Method for determining discrete nonlinear optical lattice mode based on Newton conjugate gradient method

Abstract

The invention belongs to the technical field of optics, and particularly relates to a method for determining a discrete nonlinear optical lattice mode based on a Newton conjugate gradient method.The method comprises the steps that basic parameters of discrete nonlinear optical lattices are obtained, and a discrete nonlinear Schrodinger equation is constructed based on the basic parameters of the discrete nonlinear optical lattices; solving the nonlinear Schrodinger equation by adopting a Newton conjugate gradient method to obtain a steady-state solution; the calculation framework of the Newton conjugate gradient method comprises an external Newton iteration method and an internal conjugate gradient iteration method; judging whether the steady-state solution meets predefined precision or not, if yes, outputting a result, and if not, iteratively updating the steady-state solution based on a Newton conjugate gradient method until the steady-state solution meets the predefined precision, and outputting the result; the propagation behavior of light in the photonic crystal is described by using the discrete nonlinear Schrodinger equation, the equation is solved by using the Newton conjugate gradient method, the real part and the imaginary part of the equation do not need to be separated, and the calculation cost and the requirement for high-performance calculation resources are effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of optics, and particularly relates to a method for determining discrete nonlinear optical lattice modes based on the Newton conjugate gradient method. Background Art

[0002] In engineering applications, finding modes in lattices is of crucial significance in many fields such as nonlinear physics, materials science, optics, and electronic engineering. In nonlinear photonic crystals, the identification and understanding of modes such as solitons and vortex solitons are essential for designing efficient photonic devices. By studying these modes, engineers can design photonic crystals with specific properties, such as materials with specific bandgaps or capable of transmitting light of specific wavelengths, which can be applied in devices including optical switches, optical waveguides, and laser light sources, thus promoting the progress of optical communication and laser technology. The complex phenomena such as the nonlinear effects, bandgap characteristics, and soliton behavior of photonic crystals involve the precise measurement of material parameters and complex numerical simulations. Different modeling methods and numerical solution methods will introduce different errors and computational complexities, further increasing the difficulty of analysis. The lack of a concise and general analysis process not only increases the time cost of material and device design but also is not conducive to the industrial sector quickly meeting the actual needs of different photonic crystal materials and devices.

[0003] Finding modes in discrete nonlinear optical lattices requires modeling the corresponding model to form a discrete nonlinear Schrödinger equation. The discrete nonlinear optical lattice used to describe discrete nonlinear optical lattices is one of the most fundamental and widely studied nonlinear lattice dynamics models, which is widely used to explore various phenomena, including soliton dynamics and various discrete lattice solitons, etc. Obtaining the modes in discrete nonlinear optical lattices requires solving the discrete nonlinear Schrödinger equation based on this model. In recent years, the research on the concept of topological states has accelerated the development of nonlinear physics. Compared with traditional non-topological lattices, the structure of topological lattices is usually more complex, such as higher dimensions, multiple sub-lattice nodes in a single unit cell, etc. These characteristics significantly increase the difficulty of solving the discrete nonlinear Schrödinger equation to find modes. At present, there is still no simple, fixed, and effective standardized process for obtaining lattice modes in nonlinear photonic crystals. Due to the significant differences in photonic crystals with different dimensions and structures, the processes of parameter acquisition, modeling methods, and numerical solutions involved in solving modes are different. This lack of a unified framework makes the acquisition and analysis of modes for different crystal structures particularly complex and is not conducive to the industrial sector optimizing the design of materials and devices specifically, especially in applications in the fields of optical communication, optical sensors, lasers, etc. There is an urgent need for a standardized process to improve design efficiency and accuracy.

[0004] Specifically, in the numerical solution of the discrete nonlinear Schrödinger equation based on photonic crystals, the traditional Newton method has the following problems when solving the discrete nonlinear Schrödinger equation to find modes: First, the Newton method directly solves the linearized equation, with a slow solution speed and high computational time and computing power consumption. For example, for a high-dimensional nonlinear system, its corresponding matrix is usually large and in the form of a non-tridiagonal matrix, so decomposing it requires a large amount of memory and calls a large amount of computing resources. When the system to be solved is a nonlinear topological system, this problem becomes more prominent because nonlinear topological systems usually contain multiple components, such as different spins or sublattice nodes. Second, the Newton method is mainly applicable to solving real solutions of real nonlinear equations. For the discrete nonlinear Schrödinger equation with complex coupling coefficients or complex solutions, the real and imaginary parts of the nonlinear equation usually need to be separated, which increases the matrix size and complicates the derivation process. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for determining discrete nonlinear optical lattice modes based on the Newton conjugate gradient method to solve the technical problems of low design efficiency and accuracy of discrete nonlinear optical lattice modes in the prior art.

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

[0007] In a first aspect, the present application discloses a method for determining discrete nonlinear optical lattice modes based on the Newton conjugate gradient method, including:

[0008] Obtain the basic parameters of the discrete nonlinear optical lattice, and construct a discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice;

[0009] Solve the nonlinear Schrödinger equation using the Newton conjugate gradient method to obtain a steady-state solution; the calculation framework of the Newton conjugate gradient method includes an external Newton iteration method and an internal conjugate gradient iteration method;

[0010] Judge whether the steady-state solution meets the predefined accuracy. If it meets, output the result. If it does not meet, iteratively update the steady-state solution based on the Newton conjugate gradient method until the steady-state solution meets the predefined accuracy, and output the result to obtain the discrete nonlinear optical lattice mode.

[0011] Preferably, the obtaining the basic parameters of the discrete nonlinear optical lattice and constructing a discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice specifically includes:

[0012] S101: The crystal dimension, symmetry, and nonlinear characteristics of the nonlinear photonic crystal;

[0013] S102: Determine the geometric parameters of the corresponding lattice based on the crystal dimension of the nonlinear photonic crystal;

[0014] S103: Establish a tight-binding model for the photonic crystal based on the symmetry, nonlinear characteristics of the nonlinear photonic crystal, and the geometric parameters of the corresponding lattice, and obtain the discrete nonlinear Schrödinger equation.

[0015] Preferably, the steady-state solution is obtained by solving the nonlinear Schrödinger equation using the Newton conjugate gradient method, which specifically includes:

[0016] S201: Use the Newton iteration method to expand the steady-state solution equation L 0 u (m+1) = 0 around the approximate solution u (m) , and ignore the high-order terms to obtain the linearized equation:

[0017] L 0 u (m) +L 1 (u (m+1) -u (m) ) = 0,

[0018] The above equation is rewritten as

[0019] L 1 Δu (m) = -L 0 u (m)

[0020] u (m+1) = u (m) +Δu (m)

[0021] S202: Solve the linearized equation using the conjugate gradient iteration method to obtain Δu (m) ;

[0022] S203: Update the approximate solution u (m) according to Δu (m) to obtain the steady-state solution u (m+1) ;

[0023] where u (m+1) represents the steady-state solution of a complex vector containing real and imaginary parts; L 0 represents the operator; L 1 is the linearized operator; u (m) represents the approximate solution of u (m+1) ; Δu (m) is the update amount of the solution from the m-th iteration to the m + 1-th iteration.

[0024] Preferably, S202 specifically includes:

[0025] S2021: Initialize the initial guess solution and its error of the conjugate gradient iteration method:

[0026] Δu (m,0) = 0

[0027] R (m,0) = -L 0 u (m)

[0028] D (m,0) = M -1 R (m,0)

[0029] S2022: Solve for Δu iteratively using the following equation (m) , until the stopping criterion of the conjugate gradient iteration method is satisfied:

[0030]

[0031] Δu (m,i+1) = Δu (m,i) + a (m,i) D (m,i) ,

[0032] R (m,i+1) = R (m,i) - a (m,i) L 1 D (m,i) ,

[0033]

[0034] D (m,i+1) = M -1 R (m,i+1) + b (m,i+1) D (m,i) ,

[0035] where, Δu (m,0) represents the update amount of the initial guess solution; R (m,0) is the error of the initial guess solution; L 0 represents an operator; L 1 is the linearized operator; M -1 is the inverse of a user-defined preconditioning operator for accelerating convergence; D (m,0) represents the initial iteration parameter; a (m,i) represents the i-th iteration coefficient; b (m,i+1) represents the (i + 1)-th iteration coefficient; the superscript (m, i) represents the i-th iteration of the conjugate gradient method for calculating Δu (m) .

[0036] Preferably, the stopping criterion of the conjugate gradient iteration method is:

[0037] ‖R (m,i) ‖ M < ε cg ‖R (m,0)‖ M ,

[0038] wherein, ‖R (m,i) ‖ M is the error of solving Δu (m,i) ; ‖R (m,0) ‖ M is the 2-norm of the initial error, and ε cg is the positive tolerance parameter.

[0039] Preferably, determining whether the steady-state solution satisfies a predefined accuracy specifically includes:

[0040] When the difference between the maximum value of the steady-state solution equation or the maximum value between two adjacent iterations is less than the predefined solution error limit, the corresponding steady-state solution satisfies the predefined accuracy.

[0041] In a second aspect, the present application discloses a system for determining discrete nonlinear optical lattice modes based on the Newton conjugate gradient method, including:

[0042] An acquisition unit for acquiring the basic parameters of the discrete nonlinear optical lattice and constructing a discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice;

[0043] A solving unit for solving the nonlinear Schrödinger equation by using the Newton conjugate gradient method to obtain a steady-state solution; the calculation framework of the Newton conjugate gradient method includes an external Newton iteration method and an internal conjugate gradient iteration method;

[0044] A judgment unit for judging whether the steady-state solution satisfies a predefined accuracy. If it is satisfied, the result is output. If it is not satisfied, the steady-state solution is iteratively updated based on the Newton conjugate gradient method until the steady-state solution satisfies the predefined accuracy, and then the result is output.

[0045] Preferably, in the solving unit, solving the nonlinear Schrödinger equation by using the Newton conjugate gradient method to obtain a steady-state solution specifically includes:

[0046] S201: Using the Newton iteration method to expand the steady-state solution equation L 0 u (m+1) = 0 around the approximate solution u (m) and ignoring the high-order terms to obtain a linearized equation:

[0047] L 0 u (m) + L 1 (u (m+1) - u (m) ) = 0,

[0048] The above equation is rewritten as

[0049] L 1 Δu(m) = -L 0 u (m)

[0050] u (m+1) = u (m) + Δu (m)

[0051] where L 1 is a linearization operator, and Δu (m) is the update amount of the solution from the m-th iteration to the (m + 1)-th iteration;

[0052] S202: Solve the linearized equation using the conjugate gradient iteration method to obtain Δu (m) ;

[0053] S203: Update the approximate solution u (m) according to Δu (m) to obtain the steady-state solution u (m+1) .

[0054] In a third aspect, the present application discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for determining a discrete nonlinear optical lattice mode based on the Newton conjugate gradient method as described in any one of the above are implemented.

[0055] In a fourth aspect, the present application discloses a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the method for determining a discrete nonlinear optical lattice mode based on the Newton conjugate gradient method as described in any one of the above are implemented.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1) The present application first determines the type and structure of the photonic crystal to obtain the basic parameters of the discrete nonlinear optical lattice. Based on the basic parameters, a tight-binding model is established for the photonic crystal, and the discrete nonlinear Schrödinger equation is used to describe the propagation behavior of light in the photonic crystal. Solving the nonlinear Schrödinger equation using the Newton conjugate gradient method can effectively obtain the propagation mode of the photonic crystal. During the calculation process, the present invention innovatively proposes a new numerical solution method, which significantly accelerates the speed of mode solution. Using the Newton conjugate gradient method speeds up the convergence rate of the equation, and compared with the Newton method, it greatly reduces the calculation time and hardware performance requirements.

[0058] 2) The Newton conjugate gradient method runs through a nested loop structure. The outer loop iteration is based on the Newton method, that is, linearizing the discrete nonlinear Schrödinger equation and then continuously updating the solution by solving the linear inhomogeneous equation. Since the nonlinear Schrödinger equation is discrete, the linearization operator includes a discrete translation operator. In the inner iteration, different from the Newton method that directly solves the linear operator equation, the Newton conjugate gradient operator uses conjugate gradient iteration to solve. Since the linearization operator is a self-adjoint operator, the conjugate gradient iteration is always convergent. This algorithm greatly speeds up the equation-solving speed. When dealing with the discrete nonlinear Schrödinger equation with complex coupling coefficients or complex solutions, there is no need to separate the real and imaginary parts of the equation, which greatly simplifies the theoretical derivation, reduces the calculation cost, and the demand for high-performance hardware. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can also be obtained based on these drawings without creative efforts.

[0060] Figure 1 Schematic diagram of the method flow of the present invention;

[0061] Figure 2 Schematic diagram of the process of the embodiment of the present invention;

[0062] Figure 3 Calculation result diagram of Embodiment 1 of the present invention; where, a is the amplitude and phase diagram of the fundamental soliton; b is the relationship diagram between the error and the calculation time;

[0063] Figure 4 Calculation result diagram of Embodiment 2 of the present invention; where, a is the amplitude and phase of the vortex soliton; b is the relationship between the error and the calculation time;

[0064] Figure 5 Schematic diagram of the photon Chern insulator based on the Haldane model of the present invention;

[0065] Figure 6 Calculation result diagram of Embodiment 3 of the present invention; where a is the amplitude of the bulk soliton component ψ 1 ; b is the amplitude of the bulk soliton component ψ 2 ; c is the phase of the bulk soliton component ψ 1 ; d is the phase of the bulk soliton component ψ 2 ; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0066] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some but not all of the embodiments of the present invention. Components of the embodiments of the present invention usually described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations.

[0067] Therefore, the detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0068] It should be noted that like reference numerals and letters denote like items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0069] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper", "lower", "horizontal", "inner", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, or the orientations or positional relationships in which the inventive product is customarily placed during use, it is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. In addition, terms such as "first", "second", etc. are only used for descriptive distinction and should not be construed as indicating or implying relative importance.

[0070] In addition, if the term "horizontal" appears, it does not mean that the component is required to be absolutely horizontal, but it can be slightly inclined. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but it can be slightly inclined.

[0071] In the description of the embodiments of the present invention, it should also be noted that unless otherwise clearly specified and limited, if terms such as "set", "installed", "connected", "connected" are understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0072] The following further describes the present invention in detail with reference to the accompanying drawings:

[0073] SeeFigure 1 , in view of the problems of the prior art, the present invention proposes a method for determining discrete nonlinear optical lattice modes based on the Newton conjugate gradient method, aiming to accurately obtain discrete nonlinear optical lattice modes and provide clear steps and a standardized process for obtaining photon crystal modes in engineering applications. This method clearly defines each link for obtaining nonlinear photonic crystal modes, avoiding the directional ambiguity and resource waste that occur in the process of photonic crystal research. The method includes:

[0074] S1: Obtain the basic parameters of the discrete nonlinear optical lattice, and construct a discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice;

[0075] S2: Solve the nonlinear Schrödinger equation using the Newton conjugate gradient method to obtain a steady-state solution; the calculation framework of the Newton conjugate gradient method includes an external Newton iteration method and an internal conjugate gradient iteration method;

[0076] S3: Determine whether the steady-state solution meets a predefined accuracy. If it meets the requirement, output the result. If it does not meet the requirement, iteratively update the steady-state solution based on the Newton conjugate gradient method until the steady-state solution meets the predefined accuracy, and then output the result to obtain the discrete nonlinear optical lattice mode.

[0077] This method first provides a basis for subsequent analysis by determining the type and structure of the photonic crystal, and obtains the key parameters of the photonic crystal, mainly including the lattice constant, basis vectors, nonlinear characteristics, etc. Based on these parameters, a tight-binding model is then established for the photonic crystal, and the discrete nonlinear Schrödinger equation is used to describe the propagation behavior of light in the photonic crystal. This model can effectively obtain the propagation mode of the photonic crystal through numerical solution. During the calculation process, the present invention innovatively proposes a new numerical solution method, which significantly accelerates the speed of mode solution. Through this method, the engineering community can efficiently obtain the working mode of the nonlinear photonic crystal in a short time, providing strong support for fields such as optical communication, optical device design and optimization.

[0078] This numerical solution method is run through a nested loop structure by introducing the Newton conjugate gradient method into the numerical solution algorithm of the Schrödinger equation. The outer loop iteration is based on Newton's method, that is, the discrete nonlinear Schrödinger equation is linearized, and then the solution is continuously updated by solving the linear inhomogeneous equation. Since the nonlinear Schrödinger equation is discrete, the linearization operator includes a discrete translation operator. In the inner iteration, different from Newton's method that directly solves the linear operator equation, the Newton conjugate gradient operator uses conjugate gradient iteration to solve. Since the linearization operator is a self-adjoint operator, the conjugate gradient iteration is always convergent. This algorithm greatly speeds up the equation solving speed. At the same time, this method does not need to separate the real and imaginary parts of the equation when dealing with the discrete nonlinear Schrödinger equation with complex coupling coefficients or complex solutions, effectively reducing the size of the matrix required for calculation and simplifying the derivation process, thereby reducing the calculation cost and the demand for high-performance computing resources.

[0079] In some embodiments, referring to Figure 2 , the present invention proposes a method for determining the discrete nonlinear optical lattice mode based on the Newton conjugate gradient method for a discrete nonlinear optical lattice. This method first needs to determine the type and structure of the lattice to be studied, and then obtain the basic parameters of the discrete nonlinear optical lattice, including basic parameters such as lattice constant, basis vector, and nonlinear characteristics. Then, a discrete nonlinear Schrödinger equation describing the discrete nonlinear optical lattice is formed; specifically, it includes the following steps:

[0080] 1) Determine the crystal dimension and symmetry

[0081] First, it should be pointed out that the main research object of this application is a nonlinear photonic crystal. For specific engineering requirements, we need to select the dimension and symmetry of the photonic crystal. Generally, photonic crystals can be divided into one-dimensional photonic crystals, two-dimensional photonic crystals, and three-dimensional photonic crystals according to the dimension. Among them, one-dimensional photonic crystals are suitable for simple optical device and waveguide designs, and have a periodic structure along one direction, and their geometric parameters are determined by the lattice constant a; two-dimensional photonic crystals are more common than one-dimensional photonic crystals and are widely used in the design of photonic bandgap materials, such as honeycomb lattices, Kagome photonic crystals, etc. They have periodicity in the plane and are usually described by two basis vectors ; three-dimensional photonic crystals: used for more complex optical control, capable of adjusting the propagation of light in three-dimensional space. Common ones include cubic lattices (FCC), diamond lattices, etc., and three basis vectors are required to describe the three-dimensional structure of the crystal.

[0082] 2) Based on the crystal dimension of the nonlinear photonic crystal, determine the geometric parameters of the corresponding lattice

[0083] After determining the type of the photonic crystal, it is necessary to further determine the geometric parameters of the lattice. The basic geometric parameters include the lattice constant, basis vectors, etc. As mentioned above, these parameters can determine the basic structure and optical properties of the crystal. The lattice constant is the distance between adjacent atoms, molecules or unit nodes in the lattice. Generally, there are three methods to determine the geometric parameters of the lattice, namely experimental measurement, first-principles calculation, and for known materials, they can be obtained by referring to the literature. For experimental measurement, currently, the method of X-ray diffraction is mainly adopted to measure the lattice constant and basis vectors by calculating the angles of the diffraction patterns; for first-principles calculation, it mainly uses quantum mechanical calculation methods such as density functional theory to predict the lattice constant of materials, especially for complex materials or theoretical research, this method is more commonly used; for common known materials such as silicon, gallium nitride, graphene, etc., the lattice geometric parameters given in the literature can be referred to.

[0084] 3) Determine the nonlinear characteristics of the photonic crystal

[0085] For photonic crystals, the nonlinear characteristics are one of their important characteristics, mainly including Kerr nonlinearity, saturation nonlinearity, etc. In order to model the crystal, several key parameters of the nonlinear characteristics need to be determined, among which: the nonlinear refractive index n 2 is used to describe the change in the refractive index of the material under strong light illumination. Usually, photonic crystals adjust this parameter to enhance or suppress the propagation of light; the nonlinear coupling effect refers to the nonlinear interaction between optical fields. These nonlinear effects can adjust the propagation speed of light, modulate the bandgap width and generate new optical frequencies.

[0086] After obtaining the above parameters, a tight-binding model of the photonic crystal is established, and the discrete nonlinear Schrödinger equation is used to describe the propagation of light in the photonic crystal. By solving this equation, the basic physical information of the model can be obtained, including the propagation behavior of light, soliton modes, photonic bandgaps, etc. Since the analytical solution of the equation is usually not available, especially in the case of complex structures and nonlinear effects, numerical solution methods need to be used to solve the discrete nonlinear Schrödinger equation. The calculation framework of the numerical solution method used in the present invention mainly includes two parts, namely the external Newton iteration and the internal conjugate gradient iteration.

[0087] In some embodiments, the steady-state solution is obtained by using the Newton conjugate gradient method to solve the nonlinear Schrödinger equation, specifically including:

[0088] S201: Use the Newton iteration method to expand the steady-state solution equation L 0 u (m+1) = 0 of the discrete nonlinear Schrödinger equation around the approximate solution u (m) and ignore the high-order terms to obtain the linearized equation:

[0089] L 0 u (m) +L 1 (u (m+1) -u (m) )=0,

[0090] The above equation is rewritten as

[0091] L 1 Δu (m) =-L 0 u (m)

[0092] u (m+1) =u (m) +Δu (m)

[0093] S202: Solve the linearized equation using the conjugate gradient iteration method to obtain Δu (m) ;

[0094] S203: Update the approximate solution u (m) according to Δu (m) to obtain the steady-state solution u (m+1) ;

[0095] where u (m+1) represents the steady-state solution of a complex vector containing real and imaginary parts; L 0 represents an operator; L 1 is the linearized operator; u (m) represents the approximate solution of u (m+1) ; Δu (m) is the update amount of the solution from the m-th iteration to the (m + 1)-th iteration.

[0096] In some embodiments, S202 specifically includes:

[0097] S2021: Initialize the initial guess solution and its error of the conjugate gradient iteration method:

[0098] Δu (m,0) =0

[0099] R (m,0) =-L 0 u (m)

[0100] D (m,0) =M -1 R (m,0)

[0101] where R (m,0) is the error of the initial guess solution, and M -1 is the inverse of a user-defined preconditioning operator for accelerating convergence;

[0102] S2022: Iteratively solve for Δu using the following formula (m) , until the stopping criterion of the conjugate gradient iteration method is satisfied:

[0103]

[0104] Δu (m,i+1) = Δu (m,i) + a (m,i) D (m,i) ,

[0105] R (m,i+1) = R (m,i) - a (m,i) L 1 D (m,i) ,

[0106]

[0107] D (m,i+1) = M -1 R (m,i+1) + b (m,i+1) D (m,i) ,

[0108] where the superscript (m,i) represents the i-th iteration of the conjugate gradient method for calculating Δu (m) .

[0109] In some embodiments, the stopping criterion of the conjugate gradient iteration method is:

[0110] ‖R (m,i) ‖ M < ε cg ‖R (m,0) ‖ M ,

[0111] where ‖R (m,i) ‖ M is the error of the solution Δu (m,i) ; ‖R (m,0) ‖ M is the 2-norm of the initial error, and ε cg is a positive tolerance parameter.

[0112] In some embodiments, determining whether the steady-state solution meets the predefined accuracy is specifically:

[0113] When the difference between the maximum value of the steady-state solution equation or the maximum value between two adjacent iterations is less than the predefined solution error limit, the corresponding steady-state solution meets the predefined accuracy.

[0114] In some embodiments, the present solution uses the Newton conjugate gradient method to solve the nonlinear Schrödinger equation to obtain a steady-state solution; by introducing the Newton conjugate gradient method into the algorithm, it is run through a nested loop structure. The outer loop iteration is based on Newton's method, that is, the discrete nonlinear Schrödinger equation is linearized, and then the solution is continuously updated by solving the linear inhomogeneous equation. Since the nonlinear Schrödinger equation is discrete, the linearized operator includes a discrete translation operator. In the inner iteration, different from Newton's method that directly solves the linear operator equation, the Newton conjugate gradient operator uses conjugate gradient iteration to solve. Since the linearized operator is a self-adjoint operator, the conjugate gradient iteration is always convergent. This algorithm greatly speeds up the equation-solving speed. At the same time, this method does not need to separate the real part and the imaginary part of the equation when dealing with the discrete nonlinear Schrödinger equation with complex coupling coefficients or complex solutions, effectively reducing the size of the matrix required for calculation and simplifying the derivation process, thereby reducing the calculation cost and the demand for high-performance computing resources. The main content of the algorithm is as follows. The stationary solution of the discrete nonlinear Schrödinger equation usually satisfies an equation of the following form:

[0115] L 0 u = 0, (1)

[0116] where u represents a complex vector solution containing a real part and an imaginary part, and L 0 represents an operator. Here, the following two-dimensional discrete nonlinear Schrödinger equation is taken as an example,

[0117]

[0118] where n represents the discrete nodes in the two-dimensional lattice, that is, there are ε is the coupling coefficient between lattice nodes, and g is the Kerr nonlinear coefficient. Δ 2 is the discrete two-dimensional Laplace operator:

[0119]

[0120] where is the discrete translation operator along the unit vector ±e 1,2 . Search for a steady-state solution of the following form:

[0121] U n = u n e i(μ-4ε)t , (4)

[0122] where u n is the complex solution and μ is the frequency. Substitute the steady-state solution into the discrete nonlinear Schrödinger equation to obtain that u n satisfies an equation of the following form:

[0123]

[0124] Comparing with the general form in Equation (1), it can be seen that the operator corresponding to the solution at the nth node in the two-dimensional discrete nonlinear Schrödinger equation is:

[0125]

[0126] It should be noted here that the frequency of the nonlinear state is incorporated into the operator L 0 , and L 0 depends on the solution u n . To obtain the steady-state solution of the discrete nonlinear Schrödinger equation, the iterative method is used to solve Equation (1). Similar to the Newton method, it is assumed here that the solution u (m+1) after m + 1 iterations satisfies the predefined accuracy, that is, the error of the obtained solution is less than the criterion for stopping the loop. Expand the equation L 0 u (m+1) = 0 around the approximate solution u (m) , and ignore the high-order terms to obtain the following equation:

[0127] L 0 u (m) +L 1 (u (m+1) -u (m) ) = 0, (7)

[0128] where L 1 is the linearized operator. The above equation can be rewritten as

[0129] L 1 Δu (m) =-L 0 u (m) (8)

[0130] u (m+1) =u (m) +Δu (m) (9)

[0131] where Δu (m) is the update amount of the solution from the mth iteration to the m + 1th iteration. To calculate the value of Δu (m) , the conjugate gradient method is used to solve the linear equation. The conjugate gradient method starts from an initial guess, usually Δu (m,0) = 0, and then calculates the following function:

[0132] R (m,0) =-L 0 u (m) (10)

[0133] D (m,0) =M -1 R (m,0) (11)

[0134] where R (m,0)is the error of the initial guess solution, M -1 is the inverse of a user-defined preconditioning operator for accelerating convergence. Solve for Δu (m) The iteration formula for

[0135]

[0136] Δu (m,i+1) = Δu (m,i) + a (m,i) D (m,i) , (13)

[0137] R (m,i+1) = R (m,i) - a (m,i) L 1 D (m,i) , (14)

[0138]

[0139] D (m,i+1) = M -1 R (m,i+1) + b (m,i+1) D (m,i) , (16)

[0140] where the superscript (m,i) represents the i-th iteration of the conjugate gradient method for calculating Δu (m) The inner product in the above formula is defined as

[0141]

[0142] where the superscript * represents the complex conjugate. The error of the solution Δu (m,i) is measured by the M (m,i) weighted 2-norm of R -1 :

[0143] ‖R (m,i) ‖ M = <R (m,i) , M -1 R (m,i) > 1 / 2 , (18)

[0144] The stopping criterion for conjugate gradient iteration is defined as:

[0145] ‖R (m,i) ‖ M < ε cg ‖R (m,0) ‖ M , (19)

[0146] where ||R (m,0) || Mis the 2-norm of the initial error, ε cg is the positive tolerance parameter. An appropriate value of ε cg is important for solving the equation. If ε cg is too small, the computational efficiency decreases; if ε cg is too large, the value of the solution Δu (m) may be inaccurate, which may lead to the divergence of the Newton iteration process. When the stopping criterion is satisfied after several conjugate gradient iterations, the latest value of Δu (m) is used to calculate u (m+1) . When the difference between the maximum value of L 0 u (m+1) or the maximum value between two adjacent iterations is less than the predefined solution error limit, the outer iteration of u (m+1) stops. The flowchart of this algorithm is shown in Figure 2 . It should be noted that to ensure that the linearized operator L 1 is always self-adjoint, the linearized operator can be redefined as where the superscript represents the Hermitian of the vector. This new linearized operator is always self-adjoint. At this time, Equation (8) becomes:

[0147]

[0148] Similarly, conjugate gradient iteration can be used to solve this equation.

[0149] In the algorithm described above, since Equation (1) is applicable to any-dimensional space, this algorithm can be used to identify nonlinear states in high-dimensional systems, such as topological solitons in four-dimensional or even five-dimensional nonlinear topological insulators.

[0150] The algorithm described above is applicable to multi-component nonlinear systems, including topological insulators with different spin states or multiple sublattice nodes.

[0151] In the algorithm described above, since u in the equation is complex, this algorithm can be directly used to solve complex solutions, such as vortex solitons in nonlinear lattices, without separating the real and imaginary parts, reducing the complexity of solving nonlinear equations.

[0152] In the algorithm described above, since the boundary conditions are included in the definition of the translation operator, this method is applicable to lattices with periodic boundaries and open boundary conditions.

[0153] In some embodiments, in the implementation of the present invention, the inverse M of the user-defined preprocessing algorithm for accelerating convergence -1 is taken as 1. In actual engineering, selecting other acceleration matrices according to the actual calculation object also belongs to the scope of the technical solutions proposed by the present invention.

[0154] In some embodiments, the error of solving Δu in the implementation of the present invention (m,i) is measured by the M-weighted 2-norm of R. In actual engineering, selecting other error measurement equations also falls within the scope of the technical solutions proposed by the present invention. (m,i) of M -1 In some embodiments, the stopping criterion for conjugate gradient iteration in the implementation of the present invention is defined as: ‖R

[0155] In some embodiments, the stopping criterion for conjugate gradient iteration in the implementation of the present invention is defined as: ‖R (m,i) ‖ M < ε cg ‖R (m,0) ‖ M where ‖R (m,0) ‖ M is the 2-norm of the initial error, and ε cg is the positive tolerance parameter. In actual engineering, selecting other iteration stopping criteria also falls within the scope of the technical solutions proposed by the present invention.

[0156] The following is a simulation experiment with examples to further illustrate the effect of the present invention.

[0157] 1. Simulation experiment conditions.

[0158] The hardware platform for the simulation experiment of the present invention is a personal computer, and its detailed configuration is: the processor is an Intel Core i9-10980XE CPU, the memory is 256GB, and it runs on MATLAB (R2024b) software. In order to evaluate the performance of the Newton conjugate gradient algorithm, the present invention uses two key indicators: the number of iterations and the solution time.

[0159] 2. Simulation experiment content

[0160] Example 1 Fundamental soliton in a two-dimensional discrete nonlinear optical lattice

[0161] The object of the simulation experiment of the present invention is the fundamental soliton in a two-dimensional discrete nonlinear optical lattice. Consider the following explicit form of the two-dimensional discrete nonlinear Schrödinger equation:

[0162]

[0163] The solution of the fundamental soliton can be written as: where ψ n,m is a positive real number.

[0164] The present invention uses the Newton method and the Newton conjugate gradient method respectively to solve the target equation in the simulation, and finally obtains the fundamental soliton solution in the two-dimensional discrete nonlinear optical lattice. Here, set ε = 1, g = 1, and find the soliton solution corresponding to μ = 5. Let M -1= 1, i.e., no acceleration is used in the conjugate gradient iteration. Consider a computational domain that is a rectangle containing N x × N y discrete lattice nodes, where N x = N y = 60. The error of the solution is represented by the maximum value of the absolute value of L 0 u (m+1) . Set the error limit to 10 -12 . The initial guess solution uses the solution of Equation (21) in the anti - continuous limit and ε = 0, and its guess solution form is as follows:

[0165]

[0166] That is, except for the central position, all other nodes in the computational domain are 0. With the above parameters and the initial guess solution, the fundamental soliton solution is obtained using the Newton conjugate gradient method, as shown in Figure 3 (a).

[0167] Compare the performance of the Newton conjugate gradient method with that of the Newton method. The calculation results are shown in Figure 3 . Figure 3 (a) shows the soliton amplitude distribution obtained by the solution. Under the same solution error limit and parameter values, the soliton amplitude distribution obtained by the Newton method is exactly the same as that of the Newton conjugate gradient method. Figure 3 (b) shows the relationship between the solution error and the calculation time of the Newton conjugate gradient method and the Newton method. For a fair comparison, only the number of external Newton iterations of the Newton conjugate gradient method is compared here. As can be seen from the figure, the number of iterations of the two algorithms is comparable, but the Newton conjugate gradient method runs faster than the Newton method. To make the results more intuitive, Table 1 below shows the number of iterations and the time consumption of the two methods, and the data proves the high efficiency of the Newton conjugate gradient method.

[0168] Table 1 Comparison of the two algorithms

[0169] Number of iterations Running time Newton conjugate gradient method 7 0.04 seconds Newton's method 5 6.28 seconds

[0170] Example 2 Vortex Solitons in a Two - Dimensional Discrete Nonlinear Optical Lattice

[0171] The object of the simulation experiment of the present invention is the vortex solitons in a two - dimensional discrete nonlinear optical lattice, and the form of its two - dimensional discrete nonlinear Schrödinger equation is the same as Equation (21). Since ψ n,m is a complex value, the vortex soliton solution can be written as ψ n,m = ρe -iφ , where ρ is the real - valued amplitude and φ is the phase.

[0172] In the simulation of the present invention, the Newton method and the Newton conjugate gradient method are respectively used to solve the target equation, and finally the vortex soliton solution in the two-dimensional discrete nonlinear optical lattice is obtained. Here, ε = 0.6, g = 1, and the soliton solution corresponding to μ = 3.4 is searched. Let M -1 = 1, that is, no acceleration is used in the conjugate gradient iteration. Considering that the computational domain is a rectangle containing N x ×N y discrete lattice nodes, where N x = N y = 60. The error of the solution is represented by the maximum value of the absolute value of L 0 u (m+1) . The error limit is set to 10 -8 . The initial guess solution uses the anti-continuous limit, that is, the solution when ε = 0. Specifically, the guessed solution of the vortex soliton has non-zero values at the four central lattice nodes, and there is a phase difference of π / 2 between adjacent nodes in the clockwise direction. Under the above parameters and the initial guess solution, the vortex soliton solution is obtained using the Newton conjugate gradient method. The calculation results are as shown in Figure 4 (a). It can be seen that the vortex soliton presents amplitude peaks at the four central positions, and the phase distribution shows non-zero vorticity.

[0173] The performance of the Newton conjugate gradient method is compared with that of the Newton method. Under the conditions of the same solution error limit and parameter values, the results obtained by the Newton method are exactly the same as those obtained by the Newton conjugate gradient method. Figure 4 (b) shows the relationship between the error and the calculation time of the two algorithms. For fairness, only the number of external Newton iterations of the Newton conjugate gradient method is counted here. As can be seen from the figure, the number of iterations of the two algorithms is quite the same, but the Newton conjugate gradient method runs faster than the Newton method. To make the results more intuitive, the number of iterations and the running time of the two methods are shown in Table 2 below, which proves the high efficiency of the Newton conjugate gradient algorithm.

[0174] Table 2 Comparison of the two algorithms

[0175] Number of iterations Running time Newton conjugate gradient method 5 0.05 seconds Newton's method 4 22 seconds

[0176] Example 3 Bulk Solitons in Photonic Chern Insulators

[0177] The object of the simulation experiment of the present invention is the bulk soliton in the photonic Chern insulator, and the results show that the Newton conjugate gradient method is still effective for solving more complex systems described by the discrete nonlinear Schrödinger equation. As follows Figure 5 Shown is a photonic Chern insulator based on the Haldane model, which is described by a tight-binding Hamiltonian that has real nearest-neighbor hoppings (purple line segments), complex next-nearest-neighbor hoppings (red and blue arrows), and on-site potentials (red and blue circles).

[0178] The wave functions at the sublattice sites A (red circles) and B (blue circles) can be regarded as two pseudo-spins. The length of the nearest-neighbor hopping bond is a 0 , and the lattice period Here, two sets of vectors are defined for the nearest-neighbor hopping and the next-nearest-neighbor hopping respectively and Based on the Hamiltonian of the Haldane lattice, by adding a saturated nonlinear term to the on-site potential, the nonlinear photonic Chern insulator equation is obtained as follows:

[0179]

[0180] where t 1 represents the nearest-neighbor hopping of real numbers in the sublattice, t 2 e ±iφ represents the next-nearest-neighbor hopping of complex numbers, ω A,B represents the on-site potential, characterizes the saturated nonlinearity, including the nonlinear parameter g and the saturation coefficient σ. Compared with the control equations of the fundamental solitons and vortex solitons in the discrete nonlinear optical lattice, the discrete nonlinear Schrödinger equation in the nonlinear photonic Chern insulator has two components ψ A and ψ B , so its calculation is more complex.

[0181] Here, the soliton at the point is solved. This point is a typical high-symmetry point in the Brillouin zone. The form of its soliton solution can be written as: Since φ≠0 in the photonic Chern insulator, the equation is usually complex-valued, and the bulk soliton is in the form of a semi-vortex soliton. Here, ω A = ω B = 10, g = 1, σ = 1, φ = π / 2, and a semi-vortex soliton at ω = 9.1 is searched for. By appropriately setting the initial guess solution, the bulk soliton in the nonlinear photonic Chern insulator is obtained as follows Figure 6 shown:

[0182] As can be seen from the figure, the component ψ 1 has a hump at a non-zero radius, showing non-zero vorticity, and the component ψ 2 monotonically decreases from a finite value to zero along the radial direction, with zero vorticity.

[0183] The present invention also discloses a system for determining the discrete nonlinear optical lattice mode based on the Newton conjugate gradient method, including:

[0184] An acquisition unit, configured to acquire the basic parameters of the discrete nonlinear optical lattice and construct a discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice;

[0185] A solving unit, which is used to solve the nonlinear Schrödinger equation by the Newton conjugate gradient method to obtain a steady-state solution; the calculation framework of the Newton conjugate gradient method includes an external Newton iteration method and an internal conjugate gradient iteration method;

[0186] A judging unit, which is used to judge whether the steady-state solution meets the predefined accuracy. If it meets, the result is output. If it does not meet, the steady-state solution is iteratively updated based on the Newton conjugate gradient method until the steady-state solution meets the predefined accuracy, and then the result is output.

[0187] Further preferably, in the solving unit, solving the nonlinear Schrödinger equation by the Newton conjugate gradient method to obtain a steady-state solution specifically includes:

[0188] S201: Using the Newton iteration method to expand the steady-state solution equation \(L\) of the discrete nonlinear Schrödinger equation 0 u (m+1) =0 around the approximate solution \(u\) (m) and ignoring the high-order terms to obtain the linearized equation:

[0189] L 0 u (m) +L 1 (u (m+1) -u (m) ) = 0,

[0190] The above equation is rewritten as

[0191] L 1 Δu (m) =-L 0 u (m)

[0192] u (m+1) =u (m) +Δu (m)

[0193] where \(L\) 1 is the linearized operator, and Δu (m) is the update amount of the solution from the \(m\)th iteration to the \((m + 1)\)th iteration;

[0194] S202: Using the conjugate gradient iteration method to solve the linearized equation to obtain Δu (m) ;

[0195] S203: Updating the approximate solution \(u\) (m) according to Δu (m) to obtain the steady-state solution \(u\) (m+1) .

[0196] The present invention also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for determining a discrete nonlinear optical lattice mode based on the Newton conjugate gradient method as described in any one of the above are implemented.

[0197] The present invention also discloses a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the method for determining a discrete nonlinear optical lattice mode based on the Newton conjugate gradient method as described in any one of the above are implemented.

[0198] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0199] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for realizing the functions specified in Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0200] These computer program instructions can also be stored in a computer-readable memory capable of guiding a computer or other programmable data processing devices to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device realizes the functions specified in Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0201] These computer program instructions can also be loaded onto a computer or other programmable data processing devices, such that a series of operation steps are executed on the computer or other programmable devices to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable devices provide for realizing the functions in the process Figure 1One or more processes and / or boxes Figure 1 Steps of functions specified in one or more boxes.

[0202] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific implementation manners of the present invention, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention.

Claims

1. A method for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method, characterized in that: include: Obtaining basic parameters of the discrete nonlinear optical lattice, and constructing a discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice; The Newton conjugate gradient method is used to solve the nonlinear Schrödinger equation to obtain a steady-state solution; the calculation framework of the Newton conjugate gradient method includes an external Newton iteration method and an internal conjugate gradient iteration method; Determine whether the steady-state solution meets the predefined accuracy. If so, output the result. If not, iteratively update the steady-state solution based on the Newton conjugate gradient method until the steady-state solution meets the predefined accuracy, output the result, and obtain a discrete nonlinear optical lattice pattern.

2. The method for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method according to claim 1, characterized in that: The obtaining of basic parameters of the discrete nonlinear optical lattice and constructing the discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice specifically includes: S101: Crystal dimensions, symmetry and nonlinear properties of nonlinear photonic crystals; S102: determining geometric parameters of a corresponding lattice based on the crystal dimensions of the nonlinear photonic crystal; S103: A tight binding model is established for the photonic crystal according to the symmetry and nonlinear characteristics of the nonlinear photonic crystal and the geometric parameters of the corresponding lattice, and a discrete nonlinear Schrödinger equation is obtained.

3. The method for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method according to claim 1, characterized in that: The Newton conjugate gradient method is used to solve the nonlinear Schrödinger equation to obtain a steady-state solution, which specifically includes: S201: Newton iteration method is used to solve the steady-state solution of the discrete nonlinear Schrödinger equation L0u (m+1) = 0 in the approximate solution u (m) Expanding around and ignoring higher-order terms, we get the linearized equation: L0u (m) +L1(in (m+1) -in (m) )=0, The above formula can be rewritten as L1Δu (m) =-L0u (m) u (m+1) =u (m) +Δu (m) S202: Solve the linearized equation using the conjugate gradient iteration method to obtain Δu (m) ; S203: According to Δu (m) Update the approximate solution u (m) Get the steady-state solution u (m+1) ; Among them, u (m+1) represents the steady-state solution of a complex vector containing real and imaginary parts; L0 represents the operator; L1 is the linearization operator; u (m) Indicates u (m+1) The approximate solution of Δu (m) It is the update amount of the solution from the mth iteration to the m+1th iteration.

4. The method for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method according to claim 3, characterized in that: The S202 specifically includes: S2021: Initialize the initial guess solution and its error of the conjugate gradient iteration method: Δu (m,0) =0 R (m,0) =-L0u (m) D (m,0) =M -1 R (m,0) S2022: Use the following formula to iteratively solve Δu (m) , until the stopping criterion of the conjugate gradient iteration method is met: Thu (m,i+1) =Δu (m,i) +a (m,i) D (m,i) , R (m,i+1) =R (m,i) -a (m,i) L1D (m,i) , D (m,i+1) =M -1 R (m,i+1) +b (m,i+1) D (m,i) , Among them, Δu (m,0) represents the update amount of the initial guess solution; R (m,0) is the error of the initial guess solution; L0 represents the operator; L1 is the linearization operator; M -1 is the inverse of a custom preprocessing operator used to accelerate convergence; D (m,0) represents the initial iteration parameter; a (m,i) represents the i-th iteration coefficient; b (m,i+1) Indicates the i+1th iteration coefficient; the superscript (m,i) indicates the coefficient used to calculate Δu (m) The i-th iteration of the conjugate gradient method.

5. The method for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method according to claim 4, characterized in that: The stopping criterion of the conjugate gradient iteration method is: ||R (m,i) || M <e cg ||R (m,0) || M , Among them, ||R (m,i) || M is the solution Δu (m,i) The error of ‖R (m,0) ‖ M is the 2-norm of the initial error, ε cg is the positive tolerance parameter.

6. The method for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method according to claim 1, characterized in that: The determining whether the steady-state solution satisfies the predefined accuracy is specifically as follows: When the maximum value of the steady-state solution equation or the difference between its maximum values ​​in two adjacent iterations is less than the predefined solution error limit, the corresponding steady-state solution meets the predefined accuracy.

7. A system for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method, characterized in that: include: An acquisition unit, used for acquiring basic parameters of the discrete nonlinear optical lattice, and constructing a discrete nonlinear Schrödinger equation based on the basic parameters of the discrete nonlinear optical lattice; A solution unit, used for solving the nonlinear Schrödinger equation by using Newton conjugate gradient method to obtain a steady-state solution; the calculation framework of the Newton conjugate gradient method includes an external Newton iteration method and an internal conjugate gradient iteration method; The judging unit is used to judge whether the steady-state solution satisfies the predefined accuracy. If so, the result is outputted. If not, the steady-state solution is iteratively updated based on the Newton conjugate gradient method until the steady-state solution satisfies the predefined accuracy, and the result is outputted.

8. The system for determining discrete nonlinear optical lattice modes based on Newton conjugate gradient method according to claim 7, characterized in that: In the solving unit, the Newton conjugate gradient method is used to solve the nonlinear Schrödinger equation to obtain a steady-state solution, which specifically includes: S201: Newton iteration method is used to solve the steady-state solution of the discrete nonlinear Schrödinger equation L0u (m+1) = 0 in the approximate solution u (m) Expanding around and ignoring higher-order terms, we get the linearized equation: L0u (m) +L1(in (m+1) -in (m) )=0, The above formula can be rewritten as L1Δu (m) =-L0u (m) u (m+1) =u (m) +Δu (m) Where L1 is the linearization operator, Δu (m) is the update amount of the solution from the mth iteration to the m+1th iteration; S202: Solve the linearized equation using the conjugate gradient iteration method to obtain Δu (m) ; S203: According to Δu (m) Update the approximate solution u (m) Get the steady-state solution u (m+1) .

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for determining discrete nonlinear optical lattice patterns based on Newton's conjugate gradient method as described in any one of claims 1 to 6 when executing the computer program.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for determining discrete nonlinear optical lattice modes based on the Newton conjugate gradient method as described in any one of claims 1 to 6.

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