A method for designing a structure of a graded-index optical fiber

Abstract

This invention discloses a structural design method for graded-index optical fibers, comprising the following steps: 1) Inputting initial optical fiber structure calculation parameters, including a function of the refractive index profile, operating wavelength λ, core refractive index, cladding refractive index, core radius, and cladding radius; dividing the core and cladding regions into N refractive index layers according to their refractive indices; 2) Determining the effective refractive index n of the fiber mode based on the core refractive index and cladding refractive index. eff The range of values ​​for n; eff 3) For each LP mode order m, based on the characteristic matrix corresponding to each effective refractive index sample value, calculate the effective mode refractive index n of the fiber mode. eff 4) For each LP mode order m, for n e T ff 5) Name the fiber and calculate the propagation constant of each mode; 6) Determine the graded refractive index fiber design scheme for the corresponding fiber mode based on the effective mode refractive index and propagation constant of each fiber mode.

Description

Technical Field

[0001] This invention belongs to the fields of simulation and optical fiber design, and particularly relates to a structural design method for graded refractive index optical fibers. Background Technology

[0002] Graded-index fiber, compared to step-index fiber (SIF), exhibits a radially varying refractive index distribution. During actual fiber manufacturing, due to manufacturing processes, a gradient in refractive index always exists at the core-cladding interface and in the central portion of the fiber. If the radial dimension of this gradient region is smaller than the wavelength of the incident light, the fiber can be considered a step-index fiber; otherwise, it is a graded-index fiber. By controlling the distribution of the core refractive index, the dispersion characteristics of fiber transmission can be controlled. Depending on the application, graded-index fiber can be classified into dispersion-flat fiber, dispersion-shifted fiber, and non-zero dispersion-shifted fiber. Furthermore, in multimode fiber transmission systems, the main cause of dispersion is modal dispersion. Reducing modal dispersion involves controlling the refractive index distribution of the fiber, which can be achieved using graded-index fiber with a g-power refractive index distribution (the refractive index change is proportional to the g-power of the radial position r of the core). In summary, it has broad application prospects and research value in optical fiber transmission systems.

[0003] In current fiber optic structure design, precise control of the fiber structure is required to meet system requirements regarding mode field diameter, power handling capacity, beam quality, loss, and dispersion characteristics. Mode solving for single-clad fibers typically uses analytical forms and numerical methods. However, for... Figure 1 For optical fibers with a 'triangular' or 'parabolic' structure, the derivation and solution of the characteristic equation in analytical form become extremely complex. Existing methods for designing graded-index optical fibers mainly include analytical solutions for square-rate fibers and series approximate solutions. The former is only applicable to fibers with square-rate refractive index distributions, while the latter requires expanding the refractive index and scalar Helmholtz equations into series, obtaining the field solution expressed in series, and then solving the characteristic equation. This process is cumbersome and cannot handle fibers with complex refractive index distributions, resulting in limited design freedom and applicability. Summary of the Invention

[0004] To address the problems of long design time, poor scalability and convenience, and high complexity in the design method of graded-index optical fibers for specific application scenarios described in the background art, this invention provides a graded-index optical fiber design method based on feature matrices.

[0005] This invention employs a midpoint equal-width step discretization method to divide a graded-index fiber into multiple refractive index layers radially based on differences in radius and refractive index. This discretizes the profile of the graded-index continuous refractive index fiber into an n-order step-index fiber profile. As n increases, the step-index fiber profile gradually converges to the graded-index fiber profile function. The method then solves for the non-zero solutions of the characteristic matrix to obtain parameters such as the fiber mode number, mode name, effective refractive index, and propagation constant of the graded-index fiber. This method exhibits good compatibility with a range of variable refractive index fibers, including triangular or parabolic shapes. This invention is also applicable to solving step-index fibers and can serve as a universal model for both step-index and graded-index fibers.

[0006] The technical solution of this invention is as follows:

[0007] A structural design method for graded-index optical fibers, comprising the following steps:

[0008] 1) Input the initial optical fiber structure calculation parameters, including the function of the refractive index profile, the operating wavelength λ, the refractive index of the core, the refractive index of the cladding, the radius of the core, and the radius of the cladding; divide the region containing the core and cladding into N refractive index layers according to their refractive indices, and assign the radii of each refractive index layer to r1, r2, ..., r... i ,…,r N The corresponding refractive index values ​​are represented by n1, n2, ..., n j ,…,n N express;

[0009] 2) Determine the effective refractive index n of the fiber mode based on the core refractive index and cladding refractive index. eff The range of values ​​for ; effective refractive index n eff The value range is between the cladding refractive index n out Between the highest refractive index n0 of the fiber core; for the effective refractive index n eff By performing linear discrete sampling, Z sample values ​​are obtained, denoted as Z. in This is the t-th sample value;

[0010] 3) Repeat steps a) to d) for each LP mode order m; based on the characteristic matrix corresponding to each effective refractive index sample value, calculate the effective mode refractive index of the fiber mode. Numerical solutions and the number of effective mode refractive indices;

[0011] a) For the t-th sample value Determine the normalized transverse parameters for each refractive index layer;

[0012] b) Construct the scalar mode oscillator submatrix or scalar mode attenuation submatrix at the boundary of each refractive index layer based on the numerical calculation method of the mode field distribution;

[0013] c) Construct the sampled values ​​based on the obtained scalar mode oscillator submatrix and scalar mode attenuation submatrix. The corresponding scalar modulus feature matrix;

[0014] d) Based on sampled values The corresponding scalar modulus feature matrix is ​​used to determine the sampled value. Does the condition for the existence of fiber optic mode meet? If the condition for the existence of fiber optic mode is met, then at this sample value... The exact numerical solution of the effective mode refractive index of the corresponding fiber mode is obtained by using discrete numerical methods in the vicinity of the [location].

[0015] 4) For each LP mode order m, the effective mode refractive index Sort the modes from largest to smallest, name them according to the naming rules, and calculate the propagation constant for each mode;

[0016] 5) Based on the effective mode refractive index and propagation constant corresponding to each fiber mode, determine the graded refractive index fiber design scheme for the corresponding fiber mode.

[0017] Furthermore, based on the sampled values The size determines whether each refractive index layer constructs an oscillating submatrix or an attenuation submatrix; when the refractive index of the j-th refractive index layer... When, then an oscillating submatrix is ​​constructed for the j-th refractive index layer, when Then an attenuation submatrix is ​​constructed for the j-th refractive index layer.

[0018] Furthermore, the scalar mode oscillator submatrix and the scalar mode attenuation submatrix have a 1×2 matrix structure at the innermost (first) refractive index layer. At the outermost (Nth) refractive index layer, there is a 1×2 matrix. When at the j-th refractive index layer, it is a 2×2 matrix.

[0019] When D i,j When D is a scalar modulus oscillator submatrix, i,j Let it be A i,j ;

[0020] When D i,j When D is a scalar modulus attenuation submatrix, i,j Let it be B i,j ,

[0021] Among them, J m For m-th order Bessel function of the first kind, I m For the m-th order first-order modified Bessel function, Y m Let K be an m-th order Bessel function of the second kind.m J' is an m-th order modified Bessel function of the second kind; m The derivative of the m-th order Bessel function of the first kind, I' m Y' is the derivative of the m-th order modified Bessel function of the first kind. m K' is the derivative of the m-th order Bessel function of the second kind. m For the derivative of the m-th order modified Bessel function of the second kind, r i Let X be the radius of the i-th refractive index layer. t,j Based on sampled values The normalized transverse parameters of the j-th refractive index layer, n j Let be the refractive index of the j-th refractive index layer, μ be the ratio of the radius of the i-th refractive index layer to the radius of the 1-th refractive index layer, and k0 be the wave vector in vacuum corresponding to the working wavelength λ.

[0022] Furthermore, Where k0 is the wave vector in vacuum.

[0023] Furthermore, the refractive index of the Tth effective mode Its corresponding propagation constant The relationship is

[0024] Furthermore, based on the sampled values The corresponding scalar modulus eigenvalue is obtained by solving the secant method. Corresponding effective mode refractive index

[0025] A server is characterized by comprising a memory and a processor, the memory storing a computer program configured to be executed by the processor, the computer program including instructions for performing the steps of the methods described above.

[0026] A computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the steps of the above-described method.

[0027] The method of the present invention includes the following steps:

[0028] 1) Input the initial optical fiber structure calculation parameters, including the function of the refractive index profile, the operating wavelength λ, the refractive index of the core, the refractive index of the cladding, the radius of the core, and the radius of the cladding. Divide the core and cladding into the required number of layers according to their radius and refractive index, collectively referred to as refractive index layers, with a total number of refractive index layers of N. This invention adopts a midpoint equal-width step discretization approximation method. As the number of layers N increases, the discretized optical fiber profile converges closer to the original graded optical fiber profile, such as... Figure 2As shown. The radii of each layer are successively represented by r1, r2, ..., r i ,…,r N The refractive index values ​​are represented by n1, n2, ..., n j ,…,n N The radius ordinal number is represented by the subscript i, and the refractive index is represented by the subscript j.

[0029] 2) Determine the effective refractive index n of the fiber mode based on the core refractive index and cladding refractive index. eff The effective refractive index ranges from the refractive index n of the cladding. out Between the highest refractive index n0 of the fiber core and the effective refractive index. The effective refractive index is linearly discretely measured, resulting in sampled values ​​of the effective refractive index (hereinafter referred to as sampled values). Z is the total number of sampled points, which can be denoted as: Where t represents the ordinal number of the sampling point.

[0030] 3) For the sampled value corresponding to the t-th sampling point Determine the normalized transverse parameters for each refractive index layer. (Definition) For based on The normalized transverse parameters of the j-th refractive index layer are calculated. Where k0 is the wave vector in vacuum, r1 is the radius of the first refractive index layer, and n... j Let J be the refractive index of the j-th refractive index layer. This is the sampled value of the refractive index of the t-th effective mode in step 2. When... The fiber mode employs a scalar mode oscillatory solution equation in the j-th refractive index layer, X t,j For based on The normalized transverse phase parameter of the j-th refractive index layer is calculated; when The fiber mode at this layer has a scalar mode attenuation solution equation, X. t,j For based on The normalized lateral attenuation parameter of the j-th refractive index layer is calculated. For each refractive index layer, its normalized lateral parameter is X. t,1 ,X t,2 ,…,X t,N-1 ,X t,N .

[0031] 4) Construct the scalar mode oscillator submatrix or scalar mode attenuator submatrix at the boundaries of each refractive index layer based on the numerical calculation method of the mode field distribution. The scalar mode is represented by LPmn (m = 0, 1, 2…). Here, the mode order m represents the mode number in the circumferential direction of the fiber mode, and the root ordinal number n represents the mode number in the radial direction of the fiber. The mode order m is numerically equal to the order of the Bessel function mentioned below.

[0032] Based on the weak conduction approximation and the continuity of the optical field in the optical fiber, it can be deduced that within each refractive index layer of the optical fiber... The magnitude of the value determines whether an oscillator matrix or an attenuator matrix is ​​constructed at that layer. The oscillator matrix is ​​determined by the order m (m = 0, 1, 2…) of the Bessel function and the radius r of each refractive index layer of the fiber. i Normalized lateral parameter X t,j The first kind of Bessel function J m The second kind of Bessel function Y m The attenuation submatrix is ​​a matrix with respect to the order m of the Bessel function and the radius r of each refractive index layer (boundary) of the fiber. i Normalized lateral parameter X t,j First kind of modified Bessel function I m Second-type modified Bessel function K m The matrix. For the mode order m, the effective mode refractive index sample value is... The scalar modulus eigenvalues ​​D of the innermost and outermost refractive index layers 11 D N-1,N The forms are as follows:

[0033]

[0034]

[0035] When at the j-th refractive index layer, the scalar mode oscillator submatrix or scalar mode attenuator submatrix is ​​a 2×2 matrix, and its characteristic form is:

[0036]

[0037] For ease of representation, when D in equations (1) to (3) i,j When D is a scalar modulus oscillator submatrix, i,j It can be written as A i,j ,in:

[0038]

[0039] Where J' m J is the derivative term of the first kind of Bessel function in the matrix. m Y' is the first kind of Bessel function term in the matrix. m Y is the derivative term of the second kind of Bessel function in the matrix. m Let be the second type of Bessel function term in the matrix.

[0040] When D i,j When D is a scalar modulus attenuation submatrix, i,j It can be represented as B i,j ,in:

[0041]

[0042] Where I' m Let I be the derivative term of the first kind of modified Bessel function in the matrix. m Let K' be the first kind of modified Bessel function term in the matrix. m K is the derivative term of the modified Bessel function of the second kind in the matrix. m This is the second-type modified Bessel function term in the matrix.

[0043] 5) Construct the scalar modulus characteristic matrix, which consists of the scalar modulus oscillator submatrix and the scalar modulus decay submatrix.

[0044] The scalar mode characteristic matrix of the optical fiber is formed by combining the scalar mode oscillator submatrix and the scalar mode attenuator submatrix obtained in step (4) as block matrices. By combining all the corresponding matrices from each layer, with all other elements in the matrix being 0, the characteristic matrix can be obtained. The combined form of the characteristic matrix is:

[0045]

[0046] In the determinant, the " / " symbol represents a logical OR relationship. For the matrix corresponding to the j-th refractive index layer, matrix A is specifically chosen. ij Or matrix B ij Depending on the magnitude of its refractive index, when the refractive index of the j-th refractive index layer... Take the oscillating submatrix A i,j ,when Take the attenuation submatrix B i,j By constructing and combining the scalar mode oscillator submatrices and scalar mode attenuator submatrices of each refractive index layer, the characteristic matrix of optical fibers with complex refractive index distributions can be obtained flexibly and conveniently. This simplifies the derivation and solution process of the analytical form of the characteristic equation and improves the design freedom of optical fibers with complex refractive index distributions.

[0047] 6) Based on the effective refractive index sampling value The corresponding scalar modulus eigenma is used to find the exact numerical solution of the effective refractive index that satisfies the existence of the fiber mode. This is denoted as "effective mode refractive index";

[0048] When the fiber mode exists, the determinant corresponding to the characteristic matrix (hereinafter referred to as the characteristic determinant) must be 0. For each effective refractive index sample value... First, determine if the value of its characteristic determinant is closer to zero than the characteristic determinant values ​​of adjacent sampling points. If the above condition is met, then a fiber mode exists near this sampling value, and the number of fiber modes (denoted as T, T = 0, 1, 2...) plus 1 is recorded. Discrete numerical methods such as the secant method can be used to find an exact numerical solution in the vicinity of this sampling value that makes the determinant equal to 0.

[0049] 7) For each LP mode order m (m = 0, 1, 2...), repeat steps (3) to (6) to calculate the effective mode refractive index of the fiber mode based on the characteristic matrix corresponding to each effective refractive index sample value. Numerical solutions and the number of effective mode refractive indices.

[0050] For each LP mode order m (m = 0, 1, 2...), iterate through the sampled values ​​of the effective refractive index and repeat steps (3) to (6). When step (6) yields an exact numerical solution that meets the conditions... Record it at that time.

[0051] 8) Name the fiber modes according to different LP mode orders, and... The values ​​are sorted in descending order, and the propagation constant of the scalar mode is further calculated.

[0052] In scalar model LP mn In the diagram, the modulus order is denoted as m, and the root ordinal number is denoted as n. For the m-th modulus, It decreases as n increases. For example, for LP 0n If there is a model The effective mode refractive indices for each mode are as follows:

[0053]

[0054] Effective mode refractive index and propagation constant The relationship is:

[0055] In step 8, the effective mode refractive index and propagation constant of each mode in the optical fiber are calculated, which can serve as the theoretical basis for the next step of calculating the mode field distribution, mode field diameter, insertion loss, cutoff wavelength, and fiber dispersion. By calculating the various parameters of the optical fiber, various factors of graded-index optical fibers can be comprehensively considered, providing rich and accurate design schemes for graded-index optical fibers in fiber laser systems or optical fiber communication systems.

[0056] Compared with existing technologies, the present invention provides a general method for solving the characteristic matrix of graded-index optical fibers:

[0057] ① It has a fast calculation speed, high accuracy, and high reliability.

[0058] ② The number of refractive index layers in graded-index optical fibers can be set arbitrarily, and the design of refractive index layers is flexible, providing customized design solutions for various application fields.

[0059] ③ This invention can provide technical support for the design of optical fibers in current high-power fiber lasers and optical fiber communication systems. It can simulate and calculate the characteristics of optical fibers before experiments, shorten the research and development cycle of R&D personnel, and reduce the requirements for R&D equipment.

[0060] ④ The graded-index fiber designed in this invention has flexible and controllable parameters, high design freedom, clear design requirements, and broad market prospects. The general characteristic matrix solution method for graded-index fibers described in this invention has fast computation speed, good robustness, no need to repeatedly write code, strong adaptability, good scalability and convenience, and can be customized to design different types of graded-index fibers for different application scenarios. Attached Figure Description

[0061] Figure 1 The diagram shows the graded-index optical fiber and its geometry and refractive index distribution:

[0062] (a) Cross-sectional view of optical fiber; (b) Longitudinal cross-sectional view of optical fiber; (c) Radial refractive index distribution of "parabolic" shaped optical fiber; (d) Radial refractive index distribution of "triangular" shaped optical fiber.

[0063] Figure 2 Three methods for dividing the refractive index layers of graded-index optical fibers;

[0064] (a) Divide the “parabolic” graded refractive index region into 5 layers; (b) Divide the “triangular” graded refractive index region into 5 layers; (c) Divide the “parabolic” graded refractive index region into 10 layers; (d) Divide the “triangular” graded refractive index region into 10 layers; (e) Divide the “parabolic” graded refractive index region into 15 layers; (f) Divide the “triangular” graded refractive index region into 15 layers.

[0065] Figure 3 This diagram illustrates the principle steps of a method for solving the general characteristic matrix of graded-index optical fibers. Detailed Implementation

[0066] To clearly demonstrate the purpose, technical solution, and advantages of the present invention, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0067] In one embodiment, taking the "triangular" graded-index fiber design as an example, the design methods for other graded-index fiber structures are similar and scalable. This invention calculates the LP mode of the fiber based on the fiber parameters given in Table 1. The fiber's geometric dimensions and refractive index distribution are as follows... Figure 1 As shown in (d).

[0068] Table 1 Fiber Optic Parameters

[0069]

[0070] The method flow of the present invention is as follows: Figure 3 As shown, the steps include:

[0071] (1) Input the initial structure calculation parameters of the optical fiber, including 1) the refractive index of the core and cladding; 2) the radius of the core and each cladding; 3) the refractive index distribution shape of the core and each cladding; and 4) the working wavelength λ.

[0072] (2) Based on the core refractive index and the cladding refractive index, determine the effective refractive index calculation range. The effective refractive index range lies between the refractive index of the outermost cladding and the refractive index of the core. Effective refractive index n eff Linear discrete sampling is used. The segmented boundaries of the refractive index layer radius and refractive index are determined based on the number of refractive index layers.

[0073] (3) Calculate the normalized transverse parameter X at each segment based on the sampled value of the current effective refractive index (hereinafter referred to as the sampled value). t,1 ,X t,2 ,…,X t,N-1 ,X t,N .

[0074] (4) Construct scalar mode oscillator submatrix or scalar mode attenuation submatrix for each refractive index layer. Take effective refractive index sampling values ​​in ascending order. Compare the current sampling value with the propagation constant of the fiber core and each cladding layer one by one. When the sampling value is less than the refractive index of the fiber core / cladding layer, construct a scalar mode oscillator submatrix; when the sampling value is greater than the propagation constant of the fiber core / cladding layer, construct a scalar mode attenuation submatrix.

[0075] (5) Construct the scalar mode characteristic matrix. The scalar mode oscillation / scalar mode attenuation sub-matrices of each layer of the fiber are used to form a double diagonal matrix, which is the characteristic matrix M corresponding to the sampled value of the effective refractive index.

[0076] (6) Solve for the determinant (hereinafter referred to as the characteristic determinant) of the characteristic matrix constructed from the sampled value. If the value of the characteristic determinant of the current sampled value is closer to 0 than the value of the characteristic determinant of its neighboring sampled values, the characteristic matrix has a non-zero solution, and the optical fiber supports the optical fiber mode corresponding to the sampled value. The discrete numerical methods for finding the roots of the equation can be used, such as the bisection method, Newton's method, and the secant method, to obtain a more accurate numerical solution for the effective refractive index.

[0077] (7) For each LP mode order m (m=0,1,2…), repeat steps (3)~(6) and record the numerical solution of the effective refractive index when the determinant value in step (6) is 0. This is called the “effective mode refractive index”. Continue until all effective mode refractive index sampling values ​​are traversed to obtain all the “effective mode refractive indices”.

[0078] (8) Sort the effective mode refractive index numerical solutions obtained in step (7) from largest to smallest, and name them according to the naming rules.

[0079] The results calculated using this invention for the fiber optic parameters given in Table 1 are compared with those calculated by similar software on the market as follows:

[0080] Table 2 Results for Fiber Optic Mode

[0081]

[0082]

[0083] It is evident that the calculation results of this invention are consistent with those of similar software on the market. This proves that the calculations of this invention are error-free and correct.

[0084] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.

Claims

1. A structural design method for graded-index optical fibers, comprising the following steps: 1) Input the initial fiber structure calculation parameters, including the function of the refractive index profile, the operating wavelength λ, the refractive index of the core, the refractive index of the cladding, the radius of the core, and the radius of the cladding; divide the region containing the core and cladding into N refractive index layers according to their refractive indices, and assign the radii of each refractive index layer sequentially using... The corresponding refractive index values ​​are represented by... express; 2) Determine the effective refractive index of the fiber mode based on the core refractive index and the cladding refractive index. The range of values ​​for; effective refractive index The value range is between the cladding refractive index With the highest refractive index of the fiber core Between; for effective refractive index By performing linear discrete sampling, Z sample values ​​are obtained, denoted as Z. ,in For the first t Each sample value; 3) Repeat steps a) to d) for each LP mode order m. Based on the characteristic matrix corresponding to each effective refractive index sample value, calculate the effective mode refractive index of the fiber mode. Numerical solutions and the number of effective mode refractive indices; a) For the t-th sample value Find the normalized transverse parameters of each refractive index layer; b) Construct the scalar mode oscillator submatrix or scalar mode attenuation submatrix at the boundary of each refractive index layer based on the numerical calculation method of the mode field distribution; c) Construct the sampled values ​​based on the obtained scalar mode oscillator submatrix and scalar mode attenuation submatrix. The corresponding scalar modulus feature matrix; d) Based on sampled values The corresponding scalar modulus feature matrix is ​​used to determine the sampled value. Does the condition for the existence of fiber optic mode meet? If the condition for the existence of fiber optic mode is met, then at this sample value... The exact numerical solution of the effective mode refractive index of the corresponding fiber mode is obtained by using discrete numerical methods in the vicinity of the [location]. ; 4) For each LP mode order m, the effective mode refractive index Sort the modes from largest to smallest, name them according to the naming rules, and calculate the propagation constant for each mode; 5) Based on the effective mode refractive index and propagation constant corresponding to each fiber mode, determine the graded refractive index fiber design scheme for the corresponding fiber mode.

2. The method according to claim 1, characterized in that, Based on sampled values The size determines whether each refractive index layer constructs an oscillating submatrix or an attenuation submatrix; when the refractive index of the j-th refractive index layer... When, then an oscillating submatrix is ​​constructed for the j-th refractive index layer, when Then an attenuation submatrix is ​​constructed for the j-th refractive index layer.

3. The method according to claim 2, characterized in that, The scalar mode oscillator submatrix and the scalar mode attenuation submatrix have a 1×2 matrix structure at the innermost refractive index layer. The outermost refractive index layer is a 1×2 matrix. When it is in the j-th refractive index layer, it is a 2×2 matrix. ; when When it is a scalar modulus oscillator submatrix, Recorded as ; when When it is a scalar modulus attenuation submatrix, Recorded as , ; in, For m-th order Bessel function of the first kind, For m-th order, the first kind of modified Bessel function. It is an m-th order Bessel function of the second kind. It is an m-th order modified Bessel function of the second kind; The derivative of the m-th order Bessel function of the first kind, For the derivative of the m-th order modified Bessel function of the first kind, Let be the derivative of the m-th order Bessel function of the second kind. For the derivative of the m-th order modified Bessel function of the second kind, Let the radius of the i-th refractive index layer be... Based on sampled values The normalized transverse parameters of the j-th refractive index layer were calculated. Let J be the refractive index of the j-th refractive index layer. μ The ratio of the radius of the i-th refractive index layer to that of the 1st refractive index layer. The wave vector in vacuum corresponding to the working wavelength λ.

4. The method according to claim 3, characterized in that, ;in, The wave vector in a vacuum.

5. The method according to claim 3, characterized in that, No. Refractive index of each effective mode Its corresponding propagation constant The relationship is .

6. The method according to claim 1, characterized in that, Based on sampled values The corresponding scalar modulus eigenvalue is obtained by solving the secant method. Corresponding effective mode refractive index .

7. A server, characterized in that, It includes a memory and a processor, the memory storing a computer program configured to be executed by the processor, the computer program including instructions for performing each step of the method of any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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