WO2022156762A1 - Procédé de calcul de diaphonie de fibre multicœur à faible couplage basé sur une idée de segmentation - Google Patents

Procédé de calcul de diaphonie de fibre multicœur à faible couplage basé sur une idée de segmentation Download PDF

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WO2022156762A1
WO2022156762A1 PCT/CN2022/073140 CN2022073140W WO2022156762A1 WO 2022156762 A1 WO2022156762 A1 WO 2022156762A1 CN 2022073140 W CN2022073140 W CN 2022073140W WO 2022156762 A1 WO2022156762 A1 WO 2022156762A1
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core
crosstalk
fiber
segment
calculating
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向练
汪文杰
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苏州大学
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines

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  • 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.
  • 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.
  • W-MCF weakly coupled multi-core fiber
  • SC-MCF strongly coupled multi-core fiber
  • FM-MCF few-mode multi-core fiber
  • 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 .
  • the difference between the refractive indices between different cores is zero
  • 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.
  • 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.
  • 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. .
  • 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.
  • 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].
  • 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.
  • 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.
  • 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:
  • the total crosstalk between the cores is obtained by adding the crosstalk of each segment.
  • the calculation formula of the total crosstalk XT' is:
  • ⁇ eq,mn,i (z) ⁇ eq, m,i (z)- ⁇ eq,n,i (z)
  • ⁇ eq,m,i (z) is the equivalent propagation constant of core m in the i-th segment ⁇ eq (z)
  • ⁇ eq,n , i (z) is the equivalent propagation constant ⁇ eq (z) of the core n in the i-th segment.
  • ⁇ eq (z) the equivalent propagation constant ⁇ eq (z) ⁇ c ⁇ p [R b +rcos ⁇ (z)]/R b
  • ⁇ c the undisturbed fiber Core propagation constant
  • ⁇ c n eff 2 ⁇ / ⁇
  • n eff the effective refractive index of the fundamental mode
  • R b the bending radius of the core
  • r the core spacing
  • ⁇ (z) is the core when the transmission distance is z
  • the phase of ⁇ p is the perturbation of the propagation constant along the longitudinal propagation direction.
  • phase ⁇ (z) is random when the transmission distance is z
  • 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
  • T is the solution coefficient of the matrix.
  • the value range of d is 0.0025m-0.0380m.
  • 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.
  • 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.
  • 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.
  • FIG. 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.
  • FIG. 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.
  • 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.
  • 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.
  • the optimal value range of the segment length d is 0.0025m-0.0380m, and in this embodiment, it is preferably 0.01m.
  • the average crosstalk value of a duplex fiber is calculated with different segment lengths.
  • 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
  • ⁇ L i is the segment length of different segments
  • the optical fiber is divided into N segments with lengths of ⁇ L 1 , ⁇ L 2 , . . . , ⁇ L N respectively.
  • P 0 is the incident power
  • a small part of the power is coupled into the fiber core 2 in each segment.
  • 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.
  • 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.
  • ⁇ eq,mn,i (z) that is, the difference between the propagation constants
  • the coupled mode equation is corrected by the equivalent phase mismatch ⁇ 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.
  • 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.
  • the initial electric field amplitudes of the incident fiber core m and the coupled fiber core n are 1.0 and 0.0, respectively.
  • the amount of coupled crosstalk is low, and it is assumed that the amplitude of core m remains constant.
  • ⁇ eq,mn,i (z) ⁇ eq,m,i (z)- ⁇ eq,n,i (z)
  • ⁇ eq,m,i (z) is the equivalent propagation constant ⁇ eq (z) of the core m in the i-th segment
  • ⁇ eq,n,i ( z) is the equivalent propagation constant ⁇ eq (z) of the core n in the i-th segment.
  • the bending radius R b and the phase ⁇ (z) of the core are random when the transmission distance is z, and the bending radius R b (z) and the phase ⁇ (
  • ⁇ is the twist rate
  • ⁇ 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.
  • 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:
  • 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
  • ⁇ eq,mn (z) is the fiber Equivalent phase mismatch between cores.
  • the corrected coupled mode equation of the i-th segment is:
  • z is the longitudinal transmission distance
  • A is the electric field amplitude in the core
  • j is an imaginary number
  • k mn,i (z) is the mode coupling coefficient between the core n and the core m in the i-th segment
  • Step 3 Combine the mode coupling coefficient k and the equivalent phase mismatch ⁇ 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.
  • 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 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 ⁇ ' mn (z) is the difference between the equivalent propagation constants between the cores.
  • 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.
  • a n ,i (d) and Am ,i (d) calculate the increased crosstalk ⁇ XT i in the i-th segment, and the formula for ⁇ XT 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 :
  • the core n is the incident core
  • the core m is the coupling core
  • 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:
  • each segment a small amount of power is coupled into the core m, and the normalized power of each core can be expressed as:
  • the power conversion in the coupled core can be expressed as:
  • 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:
  • 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.
  • Core n is the core n in the multi-core fiber
  • Pn is the optical power in the core n.
  • 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 ⁇ 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.
  • 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.
  • the present invention 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 core radius a 0 4um
  • the cladding refractive index n 0 1.4381
  • the twist rate ⁇ 2 ⁇ rad/m
  • the optical pulse wavelength is 1550nm
  • the incident core is the central core n
  • the coupling core is the weak coupling of the outer core m
  • the method of the present invention is compared with the classical discrete variation model in reference [1].
  • 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.
  • 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.
  • DCM discrete variation model
  • FIG 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
  • 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 .
  • Rpk critical bending radius
  • 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.
  • the present invention 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").
  • SIM 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.
  • 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.
  • 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.
  • 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%.
  • 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 .
  • 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.
  • computer-usable storage media including, but not limited to, disk storage, CD-ROM, optical storage, etc.
  • 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.

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Abstract

Procédé de calcul de la diaphonie d'une fibre multicœur à faible couplage basé sur une idée de segmentation, consistant à : acquérir un paramètre physique d'une fibre optique, paramétrer une longueur de segmentation de la fibre optique et calculer un coefficient de couplage de mode k ; réaliser une segmentation de longueur égale sur la fibre optique dans la direction de propagation selon d, calculer une désadaptation de phase équivalente Δβeq,mn,i(z) entre un cœur de fibre n et un cœur de fibre m dans un ième segment, et corriger une équation de mode couplé ; calculer un coefficient de couplage corrigé gi de chaque segment en combinaison avec k et Δβeq,mn,i(z) ; obtenir des expressions de forme fermée de champs électriques dans le cœur de fibre n et le cœur de fibre m au niveau de l'extrémité de chaque segment de fibre optique au moyen de l'équation de mode couplé corrigée, et calculer la diaphonie accrue ΔXTi dans l'ième segment ; et ajouter chaque ΔXTi pour obtenir la diaphonie totale entre les cœurs de fibre. Le remplacement de constantes aléatoires par une constante de propagation équivalente et le coefficient de couplage de mode permet de prendre pleinement en compte les influences de la constante de propagation et du coefficient de couplage de mode et d'associer les caractéristiques physiques intrinsèques du cœur de fibre grâce à la constante de propagation équivalente du cœur de fibre. Par comparaison avec un procédé de calcul de diaphonie classique, le procédé de calcul de la diaphonie d'une fibre multicœur à faible couplage basé sur une idée de segmentation est appliqué plus largement et offre un résultat de calcul précis.
PCT/CN2022/073140 2021-01-25 2022-01-21 Procédé de calcul de diaphonie de fibre multicœur à faible couplage basé sur une idée de segmentation WO2022156762A1 (fr)

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