

[0142] 3. Within the same Pareto level, further rank the targets based on the "demand level of the dominant objective" and the "crowding distance": First evaluation strategy: First, prioritize the demand level of each dominant objective (prioritize indicators with high weight and demand level, such as pulse width and background suppression), and then consider the crowding distance if the demand levels are the same; Second evaluation strategy: First, consider the crowding distance (ensuring that the distribution is as uniform as possible within the W–δ parameter space, avoiding all being squeezed into a small area), and then consider the demand level of the dominant objective if the crowding distances are the same.

[0143] The calculation of crowding distance is based on the driving power-detuned frequency plane: with each individual as the center, the density of neighbors within a set radius r is calculated; the smaller the density (the larger the crowding distance), the fewer the samples in the area and the higher the information content. Such individuals will be preferentially retained in the same level to maintain the diversity of solutions.

[0144] S4: Crossover and mutation are performed between winning individuals and elite individuals to retain the good components of the elite, resulting in ND winning crossover mutants. Crossover and mutation are also performed between losing individuals to explore the solution space to a greater extent and prevent getting trapped in local optima, resulting in R losing crossover mutants, ND winning crossover mutants, R losing crossover mutants, and E elite individuals as the next generation of individuals.

[0145] S5: Repeat steps S2-S4 to iterate over the individuals in the population. Continue to obtain the soliton cost information of each individual in the next generation population through the Ikeda coupling equation. After reaching the preset maximum number of iterations, or when the soliton state does not improve significantly after multiple iterations, output the optimal individual in the corresponding output solution. The driving power and detuning frequency contained in this individual can obtain the optimal soliton comb state in the Kerr cavity.

[0146] In this scheme, the priority rule based on cost is as follows: for individuals with different cost functions, when the cost function approaches 0, the individual is classified as optimal and therefore has a higher priority. The priority is inversely proportional to the cost function. In some special cases, when two individuals have the same cost function value, they will be compared in the following priority order:

[0147] The individual with the most dominant objective functions wins in the Pareto trade-off framework. Solutions with more dominant objective functions are considered Pareto optimal and are prioritized, while suboptimal solutions are ranked in subsequent levels. If two individuals have the same number of dominant objective functions, the crowding distance strategy is used for ranking.

[0148] This scheme significantly improves the efficiency and stability of soliton comb state generation in fiber Kerr cavity by adopting a hierarchical cost-dominated genetic algorithm. Compared with the traditional genetic algorithm, this method prioritizes high-quality solutions through a hierarchical cost-dominated strategy, avoiding the problem of local optima and better exploring a wide range of parameter spaces. In addition, by introducing refined multi-objective optimization, the algorithm not only guarantees the generation of soliton comb states, but also optimizes several key indicators during the generation process.

[0149] This embodiment provides an example, such as... Figure 3 , 4 As shown, the implementation process of a single soliton is obtained. Figure 3This indicates that before the first generation, the system was in a multi-breathing state, while in the second generation and later it was in a single-soliton state. Furthermore, the average cost function (cost) of the elites and the best cost function of each generation are being optimized (the closer the cost function is to 0, the closer it is to the target). Figure 4 It shows the changes in the indicators of the best individuals in the entire population over the generations. It can be seen that in the second generation and later, while finding single solitons, peak power, full width at half maximum (FWHM), and average noise floor were also optimized. For single solitons, the higher the peak power, the better; the narrower the FWHM, the better; and the lower the noise floor, the better.

[0150] Please see Figure 5 This embodiment compares the hierarchical cost dominance genetic algorithm with the standard genetic algorithm (GA). To maintain consistency, the population size is set to N=20 and the number of iterations is set to G=10. Figure 5 Taking single soliton SCS optimization as an example, the solutions are colored according to the cost function value: light purple indicates solutions with a high cost function (undesirable); the darker the color, the lower the cost function and the closer the solution is to the objective.

[0151] exist Figure 5 (aI) and Figure 5 In (a-II), the genetic algorithm with hierarchical cost dominance gives dark purple scatter points in multiple sub-regions of driving power and detuning parameter space, indicating that the genetic algorithm with hierarchical cost dominance can effectively guide the algorithm to approach a better solution and promote the discovery of multiple promising regions in the overall parameter space.

[0152] In contrast, Figure 5 (bI)with Figure 5 (b-II) is the result of the standard genetic algorithm. Compared with the hierarchical cost-dominated genetic algorithm, the solution distribution is excessively compressed. This clustering indicates that the algorithm lacks an effective exploration mechanism and is difficult to find the global optimum through alternative paths or intermediate paths. The risk of premature convergence to a local optimum is increased.

[0153] The results show that the hierarchical cost-dominated genetic algorithm promotes global convergence and increases the probability of obtaining robust, high-quality solutions.

[0154] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for generating soliton comb states in a Kerr cavity based on a hierarchical cost-dominated genetic algorithm, characterized in that, include: S1. Randomly generate an initial population containing multiple individuals, each individual representing a set of control parameters for the fiber optic Kerr cavity, including drive power and detuning frequency; S2. For each individual, the output solution of the fiber optic Kerr cavity is simulated by solving the Ikeda mapping equation; S3. Based on the time-frequency characteristics of the output solution, obtain soliton cost information to characterize whether a soliton exists, whether the soliton is in a stable state or a breathing state, and the number of solitons. Use the soliton cost information as the determination index for this individual / the remaining individuals. The judgment index is mapped to a score. Based on the score and the first evaluation strategy, all individuals in the population are ranked and the highest-ranked individuals are selected as elite individuals. After removing the elite individuals, the remaining individuals are ranked again according to the score and the second evaluation strategy. The top-ranked individuals are selected as winners and the rest are losers. For individuals with the same amount of cost information, a Pareto strategy is used for further ranking based on time-frequency characteristics; A Pareto trade-off framework is established, prioritizing individuals with the highest number of dominant objective functions; if two individuals have the same number of dominant objective functions, a crowding distance strategy is used for supplementary sorting; and individuals with larger crowding distances are prioritized. In the first evaluation strategy, before using the crowding distance strategy for supplementary ranking, it further includes: determining the ranking priority based on the degree of demand of the dominant objective function; if the degree of demand of the dominant objective function is the same, then the crowding distance strategy is used for supplementary ranking. In the second evaluation strategy, after supplementing the ranking using the crowding distance strategy, if the crowding distances are the same, the strategy further includes: determining the ranking priority based on the degree of demand of the dominant objective function; S4. Cross and mutate between the winning individuals and elite individuals, and cross and mutate between the losing individuals to update the population. S5. Repeat S2-S4 until the preset number of iterations is reached, then output the individual with the best output solution in the population, which is used to control the generation of soliton comb states in the fiber Kerr cavity.

2. The method for generating Kerr cavity soliton comb states based on a hierarchical cost-dominated genetic algorithm according to claim 1, characterized in that, Step S2 includes: Establish the Ikeda mapping equation, which includes the intracavity propagation equation and the boundary coupling equation: ； Where z is the spatial coordinate of the optical path propagating along the Kerr cavity, L is the length of the entire cavity, z=0 is the starting point of the Kerr cavity, and z=L is the ending point of the Kerr cavity. Let represent the pulse envelope of the optical field within the cavity in the nth cycle, and t be the fast time in the reference frame moving along the group velocity. This represents the envelope of the inner field of the nth Kerr cavity. The rate of change along the propagation direction z The second-order dispersion coefficient, Here, n is the non-linear coefficient, and n is the number of round-trip indices. The field amplitude transmission coefficient of the cavity; As the driving field, , For driving power; The phase detuning frequency per round trip caused by the angular frequency detuning between the pump and the Kerr cavity. , The driving laser frequency for pumping, This is the Kerr cavity resonant frequency; The coupling efficiency of the driving field; The Ikeda mapping equation is iteratively solved under a given driving power and detuning to obtain the physical output solution of the individual.

3. The method for generating Kerr cavity soliton comb states based on a hierarchical cost-dominated genetic algorithm according to claim 2, characterized in that, Obtain the physical output solution for this individual, including: The Ikeda mapping equation is iteratively solved under a given driving power and detuning, and the complex envelope function at the end of the Kerr cavity is obtained as the output solution.

4. The method for generating Kerr cavity soliton comb states based on a hierarchical cost-dominated genetic algorithm according to claim 3, characterized in that, The time-frequency characteristics of the output solution include the time-domain waveform, spectrum, radio spectrum, autocorrelation curve, and energy evolution curve obtained based on the complex envelope function.

5. The method for generating Kerr cavity soliton comb states based on a hierarchical cost-dominated genetic algorithm according to claim 1, characterized in that, The ranking of individuals / remaining individuals is based on scoring and evaluation strategies, including: Define the cost function: ； in, Let be the soliton cost information of the i-th individual. Information content related to the cost of the target soliton; Individuals are initially sorted from smallest to largest based on the cost function.

6. The method for generating Kerr cavity soliton comb states based on a hierarchical cost-dominated genetic algorithm according to claim 5, characterized in that, The further sorting based on time-frequency characteristics using the Pareto strategy includes: The time-frequency characteristics of individuals with the same soliton cost information are extracted as the dominant objective function, and the dominant objective functions among individuals are compared using the following formula: ； in, Here, m is the index of the time-frequency characteristic, and m is the total number of time-frequency characteristics. The dominant objective function; A Pareto trade-off framework is established, prioritizing individuals with the highest number of dominant objective functions.

7. The method for generating Kerr cavity soliton comb states based on a hierarchical cost-dominated genetic algorithm according to claim 6, characterized in that, The supplementary sorting using the crowding distance strategy includes: Establish a coordinate system based on the individual's driving power and detuning frequency. The sub-crowding distance for all individuals within a preset radius surrounding the i-th individual is determined using the following formula: ； in, For the first Individual, It is a preset radius range. For the first The coordinate system distance between individuals A constant used to control the degree of influence of congestion distance; The number is determined based on the following formula. Crowding distance between individuals: Where N is the total number of individuals; Individuals with large crowd distances are prioritized.

Images