A flat broadband wavelength conversion method based on multi-objective genetic particle swarm algorithm

Abstract

This invention discloses a flat broadband wavelength conversion method based on a multi-objective genetic particle swarm optimization algorithm, comprising: S1, performing preliminary design on a chirped periodically polarized thin-film lithium niobate waveguide structure to obtain initial waveguide-related parameters and determine the initial polarization period distribution; S2, calculating the bandwidth and flatness of the initial wavelength conversion spectrum based on the initial polarization period distribution and the initial waveguide-related parameters; S3, optimizing the bandwidth and flatness of the initial wavelength conversion spectrum using a multi-objective genetic particle swarm optimization algorithm to obtain optimal values ​​for the bandwidth and flatness of the wavelength conversion spectrum; S4, redesigning the chirped periodically polarized thin-film lithium niobate waveguide structure using the optimal values ​​for the bandwidth and flatness of the wavelength conversion spectrum to obtain a wavelength conversion spectrum. This invention enables faster and better design of periodically polarized thin-film lithium niobate waveguides with flatter broadband wavelength conversion capabilities.

Description

Technical Field

[0001] This invention relates to the field of nonlinear optical wavelength conversion technology, and more specifically, to a flat broadband wavelength conversion method based on a multi-objective genetic particle swarm optimization algorithm. Background Technology

[0002] With the rapid development of micro-nano technology, thin-film lithium niobate has begun to play an important role in the field of nonlinear optics. Wavelength converters based on second-order nonlinear effects on this material platform have begun to shine, and many wavelength converters based on periodically polarized thin-film lithium niobate waveguides have achieved significant breakthroughs in conversion efficiency and spectral broadening. However, the refractive index of thin-film lithium niobate waveguides is greatly affected by structural parameters, and the group velocity dispersion is difficult to control. Although wavelength converters based on chirped periodically polarized thin-film lithium niobate waveguides can obtain broadband second harmonic or sum-frequency generation, the spectral flatness is not high. Introducing structures such as sinusoidal chirped or Bessel chirped gratings and changing the polarization period can achieve the design of flat broadband converters, but the related designs are relatively complex and lack flexibility and scalability. Therefore, a flat broadband wavelength conversion method based on a multi-objective genetic particle swarm optimization algorithm is needed. Summary of the Invention

[0003] The purpose of this invention is to provide a flat broadband wavelength conversion method based on a multi-objective genetic particle swarm optimization algorithm to overcome the shortcomings of existing technologies.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A flat broadband wavelength conversion method based on a multi-objective genetic particle swarm optimization algorithm includes the following steps:

[0006] S1. A preliminary design of the chirped periodically polarized thin-film lithium niobate waveguide structure is carried out to obtain the initial waveguide-related parameters and determine the initial polarization period distribution.

[0007] S2. The bandwidth and flatness of the initial wavelength conversion spectrum are calculated based on the initial polarization period distribution and the initial waveguide related parameters.

[0008] S3. The bandwidth and flatness of the initial wavelength conversion spectrum are optimized using a multi-objective genetic particle swarm optimization algorithm to obtain the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum.

[0009] S4. The chirped periodically polarized thin-film lithium niobate waveguide structure is redesigned using the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum to obtain the wavelength conversion spectrum.

[0010] Furthermore, the initial waveguide-related parameters designed in step S1 include the waveguide top width, tilt angle, total thickness of the thin-film lithium niobate platform, and etching depth.

[0011] Furthermore, the calculation in step S2 is based on the wavelength conversion formula, which is:

[0012]

[0013] In the formula, L is the length of the entire chirped polarized thin-film lithium niobate waveguide, and d(y q )=±1 indicates that the crystal is cancelled along the waveguide direction, λ represents the working band, G(λ) is the Fourier transform of the d(y) function, and Δk(λ)=k ωi -k ωs -k ωp ， Represents wave vector mismatch, k ωi k ωs and k ωp These are the waveguide mode wave vectors of the sum-frequency light, signal light, and pump light, respectively. The entire chirped polarized thin-film lithium niobate waveguide contains domains of N = 2pm, each domain being between y q-1 and y q (q = 1, 2, ..., N).

[0014] Furthermore, step S3 specifically includes:

[0015] S31. Set and initialize the parameters in the genetic particle swarm, including: maximum number of iterations maxgen, particle dimension D, population size sizepop, and velocity v. ij and position x ij The limits, learning factors c1 and c2, and the maximum and minimum values ​​of the inertia factor w. max and w min Hybridization probability p c Mutation probability p m ;

[0016] S32. Using the bandwidth and flatness of the initial wavelength conversion spectrum from step S2 as the initial particles, initialize the particle velocity and substitute it into the calculation of the particle fitness value f(x). ij ), to obtain the individual optimal pbest and the global optimal gbest of the particles;

[0017] S33. Particle swarm optimization algorithm is used to update the speed;

[0018] S34. Update the position using the particle swarm optimization algorithm;

[0019] S35. Sort the particles updated by the particle swarm optimization algorithm according to their fitness, and then sort them according to the crossover probability P. c Determine the size of the hybridization pool and select particles with high fitness for hybridization calculations;

[0020] S36. Perform Gaussian mutation operation on the hybridized particles;

[0021] S37. Calculate the fitness value and update the individual best pbest and global best gbest of the particles;

[0022] S38. Determine the number of iterations N. If N = maxgen, stop the search and output the global optimal value gbest of the obtained particle and its corresponding fitness value, that is, the optimal value of the bandwidth and flatness of the wavelength conversion spectrum. Otherwise, return to step S33.

[0023] Furthermore, the bandwidth and flatness of the initial wavelength conversion spectrum in step S32 are used as fitness functions to simultaneously optimize the bandwidth and flatness of the wavelength conversion spectrum.

[0024] Furthermore, the formula for speed update in step S33 is:

[0025]

[0026] In the formula, c1 = c2 = 1.49445, r 1ij and r 2ij Given a random number in [0,1], the crossover formula is: r3 is a random number in [0,1]. Poolx1 and Poolx2 are particles from different hybridization pools after being classified according to their fitness. The mutation formula is... randn is a random number that follows a normal distribution; Represents the velocity of the updated particles. This represents the particle velocity after the Nth iteration. This represents the optimal individual value after the Nth iteration. This represents the initial position of the particle in the Nth iteration. This represents the optimal group state after the Nth iteration.

[0027] Compared with the prior art, the advantages of the present invention are: compared with the traditional design method which is complex and sometimes can only optimize a single target such as bandwidth or flatness, the present invention can design a periodically polarized thin film lithium niobate waveguide with a flatter broadband wavelength conversion function faster and better. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart of the flat broadband wavelength conversion method based on the multi-objective genetic particle swarm algorithm of the present invention.

[0030] Figure 2 This is a schematic diagram of the initial periodically polarized thin-film lithium niobate waveguide structure based on flat broadband wavelength conversion of multi-target genetic particle swarm optimization in this invention.

[0031] Figure 3 This is the iterative curve for parameter optimization using the multi-objective genetic particle swarm optimization algorithm introduced in this invention.

[0032] Figure 4 This is a comparison diagram of the polarization period distribution after the introduction of the multi-objective genetic particle swarm algorithm in this invention and the initial polarization period distribution.

[0033] Figure 5 This is a comparison diagram of the optimized wavelength conversion spectrum and the initial wavelength conversion spectrum in this invention. Detailed Implementation

[0034] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0035] See Figure 1 As shown, this embodiment discloses a flat broadband wavelength conversion method based on a multi-objective genetic particle swarm optimization algorithm, including the following steps:

[0036] Step S1: Perform preliminary design of the chirped periodically polarized thin-film lithium niobate waveguide structure, obtain the initial waveguide-related parameters, and determine the initial polarization period distribution.

[0037] Specifically, the initial waveguide parameters in the preliminary design include the waveguide top width, tilt angle, total thickness of the thin-film lithium niobate platform, and etching depth.

[0038] Step S2: Calculate the bandwidth and flatness of the initial wavelength conversion spectrum based on the initial polarization period distribution and the initial waveguide related parameters.

[0039] Step S3: Optimize the bandwidth and flatness of the initial wavelength conversion spectrum using a multi-objective genetic particle swarm optimization algorithm to obtain the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum.

[0040] Step S4: Redesign the chirped periodically polarized thin-film lithium niobate waveguide structure using the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum to obtain the wavelength conversion spectrum.

[0041] In this embodiment, the waveguide top width is set to 600 nm. The tilt angle is set to 67°, the total thickness of the thin-film lithium niobate platform is 550 nm, and the etching depth is 300 nm. The entire periodically polarized thin-film lithium niobate waveguide is a stepped chirped thin-film lithium niobate waveguide composed of 29 standard periodically polarized thin-film lithium niobate waveguides with periods increasing by 1.5 nm, wherein the period of the first periodically polarized thin-film lithium niobate waveguide is 3.02 μm.

[0042] In this embodiment, the bandwidth of the initial wavelength conversion spectrum obtained in step S2 is 180 nm, and the flatness is 1.72 dB. Flatness is defined as the peak efficiency (dB) minus the average efficiency (dB) under a 3 dB bandwidth.

[0043] In this embodiment, the calculation in step S2 is based on the wavelength conversion formula, which is:

[0044]

[0045] In the formula, L is the length of the entire chirped polarized thin-film lithium niobate waveguide, and d(y q )=±1 indicates that the crystal is cancelled along the waveguide direction, λ represents the working band, G(λ) is the Fourier transform of the d(y) function, and Δk(λ)=k ωi -k ωs -k ωp， Represents wave vector mismatch, k ωi k ωs and k ωp These are the waveguide mode wave vectors of the sum-frequency light, signal light, and pump light, respectively. The entire chirped polarized thin-film lithium niobate waveguide contains domains of N = 2pm, each domain being between y q-1 and y q (q = 1, 2, ..., N).

[0046] Combination Figure 2 As shown, the multi-objective genetic particle swarm optimization algorithm in step S3 specifically includes:

[0047] Step S31: Set and initialize the parameters in the genetic particle swarm, including: maximum number of iterations maxgen, particle dimension D, population size sizepop, and velocity v. ij and position x ij The limits, learning factors c1 and c2, and the maximum and minimum values ​​of the inertia factor w. max and w min Hybridization probability p c Mutation probability p m ;

[0048] Step S32: Using the bandwidth and flatness of the initial wavelength conversion spectrum from step S2 as the initial particles, initialize the particle velocity and substitute it into the calculation of the particle fitness value f(x).ij ), to obtain the individual optimal pbest and the global optimal gbest of the particles;

[0049] Step S33: Update the speed using the particle swarm optimization algorithm;

[0050] Step S34: Update the position using the particle swarm optimization algorithm;

[0051] Step S35: Sort the particles updated by the particle swarm optimization algorithm according to their fitness, and then sort them according to the crossover probability P. c Determine the size of the hybridization pool and select particles with high fitness for hybridization calculations;

[0052] Step S36: Perform Gaussian mutation on the hybridized particles;

[0053] Step S37: Calculate the fitness value and update the individual best pbest and global best gbest of the particles;

[0054] Step S38: Determine the number of iterations N. If N = maxgen, stop the search and output the global optimal gbest of the obtained particle and its corresponding fitness value, that is, the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum. Otherwise, return to step S33.

[0055] In step S32, the bandwidth and flatness of the initial wavelength conversion spectrum are used as fitness functions to simultaneously optimize the bandwidth and flatness of the wavelength conversion spectrum.

[0056] Furthermore, the formula for speed update in step S33 is:

[0057]

[0058] In the formula, c1 = c2 = 1.49445, r 1ij and r 2ij Given a random number in [0,1], the crossover formula is: r3 is a random number in [0,1]. Poolx1 and Poolx2 are particles from different hybridization pools after being classified according to their fitness. The mutation formula is... randn is a random number that follows a normal distribution; Represents the velocity of the updated particles. This represents the particle velocity after the Nth iteration. This represents the optimal individual value after the Nth iteration. This represents the initial position of the particle in the Nth iteration. This represents the optimal group state after the Nth iteration.

[0059] Figure 3The iterative curves for parameter optimization using a multi-objective genetic particle swarm optimization algorithm introduced in this embodiment are shown in detail. The iterative process for bandwidth and flatness is described in detail. This algorithm can converge quickly and has good iterative results.

[0060] Figure 4 The diagram shows a comparison between the polarization period distribution after introducing the multi-objective genetic particle swarm optimization algorithm in this embodiment and the initial polarization period distribution. Obviously, the optimized polarization period distribution is significantly different from the original linearly increasing polarization period distribution. This also indicates that the optimal result obtained by the algorithm has escaped the local optimum and is in line with expectations.

[0061] Figure 5 This is a comparison chart of the optimized wavelength conversion spectrum and the initial wavelength conversion spectrum in the embodiment. It can be seen that the optimized spectrum is flatter and the bandwidth is significantly broadened.

[0062] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, the patent owner may make various modifications or alterations within the scope of the appended claims, as long as they do not exceed the protection scope described in the claims of the present invention, they shall be within the protection scope of the present invention.

Claims

1. A flat broadband wavelength conversion method based on a multi-objective genetic particle swarm optimization algorithm, characterized in that, Includes the following steps: S1. A preliminary design of the chirped periodically polarized thin-film lithium niobate waveguide structure is carried out to obtain the initial waveguide-related parameters and determine the initial polarization period distribution. S2. The bandwidth and flatness of the initial wavelength conversion spectrum are calculated based on the initial polarization period distribution and the initial waveguide related parameters. S3. The bandwidth and flatness of the initial wavelength conversion spectrum are optimized using a multi-objective genetic particle swarm optimization algorithm to obtain the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum. S4. The chirped periodically polarized thin-film lithium niobate waveguide structure is redesigned using the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum to obtain the wavelength conversion spectrum. Step S3 specifically includes: S31. Set and initialize the parameters in the genetic particle swarm, including: maximum number of iterations maxgen, particle dimension D, population size sizepop, and velocity v. ij and position x ij The limits, learning factors c1 and c2, and the maximum and minimum values ​​of the inertia factor w. max and w min Hybridization probability p c Mutation probability p m ; S32. Using the bandwidth and flatness of the initial wavelength conversion spectrum from step S2 as the initial particles, initialize the particle velocity and substitute it into the calculation of the particle fitness value f(x). ij ), to obtain the individual optimal pbest and the global optimal gbest of the particles; S33. Particle swarm optimization algorithm is used to update the speed; S34. Update the position using the particle swarm optimization algorithm; S35. Sort the particles updated by the particle swarm optimization algorithm according to their fitness, and then sort them according to the crossover probability P. c Determine the size of the hybridization pool and select particles with high fitness for hybridization calculations; S36. Perform Gaussian mutation operation on the hybridized particles; S37. Calculate the fitness value and update the individual best pbest and global best gbest of the particles; S38. Determine the number of iterations N. If N = maxgen, stop the search and output the global optimal gbest of the obtained particle and its corresponding fitness value, that is, the optimal values ​​of bandwidth and flatness of the wavelength conversion spectrum. Otherwise, return to step S33. The bandwidth and flatness of the initial wavelength conversion spectrum in step S32 are used as fitness functions to simultaneously optimize the bandwidth and flatness of the wavelength conversion spectrum.

2. The flat broadband wavelength conversion method based on multi-objective genetic particle swarm optimization algorithm according to claim 1, characterized in that, The initial waveguide parameters designed in step S1 include the waveguide top width, tilt angle, total thickness of the thin-film lithium niobate platform, and etching depth.

3. The flat broadband wavelength conversion method based on multi-objective genetic particle swarm optimization algorithm according to claim 1, characterized in that, The calculation in step S2 is based on the wavelength conversion formula, which is: In the formula, L is the length of the entire chirped polarized thin-film lithium niobate waveguide. d ( y q ) = ±1 indicates that the crystal along the waveguide direction is cancelled. λ Represents the working band, G( λ ) is d( y Fourier transform of the function, Δ k ( λ ) = k ωi - k ωs - k ωp， This represents wave-vector mismatch. k ωi , k ωs and k ωp These are the waveguide mode wave vectors of the sum-frequency light, signal light, and pump light, respectively. The entire chirped polarized thin-film lithium niobate waveguide contains domains of N = 2 pm, each domain being intermediate between y q - 1 and y q (q = 1,2, ...,N).

4. The flat broadband wavelength conversion method based on multi-objective genetic particle swarm optimization algorithm according to claim 1, characterized in that, The formula for speed update in step S33 is: In the formula, c1=c2=1.49445, r 1ij and r 2ij Given a random number in [0,1], the crossover formula is: , r 3 is a random number in the range [0,1]. Poolx 1 and Poolx 2 represents particles from different hybridization pools after being classified according to fitness levels. The mutation formula is... , randn These are random numbers that follow a normal distribution. Represents the velocity of the updated particles. This represents the particle velocity after the Nth iteration. This represents the optimal individual value after the Nth iteration. This represents the initial position of the particle in the Nth iteration. This represents the optimal group state after the Nth iteration.

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