A Parity-Time Symmetric Imaging Model Based on the RUN Optimization Algorithm

Abstract

The present invention proposes a parity-time symmetry imaging model based on RUN (RUNge Kutta optimizer), including: a point light source, two groups of multilayer films, and an air layer, where the two groups of multilayer films satisfy the PT symmetry characteristic. The light rays emitted by the point light source undergo negative refraction between the two groups of multilayer films, thereby generating an image at the output end. The optimization module analyzes the image signal and uses the RUN optimizer to adjust the dielectric constant and thickness of the multilayer films. The present invention can effectively reduce aberration and achieve ideal aberration-free imaging; compared with the existing models, the present invention uses fewer materials, has a simpler process, and does not require setting other data; compared with other existing meta-heuristic optimization algorithms, the present invention shows higher efficiency in the design of the PT symmetry imaging model, has a faster convergence speed, a low probability of falling into local extrema, and strong adaptability to different dielectric parameters, and can fully exert the imaging ability of the PT symmetry imaging system.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical imaging, and specifically relates to a parity-time symmetric imaging model based on the RUN optimization algorithm. It is a parity-time symmetry (PT symmetry) multilayer film structure designed based on the RUN optimization algorithm, which is used to achieve ideal spatial imaging of a planar lens. Background Art

[0002] Imaging is the process of accurately converting a point source in a three-dimensional (3D) space to another three-dimensional image space. However, due to the limitations of traditional imaging systems, this process can usually only be carried out on two two-dimensional (2D) planes, resulting in images that are often not completely real. Although the PT symmetry theory has provided new perspectives and made progress in optical imaging, its effective application in optical imaging still faces many challenges.

[0003] Optical imaging systems often exhibit various monochromatic aberrations, such as spherical aberration, coma aberration, and astigmatism, which makes it difficult to obtain a perfect image, even for a simple object plane. Therefore, a related question is whether there is a two-dimensional or three-dimensional optical imaging system that is completely free of aberrations in theory, and whether such ideal imaging still conforms to the laws of reflection and refraction. For more than a century, it has been generally believed that the only true example of a planar optical instrument is a plane mirror. However, this understanding has its limitations because the image points produced by a plane mirror are virtual, that is, these image points cannot be directly projected onto a screen unless additional lenses (which may introduce aberrations) are used.

[0004] The PT symmetry system based on RUN (RUNge Kutta optimizer) utilizes the symmetry of space and time and aims to achieve specific physical properties. In recent years, several optimization algorithms have been commonly used in the design of PT symmetry imaging systems, such as genetic algorithms, particle swarm optimization algorithms, and differential evolution algorithms, etc. These methods often suffer from problems such as slow convergence speed or insufficient global search efficiency, which makes them face challenges in practical applications. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides a parity-time symmetric imaging model based on the RUN optimization algorithm, and designs an appropriate PT symmetry system to reduce aberrations and achieve ideal aberration-free imaging.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention provides a parity-time symmetric imaging model based on the RUN optimization algorithm, which is characterized by including: a point light source, two groups of multilayer films, an air layer, and an optimization module; the two groups of multilayer films satisfy the PT symmetry characteristic, and there is an air layer between the two groups of multilayer films; the light rays emitted by the point light source irradiate the two groups of multilayer films composed of multilayer lossy materials, and negative refraction occurs between the two groups of multilayer films, so as to generate an image at the output end; the optimization module analyzes the image signal and uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer films.

[0008] Optionally, the optimization module uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer films, which specifically includes the following steps:

[0009] Step 1: Use the sum of the reflectivity and transmittance at different angles of the multilayer film as the objective function of the optimization algorithm;

[0010] Step 2: Set the initial population x and set the population size np, x n , n = 1, 2,..., np, which is used to solve the optimization problem of dim dimensions, and the size of dim depends on the number of layers of the multilayer film;

[0011] Step 3: Apply the initialized population x as input parameters to the multilayer film as its initial dielectric constant and thickness, calculate the objective function through the transfer matrix and scattering matrix operations, and analyze the current global optimal solution x-best;

[0012] Step 4: Update the position of each particle in the population and adjust the optimal value x-best at the same time, apply x-best as the current optimal design parameter to the multilayer film for aberration correction, and complete the current iteration;

[0013] Step 5: Repeat Step 3 and Step 4. When the global optimal design parameter meets the correction requirements, complete the optimization design.

[0014] Optionally, in Step 2, the population is initialized by the following formula:

[0015] x = rand·(UB - LB) + LB;

[0016] In the formula, x is a one-dimensional vector composed of the dielectric constant and thickness of each layer of the film, LB and UB are the lower and upper boundaries of the search space respectively, and rand is a random number within the range of [0, 1].

[0017] Optionally, Step 4 specifically includes the following steps:

[0018] Step 4.1: Use the RUN method to calculate the exploration mechanism SM, and then randomly generate a value rand between [0, 1]. If rand < 0.5, the particle enters the exploration phase, conducts a global search in the search space, and performs a local search near the current position. Update the position x-new according to the search results.

[0019] Step 4.2: If rand ≥ 0.5, the particle enters the exploitation phase, conducts a local search around the new position generated by the current global optimal solution and the optimal solution of each iteration, and updates the position x-new according to the search results.

[0020] Optionally, in step 4.1, the quality of the solution is enhanced through the ESQ phase.

[0021] Optionally, enhancing the quality of the solution through the ESQ phase is specifically as follows:

[0022] Generate a perturbation factor w:

[0023] w = rand(a, b)·exp(-c(rand));

[0024] In the formula, a, b, and c are constants, and rand is a random number less than 0.5. If w < 1, the particle enters the exploitation phase and obtains a new position x-new2 according to the exploitation results. If w ≥ 1, the particle enters the exploration phase and obtains a new position x-new2 according to the exploration results. If the fitness of the new solution x-new2 is not better than the current solution and satisfies the condition rand < w, a local search is performed near x-new to obtain a new position x-new.

[0025] Complete the position update by comparing the fitness of the solution of ESQ and the current optimal solution.

[0026] The beneficial effects of the present invention are: (1) The parity-time symmetric imaging model based on the RUN optimization algorithm proposed by the present invention can effectively reduce aberrations and achieve ideal aberration-free imaging; (2) Compared with other existing models, the model proposed by the present invention uses less materials, has a simpler process, and does not require setting other data; (3) Compared with other existing metaheuristic optimization methods, the present invention shows higher efficiency in the design of the PT symmetric imaging model and has a faster convergence speed; (4) The present invention has a low probability of falling into local extrema, strong adaptability to different dielectric parameters, and can fully exert the imaging ability of the PT symmetric imaging system. Description of the Drawings

[0027] Figure 1 It is a schematic structural diagram of the parity-time symmetric imaging model based on the RUN optimization algorithm of the present invention.

[0028] Figure 2Schematic diagram of the RUN optimization algorithm process of the present invention.

[0029] Figure 3 Optical field distribution diagram before optimization of the present invention.

[0030] Figure 4 Optical field distribution diagram after optimization of the present invention. Specific implementation manners

[0031] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application.

[0032] The PT-symmetric system based on RUN (RUNge Kutta optimizer) utilizes the symmetry of space and time and aims to achieve specific physical properties. To achieve this symmetry, the present invention takes a structure containing ten layers of lossy materials as an example, and sets the value of the specific parameter reflectivity R to -0.5 and the transmittance T to 0.5.

[0033] To optimize the transmission and reflection characteristics, an objective function is designed:

[0034] REFLECTION = ∑(|k1 - 0.5|) + ∑(|k2|) + ∑(|k3 + 0.5|) + ∑(|k4|) (1)

[0035] In the formula, the four coefficient factors k1, k2, k3, and k4 are the real part of transmission, the imaginary part of transmission, the real part of reflection, and the imaginary part of reflection respectively. |k1 - 0.5| ensures that the real part of the transmitted wave is close to 0.5, representing the desired transmission characteristics of the system under specific conditions. |k2| ensures that the imaginary part of the transmitted wave is as small as possible. |k3 + 0.5| focuses on the real part of the reflected wave and makes it as close to -0.5 as possible. |k4| ensures that the imaginary part of the reflected wave is as small as possible, reducing the negative impact on the system transmission characteristics.

[0036] This function aims to minimize the real part of the transmittance close to 0.5 and the imaginary part as small as possible, as well as the real part of the reflectivity close to -0.5 and the imaginary part as small as possible, so as to achieve an ideal imaging effect and ensure the superior imaging ability of the system under specific conditions.

[0037] As Figure 1As shown in the figure, a parity-time symmetric imaging model based on the RUN optimization algorithm proposed by the present invention has an overall structure that is symmetric left and right. The model includes: a point light source, a multilayer film, an air layer, and an optimization module. The two groups of multilayer films satisfy the PT symmetry (Parity Time Symmetry) property. The light emitted by the point light source irradiates a thin film composed of ten lossy materials, thereby generating an image. The optimization module analyzes the image signal and calculates the objective function value using the RUN optimization algorithm. According to the objective function value, the permittivity and thickness of the multilayer film are adjusted to complete the optimization design.

[0038] As Figure 2 shown, the optimization module uses the RUN optimization algorithm to adjust the permittivity and thickness of the multilayer film, including the following steps:

[0039] Step 1: Use the sum of the reflectivity and transmittance at different angles of the multilayer film as the objective function of the optimization algorithm. As the RUN algorithm continuously optimizes the design parameters, the objective function gradually becomes smaller.

[0040] Step 2: Initialize all the parameters of the RUN optimizer and set the population size np. According to the dielectric parameters, set the population particle dimension and the number of optimization parameters dim; specifically, it includes the following steps:

[0041] Step 2.1: Generate the initial position of the population through the initialization formula to generate the initial population x:

[0042] x = rand(np, dim)·(UB - LB)+LB (2)

[0043] In the formula, x is a one-dimensional vector composed of the permittivity and thickness of each layer of the film, LB and UB are the lower and upper boundaries of the search space respectively, and rand is a random number within the range of [0, 1].

[0044] Step 3: Apply the initialized population as the input parameter to the multilayer film as its initial permittivity. Through the transfer matrix and scattering matrix operations, calculate the objective function and analyze the current global optimal solution x-best; specifically, it includes the following steps:

[0045] Step 3.1: Calculate the wave number in the z direction in the material at this time according to the permittivity of the multilayer film and the wave number in free space and ensure that it is positive;

[0046] Step 3.2: Judge the electromagnetic wave mode at this time and calculate the characteristic impedance in different modes according to different electromagnetic wave modes. TE is the transverse electric mode (Transverse Electric), and TM is the transverse magnetic mode (Transverse Magnetic). The calculation methods of the characteristic impedance zc in the TE and TM modes are different:

[0047] For the TE mode:

[0048]

[0049] For the TM mode:

[0050]

[0051] Step 3.3: Calculate layer by layer:

[0052] For each layer, the code extracts the relative permittivity ε and thickness d from the x vector. The wave number (kzi) in the z direction is calculated by the formula:

[0053]

[0054] Where is the wave number in vacuum; μ is the magnetic permeability of vacuum, and θ is the light angle.

[0055] The phase difference (delta) of each layer is calculated as:

[0056] δ = kzi·d (6)

[0057] The matrix Mt of each layer is:

[0058]

[0059] The overall transfer matrix M is updated by multiplying with Mt.

[0060] Calculate the final reflection and transmission coefficients: After processing all layers, the code calculates the characteristic impedance of the medium outside the last layer, which is calculated in two modes:

[0061] For the TE mode:

[0062]

[0063] For the TM mode:

[0064]

[0065] Where ηO is the wave impedance constant in vacuum. After the calculation is completed, the final reflection coefficient R and transmission coefficient T are calculated and determined from the elements A, B, C, and D of the transfer matrix:

[0066]

[0067] Further calculate the objective function according to formula (1).

[0068] Step 4: Update the position of each particle in the population and adjust the optimal value x-best, and apply x-best as the current optimal design parameter to the multilayer film to complete the current iteration; specifically, it includes the following steps:

[0069] Step 4.1: Use the Runge-Kutta method to calculate the exploration mechanism SM, and then randomly generate a value rand between [0, 1]. If rand < 0.5, the particle will enter the exploration phase, perform a global search in the search space, and perform a local search near the current position, and update the position x-new according to the search results;

[0070] Step 4.2: If rand ≥ 0.5, the particle will enter the exploitation phase. In this phase, the particle performs a local search around the new position generated by the current global optimal solution and the optimal solution of each iteration, and updates the position x-new according to the search results

[0071] In some embodiments, in Step 4.1, the quality of the solution is enhanced through the ESQ (ESQ-Enhanced Solution Quality) phase.

[0072] When rand < 0.5, the specific method of enhancing the solution quality through the ESQ phase is: generate a perturbation factor w:

[0073] w = rand(1, dim)·exp(-5·rand) (12)

[0074] In the formula, dim is the number of optimization parameters, and rand is a random number less than 0.5; if w < 1, the particle will enter the exploitation phase and obtain a new position x-new2 according to the exploitation results; if w ≥ 1, the particle will enter the exploration phase and obtain a new position x-new2 according to the exploration results; if the fitness of the new solution x-new2 is not better than the current solution and satisfies the condition rand < w, a local search will be performed near x-new to explore potential regions, thereby obtaining a new position x-new. Finally, compare the fitness of the solution of ESQ and the current optimal solution to complete the position update.

[0075] Step 5: When the global optimal design parameter meets the design requirements, complete the optimization design. If not, increase the number of iterations and return to Step 4 to continue processing.

[0076] As Figure 3 、 4 shown, where Figure 3 is the light field distribution diagram before optimization, Figure 4 is Figure 3The corresponding optical field distribution map obtained based on the optimized RUN parameters. It can be seen from this that the present invention uses the sum of the reflectivity and transmittance of different angles of the multilayer film as the objective function of the optimization algorithm, uses the RUN algorithm to optimize the parameters of the PT-symmetric imaging system, and obtains the optimal dielectric constant and thickness values of the multilayer film through multiple iterations of the algorithm, so as to obtain an imaging close to the ideal one.

[0077] The above is only the preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A parity-time symmetric imaging model based on the RUN optimization algorithm, characterized in that: Including: A point light source, two groups of multilayer films, an air layer, and an optimization module; the two groups of multilayer films satisfy PT symmetry characteristics, and there is an air layer between the two groups of multilayer films; the light emitted by the point light source irradiates the two groups of multilayer films composed of multilayer lossy materials, and negative refraction occurs between the two groups of multilayer films, so as to generate an image at the output end; the optimization module analyzes the image signal and uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer film, specifically including the following steps: Step 1: Use the sum of the reflectance and transmittance at different angles of the multilayer film as the objective function of the optimization algorithm; Step 2: Set the initial population x and the population size np, x n ,n=1,2,…,np, used to solve the dim dimension optimization problem, the size of dim depends on the number of layers of the multilayer film; Step 3: Apply the initialized population x as an input parameter to the multilayer film as its initial dielectric constant and thickness, calculate the objective function through the transfer matrix and scattering matrix operations, and analyze the current global optimal solution x-best; Step 4: Update the position of each particle in the population and adjust the optimal value x-best at the same time, apply x-best as the current optimal design parameter to the multilayer film, and complete the current iteration; Step 4 specifically includes the following steps: Step 4.1: Use the RUN method to calculate the exploration mechanism SM, and then randomly generate a value rand between [0, 1]. If rand < 0.5, the particle enters the exploration stage, performs global search in the search space, and performs local search near the current position, and updates the position x-new according to the search results; in Step 4.1, the quality of the solution is enhanced through the ESQ stage, specifically: Generate a perturbation factor w: w = rand(a, b)·exp(-c(rand)); In the formula, a, b, and c are constants, and rand is a random number less than 0.5; if w < 1, the particle enters the exploitation stage and obtains a new position x-new2 according to the exploitation result; if w ≥ 1, the particle enters the exploration stage and obtains a new position x-new2 according to the exploration result; if the fitness of the new solution x-new2 is not better than the current solution and satisfies the condition rand < w, local search is performed near x-new to obtain a new position x-new; Complete the position update by comparing the fitness of the solution of ESQ and the current optimal solution; Step 4.2: If rand ≥ 0.5, the particle enters the exploitation stage, performs local search around the current global optimal solution and the new position generated by the optimal solution of each iteration, and updates the position x-new according to the search results; Step 5: Repeat Step 3 and Step 4. When the global optimal design parameter meets the design requirements, the optimization design is completed.

2. A parity-time symmetric imaging model based on the RUN optimization algorithm as claimed in claim 1, characterized in that: In Step 2, the population is initialized using the following formula: x = rand·(UB - LB) + LB; In the formula, x is a one-dimensional vector composed of the dielectric constant and thickness of each layer of the film, LB and UB are the lower and upper boundaries of the search space respectively, and rand is a random number in the range of [0, 1].

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