WO2022156762A1

WO2022156762A1 - Weakly-coupled multi-core fiber crosstalk calculation method based on segmentation idea

Info

Publication number: WO2022156762A1
Application number: PCT/CN2022/073140
Authority: WO
Inventors: 向练; 汪文杰
Original assignee: 苏州大学
Priority date: 2021-01-25
Filing date: 2022-01-21
Publication date: 2022-07-28
Also published as: CN112859329A

Abstract

A weakly-coupled multi-core fiber crosstalk calculation method based on a segmentation idea, comprising: acquiring a physical parameter of an optical fiber, setting a segmentation length d of the optical fiber, and calculating a mode coupling coefficient k; performing equal-length segmentation on the optical fiber along the propagation direction according to d, calculating an equivalent phase mismatch Δβeq,mn,i(z) between a fiber core n and a fiber core m in an i-th segment, and correcting a coupled-mode equation; calculating a corrected coupling coefficient gi of each segment in combination with k and Δβeq,mn,i(z); obtaining closed-form expressions of electric fields in the fiber core n and the fiber core m at the tail of each segment of optical fiber by means of the corrected coupled-mode equation, and calculating the increased crosstalk ΔXTi in the i-th segment; and adding each ΔXTi to obtain the total crosstalk between the fiber cores. By replacing random constants with an equivalent propagation constant and the mode coupling coefficient, the influences of the propagation constant and the mode coupling coefficient are fully considered, and the intrinsic physical characteristics of the fiber core are associated by means of the equivalent propagation constant of the fiber core. Compared with a traditional crosstalk calculation method, the weakly-coupled multi-core fiber crosstalk calculation method based on a segmentation idea is applied more widely, and has an accurate calculation result.

Description

Crosstalk calculation method of weakly coupled multi-core fiber based on segmentation idea

technical field

The invention relates to the technical field of optical fiber crosstalk calculation, in particular to a weakly coupled multi-core optical fiber crosstalk calculation method based on a segmentation idea.

Background technique

With the rapid growth of data services such as cloud computing, online games, and the Internet of Things, Internet traffic continues to grow. As the backbone transmission network of the Internet, the optical network is the backbone of the Internet. The growth trend of traffic has put forward higher requirements for the transmission bandwidth of optical networks. However, with the full utilization of physical dimensions such as time, frequency, wavelength, and polarization in the optical fiber communication system by modern communication technology, in the optical network environment with optical fiber as the main propagation medium, the single-core single-mode fiber (Single Mode Fiber, SMF The experimental transmission capacity of ) has gradually approached the nonlinear Shannon theoretical limit of 100Tbit/s, and the multi-core fiber technology based on space division multiplexing (SDM) can greatly expand the last remaining physical dimension (spatial dimension) in optical fiber communication. The communication capacity has therefore begun to be widely studied.

Multi-core fiber (Multi Core Fiber) is a common cladding area with multiple cores. Existing space division multiplexing (SDM) fibers include weakly coupled multi-core fiber (WC-MCF), strongly coupled multi-core fiber. (SC-MCF) and few-mode multi-core fiber (FM-MCF), etc. In weakly coupled multi-core fibers, the physical distance between the cores is very small, and the optical signals in different cores interact with each other to generate coupling crosstalk, which will seriously affect the quality of optical communication. The coupled mode theory provides a theoretical basis for the study of the coupling crosstalk between the cores, and it is found that the power coupling between the cores in an ideal weakly coupled multi-core fiber (the difference between the refractive indices between different cores is zero) exhibits periodic oscillation characteristics . However, due to the error of the manufacturing process, there will be slight differences in the refractive index between different cores of the actual multi-core fiber, and in the actual transmission process, the random longitudinal disturbance caused by the bending and twisting of the fiber must also be considered. Therefore, in order to study the coupling crosstalk problem of practical multi-core fibers, it is necessary to solve the modified coupled mode equation including random longitudinal disturbance to study the characteristics of coupling crosstalk.

Based on the random characteristics of longitudinal perturbation, Tetsuya Hayashi et al. used the probability and statistical method to analyze the statistical characteristics of coupled crosstalk in a constant bending rate twin-core fiber to solve the problem of random evolution of crosstalk, and proposed a general expression of coupled crosstalk[1] , it can be seen that in the phase matching region, the average power of the inter-core crosstalk varies linearly with the bending radius and transmission length. In this method, the discrete variation model is used to regard crosstalk as a random variable. It is necessary to use the central limit theory to find the variance of the real and imaginary parts of the crosstalk, so as to obtain the probability density function and distribution function of the crosstalk, and finally obtain the expression of the mean value of the crosstalk. . In the process of theoretical derivation, it is assumed that the propagation constants between different cores are exactly the same (the intrinsic refractive indices of different cores are exactly the same). However, the propagation constants of different cores of an actual multi-core fiber will be slightly different and cannot be exactly the same. Therefore, this model does not apply to practical multi-core fibers. Moreover, this model can only be applied in the phase-matched region, not in the non-phase-matched region. In practical multi-core fibers, its application range is small.

Ming-Jun Li et al. proposed to use the idea of segment statistics to deduce the average crosstalk value of the two-core fiber, and obtained the expression of the average crosstalk value of the two-core fiber under the condition of different segment lengths [2]. The methods and theoretical expressions proposed in this method are not complete enough. In actual fibers, even if there are two homogeneous cores, their propagation constants cannot be exactly the same, and their propagation constants will change due to longitudinal perturbations of bending and torsion. In addition, the processing of segmentation is not perfect. It assumes that the propagation constant k and the propagation constant g remain unchanged. This assumption does not hold in the actual multi-core fiber, because the propagation constant k and the modified propagation constant g are subject to bending. and torsional effects vary longitudinally along the fiber. Therefore, these factors must be taken into account when solving the coupled-mode equations and calculating crosstalk.

Lin Gan et al. proposed a numerical solution method to solve the coupled mode equation directly by using a computer [3]. In this method, the fourth-order Runge-Kutta method and the Simpson integration method are combined to deal with the phase integration problem in the coupled mode equation, so as to realize the coupled mode equation. Numerical solution of the equation. Although the final analytical results of this method are consistent with the theoretical results, it is time-consuming to solve the coupled mode equations numerically and cannot provide the intrinsic physical properties of the crosstalk variation.

References of the present invention are as follows:

[1] Tetsuya Hayashi, Toshiki Taru, Osamu Shimakawa, Takashi Sasaki, and Eisuke Sasaoka, "Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber," Optics Express, 19(17), 16576-16592 ( 2011).

[2] Ming-Jun Li, Shenping Li, and Robert A. Modavis, "Coupled mode analysis of crosstalk in multicore fiber with random perturbations," in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper W2A .35.

[3] Lin Gan, Li Shen, Ming Tang, Chen Xing, Yanpeng Li, Changjian Ke, Weijun Tong, Borui Li, Songnian Fu, and Deming Liu, "Investigation of channel model for weakly coupled multicore fiber," Optics Express, 26 (5), 5182-5199 (2018).

SUMMARY OF THE INVENTION

Therefore, the technical problem to be solved by the present invention is to overcome the problems in the prior art that the influence of the propagation constant and the mode coupling coefficient are not considered at the same time, the intrinsic physical characteristics of the fiber core cannot be correlated, and the application scope is limited.

In order to solve the above technical problems, the present invention provides a method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the idea of segmentation, which includes the following steps:

Obtain the physical parameters of the fiber, set the segment length d of the fiber, and calculate the mode coupling coefficient k;

Divide the optical fiber into equal-length segments along the propagation direction by the length d, and calculate the equivalent phase mismatch Δβ _eq,mn,i (z) between the core n and the core m in the i-th segment, using the equal-length segment Δβ _eq,mn,i (z) modifies the coupled mode equation, and the modified coupled mode equation of the i-th segment is:

where z is the longitudinal transmission distance, A is the electric field amplitude in the core, j is an imaginary number, and k _mn,i (z) is the mode coupling coefficient between the core n and the core m in the i-th segment;

Combine the mode coupling coefficient and the equivalent phase mismatch to calculate the modified coupling coefficient _gi of each segment. The calculation formula of _gi is:

where k _i (d) is the coupled mode coefficient of the i-th segment;

The analytical solution of the electric field in the core n at the end of each fiber, A _n,i (d) and the analytical solution of the electric field in the core m, Am _,i (d), are obtained through the revised coupled mode equation. According to An _,i ( d) and Am _,i (d) calculate the increased crosstalk ΔXT _i of the i-th segment;

The total crosstalk between the cores is obtained by adding the crosstalk of each segment. The calculation formula of the total crosstalk XT' is:

Further, the calculation formula of the mode coupling coefficient k is:

where Δ ₁ is the relative refractive index difference between the core and the cladding, a ₁ is the core radius, and Λ is the distance between the cores;

β is the propagation constant of the fiber core; V ₁ =k ₀ a ₁ n ₁ (2Δ ₁ ) ^1/2 is the normalized frequency of the transmission mode in the fiber, k ₀ =2π/λ is the light wave number, λ is the light wave wavelength; K ₁ (W ₁ ) is the modified second-order first-order Bessel function.

Further, the calculation formula of the equivalent phase mismatch Δβ _eq,mn,i (z) between the core n and the core m in the i-th segment is: Δβ _eq,mn,i (z)=β _{eq, m,i} (z)-β _eq,n,i (z), where β _eq,m,i (z) is the equivalent propagation constant of core m in the i-th segment β _eq (z),β _{eq,n , i} (z) is the equivalent propagation constant β _eq (z) of the core n in the i-th segment.

Further, the calculation formula of the equivalent propagation constant β _eq (z) is: β _eq (z)≈β _c β _p [R _b +rcosθ(z)]/R _b , where β _c is the undisturbed fiber Core propagation constant, β _c =n _eff 2π/λ; n _eff is the effective refractive index of the fundamental mode, R _b is the bending radius of the core, r is the core spacing; θ(z) is the core when the transmission distance is z The phase of β _p is the perturbation of the propagation constant along the longitudinal propagation direction.

Further, the bending radius R _b of the fiber core is random when the transmission distance is z, and the calculation formula of the bending radius R _b (z) when the transmission distance is z is: R _b (z)=R _b ( 1+ _SR (z)), where _SR is an introduced random variable, and _SR is uniformly distributed along the longitudinal transmission distance.

Further, the phase θ(z) is random when the transmission distance is z, and the calculation formula of the phase θ(z) when the transmission distance is z is: θ(z)=γ(1+S _T (z ))z+φ, where γ is the twist rate, φ is the initial phase of the fiber core, _ST are the random variables introduced respectively, and _ST is uniformly distributed along the longitudinal transmission distance.

Further, the calculation formulas of the analytical solution A _n,i (d) of the electric field in the core n at the end of each fiber segment and the analytical solution of the electric field in the core m A _m,i (d) are:

The core n is the incident core, the core m is the coupling core, and T is the solution coefficient of the matrix.

Further, the solution coefficient T of the matrix is:

Further, according to A _n,i (d) and A _m,i (d) to calculate the increased crosstalk ΔXT _i in the i-th segment, the calculation formula of ΔXT _i is:

Further, when the segment length d of the optical fiber is set, the value range of d is 0.0025m-0.0380m.

Beneficial effects of the present invention: the method for calculating crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea fully considers the influence of propagation constant and mode coupling coefficient according to the characteristics of crosstalk in different working ranges and the relationship between crosstalk and optical fiber parameters, and uses The equivalent propagation constant of the fiber core is related to the intrinsic physical properties of the fiber core. The calculation method of universal crosstalk is proposed by using the equivalent propagation constant and mode coupling coefficient instead of random constants on the basis of equal length segments. Compared with the traditional crosstalk calculation method, the present invention has a wider application range, not only in the phase matching area, but also in the non-phase matching area, homogeneous and heterogeneous multi-core fibers, and the calculation is fast and the result is accurate.

The above description is only an overview of the technical solution of the present invention. In order to understand the technical means of the present invention more clearly, and implement it according to the content of the description, the preferred embodiments of the present invention are described in detail below with the accompanying drawings.

Description of drawings

Figure 1 is a flow chart of the present invention.

FIG. 2 is a schematic diagram of power coupling between fiber cores in the present invention.

Figure 3 is a schematic diagram of the seven-core fiber used in the simulation.

4 is a schematic diagram of the relationship between the crosstalk between cores of the present invention and the discrete variation model and the longitudinal signal transmission distance when the segment lengths d are 0.001m, 0.01m and 0.05m respectively in the simulation.

5 is a schematic diagram of the relationship between the inter-core crosstalk and optical wavelength, inter-core distance, fiber bending radius and twist rate of the present invention and the discrete variation model under the condition of longitudinal transmission distance z=200m in the simulation.

6 is a schematic diagram of the relationship between the crosstalk and the bending radius of the present invention and the use of power coupling theory and discrete variation model in the case of an actual homogeneous multi-core fiber and a heterogeneous multi-core fiber in the simulation.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

Referring to the flowchart shown in FIG. 1 , an embodiment of a method for calculating crosstalk of weakly coupled multi-core optical fibers based on a segmentation idea of the present invention includes the following steps:

Step 1: Obtain the physical parameters of the optical fiber. In this embodiment, the physical parameters of the optical fiber are initialized, including the distance between cores, the core radius, the bending radius of the optical fiber, and the twist rate of the optical fiber, and the segment length d of the optical fiber is set. After a large number of simulation and comparison experiments, it is obtained that the optimal value range of the segment length d is 0.0025m-0.0380m, and in this embodiment, it is preferably 0.01m. Calculate the mode coupling coefficient k, the formula for k is:

In Ref. [2], the average crosstalk value of a duplex fiber is calculated with different segment lengths. In this paper, core 1 is the incident core, P ₁ is the output power of the incident core; core 2 is the coupled core, P ₂ is the output power of the coupled core, P _2i is the power coupled into the core 2 for each segment, ΔL _i is the segment length of different segments, and the optical fiber is divided into N segments with lengths of ΔL ₁ , ΔL ₂ , . . . , ΔL _N respectively. When P ₀ is the incident power, a small part of the power is coupled into the fiber core 2 in each segment. Assuming that each segment is uniform, the electric field amplitude _Am of each core is described by the coupled mode equation:

where k _j is the mode coupling coefficient of the jth segment, Δβ _j is the difference between the propagation constants between the two cores, which includes a constant term Δβ ₀ and a random disturbance term Δβ _pj , usually Δβ _j =Δβ ₀ + Δβ _pj . By solving the coupled mode equation, the electric field amplitude in the coupled core at the end of each segment can be obtained as:

in

Because the phases in the different segments of the random perturbation can be uncorrelated, the powers of all the different segments can be added incoherently. In the present invention, the idea of segmentation is also used to divide the optical fiber into N segments, and the problem of inaccurate calculation of crosstalk will be caused when the segment lengths are different. Therefore, the segmented method of equal length is adopted in the present invention, thereby simplifying the Correct the integral term in the coupled mode equation to improve the accuracy of crosstalk calculation.

Step 2: Divide the optical fiber into equal-length segments along the propagation direction according to the length d, divide the optical fiber into N uncorrelated equal-length uniform segments d, and calculate the equivalent phase loss between the core n and the core m in the i-th segment. With Δβ _eq,mn,i (z) (that is, the difference between the propagation constants), the coupled mode equation is corrected by the equivalent phase mismatch Δβ _eq,mn,i (z) under equal-length segments. Solving the coupled-mode equations numerically is time-consuming and does not provide the intrinsic physics of the crosstalk variation. Therefore, the present invention correlates the intrinsic physical properties of the fiber core through the equivalent propagation constant of the fiber core, which is determined by the effective refractive index of the fundamental mode of the fiber core, the bending radius of the fiber core, the core spacing, the twist rate, the light wavelength, etc. reflect.

In this embodiment, it is assumed that the initial electric field amplitudes of the incident fiber core m and the coupled fiber core n are 1.0 and 0.0, respectively. In the case of weak coupling, the amount of coupled crosstalk is low, and it is assumed that the amplitude of core m remains constant. The calculation formula of the equivalent phase mismatch Δβ _eq,mn,i (z) between the core n and the core m in the i-th segment is: Δβ _eq,mn,i (z)=β _eq,m,i (z)-β _eq,n,i (z), where β _eq,m,i (z) is the equivalent propagation constant β _eq (z) of the core m in the i-th segment, β _eq,n,i ( z) is the equivalent propagation constant β _eq (z) of the core n in the i-th segment. The calculation formula of the equivalent propagation constant β _eq (z) is: β _eq (z)≈β _c β _p [R _b +rcosθ(z)]/R _b , where β _c is the undisturbed core propagation constant , β _c =n _eff 2π/λ; n _eff is the effective refractive index of the fundamental mode, R _b is the bending radius of the core, r is the core spacing; θ(z) is the phase of the core when the transmission distance is z; β _p is the perturbation of the propagation constant along the longitudinal propagation direction, which is a random variable.

In an actual multi-core fiber, the bending radius R _b and the phase θ(z) of the core are random when the transmission distance is z, and the bending radius R _b (z) and the phase θ ( The calculation formula of z) is: R _b (z)=R _b (1+S _R (z)), θ(z)=γ(1+S _T (z))z+φ. Among them, γ is the twist rate, φ is the initial phase of the fiber core; S _R and S _T are the random variables introduced respectively, and they are uniformly distributed along the longitudinal transmission distance. Due to the existence of _SR and _ST random variables, it is difficult to solve the above traditional coupled mode equations. Therefore, we adopt the idea of piecewise to deal with the modified coupled mode equations. When the fiber is divided into N uncorrelated equal-length uniform segments d, these random variables can be reduced to a constant within the interval of this segment.

The main external factors that affect the crosstalk function in a homogeneous fiber are the bending and twisting of the fiber, and the main internal factors are the core distance and refractive index. The traditional coupled mode equation is:

where z is the longitudinal transmission distance, A is the electric field amplitude in the core, M is the number of cores in the multi-core fiber, k _nm (z) is the mode coupling coefficient between the cores, Δβ _eq,mn (z) is the fiber Equivalent phase mismatch between cores.

Using the equivalent phase mismatch Δβ _eq,mn,i (z) under the equal length segment to correct the coupled mode equation, the corrected coupled mode equation of the i-th segment is:

Step 3: Combine the mode coupling coefficient k and the equivalent phase mismatch Δβ _eq,mn,i (z) to calculate the modified coupling coefficient g _i of each segment,

where k _i (d) is the coupled mode coefficient of the i-th segment, k _i (d)≈k _mn,i (d)≈k _nm,i (d). gi is the corrected coupled mode coefficient, _gi contains both the coupled mode coefficient and the difference between the equivalent propagation constants, fully considering the influence of the propagation constant and the mode coupling coefficient, which can improve the accuracy of the calculation and expand the application scope.

In order to evaluate the crosstalk in the multi-core fiber more easily, the power coupling theory is introduced in the present invention to solve the crosstalk estimation problem in the multi-core fiber. Crosstalk estimation method based on power coupling theory Starting from the power coupling theory, the power coupling equation in multi-core fibers is:

Among them, P _m is the average power of the core m, and h _mn is the power coupling coefficient between the cores. The power coupling coefficient based on the exponential autocorrelation function is:

where d is the correlation length and Δβ' _mn (z) is the difference between the equivalent propagation constants between the cores. If the bending rate R _b and the twist rate γ of a multi-core fiber are assumed to be constant, then the average value of the power coupling coefficient over torque is:

The final crosstalk estimation expression obtained is:

is the average power coupling coefficient. Under different transmission conditions, the average power coupling coefficient has different mathematical expressions.

Step 4: Obtain the analytical solution A _n,i (d) of the electric field in the core n at the end of each fiber segment and the analytical solution A _m,i (d) of the electric field in the core m through the modified coupled mode equation. According to A _{n ,i} (d) and Am _,i (d) calculate the increased crosstalk ΔXT _i in the i-th segment, and the formula for ΔXT _i is:

The analytical solution of the electric field in the fiber core n at the end of each fiber segment, A _n,i (d), and the analytical solution of the electric field in the fiber core m, Am _,i (d), can be obtained by solving the coupled mode equation, which is expressed as :

Among them, the core n is the incident core, the core m is the coupling core, and T is the solution coefficient of the matrix. The solution coefficient T of the matrix is:

Step 5: Add the crosstalk of each segment to obtain the total crosstalk between the cores. The calculation formula of the total crosstalk XT' is:

In each segment, a small amount of power is coupled into the core m, and the normalized power of each core can be expressed as:

;in:

Therefore, from segment i-1 to segment i, the power conversion in the coupled core can be expressed as:

ΔP _m,i =|A _m,i (d)-A _m,i-1 (d)| ² ;

Therefore, the increased crosstalk of the i-th segment can be expressed as:

The crosstalk of different segments can be seen as uncorrelated due to the effects of core bending and twisting. Therefore, the crosstalk of different segments can be superimposed together. The total crosstalk between the cores can be expressed as:

N is the number of segments, N=z/d, and z is the longitudinal transmission distance of the optical signal. In a weakly coupled multi-core fiber, the power in the coupled core is much less than the power in the incident core, so the total crosstalk XT' can be simplified as:

FIG. 2 is a schematic diagram of the power coupling between cores in the present invention, wherein Core n is the core n in the multi-core fiber, and Pn is the optical power in the core n. During the longitudinal transmission of the optical pulse signal along the optical fiber, the optical power in each fiber core should be continuously coupled with each other in a wave-like manner along the transmission direction. Due to the segmented nature, the model is applicable even if the intrinsic propagation constant β _c of the core and the mode coupling coefficient k _mn(nm) (z) vary randomly along the longitudinal direction. Because we only need to find the value of the equivalent propagation constant and the mode coupling coefficient in each segment to get the variation of the crosstalk in this segment.

Beneficial effects of the present invention: the method for calculating crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea fully considers the influence of propagation constant and mode coupling coefficient according to the characteristics of crosstalk in different working ranges and the relationship between crosstalk and optical fiber parameters, and uses The equivalent propagation constant of the fiber core is related to the intrinsic physical properties of the fiber core, and a calculation method of universal crosstalk is proposed by using the equivalent propagation constant and mode coupling coefficient instead of random constants on the basis of equal-length segments. Compared with the traditional crosstalk calculation method, the present invention has a wider application range, not only in the phase matching area, but also in the non-phase matching area, homogeneous and heterogeneous multi-core fibers, and the calculation is fast and the result is accurate.

In order to further illustrate the beneficial effects of the present invention, as shown in FIG. 3 , the core radius a ₀ =4um, the cladding refractive index n ₀ =1.4381, the core refractive index is about n ₁ =1.4453, and the bending radius is R _b =200mm , the twist rate γ=2πrad/m, the core spacing is D _nm =30um, the optical pulse wavelength is 1550nm, the transmission distance is z=200m, the incident core is the central core n, and the coupling core is the weak coupling of the outer core m In the case of a seven-core fiber, the method of the present invention is compared with the classical discrete variation model in reference [1]. As shown in the relationship between the crosstalk between cores and the longitudinal transmission distance of the signal in Fig. 4, when the segment length d is set to 0.001m, 0.01m and 0.05m respectively, the crosstalk value calculated by the method of the present invention and the discrete change model are obtained. The crosstalk values are compared, and the results are shown in Figure 4. Fig. 4(b) is a partial enlarged view of the corresponding cells indicated by the arrows in Fig. 4(a), and the boxes in Fig. 4(a) and Fig. 4(b) represent the corresponding corresponding arrows A zoomed-in view of the area within the cell. In Figure 4, Sim is the crosstalk value obtained by directly using the power coupling theory, which is represented by "x" in the figure; DCM is the crosstalk value obtained by the discrete variation model, which has nothing to do with the segment length d, which is represented by "+—+" in the figure. ; (16) in Figure 4 represents the exact solution by the present invention

The result obtained, (19) represents the simplified solution from the present invention

The obtained results; in Figure 4, "o-o" represents the simulation result of (16) under the condition of d=0.01, "o--o" represents the simulation result of (16) under the condition of d=0.001, "o- _· -o" indicates the simulation result of (16) under the condition of d=0.05; "*-*" indicates the simulation result of (19) under the condition of d=0.01, "*--*" indicates (19) under the condition of d=0.001 The simulation result under the condition, "*-·-*" represents the simulation result of (19) under the condition of d=0.05. It can be seen from FIG. 4 that the inter-core crosstalk value increases with the increase of the transmission distance, and the method for calculating the crosstalk in the present invention is very consistent with the crosstalk value obtained by the discrete variation model. It can be seen that the calculation result of the present invention is highly accurate. Meanwhile, it can also be seen from FIG. 4 that when the preferred d=0.01m in the embodiment is used, the present invention is applicable and can provide an accurate crosstalk estimation.

Next, in this embodiment, the present invention (USAM) is also compared with the discrete variation model (DCM) in the case of longitudinal transmission distance z=200m. The relationship between inter-core crosstalk and optical wavelength, inter-core distance, fiber bending radius and twist rate is shown in Figure 5. In Figure 5 (a) is the relationship between crosstalk and light wavelength, (b) is the relationship between crosstalk and inter-core distance , (c) is the relationship between the crosstalk and the bending radius of the fiber, (d) is the relationship between the crosstalk and the twist rate of the fiber, it can be seen from Figure 5 that under the same transmission conditions, the crosstalk will increase with the increase of the transmission wavelength, It decreases with the increase of the distance between the cores, and increases with the increase of the bending radius. It has nothing to do with the twist rate of the fiber core. The present invention is in good agreement with the estimated value of the crosstalk obtained by the discrete change model. Modeling is fairly reliable. The phase matching region is related to the bending radius, and the inter-core crosstalk will reach a maximum value at the critical bending radius _Rpk . When the bending radius of the fiber is less than R _pk , the fiber is said to work in the phase matching region; when the bending radius of the fiber is greater than R _pk , the fiber is said to be working in the non-phase matching region. The simulation results shown in Fig. 5 are all obtained when the bending radius is less than _Rpk , from which it can be seen that the present invention is in the phase matching region and under different transmission conditions (including changes with optical wavelength, core spacing, bending radius, and torsion rate) The following are applicable.

In addition, in order to illustrate that the method of the present invention is applicable to actual homogeneous multi-core fibers and heterogeneous multi-core fibers (refractive indices between different cores are not exactly the same, there will be slight differences), in actual homogeneous multi-core fibers and heterogeneous multi-core fibers In the case of multi-core fibers, the present invention (USAM) is combined with the use of power coupling theory (SIM) (see document "Koshiba M, Saitoh K, Takenaga K, et al. Analytical Expression of Average Power-Coupling Coefficients for Estimating Intercore Crosstalk"). in Multicore Fibers[J].IEEE Photonics Journal,2012,4(5):1987-1995.”), discrete variation model (DCM) for comparison. The method in the present invention adopts the derivation based on the coupled mode theory, which is different from the method using the power coupling theory (SIM) in the power coupling theory. Fig. 6(a) is a discrete variation model, the present invention when the refractive index difference between the cores is 0.012% and 0.020%, respectively, and the power coupling when the refractive index difference between the cores is 0.012% and 0.020%, respectively Schematic diagram comparing the relationship between crosstalk and bending radius in the actual homogeneous multi-core fiber obtained theoretically; as shown in Fig. 6(b), it is a discrete variation model and the difference between the refractive indices between the cores is 0.046% and 0.092%, respectively A schematic diagram comparing the relationship between crosstalk and bending radius in a heterogeneous multi-core fiber obtained by using the power coupling theory in the present invention, and the difference in refractive index between cores is 0.046% and 0.092%, respectively. The discrete variation model is only suitable for completely homogeneous multi-core fibers, not for multi-core fibers with refractive index differences, so the discrete variation model in Figure 6 does not involve multi-core fibers with refractive index differences. In Fig. 6(a), R _pk1 is the critical bending radius when the refractive index difference between the cores is 0.012%, and R _pk2 is the critical bending radius when the refractive index difference between the cores is 0.020%; R _pk3 in Fig. 6(b) is the critical bending radius when the refractive index difference between the cores is 0.046%, and R _pk4 is the critical bending radius when the refractive index difference between the cores is 0.092%. It can be seen from Figure 6 that in the phase-matched region, the inter-core crosstalk increases with the increase of the bending radius; in the non-phase-matched region, the inter-core crosstalk decreases with the increase of the bending radius, and with the increase of the bending radius, The crosstalk will gradually tend to a stable value. It can be seen that the estimated value of the crosstalk obtained by the present invention is very consistent with the result obtained by using the power coupling theory. At the same time, it can be seen from Figure 6(b) that the variation trend of inter-core crosstalk is almost the same as that of homogeneous multi-core fibers, but for heterogeneous multi-core fibers, the critical bending radius is smaller than that of homogeneous multi-core fibers. , and the greater the intrinsic refractive index difference between the cores, the smaller the critical bending radius, and the performance of the discrete variation model in these ranges is not as good as the present invention. It can be seen that the present invention is also quite reliable for crosstalk modeling of heterogeneous multi-core fibers. It can be seen that the beneficial effects of the present invention are further illustrated through the simulation and comparison experiments in FIG. 3 , FIG. 4 , FIG. 5 and FIG. 6 .

As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations of methods and computer program products according to embodiments of the present application. It will be understood that each process in the flowchart can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce A device that implements the functions specified in one or more of the flow charts.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The device implements the functions specified in one or more of the flow charts.

These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that Instructions provide steps for implementing the functions specified in a flow or flows of the flowchart.

Obviously, the above-mentioned embodiments are only examples for clear description, and are not intended to limit the implementation manner. For those of ordinary skill in the art, other different forms of changes or modifications can also be made on the basis of the above description. There is no need and cannot be exhaustive of all implementations here. And the obvious changes or changes derived from this are still within the protection scope of the present invention.

Claims

A method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the idea of segmentation, which is characterized by comprising the following steps:

Obtain the physical parameters of the fiber, set the segment length d of the fiber, and calculate the mode coupling coefficient k;

Divide the optical fiber into equal-length segments along the propagation direction by the length d, and calculate the equivalent phase mismatch Δβ eq,mn,i (z) between the core n and the core m in the i-th segment, using the equal-length segment Δβ eq,mn,i (z) modifies the coupled mode equation, and the modified coupled mode equation of the i-th segment is:

where z is the longitudinal transmission distance, A is the electric field amplitude in the core, j is an imaginary number, and k mn,i (z) is the mode coupling coefficient between the core n and the core m in the i-th segment;

Combine the mode coupling coefficient k and the equivalent phase mismatch Δβ eq,mn,i (z) to calculate the modified coupling coefficient gi of each segment. The calculation formula of gi is:
where k i (d) is the coupled mode coefficient of the i-th segment;

The analytical solution of the electric field in the core n at the end of each fiber, A n,i (d) and the analytical solution of the electric field in the core m, Am ,i (d), are obtained through the revised coupled mode equation. According to An ,i ( d) and Am ,i (d) calculate the increased crosstalk ΔXT i of the i-th segment;

The total crosstalk between the cores is obtained by adding the crosstalk of each segment. The calculation formula of the total crosstalk XT' is:
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 1, wherein the calculation formula of the mode coupling coefficient k is:

where Δ 1 is the relative refractive index difference between the core and the cladding, a 1 is the core radius, and Λ is the distance between the cores;
β is the propagation constant of the fiber core; V 1 =k 0 a 1 n 1 (2Δ 1 ) 1/2 is the normalized frequency of the transmission mode in the fiber, k 0 =2π/λ is the light wave number, λ is the light wave wavelength; K 1 (W 1 ) is the modified second-order first-order Bessel function.
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 1, wherein the calculation formula of the equivalent phase mismatch Δβ eq,mn,i (z) is:

Δβ eq,mn,i (z)=β eq,m,i (z)−β eq,n,i (z),

where β eq,m,i (z) is the equivalent propagation constant of core m in the i-th segment β eq (z), and β eq,n,i (z) is the equivalent propagation of the core n in the i-th segment Constant β eq (z).
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 3, wherein the calculation formula of the equivalent propagation constant β eq (z) is:

β eq (z)≈β c β p [R b +r cosθ(z)]/R b ,

where β c is the undisturbed core propagation constant, β c =n eff 2π/λ; n eff is the effective refractive index of the fundamental mode, R b is the bending radius of the fiber core, r is the core spacing; θ(z) is The phase of the core at propagation distance z, β p is the perturbation of the propagation constant along the longitudinal propagation direction.
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 4, characterized in that: the bending radius R b of the fiber core is random when the transmission distance is z, and when the transmission distance is z The calculation formula of the bending radius R b (z) is:

R b (z)=R b (1+S R (z)),

Among them, SR is an introduced random variable, and SR is uniformly distributed along the longitudinal transmission distance.
The method for calculating crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 4, wherein the phase θ(z) is random when the transmission distance is z, and the phase when the transmission distance is z is random. The formula for calculating θ(z) is:

θ(z)=γ(1+S T (z))z+φ,

Among them, γ is the torsion rate, φ is the initial phase of the fiber core, ST are the random variables introduced respectively, and ST is uniformly distributed along the longitudinal transmission distance.
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 1, characterized in that: the analytical solution of the electric field in the core n at the end of each segment of the optical fiber An ,i (d) and the core m The calculation formula of the analytical solution of the medium electric field Am ,i (d) is:

The core n is the incident core, the core m is the coupling core, and T is the solution coefficient of the matrix.
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 7, characterized in that: the solution coefficient T of the matrix is:
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to claim 1, characterized in that: calculating the increased crosstalk of the i-th segment according to A n,i (d) and A m,i (d) ΔXT i , the calculation formula of ΔXT i is:
The method for calculating the crosstalk of weakly coupled multi-core optical fibers based on the segmentation idea according to any one of claims 1 to 9, wherein: when the segment length d of the optical fiber is set, the value range of d is 0.0025m- 0.0380m.