A design method for optical phased array based on multi-objective optimization algorithm

Abstract

The present invention discloses a design method for an optical phased array based on a multi-objective optimization algorithm, comprising: S1, initializing a population; S2, normalizing the objective functions of all solutions in the population; S3, performing non-dominated sorting on the population and associating it with a reference point; S4, judging whether the current population meets a termination condition, and if so, entering S5, and if not, entering S6; S5, outputting a Pareto front solution; S6, selecting, crossover, and mutating the population; S7, merging the offspring population obtained in S6 and the parent population to obtain a new population; S8, normalizing the objective functions of all solutions in the new population; sorting the new population through non-dominated sorting and associating with a reference point, selecting solutions layer by layer according to the non-dominated layer, and giving priority to solutions closest to the reference point until N solutions are filled, wherein N is the population size defined when the population is initialized; S9, using the solution selected in step S8 as the next generation population, updating the reference point and normalization parameters, and returning to step S4.

Description

Technical Field

[0001] The present invention relates to the technical field of optical phased arrays, and in particular to a design method for an optical phased array based on a multi-objective optimization algorithm. Background Art

[0002] In recent years, optical phased arrays (OPAs) have shown great potential for application in laser communications and lidar systems. OPAs operate by controlling the phase of light waves in an array of transmitters, thereby steering a beam without mechanical motion. This capability offers advantages such as high precision and speed, making OPAs a crucial component of advanced optical systems. Unlike microwave phased arrays, the antennas and optical phase shifters in OPAs are often larger than the operating wavelength. Therefore, the spacing between antennas in the array typically exceeds one wavelength. Optical phased arrays typically use uniform antenna spacing. This large spacing creates grating lobes in the far field—unwanted radiation lobes that appear at specific angles. These grating lobes not only increase noise, thereby degrading the performance of the antenna array, but also limit the range of effective beam steering. To address this issue, innovative design methods must be adopted to minimize grating lobes and achieve lower sidelobe suppression levels. This requires exploring non-uniform array configurations by optimizing antenna spacing.

[0003] Currently, the design of non-uniform optical antenna arrays mostly uses single-objective optimization algorithms, but the non-uniformity of optical arrays brings complex optimization objectives and balancing requirements, and existing optimization methods have many challenges. When designing OPAs, not only sidelobes should be considered, but other key performance indicators should also be comprehensively evaluated. These indicators include steering range, beamwidth, and mainlobe power ratio. Balancing these factors is crucial to finding the best design that meets the needs of specific applications. Each of these indicators plays an important role in the overall performance of the array: the steering range determines the effective direction of the light beam at different angles; the beam width affects the resolution and accuracy of the system; and the mainlobe power ratio affects the strength and quality of the main signal. To achieve the best design, these parameters must be carefully balanced to enhance the functionality and reliability of the optical phased array. Summary of the Invention

[0004] The main purpose of the present invention is to propose a design method for an optical phased array based on a multi-objective optimization algorithm. By optimizing the array spacing to adjust the interference pattern of the array, while ensuring a small beamwidth, the sidelobe suppression level (SLL) and mainlobe energy loss are reduced to improve the overall performance of the OPA.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A design method for an optical phased array based on a multi-objective optimization algorithm comprises the following steps: S1, initializing a population; S2, normalizing the objective functions of all solutions in the population; S3, performing non-dominated sorting on the population and associating it with a reference point; S4, judging whether the current population satisfies a termination condition, and if so, proceeding to step S5; if not, proceeding to step S6; S5, outputting a Pareto front solution; S6, performing selection, crossover, and mutation on the population; S7, merging the offspring population obtained after step S6 and the parent population to obtain a new population; S8, normalizing the objective functions of all solutions in the new population; sorting the new population by non-dominated sorting and associating it with a reference point, and then selecting solutions layer by layer according to the non-dominated layer, with the solution closest to the reference point being preferentially selected until N solutions are filled, wherein N is the population size defined when the population is initialized; S9, using the solution selected in step S8 as the next generation population, updating the reference point and normalization parameters, and returning to step S4.

[0007] Furthermore, the initialization of the population described in step S1 includes: defining the population size N and the dimension M of the objective function, randomly generating N solutions in the search space, each solution containing an initial value of the array spacing; and initializing a reference point set for guiding the target space distribution.

[0008] Furthermore, the normalization process described in step S2 includes: performing normalization by subtracting ideal points and using a hyperplane intercept to ensure that all objective function values ​​are within the same scale range while eliminating dimensional effects.

[0009] Furthermore, the non-dominated sorting of the population and associating it with the reference point described in step S3 includes: hierarchically sorting the population according to the Pareto dominance relationship to divide different dominance levels; for each non-dominated solution, calculating its distance to all reference points, and associating the solution to the nearest reference point.

[0010] Furthermore, in step S4, determining whether the current population satisfies the termination condition includes determining whether the current population reaches a maximum number of iterations.

[0011] Furthermore, the Pareto front solution in step S5 includes: a solution set on the Pareto front and association information between the solution and the reference point; wherein the solution set on the Pareto front includes each spacing distribution and the corresponding M objective function values; the association information between the solution and the reference point includes the distance from the solution to its associated reference point.

[0012] Furthermore, in step S6, the population is selected, crossover and mutated, specifically including: selecting a solution from the sorting results and the association of the reference points, and using simulated linear crossover and uniform mutation methods.

[0013] Furthermore, in step S8, the objective functions of all solutions of the new population are normalized by using the same normalization method as in step S2, and the new population is sorted by using the same non-dominated sorting method as in step S3.

[0014] The present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the aforementioned optical phased array design method can be implemented.

[0015] The beneficial effects of the technical solution of the present invention are embodied in:

[0016] 1. Traditional optimization methods struggle to balance the conflicting performance requirements of an array, such as beamwidth, sidelobe suppression, and mainlobe power, limiting overall performance. The design method of the present invention adjusts the array's interference pattern by optimizing the array spacing, reducing the beamwidth while ensuring the lowest possible sidelobe suppression level (SLL). Furthermore, the optimized design concentrates more energy in the mainlobe region, improving the mainlobe power ratio. This design method of the present invention enables the production of a non-uniform optical phased array with low sidelobe suppression, narrow beamwidth, and high mainlobe power ratio.

[0017] 2. By optimizing the design of non-uniform optical antenna arrays, this invention significantly improves system performance while maintaining the miniaturization and high integration of optical phased array chips, meeting the requirements of modern high-precision beam control. This optimized design approach not only reduces development costs and improves system feasibility, but also lays a solid foundation for the widespread application of photonic integrated phased array technology in optical communications, remote sensing, and autonomous driving. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of a design method for an optical phased array based on a multi-objective optimization algorithm according to an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram of the spacing design of a 64-antenna array according to an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described below with reference to the accompanying drawings, specific implementation methods, and examples. It should be understood that the examples are provided for the purpose of illustration only and are not intended to be limiting.

[0021] This invention aims to address the design and optimization requirements of non-uniform optical antenna arrays in integrated optical phased arrays (OPAs) by proposing an efficient multi-objective optimization method to improve the overall performance of the OPA. By optimizing the array spacing to adjust the interferometry pattern, the method reduces the sidelobe suppression level (SLL) and mainlobe energy loss while ensuring a small beamwidth.

[0022] In an embodiment of the present invention, we use a genetic algorithm for optimization design. The genetic algorithm uses a population composed of many individuals (solutions) to search and optimize, simulating the process of natural selection and genetic variation to generate new solutions. NSGA-III (Non-dominated Sorting Genetic Algorithm III) is a genetic algorithm for solving multi-objective optimization problems, which uses an improved survival selection mechanism. Based on the NSGA-III algorithm, an embodiment of the present invention introduces a multi-objective OPA optimization method that guides population evolution by using reference points and non-dominated sorting. If the objective value of a solution cannot be improved without reducing some other objective values, then the solution is considered to be non-dominated. The design method of the present invention combines the advantages of non-periodicization and sparsification, and takes the distance between two adjacent array elements as the optimization variable. First, the population is initialized. In the process of finding the optimal solution, it is necessary to calculate the fitness value of each individual to evaluate its performance in solving the problem.

[0023] Based on this, the embodiment of the present invention proposes a design method of an optical phased array based on a multi-objective optimization algorithm. Figure 1 , the design method includes the following steps S1 to S9:

[0024] S1. Initialize the population: Define the population size N and the dimension M of the objective function. Randomly generate N solutions within the search space, each containing an initial value for the array spacing. Initialize a set of reference points to guide the target spatial distribution. In this implementation, the population size N can be determined based on the number of objective functions, the number of decision variables (number of spacings), and computational resources. In this embodiment, N ranges from 20 to 100.

[0025] S2. Normalization: Normalization is to normalize the objective function values ​​of all individuals in the population by subtracting the ideal point and using the hyperplane intercept to ensure that all objective function values ​​are within the same scale range and eliminate the dimension effect.

[0026] S3. Sort the population by non-dominance and associate it with a reference point. In this step, the population is hierarchically sorted according to the Pareto dominance relationship, dividing it into different dominance levels. For each non-dominated solution, its distance to all reference points is calculated, and the solution is associated with the closest reference point.

[0027] S4. Check the termination condition: determine whether the current population has reached the preset maximum number of iterations. If so, it is determined that the termination condition is met and the process goes to step S5. If not, it is determined that the termination condition is not met and the process goes to step S6.

[0028] S5. Output the Pareto frontier solution. The Pareto frontier solution includes: a set of solutions on the Pareto frontier (each spacing distribution and the corresponding M objective function values), and association information between the solution and the reference point (the distance to its associated reference point).

[0029] S6. Perform selection, crossover, and mutation on the population. In this step, N solutions are selected from the sorted results and the association with the reference point. That is, solutions are selected layer by layer according to the non-dominated layer, and the solution closest to the reference point is prioritized during the layer-by-layer selection process. Simulated linear crossover and uniform mutation are used.

[0030] S7. Merge the offspring population Q obtained in step S6 and the parent population P to obtain a new population P', where P'=P∪Q.

[0031] S8. Normalize the objective functions of all solutions of the new population P' as in step S2. Then, refer to step S3, sort the new population by non-dominated sorting and association with the reference point, and select solutions layer by layer according to the non-dominated layer. In the layer-by-layer selection process, give priority to the solution closest to the reference point until N solutions are filled.

[0032] S9. Use the solution selected in step S8 as the next generation population, update the reference point and normalization parameters and return to step S4.

[0033] The far-field radiation pattern formula of OPA is:

[0034]

[0035] Where E(θ) represents the far-field radiation distribution of the optical phased array, θ represents the far-field direction angle, j is the imaginary unit, λ is the wavelength, and A i and d i Represent the amplitude excitation and position of the i-th array element, θ s Indicates the beam pointing angle.

[0036] In the embodiment of the present invention, three indicators (i.e., the dimension of the objective function M=3) are selected for fitness evaluation, namely, sidelobe suppression level (SLL), beamwidth, and mainlobe power ratio. The formula is as follows:

[0037]

[0038] θ beamwith =2θ 0.5 (3)

[0039]

[0040] Among them, E 2 (θ) max-sidelobe 、E 2 (θ)mainlobe and E 2 (θ) represents the maximum sidelobe power, mainlobe power and power distribution in the far field direction θ, respectively. 0.5 is the angle at which the power of the far-field pattern decreases to half relative to the maximum power, θ beamwith Indicates the main beam width (in angular form), R mainlobe Represents the main lobe power ratio.

[0041] The optimization design algorithm of the embodiment of the present invention can evenly distribute the solution set in the target space composed of three objectives, ensuring that the solutions in multi-objective optimization have good diversity and wide distribution. The use of random mutation during the optimization process can randomly explore different areas of the solution space and promote the improvement of global optimization capabilities. The algorithm can find Pareto frontier solutions between multiple objective functions, that is, no solution can outperform another solution in all objectives. This method can help find multiple trade-off solutions for decision makers to choose from.

[0042] Because multiple objectives inherently trade off, optimizing one often leads to degradation of others, making it difficult to find a single optimal solution. The key lies in achieving coordination and compromise among these objectives, thereby optimizing the overall performance. This algorithm uses a reference point to guide the evolution of the population, ensuring that the final solution set is evenly distributed across the objective space. This uniform distribution ensures that the solution set encompasses various trade-offs between different objectives, providing decision makers with a diverse range of options. The final optimal solution set consists of a set of non-dominated solutions, meaning no other solution outperforms them across all objective functions. The antenna spacing design we ultimately selected was derived from a solution in this set.

[0043] Through the above method, we can find the antenna distribution scheme that meets the specific application requirements in the solution set and use it in the design of actual OPA chips. For example, Figure 2 The optical phased array design method according to an embodiment of the present invention is applied to the spacing design of a 64-antenna array, where the horizontal axis Channel represents the sequence number of the antenna spacing and the vertical axis Pitch represents the spacing value.

[0044] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. Those skilled in the art will recognize that several equivalent substitutions or obvious variations can be made without departing from the scope of the present invention, and that any equivalent performance or application should be considered to fall within the scope of protection of the present invention.

Claims

1. A design method for an optical phased array based on a multi-objective optimization algorithm, characterized in that: The steps include: S1. Initialize the population, including: defining the population size N and the dimension M of the objective function, randomly generating N solutions in the search space, each solution containing the initial value of the array spacing; initializing the reference point set for guiding the target space distribution; S2, normalize the objective functions of all solutions in the population; S3, perform non-dominated sorting on the population and associate it with the reference point; S4, determine whether the current population meets the termination condition, if so, proceed to step S5, if not, proceed to step S6; S5. Output Pareto front solution; S6. Perform selection, crossover, and mutation on the population; S7, merging the offspring population obtained in step S6 and the parent population to obtain a new population; S8. Normalize the objective functions of all solutions in the new population; sort the new population by non-dominated sorting and association with the reference point, then select solutions layer by layer according to the non-dominated layer, and give priority to solutions closest to the reference point until N solutions are filled; where N is the population size defined when the population is initialized; S9, taking the solution selected in step S8 as the next generation population, updating the reference point and normalization parameters and returning to step S4; In the process of finding the optimal solution, the design method needs to calculate the fitness value of each individual. Among them, three indicators, namely the sidelobe suppression level (SLL), beamwidth, and mainlobe power ratio, are selected for fitness evaluation. The formula is as follows: i beamwith =2θ 0.5 Where θ represents the far-field direction angle, E 2 (θ) max-sidelobe 、E 2 (θ) mainlobe and E 2 (θ) represents the maximum sidelobe power, mainlobe power and power distribution at the far-field angle θ, respectively. 0.5 is the angle at which the power of the far-field pattern decreases to half relative to the maximum power, θ beamwith represents the main beam width, R mainlobe Represents the main lobe power ratio.

2. The optical phased array design method according to claim 1, wherein: The normalization process described in step S2 includes: performing normalization by subtracting ideal points and using the hyperplane intercept to ensure that all objective function values ​​are within the same scale range and eliminate dimensional effects.

3. The optical phased array design method according to claim 1, wherein: The non-dominated sorting of the population and associating it with the reference point described in step S3 includes: hierarchically sorting the population according to the Pareto dominance relationship to divide different dominance levels; for each non-dominated solution, calculating its distance to all reference points, and associating the solution to the reference point closest to it.

4. The optical phased array design method according to claim 1, wherein: In step S4, determining whether the current population meets the termination condition includes: determining whether the current population reaches the maximum number of iterations.

5. The optical phased array design method according to claim 1, wherein: The Pareto front solution described in step S5 includes: a solution set on the Pareto front and association information between the solution and the reference point; wherein the solution set on the Pareto front includes each spacing distribution and the corresponding M objective function values; the association information between the solution and the reference point includes the distance from the solution to its associated reference point.

6. The optical phased array design method according to claim 1, wherein: In step S6, the population is selected, crossover and mutated, specifically including: selecting a solution from the sorting results and the association of the reference points, and using simulated linear crossover and uniform mutation methods.

7. The optical phased array design method according to claim 1, wherein: In step S8, the objective functions of all solutions of the new population are normalized by the same normalization method as in step S2, and the new population is sorted by the same non-dominated sorting method as in step S3.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the optical phased array design method according to any one of claims 1 to 7 can be implemented.

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