CN114942490A - Multi-cladding step optical fiber design method based on characteristic matrix - Google Patents
Multi-cladding step optical fiber design method based on characteristic matrix Download PDFInfo
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Abstract
The invention discloses a multi-cladding step optical fiber design method based on a characteristic matrix. The method comprises the following steps: 1) inputting calculation parameters of an initial structure of the optical fiber; 2) discrete sampling is carried out in the effective propagation constant calculation range determined according to the refractive index of the fiber core and the refractive index of the outermost cladding, and an effective propagation constant sampling value is obtained; 3) determining a segment boundary according to the number of claddings; calculating the normalization parameters of the corresponding refractive index layers for each effective propagation constant sampling value; 4) constructing an oscillation submatrix or an attenuation submatrix of each effective propagation constant sampling value in the optical fiber; 5) constructing a characteristic matrix according to the oscillator sub-matrix and the attenuator sub-matrix; 6) when the determinant value of the characteristic matrix is solved to be 0, the constant value is effectively propagated; 7) calculating equivalent refractive indexes corresponding to effective propagation constant values under different mode orders; 8) and (4) the obtained equivalent refractive index is substituted back into the characteristic matrix to obtain an equation set of the corresponding mode, and the mode field distribution in the optical fiber under each corresponding mode is obtained through calculation.
Description
Technical Field
The invention relates to the field of simulation and the field of optical fiber design, in particular to a multi-cladding step type optical fiber mode characteristic equation matrix solving method.
Background
The Step Index Fiber (SIF) has a simple structure and is easy to draw, and the SIF-based optical Fiber device manufacturing process and technology are mature. In the aspect of application, most of the high-power fiber lasers close to the diffraction limit are realized on the basis of SIF, SIF fibers adopted by the high-average-power high-beam-quality fiber lasers are generally not strict single-mode fibers but few-mode fibers supporting a certain mode number, the beam quality is determined by the components of a basic mode and a high-order mode in an output beam, so that the mode precision control needs to be carried out on a multi-cladding step-type fiber structure, and the improved SIF design of the multi-cladding structure becomes a research hotspot in the field of fiber design.
In the current optical fiber structure design, for a single-cladding optical fiber, no matter a scalar mode or a vector mode is calculated, an analytic form is mostly adopted, and a common numerical method for solving a root is combined with an equation to solve the root. For a triple-clad fiber with a 'W' type structure as shown in fig. 1 or a fiber with more clad structures, the derivation and derivation process of the analytical form of the characteristic equation becomes complicated. In specific applications such as fiber lasers/amplifiers and fiber communication systems, in order to meet the requirements of a fiber such as a larger mode field diameter, higher bearable power, better output beam quality and low loss, the structure of the fiber needs to be accurately controlled. Most of the existing methods for designing multi-clad fibers are based on calculation of specific cladding refractive index distribution or design based on experience. The corresponding relation between linear polarization and a vector mode is utilized for specific cladding refractive index distribution, the effective refractive index or the propagation constant of an LP mode replaces the corresponding vector mode, the calculation result is very inaccurate, the design freedom degree is not high, and the applicability is not strong. The method for adjusting the number of optical fiber layers and calculating the mode by using experience is too complicated, needs to occupy a large amount of time and cost to optimize the method, and is difficult to obtain parameters meeting the requirements.
Disclosure of Invention
The invention provides a multi-cladding step optical fiber design method based on a characteristic matrix, aiming at solving the problems of long time consumption, poor expandability and convenience and higher complexity of the multi-cladding optical fiber design in the background technology for designing the optimal performance optical fiber in a specific application scene.
The method comprises the following steps:
1) and inputting calculation parameters of the initial structure of the optical fiber, including the working wavelength lambda, the refractive index from the fiber core to the outermost cladding, the radius and the like. If the core and each cladding are collectively referred to as the refractive index layer of the optical fiber, the total number of layers is N, and the radii of the layers are r in order 1 ,r 2 ,…,r i ,…,r N Expressed by the refractive index values n 1 ,n 2 ,…,n j ,…,n N And (4) showing. Where the radius ordinal number is denoted by the index i and the refractive index is denoted by the index j.
2) And determining the effective propagation constant range according to the refractive index of the fiber core and the refractive index of the outermost cladding. The effective propagation constant range is between the propagation constant of the outermost cladding and the propagation constant of the fiber core, sampling is performed according to linear dispersion, Z is the total number of sampling points, and each point is recorded as beta-beta 1 ,β 2 ,β 3 ,…β t …β Z Where t represents the ordinal number of the sample point.
3) For beta t And calculating the normalized transverse phase parameter or the normalized attenuation parameter of each refractive index layer. Definition of
Normalized transverse phase parameter or normalized attenuation parameter corresponding to j-th refractive index layer, wherein k 0 Is the wave vector in vacuum, n j Is the refractive index of the refractive index layer, beta t Are samples of the valid constants in step 2. When (k) 0 n j ) 2 -β t 2 > 0, fiber mode has an oscillatory solution at this layer, f j Is the normalized transverse phase parameter of the layer; when (k) 0 n j ) 2 -β t 2 < 0, the fiber mode has an attenuation solution at this layer, f j For normalization of the layerA lateral attenuation parameter. For each refractive index layer, according to the refractive index of each refractive index layer of the set optical fiber, the normalized transverse parameter is f 1 ,f 2 ,…,f j ,…,f N 。
4) Construction of the model for beta according to the mode calculation method (vector norm/scalar norm) t Each of the oscillator submatrix and the attenuator submatrix. Scalar modulo Using LP mn (m is 0,1,2 …) and TE is used as a vector mode 0n 、TE 0n (m＝0)、HE mn 、EH mn And (m-1, 2 …). The mode order m represents the mode number in the circumferential direction of the optical fiber mode, the root number n represents the mode number in the radial direction of the optical fiber, and the two are used as subscripts to name the optical fiber mode. Where the mode order m is numerically equal to the order of the bessel function in the following.
For beta t Comprises an oscillation submatrix or an attenuation submatrix of each fiber refractive index layer. Within each fiber index layer, β t The size of the value determines whether an oscillatory submatrix or an oscillatory submatrix is constructed at that layer. When (k) 0 n j ) 2 -β t 2 When the value is more than 0, constructing an oscillatory submatrix of the layer; when (k) 0 n j ) 2 -β t 2 < 0, constructing the attenuator matrix of the layer. The oscillator matrix is the order m (m is 0,1,2 …) of the Bessel function and the radius r of each refractive index layer of the optical fiber i Normalized transverse parameter f j Bessel function J of the first kind m And a second type of modified Bessel function N m Of the matrix of (a). The attenuation submatrix is related to the order m of the Bessel function and the radius r of each refractive index layer of the optical fiber i Normalized transverse phase parameter or normalized transverse attenuation parameter f j Modified Bessel function K of the first kind m And a Bessel function I of the second kind m Of the matrix of (a). When scalar mode is considered, the fiber core oscillation submatrix and the outmost cladding attenuation submatrix are 2 multiplied by 1 matrixes, and the characteristic forms are respectively as follows:
in the non-outermost cladding layer, the oscillator sub-matrix or the attenuator sub-matrix formed by the middle cladding layer is a 2 x 2 matrix, and the characteristic forms of the oscillator sub-matrix or the attenuator sub-matrix are respectively as follows:
when the vector mode is considered, the treatment method is the same as the treatment method of the scalar mode fiber core, the outermost layer cladding and the non-outermost layer cladding. The fiber core oscillator sub-matrix and the outmost cladding attenuator matrix are 4 multiplied by 2 matrixes, and the characteristic forms of the fiber core oscillator sub-matrix and the outmost cladding attenuator matrix are respectively as follows:
where ω is the circular frequency, ω is 2 π c/λ, c is the propagation velocity of light in vacuum, ε 0 、μ 0 Is dielectric constant, magnetic permeability in vacuum j Is a refractive index dependent dielectric constant, ε j ＝ε 0 n j 2 。
The oscillator sub-matrix or attenuator sub-matrix formed by the middle cladding is a 4 x 4 matrix, and the characteristic forms are respectively as follows:
5) and constructing a characteristic matrix which is composed of an oscillation submatrix and an attenuation submatrix.
And (4) combining the characteristic matrix of the optical fiber by using the oscillation submatrix or the attenuation submatrix obtained in the step (4) as a block matrix. The number of the oscillation/attenuation submatrices is determined by the total number of refractive index layers of the optical fiber, the number of the submatrices is one in the fiber core and the outermost cladding, the number of the submatrices is two in the non-outermost cladding, and the characteristic matrixes can be obtained by combining all the matrixes. Feature matrix
The combination form of (A) is as follows:
wherein the "/" symbol in the determinant represents a logical OR relationship, specifically selecting the matrix A ij Or matrix B ij Depending on the refractive index, when k 0 n j ≥β t Taking an oscillator matrix A i,j When k is 0 n j ＜β t Taking an attenuator matrix B i,j 。
6) The steps (3) to (5) are repeated to obtain the number of fiber modes existing and the propagation constant corresponding to each bessel function order m (m is 0,1,2 …).
When the fiber mode exists, the determinant corresponding to the feature matrix must be zero. It can be deduced that if there are some propagation constants
Can make the determinant of the characteristic matrix be zero, then the propagation constant
The corresponding fiber mode may be transmitted in the optical fiber. Therefore, solving for propagationConstant number
Comprises the following steps: first, each beta is obtained in turn t The values of the corresponding characteristic matrix determinant are found by the zero point existence theorem for intervals in which all the values satisfying the determinant can exist zero points, and for example, if there are G intervals satisfying the existence of zero points, each of the intervals is expressed as (β) g ,β g+1 ) G is the ordinal number of solution interval, G is 1,2,3, … G; ② adopting discrete numerical method such as Newton method in all intervals (beta) satisfying conditions g ,β g+1 ) A numerical solution is found that can make the determinant of the feature matrix 0. Assuming that the number of numerical solutions that can exist in the optical fiber mode is x, the propagation constant corresponding to each numerical solution is recorded as
T represents the ordinal number of the numerical solution.
7) For optical fiber mode according to mode order m pairs
The values are ordered and named in the order from big to small, and the equivalent refractive index of a scalar mode or a vector mode is further calculated.
Increase by n by a value beta T Decrease; the vector mode is represented by TE mode, TM mode, EH mode, and HE mode, and when m is 0, TE can be obtained by calculation 0n And TM 0n Of modes
Value, increasing with n
The value increases, and TE 0n Has a beta value slightly larger than TM 0n Is/are as follows
The value is obtained. When m ≠ 0, EH can be calculated ln And HE ln Value of mode, increasing with n
Increase in value, HE ln Is/are as follows
Value slightly greater than EH ln Is/are as follows
A value; equivalent refractive index n eff Propagation constant
The relationship of sum is:
8) and obtaining the mode field distribution of each optical fiber mode in the optical fiber.
The propagation constant of each mode is solved as step 7
And then, sequentially substituting the characteristic matrixes back into the characteristic matrix shown in the formula (9) in the step 5). If scalar method is used, the feature matrix is 2(N-1) multiplied by 2(N-1) order matrix; if vectorial, the feature matrix is a 4 (N-1). times.4 (N-1) order matrix. For scalar norm, characteristic equation set for each mode
As shown in equation (10):
wherein C k Is (k ═ 1,2,3.. 2N-1) each term bessel function coefficient in the electric field component. C 1 Coefficient of Bessel function, C, being the electric field component of the core 2N-1 Coefficient of Bessel function of electric field component of outermost cladding, C in the middle k The Bessel function coefficients of the non-outermost cladding are respectively Bessel function coefficients of electric field components in sequence from the inside to the outside in every 2 groups. Order to
Different propagation constants can be sequentially obtained
Corresponding electric field component C k . So far, the invention has obtained the correspondence of the optical fiber mode
The electric field component expression coefficients are substituted into the electric field component expression to obtain the mode field distribution of the optical fiber mode in the optical fiber.
The solution of the vector solution is similar to the above, and the propagation constant of each mode is determined
And (5) back substituting the feature matrix shown in the formula (9). For the vector mode, the characteristic equation set of each mode
As shown in formula (11):
at this time, C k Is (k ═ 1,2,3.. 4N-1) bessel function coefficients, C, in the electric and magnetic field components 1 Coefficient of Bessel function, C, being the electric field component of the core 2 Coefficient of Bessel function, C, being the magnetic field component of the core 4(N-1)-1 Coefficient of Bessel function, C, being the electric field component of the outermost cladding 4(N-1) Is the Bezier function coefficient of the magnetic field component of the outermost cladding. Intermediate C k The Bezier function coefficients of the non-outermost cladding are set into 4 groups, the first 2 of each group are the Bezier function coefficients of the electric field components of the inner cladding in sequence from the fiber core to the outer cladding, and the last 2 are the Bezier function coefficients of the magnetic field components of the inner cladding. Order to
Different propagation constants can be sequentially obtained
Corresponding electric and magnetic field components C k . So far, the invention has obtained the correspondence of the optical fiber mode
The electric field component expression coefficients are substituted into the electric field component expression to obtain the vector mode field distribution of the optical fiber mode in the optical fiber.
After the equivalent refractive index and the propagation constant of the optical fiber and each transmission mode of the optical fiber are calculated, the method can be used as a theoretical basis for calculating the mode field diameter, the insertion loss, the cut-off wavelength and the optical fiber dispersion of the optical fiber in the next step. A variety of different multi-clad fiber designs are provided by single mode/few mode fiber laser/amplifier systems.
Compared with the prior art, the multi-cladding step optical fiber design method based on the characteristic matrix comprises the following steps:
the method has the advantages of high calculation speed, high precision and high reliability.
The number of layers of the multi-clad optical fiber can be set at will, the fiber core and the cladding are flexible in design, and customized design schemes can be provided for various application fields.
The invention can provide theoretical support for the optical fiber design scheme of the prior high-power optical fiber laser/amplifier project, and can carry out analog calculation on the characteristics of the optical fiber laser/amplifier before the experiment, thereby saving precious research and development time and research and development expenses.
The multi-clad step optical fiber designed by the invention has the advantages of flexible and controllable parameters of each layer, high design freedom degree and wide application scenes.
Drawings
FIG. 1 shows the geometry and refractive index profile of a "W" -shaped triple-clad fiber;
(a) a transverse cross-sectional view of the optical fiber; (b) refractive index distribution of the optical fiber in the radial direction; (c) cross-sectional view of the optical fiber in the radial direction.
Fig. 2 shows the mode field distribution image of the three-clad fiber partial mode obtained after the solution.
FIG. 3 is a schematic diagram of the steps of a multi-cladding step-index fiber design method based on a feature matrix.
Detailed Description
For clearly showing the objects, technical solutions and advantages of the present invention, the following detailed description of the embodiments of the present invention will be made with reference to the accompanying drawings and examples.
In one embodiment, the multi-clad structure design approach is similarly scalable, taking the "W" type triple clad fiber design as an example. The present invention calculates the LP mode of the fiber from the fiber parameters given in Table 1, and the fiber geometry and refractive index profile are shown in FIG. 1.
TABLE 1 triple clad fiber parameters
The method flow of the invention is shown in fig. 3, and the steps comprise:
(1) inputting calculation parameters of an initial structure of the optical fiber, wherein the calculation parameters comprise 1) working wavelength lambda; 2) the radius of the core and each cladding; 3) the number N of refractive index layers of the optical fiber; 4) the refractive index of the core and each cladding.
(2) And determining an effective propagation constant calculation range according to the refractive index of the fiber core and the refractive index of the outermost cladding, wherein the effective propagation constant range is between the propagation constant of the outermost cladding and the propagation constant of the fiber core. The effective propagation constant beta is sampled according to linear discrete, dense sampling is carried out firstly, then sparse sampling is carried out gradually, and the influence of the number of stable solutions and the solving efficiency is balanced.
(3) Segment boundaries determination based on cladding quantityTaking effective propagation constant sampling values in the order from small to large, calculating the frequency of each segment corresponding to the sampling values, and taking the absolute value f of the frequency 1 ,f 2 ,…,f j ,…,f N 。
(4) And selecting the mode field distribution by using a scalar method or a vector method. If scalar method is used, the characteristic matrix is 2(N-1) multiplied by 2(N-1) order matrix; if vectorial, the feature matrix is a 4 (N-1). times.4 (N-1) order matrix.
(5) And constructing a characteristic matrix which is composed of an oscillation submatrix and an attenuation submatrix. The effective propagation constant samples are taken in order of magnitude. Comparing the sampling value with the propagation constants of the fiber core and each cladding layer one by one, and constructing an oscillator matrix when the sampling value is greater than the propagation constant of the fiber core/the cladding layer; when the sample value is less than the propagation constant of the core/cladding, an attenuator matrix is constructed. And forming a dual diagonal matrix by using the obtained oscillation/attenuation submatrices of each layer of the optical fiber, wherein the dual diagonal matrix is the characteristic matrix of the optical fiber.
(6) And when the determinant value of the solved feature matrix is 0, the variable effectively propagates the constant value. The characteristic matrix is a square matrix, and if a homogeneous equation set needs to have a non-zero solution, the determinant of the homogeneous equation set needs to be zero. The method for solving the equation root discrete solution can adopt equation root discrete numerical methods such as dichotomy, Newton method, chord-section method and the like.
(7) And sequencing the effective propagation constant values according to different mode orders, and obtaining the equivalent refractive index of a scalar mode or a vector mode through formula conversion.
(8) And (4) substituting the equivalent refractive index into the characteristic matrix to obtain an equation set of a corresponding mode, and calculating the mode field distribution condition in the optical fiber in the mode. The fiber mode part results are shown in table 2. Through further calculation, information such as amplitude, light intensity, phase distribution, etc. of each mode can be obtained, which is shown in fig. 2.
TABLE 2 fiber mode partial results
Although specific embodiments of the invention have been disclosed for purposes of illustration, and for purposes of aiding in the understanding of the contents of the invention and its implementation, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (9)
1. A multi-cladding step optical fiber design method based on a characteristic matrix comprises the following steps:
1) inputting calculation parameters of the initial structure of the optical fiber, wherein the calculation parameters comprise an operating wavelength lambda, the radius from the fiber core to each cladding, the refractive index of the fiber core and the refractive index of each cladding; the fiber core and each cladding are collectively called the refractive index layer of the optical fiber, the total number of the refractive index layers is N, and the radius from the fiber core to the outermost cladding is r 1 ,r 2 ,…,r i ,…,r N Expressed by the refractive index values n 1 ,n 2 ,…,n j ,…,n N Is represented by r i Is the radius of the i-th refractive index layer, n j Is the refractive index of the jth refractive index layer;
2) determining the effective propagation constant calculation range according to the refractive index of the fiber core and the refractive index of the outermost cladding; discrete sampling is carried out in the effective propagation constant calculation range to obtain an effective propagation constant beta sampling value which is recorded as beta-beta 1 ,β 2 ,β 3 ,…β t …β Z (ii) a Wherein, beta t The value is the t effective propagation constant sampling value, and Z is the total number of sampling points;
3) determining a segment boundary according to the number of the cladding layers; for each effective propagation constant sampling value, calculating the normalized transverse phase parameter or normalized transverse attenuation parameter of each refractive index layer corresponding to the effective propagation constant sampling value, and recording as f 1 ,f 2 ,…,f j ,…,f N ；
4) Constructing an oscillation submatrix or an attenuation submatrix of each effective propagation constant sampling value in the designed optical fiber;
5) constructing a characteristic matrix of the designed optical fiber according to the oscillator matrix and the attenuator matrix;
6) when the determinant value of the solved feature matrix is 0, the effective propagation constant value
7) Calculating effective propagation constant values at different mode orders
Corresponding equivalent refractive index n eff ；
8) The obtained equivalent refractive index n eff And (4) substituting the characteristic matrix to obtain an equation set of the corresponding mode, and calculating to obtain the mode field distribution in the optical fiber under each corresponding mode.
2. The method of claim 1, wherein the effective propagation constant sample value is β t Normalized transverse phase parameter or normalized transverse attenuation parameter of the j-th refractive index layer
Wherein k is 0 Is the wave vector in vacuum when (k) 0 n j ) 2 -β t 2 ＞0，f j To normalize the transverse phase parameter, when (k) 0 n j ) 2 -β t 2 ＜0，f j To normalize the transverse attenuation parameter.
3. The method of claim 2, wherein (k) is 0 n j ) 2 -β t 2 When the refractive index is more than 0, constructing an oscillator matrix of the jth refractive index layer; when (k) 0 n j ) 2 -β t 2 < 0, constructing an attenuator matrix for the j-th refractive index layer.
4. The method of claim 3, wherein the feature matrix is
5. The method according to claim 4, wherein in the step 6), the effective propagation constant value is solved
Comprises the following steps: first, each beta is obtained in turn t Finding out intervals in which all values meeting the determinant have zero points by utilizing the zero point existence theorem for the corresponding characteristic matrix determinant values; secondly, a discrete numerical method is adopted to obtain a numerical solution with a determinant of 0 in all the intervals meeting the conditions
Where x is the number of numerical solutions for the presence of a fiber mode,
and solving the corresponding effective propagation constant value for the Tth numerical value.
6. The method of claim 1, wherein the mode field diameter, insertion loss, cut-off wavelength, and fiber dispersion of the designed fiber are determined according to the mode field distribution, thereby determining the application scenario of the designed fiber.
7. The method of claim 1, wherein discrete sampling is performed over the effective propagation constant calculation range.
8. A server, comprising a memory and a processor, the memory storing a computer program configured to be executed by the processor, the computer program comprising instructions for carrying out the steps of the method according to any one of claims 1 to 7.
9. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 7.
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| CN114942490B (en) | 2023-03-24 |
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