Multilayer slab waveguide mode processing method, device, equipment, medium and program

Abstract

The invention relates to the technical field of electromagnetism, in particular to a multi-layer slab waveguide mode processing method, device, equipment, medium and program, and the method comprises the steps: constructing a transfer matrix model of a multi-layer slab waveguide; obtaining boundary conditions of the infinite space, and determining a corresponding real number domain characteristic equation and a complex number domain characteristic equation according to the transfer matrix model and the boundary conditions so as to determine a guided mode and a leakage mode of the multilayer slab waveguide in the infinite space; introducing a perfect matching layer to convert a radiation condition of an infinite space into an absorption boundary in a finite computational domain, constructing a finite space characteristic equation according to the thicknesses of the perfect matching layer and the absorption boundary, and positioning a plurality of correction leakage modes according to the finite space characteristic equation to generate a Bereger mode; and generating complete mode distribution according to the guided mode, the leakage mode and the Bereger mode. Therefore, the problems of relatively poor calculation precision, relatively slow calculation speed, limitation of complete mode solving in the multilayer slab waveguide and the like in related technologies are solved.

Description

Technical Field

[0001] This application relates to the technical field of electromagnetics, and particularly to a method, apparatus, device, medium, and program for processing multi-layer planar waveguide modes. Background Technique

[0002] The theory of optical waveguide modes is the basic work for studying optical waveguides, mainly focusing on studying the propagation modes and characteristics of light in waveguide structures. A waveguide structure refers to a dielectric layer or optical fiber that can confine and guide the propagation of light waves. According to Maxwell's equations and the theory of wave optics, the theory of optical waveguide modes can be described as the relationship between the electromagnetic field distribution and propagation constant of light waves propagating in a waveguide structure. Here, the so-called modes are actually the roots of the Helmholtz equation, which is a generalized form of solving Maxwell's equations, to describe the allowed light wave propagation states in the waveguide. In the field of optics, a multi-layer planar waveguide is usually composed of a high-refractive-index slab sandwiched between two or more low-refractive-index slabs, forming a step-type waveguide structure.

[0003] In related technologies, the analytical method can solve leakage modes, but it is limited to finite structures, and the derivation process is quite complicated. To overcome these problems, numerical methods are widely used. For example, by introducing a perfectly matched layer or ideal electric conductor boundary conditions, the effect of an infinite space can be simulated in a finite space. However, this method requires calculating complete roots in the complex domain, increasing the computational difficulty. As an effective analytical method, the transfer matrix method has been used to analyze waveguide modes by establishing a basis matrix using the continuity conditions of the electric and magnetic fields. Nevertheless, the existing methods still have deficiencies in terms of accuracy, computational speed, and solving the problem of complete mode solutions in multi-layer planar waveguides. Summary of the Invention

[0004] This application provides a method, apparatus, device, medium, and program for processing multi-layer planar waveguide modes to solve problems such as poor computational accuracy, slow computational speed, and limitations in solving complete modes in multi-layer planar waveguides in related technologies.

[0005] The first aspect of the present application provides a method for processing multi-layer planar waveguide modes, including the following steps: identifying the propagation characteristics and field distributions of light waves in each layer of the multi-layer planar waveguide, and constructing a transfer matrix model of the multi-layer planar waveguide according to the propagation characteristics and the field distributions; obtaining the boundary conditions of the infinite space, determining the corresponding real-domain characteristic equation and complex-domain characteristic equation according to the transfer matrix model and the boundary conditions, and determining the guided modes and leakage modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation; introducing a perfectly matched layer to transform the radiation condition of the infinite space into an absorbing boundary in the finite computational domain, constructing a finite-space characteristic equation according to the thickness of the perfectly matched layer and the absorbing boundary, so as to locate the complex roots according to the finite-space characteristic equation to correct the leakage modes to generate Berenger modes; generating a complete mode distribution according to the guided modes and leakage modes of the infinite space and the Berenger modes of the perfectly matched layer in the finite space.

[0006] Optionally, the transfer matrix model of the multi-layer planar waveguide is composed of multiple single-layer transfer matrices, and the formula is as follows:

[0007] M = M1·M2……M j ;

[0008] Among them, the formula for the transfer matrix of the j-th layer waveguide is as follows:

[0009]

[0010] Among them, λ is the wavelength, n j represents the refractive index of the j-th layer of the planar waveguide, β is the propagation constant, h j represents the thickness of the j-th layer of the planar waveguide.

[0011] Optionally, the determining the guided modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation includes: traversing all real refractive indices; inputting each real refractive index into the real-domain characteristic equation to calculate the corresponding characteristic equation value; identifying the root at the position of the sign change of the characteristic equation value as the initial value of the characteristic equation for iterative solution; using the bisection method and the secant method to iteratively solve the initial value of the characteristic equation until the convergence condition is satisfied, then determining the guided modes of the multi-layer planar waveguide in the infinite space.

[0012] Optionally, determining the leaky modes of the multi-layer planar waveguide in infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation includes: calculating three groups of corresponding initial effective refractive index distributions of the leaky modes by the second, third, and fourth-order asymptotic methods; identifying the difference between the maximum and minimum absolute values of the initial effective refractive index of the three groups of leaky modes; extracting the complex values of the effective refractive index that do not meet the target accuracy condition to determine the solution range of the target algorithm, and using the target algorithm to solve the corresponding initial values; combining the initial values solved by the target algorithm and the complex values of the effective refractive index that meet the target accuracy condition; calculating the corresponding characteristic equation values according to the complex values of the effective refractive index and inputting them into the complex-domain characteristic equation, so as to iteratively solve the leaky modes according to the difference between the maximum and minimum values and the characteristic equation values.

[0013] Optionally, the calculation formula of the target algorithm is:

[0014]

[0015] where N z is the number of zeros in the current solution range, M represents the number of sampling points on each side, i is the i-th sampling point, f() represents the function value at this point, arg represents taking the argument, and Φ t represents the total phase accumulation.

[0016] Optionally, the calculation formula for introducing a perfectly matched layer to transform the radiation condition of infinite space into an absorbing boundary in a finite computational domain is:

[0017]

[0018]

[0019] where ρ R , ρ L is the thickness of the equivalent perfectly matched layer, d L , d R represent the thicknesses of the left and right perfectly matched layers respectively, h L , h R is the boundary wave thickness, i is the imaginary unit is the stretching factor, τ is the integration variable, κ L is n L is the refractive index of the left-end waveguide, λ is the wavelength, β is the propagation constant, M equal is M j is the transfer matrix of the j-th layer, κ R is n R is the refractive index of the right-end waveguide.

[0020] The second aspect of the present application provides a processing device for a multi-layer planar waveguide mode, including: an identification module, configured to identify the propagation characteristics and field distribution of light waves in each layer of the multi-layer planar waveguide, and construct a transfer matrix model of the multi-layer planar waveguide according to the propagation characteristics and the field distribution; an acquisition module, configured to acquire the boundary conditions of the infinite space, determine the corresponding real-domain characteristic equation and complex-domain characteristic equation according to the transfer matrix model and the boundary conditions, and determine the guided modes and leaky modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation; an introduction module, configured to introduce a perfectly matched layer to convert the radiation condition of the infinite space into an absorbing boundary in the finite computational domain, and construct a finite-space characteristic equation according to the thickness of the perfectly matched layer and the absorbing boundary, so as to locate the complex roots according to the finite-space characteristic equation to correct the leaky modes to generate Berenger modes; a generation module, configured to generate a complete mode distribution according to the guided modes and leaky modes of the infinite space and the Berenger modes of the perfectly matched layer in the finite space.

[0021] The third aspect of the present application provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the program to perform the processing method of the multi-layer planar waveguide mode as described in the above embodiments.

[0022] The fourth aspect of the present application provides a computer-readable storage medium, on which a computer program is stored, and the program is executed by a processor to perform the processing method of the multi-layer planar waveguide mode as described in the above embodiments.

[0023] The fifth aspect of the present application provides a computer program product, including a computer program or instruction, and when the computer program or instruction is executed, it realizes the processing method of the multi-layer planar waveguide mode as described in the above embodiments.

[0024] Therefore, the present application has at least the following beneficial effects:

[0025] The embodiments of the present application can use the transfer matrix method to establish a unified mathematical model for the one-dimensional multi-layer planar waveguide problem, making it compatible with the PML (Perfectly Matched Layer) boundary problem, and proving that this method can be conveniently compatible with any different boundary conditions, so as to complete the calculation of guided modes, leaky modes, and Berenger modes by modifying some boundary conditions. For the calculation of guided modes, the real transfer matrix method is used to establish a characteristic equation in the real number domain to avoid finding the roots of the equation in the complex number domain; for the difficult calculation of PML modes, the root search speed of the algorithm is accelerated by a reasonable initial root solving order and by constraining the solution range through the main axis prediction technique; and the DFZEPE (Derivative-free Zero Extraction By Phase-based Enclosure) algorithm is improved by adopting dynamic sampling calculation and boundary reuse technology to improve the calculation speed. The overall algorithm far exceeds the native DFZEPE complex number domain solver in terms of speed, and at the same time solves the problem of setting the complex number domain solution range boundary of the one-dimensional multi-layer planar waveguide, and gives a complete high-speed solution scheme for the complete mode root solution of the multi-layer planar waveguide.

[0026] Additional aspects and advantages of the present application will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The above and / or additional aspects and advantages of the present application will become apparent and be readily understood from the following description of the embodiments in conjunction with the drawings, where:

[0028] Figure 1 is a flowchart of a method for processing multi-layer planar waveguide modes according to an embodiment of the present application;

[0029] Figure 2 is a brief flowchart of a fast one-dimensional multi-layer planar waveguide mode solver according to an embodiment of the present application;

[0030] Figure 3 is a schematic diagram of a one-dimensional multi-layer planar waveguide model according to an embodiment of the present application;

[0031] Figure 4 is an argument quadrant mapping diagram of a complex number domain nonlinear equation according to an embodiment of the present application;

[0032] Figure 5 is a brief flowchart of the improved DFZEPE according to an embodiment of the present application;

[0033] Figure 6 is an edge reuse diagram according to an embodiment of the present application;

[0034] Figure 7 Schematic diagram of uniform dynamic sampling provided according to an embodiment of the present application;

[0035] Figure 8 Schematic diagram of the mode distribution of a four-layer planar waveguide provided according to an embodiment of the present application;

[0036] Figure 9 Schematic diagram of the root locus prediction of a three-layer planar waveguide provided according to an embodiment of the present application;

[0037] Figure 10 Schematic diagram of arbitrary boundary search and subdomain merging provided according to an embodiment of the present application;

[0038] Figure 11 Schematic diagram of the leakage mode root distribution of the asymptotic method and the improved DEPEZE for solving a five-layer planar waveguide provided according to an embodiment of the present application;

[0039] Figure 12 Schematic diagram of the comparison of the solution speeds of three methods provided according to an embodiment of the present application;

[0040] Figure 13 Example diagram of a processing device for the mode of a multi-layer planar waveguide provided according to an embodiment of the present application;

[0041] Figure 14 Schematic diagram of the structure of an electronic device provided according to an embodiment of the present application. Detailed implementation manners

[0042] The embodiments of the present application will be described in detail below. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application, and should not be construed as a limitation of the present application.

[0043] The following describes a method, device, vehicle, storage medium, and program for processing the mode of a multi-layer planar waveguide according to an embodiment of the present application with reference to the drawings.

[0044] Specifically, Figure 1 Schematic flowchart of a method for processing the mode of a multi-layer planar waveguide provided according to an embodiment of the present application.

[0045] As Figure 1 shown, the method for processing the mode of the multi-layer planar waveguide includes the following steps:

[0046] In step S101, identify the propagation characteristics and field distribution of light waves in each layer of the multi-layer planar waveguide, and construct a transfer matrix model of the multi-layer planar waveguide according to the propagation characteristics and field distribution.

[0047] Among them, the transfer matrix model of the multi-layer planar waveguide is composed of multiple single-layer transfer matrices, and the formula is as follows:

[0048] M = M1·M2……M j ;

[0049] Among them, the formula for the transfer matrix of the j-th layer waveguide is as follows:

[0050]

[0051] Among them, λ is the wavelength, n j represents the refractive index of the j-th layer of planar waveguide, β is the propagation constant, and h j represents the thickness of the j-th layer of planar waveguide.

[0052] It can be understood that by identifying the propagation characteristics and field distribution of light waves in each layer of the multi-layer planar waveguide and constructing a transfer matrix model accordingly, the embodiments of the present application can not only significantly improve the analysis accuracy, but also greatly improve the calculation efficiency, and at the same time enhance the adaptability to different types of waveguide structures and boundary conditions.

[0053] Specifically, the conceptual diagram of the multi-layer planar waveguide structure is as Figure 3 shown, and each matrix represents a different refractive index n j , and its structural width is h j , j ∈ L, R, 1, 2... l-2, and l represents that the waveguide has l layers of structure.

[0054] First, establish a mathematical calculation model according to the transfer matrix formula:

[0055]

[0056] Among them, i is the imaginary unit M j represents the transfer matrix of the j-th layer; This formula indicates that any one-dimensional multi-layer planar waveguide can be equivalent to a one-dimensional three-layer planar waveguide, and its characteristic equation is described by the left boundary condition × equivalent transfer matrix × right boundary situation. β is the propagation constant (it is agreed that the propagation constant β is in the first quadrant, with a positive real part and an imaginary part), and the wave number λ is the wavelength.

[0057]

[0058] Among them, h j represents the thickness of the j-th layer of planar waveguide. It can be easily verified that when the propagation constant β is real, in order to satisfy the guided mode condition, all the coefficients in formula (1) are real, so a real characteristic equation can be conveniently established.

[0059] In step S102, obtain the boundary conditions of the infinite space, determine the corresponding real-domain characteristic equation and complex-domain characteristic equation according to the transfer matrix model and the boundary conditions, and determine the guided modes and leaky modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation.

[0060] It can be understood that the embodiments of the present application can determine the guided modes and leaky modes by obtaining the boundary conditions of the infinite space and establishing the characteristic equation accordingly, which can not only significantly improve the accuracy of mode solution, but also enhance the calculation efficiency and support the accurate simulation of complex structures.

[0061] In the embodiments of the present application, determining the guided modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation includes: traversing all real refractive indices; inputting each real refractive index into the real-domain characteristic equation to calculate the corresponding characteristic equation value; identifying the root at the position of the sign change of the characteristic equation value as the initial value of the characteristic equation for iterative solution; using the bisection method and the secant method to perform iterative solution of the initial value of the characteristic equation until the convergence condition is met, then determining the guided modes of the multi-layer planar waveguide in the infinite space.

[0062] It can be understood that the embodiments of the present application can perform iterative solution of the characteristic equation by traversing all real refractive indices and combining the bisection method and the secant method, which can not only significantly improve the accuracy and efficiency of guided mode solution, but also enhance the stability and robustness of the entire solution process.

[0063] In the embodiments of the present application, determining the leaky modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation includes: calculating three groups of corresponding initial effective refractive index distributions of the leaky modes by the second, third, and fourth order asymptotic methods; identifying the difference between the maximum and minimum values of the absolute values of the three groups of initial effective refractive indices of the leaky modes; extracting the complex values of the effective refractive indices that do not meet the target accuracy condition to determine the solution range of the target algorithm, and using the target algorithm to solve the corresponding initial values; combining the initial values solved by the target algorithm and the complex values of the effective refractive indices that meet the target accuracy condition; inputting the complex values of the effective refractive indices into the complex-domain characteristic equation to calculate the corresponding characteristic equation value, so as to iteratively solve the leaky modes according to the difference between the maximum and minimum values and the characteristic equation value.

[0064] Among them, the calculation formula of the target algorithm is:

[0065]

[0066] Among them, N z is the number of zeros of the characteristic equation within the solution range, M represents the number of sampling points on each side, i is the i-th sampling point, f() represents the function value at this point, arg represents taking the argument, and Φ t represents the total phase accumulation.

[0067] It can be understood that the embodiments of the present application can calculate the initial effective refractive index distribution of the leaky mode by the second, third, and fourth order asymptotic methods, and combine other steps to finally iteratively solve the leaky mode, which not only improves the accuracy of the initial value selection, but also optimizes the solution range and enhances the efficiency and reliability of the entire solution process.

[0068] It should be noted that the method for calculating the leaky mode in the infinite space and the finite space in the present application is the same, and will be specifically described below.

[0069] In step S103, a perfectly matched layer is introduced to transform the radiation condition in the infinite space into an absorbing boundary in the finite computational domain, and a finite-space characteristic equation is constructed according to the thickness of the perfectly matched layer and the absorbing boundary, so as to locate the complex roots according to the finite-space characteristic equation to correct the leaky mode and generate the Berenger mode.

[0070] Among them, the calculation formula for introducing a perfectly matched layer to transform the radiation condition in the infinite space into an absorbing boundary in the finite computational domain is:

[0071]

[0072] Among them, ρ R , ρ L is the thickness of the equivalent perfectly matched layer, d L , d R represent the thicknesses of the left and right perfectly matched layers respectively, h L , h R is the boundary wave thickness, i is the imaginary unit is the stretching factor, τ is the integration variable, κ L is the wave number λ is the wavelength, n L is the refractive index at the left end of the waveguide, β is the propagation constant, M equal is M j is the transfer matrix of the jth layer, κ R is

[0073] It can be understood that the embodiments of the present application can introduce PML to transform the radiation condition in the infinite space into an absorbing boundary in the finite computational domain, and locate the complex roots based on the finite-space characteristic equation to generate the Berenger mode, which not only realizes the accurate simulation from the infinite space to the finite space, but also significantly improves the solution efficiency and accuracy, and enhances the adaptability to complex waveguide structures.

[0074] Specifically, (1) the asymptotic method is a method that can approximately solve the leaky mode and the Berenger mode when |β| is large enough. The solution method for the leaky mode is given by the following formula (6):

[0075]

[0076] where n1 represents the refractive index of the first non-boundary waveguide, λ is the wavelength, β is the propagation constant, and W m is the value of the LambertW function, i is the imaginary unit δ1 and δ3 are respectively δ2 - δ0, δ0, and δ2 are respectively n L is the refractive index of the left boundary waveguide, and n l-2 is the refractive index of the last non-boundary waveguide, and n R is the refractive index of the right boundary waveguide; a0 is i is the imaginary unit d is h j is the thickness of the j-th waveguide, and l is the total number of slab waveguides; a2 is a3 is a4 is where b4 is

[0077] The higher the order of the asymptotic method, the weaker the approximation and the higher the accuracy. The first, second, third, and fourth order approximations are respectively

[0078]

[0079] The asymptotic solution method for the Berenger mode has an approximate form with equation (6),

[0080]

[0081] where the parameters e0, e2, e3, e4, are respectively expressed as follows:

[0082]

[0083] where, (the parentheses take the negative sign when p = 0, the positive or negative sign when p > 0, p = 0, 1, 2,...), R.

[0084] It should be noted that the parameters in

[0085] (2) The improved DFZEPE method is a method based on the phase-based closed-form derivative-free zero extraction technique, and its core principle is derived from the Cauchy argument principle. As Figure 4 shown, this is the result of taking the argument of the range of the complex-domain nonlinear equation in the real domain [1.25, 1.5] and the complex domain [-0.5, 0.5]. Each color represents a different quadrant. Obviously, if we want to find the zeros of the characteristic equation, we actually need to find the overlapping positions of the four quadrants, that is, the regions of the two black frames in the image. The number of zeros N in the region z can be expressed by the following formula (8):

[0086]

[0087] where M represents the number of sampling points on each side, f() represents the function value at that point, arg represents taking the argument, and Φ t represents the total phase accumulation. The general brief process of this algorithm can be represented by Figure 5 shown.

[0088] Since the number of zeros in the range can be determined by formula (8) each time the root-solving range is delimited, by continuously bisecting the root-solving range, the number of zeros in the sub-region can be recalculated. By continuously refining the possible root region, the initial root that meets the accuracy can be finally obtained. Using the iterative method to solve the initial root, a solution with higher accuracy can be obtained. The edge reuse technology is to not recalculate the entire sub-region within the selected range, but only calculate the phase accumulation of the newly generated edges, as Figure 6 .

[0089] Numbers one to four are the new edges calculated by the bisection method, as Figure 6 shown. The total number of samples calculated is 4M + 4×M. At the same time, considering that the number of samples may not ensure the correct phase accumulation in the region, the method of dynamic sampling estimation is adopted here to ensure the accuracy of the phase accumulation, as Figure 7 shown.

[0090] Each side is augmented with two additional samples, and the phase accumulations calculated at three different sampling rates (such as M, M / 2, M / 4) are compared for each single side. If it cannot be kept constant, the basic sampling rate is increased to 2 times the original, and then the phase accumulations of 2M, M, and M / 2 sampling points are compared. This cycle continues until the calculation is stable. It can be seen that only one more point of the basic sampling rate needs to be calculated for each iteration. The sampling rate increase in powers of 2 is to maintain integer division during the bisection method for better reuse of calculations. Since it is impossible to use the global DFZEPE method in the entire first quadrant, in order to constrain the calculation interval, using the structural properties of the waveguide mode solutions, the asymptotic method is adopted to provide the initial stable imaginary part interval to constrain the extension of the solution along the imaginary number axis.

[0091] As Figure 8As shown, the green line is the stable imaginary interval defined by the asymptotic method with a tolerance of 1e-5. Below the green line, the improved DFZEPE calculation is performed. Only constraining the imaginary part may not guarantee sampling stability. Here, a method with root distribution prediction is used for real number domain partitioning. Figure 9 Show the prediction algorithm for solving the Berenger mode. The red boxes show the improved DFZEPE calculation ranges in each sub-region layer. The red sub-regions closer to the 0 point represent lower layer sub-regions. Root distribution prediction utilizes the monotonicity of the root distribution (i.e., the roots are approximately monotonically increasing along the imaginary axis and the real axis), and is piecewise approximately linearly distributed. Set the initial sub-imaginary solution interval along the imaginary axis, set the real initial solution width, and the attenuation factor to ensure that the search interval has a larger real solution width at low imaginary values and converges to a smaller real search interval on the high imaginary axis.

[0092] After solving for the roots of the current layer sub-region, the real search width of the next layer sub-region updates the starting coordinate x1 and the final coordinate x2 using the following formula (9):

[0093]

[0094] where α is the relaxation factor, and the width of the sub-search real number interval is α×belt new , Center new and belt new are calculated as follows:

[0095]

[0096] P last , P last-1 are respectively the largest and the second largest real roots among the currently searched roots, {P i} are all the searched roots in the current search region, Re() is to take the real part, mean() is to take the average of all the roots, and belt base is the set initial real search width, which is generally relatively large to ensure a larger search space when searching for roots of low-order modes; ω(t) is the coefficient that decays with the call times t, where a is the attenuation coefficient factor, less than 0, controlling the attenuation speed of the overall ω(t); b is the call relaxation factor, the larger b is, the less ω(t) decays as t increases, greater than 0; c is the minimum weight, controlling the minimum attenuation coefficient, which needs to be less than 1 and greater than 0, so t∈(0, +∞), ω(t)∈(0, c).

[0097] And belt old =max(Re({P i}) - min(Re({P i}(}) represents the span range of real numbers in the current search domain; belt min is the defined minimum span range, providing a relaxation range. Since the algorithm needs the distribution of multiple roots for prediction, the height of the sub-region generated by each call will also be adjusted dynamically ( Figure 9 (height of the red box).

[0098] The improved DFZEPE method can also be used to solve the cases with arbitrary boundary conditions, such as Figure 10 As shown, when the given solution region is an arbitrary polygon, it can be automatically divided into sub-solution regions according to the boundary conditions, and an attempt is made to perform optimal sub-domain merging for adjacent search intervals (no constraint in the x direction here). The improved DFZEPE is performed for each merged sub-domain respectively to satisfy any sub-domain division. When the root search sub-range that meets the accuracy is obtained, the upper left coordinate, the lower right coordinate, and the midpoint data of the two are used as the three groups of initial roots for output.

[0099] In step S104, a complete mode distribution is generated based on the guided modes and leaky modes in the infinite space and the Berenger modes of the perfectly matched layer in the finite space.

[0100] It can be understood that the embodiments of the present application can generate a complete mode distribution by combining the guided modes and leaky modes in the infinite space and the Berenger modes generated by the finite space PML. This method not only achieves a comprehensive coverage of all possible modes but also significantly improves the accuracy and applicability of mode analysis.

[0101] According to the method for processing multi-layer planar waveguide modes proposed in the embodiments of the present application, by identifying the propagation characteristics and field distributions of light waves in each layer of the multi-layer planar waveguide and constructing the corresponding transfer matrix model, the propagation characteristics of electromagnetic fields between different dielectric layers can be described more accurately. Using the characteristic equations in the real number domain and the complex number domain, not only the guided modes in the infinite space can be determined, but also the leaky modes can be accurately calculated, improving the solution accuracy for complex modes. By introducing the perfectly matched layer and combining with the characteristic equation of the finite space to calculate the Berenger modes, an efficient and accurate solution for the multi-layer planar waveguide modes is realized, solving the problems of low accuracy and slow calculation speed existing in the prior art.

[0102] Next, it will be combined with Figure 2 to elaborate in detail on the method for processing multi-layer planar waveguide modes of the present application, specifically as follows:

[0103] 1. To solve the guided mode, a suitable step size is selected to traverse the possible real refractive index values (usually within the range of the maximum and minimum refractive indices), and the sign change positions of the characteristic equation are checked. Since the equation is established as a real equation, the sign change detection can quickly detect the existence of zeros. Through the single-step secant method, a rough initial value is determined. After obtaining a reasonable initial value, a combination of the bisection method and the secant method is used to accurately solve the mode, and the solution stops when the solution accuracy is lower than a certain threshold.

[0104] 2. For solving the leaky mode, the leaky mode uses the same characteristic equation as the guided mode. Using the second, third, and fourth-order asymptotic methods, multiple groups of different effective refractive index distributions are calculated. The matrix dimension can be written as [mode_num, 3], indicating that there are mode_num groups of effective refractive index distributions, and each group of effective refractive index distributions consists of three different-order asymptotic methods. Then, calculate the difference between the maximum and minimum absolute values of the different-order asymptotic methods in each group of effective refractive indices to judge the stability of the asymptotic method. Extract the complex modes of the effective refractive indices that do not meet the accuracy conditions and determine the initial solution range of the improved DFZEPE. Within the given solution range, use the improved DFZEPE to find three groups of initial roots. Combine the obtained initial roots with the initial roots of the asymptotic method and use the Muller method to iteratively solve the leaky mode.

[0105] 3. Introduce a perfectly matched layer into the Helmholtz equation and establish a multi-layer transfer matrix and a finite-space domain nonlinear equation. Use the second, third, and fourth-order iterative methods to determine three groups of different effective refractive index distributions of the Berenger mode under the PML condition. Based on the complex domain values of the effective nonlinear refractive indices that do not meet the accuracy conditions extracted in the infinite space (such as Figure 8 the green line), determine the solution range of the improved DFZEPE in the finite space and find the initial solution of the overall Berenger mode. Then, directly use the leaky mode obtained in the infinite space as the initial value, combine the initial solutions obtained above, and use the characteristic equation with PML and the Muller method iterative method to solve all the exact modes under the PML condition.

[0106] 4. Combine all the above solutions to obtain the guided mode, leaky mode defined in the infinite space, and the leaky mode and Berenger mode under the PML constraint.

[0107] In summary, the solution accuracy of this application is compared with that of the asymptotic method and the DFZEPE method respectively. At the same time, the calculation speed of the improved DFZEPE is compared with that of the existing root-solving software package and the original DFZEPE alone. The specific implementation scheme is as follows: For the comparison of solution accuracy, the same PML characteristic equation is used for calculation, and it is compared whether the roots that meet the accuracy in the root-finding interval are complete; for the calculation speed, calculations are carried out in the same computer environment, and the time consumed by the improved DFZEPE technology proposed in this application, the existing root-solving software package and the original DFZEPE method to complete the calculation is compared. The simulation environment is as follows: the CPU is Intel(R) Core(TM) i5-9300H CPU@2.40GHz, the Ram is 16G, and the operating system is Windows10. From Figure 11 It can be seen that the improved DFZEPE method is more complete than the asymptotic method in solving the mode. The missed root situation of the asymptotic method is shown in the black box in the figure, and the root in the lower right corner of the figure is missed. From Figure 12 It can also be seen that, compared with the original DFZEPE and the existing software package GRPF, the technology proposed in this application has the advantage of fast speed.

[0108] Secondly, a processing device for multi-layer planar waveguide modes proposed according to an embodiment of the present application is described with reference to the accompanying drawings.

[0109] Figure 13 It is a block diagram of a processing device for multi-layer planar waveguide modes according to an embodiment of the present application.

[0110] As Figure 13 shown, the processing device 10 for multi-layer planar waveguide modes includes: an identification module 100, an acquisition module 200, an introduction module 300, and a generation module 400.

[0111] Among them, the identification module 100 is used to identify the propagation characteristics and field distribution of light waves in each layer of the multi-layer planar waveguide, and construct a transfer matrix model of the multi-layer planar waveguide according to the propagation characteristics and the field distribution; the acquisition module 200 is used to acquire the boundary conditions of the infinite space, and determine the corresponding real-domain characteristic equation and complex-domain characteristic equation according to the transfer matrix model and the boundary conditions, and determine the guided modes and leaky modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation; the introduction module 300 is used to introduce a perfectly matched layer to convert the radiation condition of the infinite space into an absorbing boundary in the finite calculation domain, and construct a finite-space characteristic equation according to the perfectly matched layer and the thickness of the absorbing boundary, so as to locate the complex roots according to the finite-space characteristic equation and correct the leaky modes to generate Berenger modes; the generation module 400 is used to generate a complete mode distribution according to the guided modes and leaky modes of the infinite space and the Berenger modes of the perfectly matched layer in the finite space.

[0112] It should be noted that the foregoing explanation of the embodiments of the method for processing multi-layer planar waveguide modes also applies to the device for processing multi-layer planar waveguide modes in this embodiment, and will not be elaborated here.

[0113] The device for processing multi-layer planar waveguide modes proposed according to the embodiments of the present application can more accurately describe the propagation characteristics of electromagnetic fields between different dielectric layers by identifying the propagation characteristics and field distributions of light waves in each layer of the multi-layer planar waveguide and constructing a corresponding transfer matrix model. By using the characteristic equations in the real number domain and the complex number domain, not only can the guided modes in infinite space be determined, but also the leaky modes can be accurately calculated, improving the solution accuracy for complex modes. By introducing a perfectly matched layer and combining it with the characteristic equation of the finite space to calculate the Berenger mode, an efficient and accurate solution for multi-layer planar waveguide modes is achieved, solving the problems of low accuracy and slow calculation speed in the prior art.

[0114] Figure 14 The structure diagram of the electronic device provided by the embodiments of the present application. The electronic device may include:

[0115] A memory 1401, a processor 1402, and a computer program stored on the memory 1401 and executable on the processor 1402.

[0116] When the processor 1402 executes the program, it implements the method for processing multi-layer planar waveguide modes provided in the foregoing embodiments.

[0117] Furthermore, the electronic device further includes:

[0118] A communication interface 1403 for communication between the memory 1401 and the processor 1402.

[0119] The memory 1401 is used to store a computer program executable on the processor 1402.

[0120] The memory 1401 may include a high-speed RAM memory, and may also include a non-volatile memory, such as at least one disk memory.

[0121] If the memory 1401, the processor 1402, and the communication interface 1403 are implemented independently, the communication interface 1403, the memory 1401, and the processor 1402 can be interconnected via a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 14 only a thick line is used in Figure 14 , but it does not mean that there is only one bus or one type of bus.

[0122] Optionally, in a specific implementation, if the memory 1401, the processor 1402, and the communication interface 1403 are integrated on a single chip, the memory 1401, the processor 1402, and the communication interface 1403 can communicate with each other through an internal interface.

[0123] The processor 1402 may be a Central Processing Unit (CPU), or an Application Specific Integrated Circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0124] The embodiments of the present application further provide a computer-readable storage medium, on which a computer program or instruction is stored. When the computer program or instruction is executed by a processor, the processing method of the multi-layer planar waveguide mode as described above is implemented.

[0125] The embodiments of the present application further provide a computer program product, including a computer program or instruction. When the computer program or instruction is executed, the processing method of the multi-layer planar waveguide mode as described above is implemented.

[0126] In the description of this specification, the descriptions with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of this application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0127] In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of this application, the meaning of "N" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0128] Any process or method description in a flowchart or described in other ways herein can be understood to represent a module, segment, or part of code including one or N executable instructions for implementing a customized logical function or process, and the scope of the preferred embodiments of this application includes additional implementations, where the functions can be executed in a substantially simultaneous manner or in a reverse order according to the involved functions, rather than in the order shown or discussed, which should be understood by those skilled in the art to which the embodiments of this application belong.

[0129] It should be understood that each part of this application can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one or a combination of the following technologies known in the art: discrete logic circuits with logic gate circuits for implementing logical functions on data signals, application-specific integrated circuits with appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0130] Those of ordinary skill in the art of this technology can understand that all or part of the steps carried by the methods of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiments.

Claims

1. A method for processing a multi-layer planar waveguide mode, characterized in that, It includes the following steps: Identify the propagation characteristics and field distribution of light waves in each layer of the multi-layer planar waveguide, and construct a transfer matrix model of the multi-layer planar waveguide according to the propagation characteristics and the field distribution; Obtain the boundary conditions of the infinite space, determine the corresponding real-domain characteristic equation and complex-domain characteristic equation according to the transfer matrix model and the boundary conditions, and determine the guided modes and leaky modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation; Introduce a perfectly matched layer to transform the radiation condition of the infinite space into an absorbing boundary in the finite computational domain, and construct a finite-space characteristic equation according to the thickness of the perfectly matched layer and the absorbing boundary, so as to locate the complex roots to correct the leaky modes and generate Berenger modes; Generate a complete mode distribution according to the guided modes and leaky modes of the infinite space and the Berenger modes of the perfectly matched layer in the finite space.

2. The calculation method of the multi-layer planar waveguide mode according to claim 1, characterized in that, The transfer matrix model of the multi-layer planar waveguide is composed of multiple single-layer transfer matrices, and the formula is as follows: M = M1·M2……M j ; Among them, the formula for the transfer matrix of the j-th layer waveguide is as follows: Among them, λ is the wavelength, n j represents the refractive index of the j-th layer of the planar waveguide, β is the propagation constant, h j represents the thickness of the j-th layer of the planar waveguide.

3. The calculation method of the multi-layer planar waveguide mode according to claim 1, characterized in that The determination of the guided modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation includes: Traverse all real refractive indices; Input each real refractive index into the real-domain characteristic equation to calculate the corresponding characteristic equation value; Identify the root at the position of the sign change of the characteristic equation value as the initial value of the characteristic equation for iterative solution; Use the bisection method and the secant method to perform iterative solution of the initial value of the characteristic equation until the convergence condition is satisfied, then determine the guided modes of the multi-layer planar waveguide in the infinite space.

4. The calculation method of the multi-layer planar waveguide mode according to claim 1, wherein The determination of the leaky modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation includes: Calculate three groups of corresponding initial effective refractive index distributions of the leaky modes by the second, third, and fourth order asymptotic methods; Identify the difference between the maximum and minimum absolute values of the three groups of initial effective refractive indices of the leaky modes; Extract the complex values of the effective refractive indices that do not meet the target accuracy condition to determine the solution range of the target algorithm, and use the target algorithm to solve the corresponding initial values; Combine the initial values solved by the target algorithm and the complex values of the effective refractive indices that meet the target accuracy condition; Input the complex values of the effective refractive indices into the complex-domain characteristic equation to calculate the corresponding characteristic equation values, so as to iteratively solve the leaky modes according to the difference between the maximum and minimum values and the characteristic equation values.

5. The calculation method of the multi-layer planar waveguide mode according to claim 4, characterized in that The calculation formula of the target algorithm is: Among them, N z is the number of zeros in the current root-finding range, M represents the number of sampling points on each side, i is the i-th sampling point, f() represents the function value at this point, arg represents taking the argument, and φ t represents the total phase accumulation.

6. The calculation method of the multi-layer planar waveguide mode according to claim 1, characterized in that The calculation formula for introducing a perfectly matched layer to transform the radiation condition of the infinite space into an absorbing boundary in the finite computational domain is: Among them, ρ R , ρ L is the thickness of the equivalent perfectly matched layer, d L , d R represent the thicknesses of the left and right perfectly matched layers respectively, h L , h R are the thicknesses of the left and right boundary waveguides, i is the imaginary unit is the integral value of the stretching factor, τ is the integration variable, κ L is n L is the refractive index of the left - hand waveguide, λ is the wavelength, β is the propagation constant, M equal is M j is the transfer matrix of the j - th layer, κ R is n R is the refractive index of the right - hand waveguide.

7. A processing device for multi-layer planar waveguide modes, characterized in that It includes: An identification module for identifying the propagation characteristics and field distribution of light waves in each layer of the multi-layer planar waveguide, and constructing a transfer matrix model of the multi-layer planar waveguide according to the propagation characteristics and the field distribution; An acquisition module for acquiring the boundary conditions of the infinite space, determining the corresponding real-domain characteristic equation and complex-domain characteristic equation according to the transfer matrix model and the boundary conditions, and determining the guided modes and leaky modes of the multi-layer planar waveguide in the infinite space according to the real-domain characteristic equation and the complex-domain characteristic equation; An introduction module for introducing a perfectly matched layer to transform the radiation condition of an infinite space into an absorbing boundary within a finite computational domain, constructing a characteristic equation for the finite space based on the thickness of the perfectly matched layer and the absorbing boundary, and locating complex roots according to the characteristic equation of the finite space to correct leaky modes to generate Berenger modes; A generation module for generating a complete mode distribution based on the guided modes and leaky modes of the infinite space and the Berenger modes of the perfectly matched layer of the finite space.

8. An electronic device, characterized in that, Comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the method for processing multi-layer planar waveguide modes according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to be used for implementing the method for processing multi-layer planar waveguide modes according to any one of claims 1-6.

10. A computer program product, characterized in that, Comprising a computer program, which is used for implementing the method for processing multi-layer planar waveguide modes according to any one of claims 1-6 when executed by the processor.

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