A method, system and device for detecting inter-modal crosstalk of a weakly coupled few-mode multi-core optical fiber

Abstract

The present invention relates to the field of optical fiber communication technologies, and in particular to a method, system and device for detecting inter-modal crosstalk of a weakly-coupled few-mode multi-core optical fiber. The method includes: S1: obtaining optical fiber parameters and injection power, where the optical fiber parameters include core refractive index, cladding refractive index, core radius, core propagation constant and optical wavelength; S2: calculating the electric field strength in the core region of the optical fiber and the electric field strength in the cladding region of the optical fiber based on the optical fiber parameters; S3: calculating the inter-modal coupling mode coefficient based on the electric field strength in the core region, the electric field strength in the cladding region and the injection power; S4: constructing an inter-modal crosstalk calculation equation according to the inter-modal coupling mode coefficient to obtain the inter-modal crosstalk value of the optical fiber. The present invention takes into account the inter-modal coupling mode coefficients under different LP modes, improves the calculation accuracy of inter-modal crosstalk, is more in line with the actual optical fiber laying situation, and has a wide application range.

Description

Technical Field

[0001] The present invention relates to the technical field of optical fiber communication, and in particular to a method, system and device for detecting inter-modal crosstalk of a weakly coupled few-mode multi-core optical fiber. Background Art

[0002] The rapid development of current information technology has led to a huge increase in the data volume of optical communication networks. The transmission capacity based on standard single-mode optical fibers has approached the non-linear Shannon limit. To solve the communication capacity crisis, multi-core optical fibers, few-mode optical fibers, and few-mode multi-core optical fibers based on space division multiplexing (SDM) make full use of the spatial dimension and are expected to solve the transmission tolerance problem of single-mode optical fibers and improve the optical fiber communication capacity.

[0003] For a multi-core fiber (MCF), multiple independent single-mode cores are introduced in the cladding. When the core pitch is large, the coupling degree between the cores is small. At this time, each core of the multi-core fiber can be used as a relatively independent spatial channel to transmit different optical signals, and the transmission capacity of the optical fiber increases exponentially with the increase in the number of cores. However, due to the limitation of the manufacturing process, the cladding diameter of the optical fiber is limited. Under this condition, the increase in the number of cores will lead to a decrease in the core pitch, which means that the coupling between the cores will become stronger, that is, the inter-core crosstalk will become larger. However, the optical fiber used for transmission should have the optical characteristic of low crosstalk. Therefore, the number of cores cannot be increased blindly. A few-mode fiber (FMF) is a fiber in which multiple mutually orthogonal transmission modes are transmitted in one core, and each mode can be used as an independent channel to transmit different optical signals. Therefore, the transmission capacity of the optical fiber increases with the increase in the number of transmission modes in the core. However, when the number of modes is larger, the interference between the modes will become stronger.

[0004] In an optical communication system, excessive inter-core crosstalk will affect the transmission distance. To ensure good crosstalk performance, the core pitch of the multi-core fiber cannot be reduced. On the other hand, the limited cladding diameter limits the increase in the number of its cores. When the number of modes in a few-mode fiber increases, the complexity of signal processing at the receiving end of its transmission system increases. Therefore, in order to better solve the capacity problem, a few-mode multi-core fiber (FM-MCF) is proposed, that is, the number of spatial channels is increased from both the number of cores and the number of modes, thereby improving the transmission energy of the few-mode multi-core fiber.

[0005] Few-mode multi-core fibers have great advantages in achieving ultra-high capacity and improving spectral transmission efficiency. However, few-mode multi-core fibers also have some disadvantages, including crosstalk caused by mode coupling (abbreviated as MC) and differential mode group delay (abbreviated as DMGD) caused by the transmission of different modes. At present, great progress has been made in the research on DMGD, but little is still known about inter-modal crosstalk. Therefore, studying inter-modal crosstalk is of great significance for improving the capacity of few-mode multi-core fibers.

[0006] In the prior art, the research on inter-modal crosstalk of few-mode multi-core fibers, such as the patent with the application publication number CN115455355A, provides a method for detecting inter-core crosstalk in the case of single-mode multi-core. However, only the electric field distribution of a linear polarization (LP) mode is obtained. Since the electric field distributions of LP modes are different, there are limitations in using this method and it is impossible to obtain the inter-modal coupling coefficients of multiple LP modes simultaneously. Summary of the Invention

[0007] To solve the above technical problems, the present invention provides a method, system and device for detecting inter-modal crosstalk of weakly coupled few-mode multi-core fibers. Based on the coupled-mode theory with random perturbations existing in multi-core fibers and the Maxwell equations between modes, new inter-modal coupling coefficients are obtained, which are more accurate for the change process of inter-modal crosstalk. It can not only obtain the inter-modal crosstalk of low-order LP modes, but also obtain the inter-modal crosstalk of high-order LP modes.

[0008] The steps of the method for detecting inter-modal crosstalk of weakly coupled few-mode multi-core fibers include:

[0009] S1: Obtain fiber parameters and injection power, where the fiber parameters include core refractive index, cladding refractive index, core radius, core propagation constant and optical wavelength;

[0010] S2: Based on the fiber parameters, calculate the electric field strength in the core region of the fiber and the electric field strength in the cladding region of the fiber;

[0011] S3: Based on the electric field strength in the core region, the electric field strength in the cladding region and the injection power, calculate the inter-modal coupled-mode coefficients;

[0012] S4: According to the inter-modal coupled-mode coefficients, construct an equation for calculating inter-modal crosstalk of the fiber to obtain the value of inter-modal crosstalk of the fiber;

[0013] Among them, the calculation method of the inter-modal coupled-mode coefficients is: divide the fiber into multiple small segments to obtain the relationship between the inter-modal coupled-mode coefficients in each small segment and the electric field distribution of the linear polarization mode, and calculate the initial inter-modal coupled-mode coefficient k' according to the relationship mn:

[0014]

[0015] where ω is the angular frequency, ε0 is the vacuum permittivity, and E m and H m represent the electric field strength and the magnetic field strength in the core region respectively, and E n represents the electric field strength within the cladding, e z represents the unit vector in the z direction, n1 and n2 represent the refractive index of the core and the refractive index of the cladding respectively, the symbol * represents the conjugate operation on the matrix, m represents core m, and n represents core n;

[0016] Based on the electric field strength in the core region and the electric field strength in the cladding region, the electric field strength of the linearly polarized mode LP mn is obtained;

[0017] Based on the electric field strength of the linearly polarized mode LP mn the initial inter-mode coupling coefficient k' mn is optimized to obtain the final inter-mode coupling coefficient k mn .

[0018] In an embodiment of the present invention, the calculation method of the electric field strength in the core region and the electric field strength in the cladding region includes:

[0019] Since the optical fiber is a cylindrical structure, the LP mn mode electric field is expanded into a cylindrical polar coordinate form, so that the electric field vector is represented as the superposition of three dimensions. Based on the longitudinal electric field component in the core region and the transverse electric field component in the core region, the electric field strength E m in the core region is obtained:

[0020]

[0021] Based on the longitudinal electric field component in the cladding region and the transverse electric field component in the core region, the electric field strength E n in the cladding region is obtained:

[0022]

[0023] where e r represents the unit vector in the r direction, represents the unit vector in the z direction, and e z1 and E z2 represent the longitudinal electric field component in the core region and the longitudinal electric field component in the cladding region respectively; Er1 and both represent the transverse electric field component in the core region, E r2 and both represent the components of the transverse electric field in the cladding region.

[0024] In an embodiment of the present invention, the method for calculating the longitudinal electric field components in the core region and the cladding region includes:

[0025] Calculating the longitudinal electric field components in the core region and the cladding region by using the homogeneous Helmholtz equation:

[0026]

[0027] where, E z1 and E Z2 respectively represent the longitudinal electric field component in the core region and the longitudinal electric field component in the cladding region, A = jUC / aβ, j is the imaginary unit, C is a system constant, n1 is the core refractive index, β is the core propagation constant, a is the core radius, k = λ / 2π is the wave number, λ represents the optical wavelength, J m (x) represents the Bessel function of the first kind of order m, K m (x) represents the modified Bessel function of the second kind of order m, n2 is the cladding refractive index, r represents the radial direction in the cylindrical coordinate system, represents the circumferential direction in the cylindrical coordinate system.

[0028] In an embodiment of the present invention, substituting the longitudinal electric field components in the core region and the cladding region into the Maxwell equation, the transverse electric field components in the core region and the cladding region are obtained:

[0029]

[0030]

[0031] where, E r1 and both represent the transverse electric field components in the core region, E r2 and both represent the components of the transverse electric field in the cladding region; J' m (x) is the m - order derivative of J m (x); K' m (x) is the m - order derivative of K m (x).

[0032] In an embodiment of the present invention, the linearly polarized mode LP mnThe electric field strength I m The calculation method is as follows:

[0033]

[0034] Wherein, represents the conjugate of the longitudinal electric field component E z1 in the core region; E z2 represents the longitudinal electric field component in the cladding region; represents the conjugate of the transverse electric field component E r1 in the core region; E r2 represents the transverse electric field component in the cladding region; represents the transverse electric field component in the core region conjugate; represents the transverse electric field component in the cladding region; A = jUC / aβ, j is the imaginary unit, C is a system constant, n1 is the core refractive index, β is the core propagation constant, a is the core radius, k = λ / 2π is the wave number, λ represents the optical wavelength; J m (x) represents the Bessel function of the first kind of order m; K m (x) represents the modified Bessel function of the second kind of order m, n2 is the cladding refractive index, r represents the radial direction in the cylindrical coordinate system, represents the circumferential direction in the cylindrical coordinate system; J' m (x) is the m-th derivative of J m (x); K' m (x) is the m-th derivative of K m (x).

[0035] In an embodiment of the present invention, the method for obtaining the final inter-mode coupling mode coefficient k mn is as follows:

[0036] Perform a normalization operation on the denominator in Equation (1), which is expressed as:

[0037]

[0038] Wherein, P represents the injection power;

[0039] Substitute the electric field strength I mn of the linearly polarized mode LP m into the numerator of Equation (1) to obtain

[0040]

[0041] Substitute Equation (12) into Equation (1) to obtain the final inter-mode coupling mode coefficient k mn :

[0042]

[0043] In one embodiment of the present invention, the method for obtaining the intermodal crosstalk value IMXT of the optical fiber includes:

[0044]

[0045] where N represents the number of segments after the optical fiber is segmented, d represents the segment length after the optical fiber is segmented, and Δβ mn,i represents the equivalent phase mismatch of the i-th segment, and g mn,i represents the corrected coupling mode coefficient of the i-th segment, and k mn,i represents the coupling mode coefficient of the i-th segment between the core m and the core n.

[0046] Based on the same inventive concept, the present invention also provides a weak-coupling few-mode multi-core optical fiber intermodal crosstalk detection system, which includes the following modules:

[0047] An optical fiber parameter and injection power acquisition module, configured to acquire optical fiber parameters and injection power, where the optical fiber parameters include core refractive index, cladding refractive index, core radius, core propagation constant, and optical wavelength;

[0048] An electric field strength calculation module for the core region and the cladding region, configured to calculate the electric field strength in the core region of the optical fiber and the electric field strength in the cladding region of the optical fiber based on the optical fiber parameters;

[0049] An inter-mode coupling mode coefficient calculation module, configured to calculate the inter-mode coupling mode coefficient based on the electric field strength in the core region, the electric field strength in the cladding region, and the injection power;

[0050] An optical fiber intermodal crosstalk value acquisition module, configured to construct an optical fiber intermodal crosstalk calculation equation according to the inter-mode coupling mode coefficient, and obtain the optical fiber intermodal crosstalk value.

[0051] The present invention also provides a weak-coupling few-mode multi-core optical fiber intermodal crosstalk detection device, which calculates the optical fiber intermodal crosstalk value by using the weak-coupling few-mode multi-core optical fiber intermodal crosstalk detection system.

[0052] In one embodiment of the present invention, the weak-coupling few-mode multi-core optical fiber intermodal crosstalk detection device is applied to a homogeneous few-mode multi-core optical fiber or a heterogeneous few-mode multi-core optical fiber.

[0053] The above technical solutions of the present invention have the following advantages compared with the prior art:

[0054] First, the inter-modal crosstalk detection method described in the present invention is of great significance for improving communication capacity in a multi-core few-mode optical fiber communication system. This method can not only study the inter-modal crosstalk of low-order polarization (LP) modes, but also study the inter-modal crosstalk of high-order LP modes.

[0055] Second, based on the coupled-mode theory with random perturbations in multi-core optical fibers and the Maxwell equations between modes, the present invention obtains a new inter-modal coupling coefficient, which is more accurate for the change process of inter-modal crosstalk. Moreover, this method is applicable not only to heterogeneous optical fibers, but also to ideal homogeneous optical fibers and actual homogeneous optical fibers. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the drawings, where

[0057] Figure 1 is a schematic diagram of the transmission paths of different modes in the cores of a step-type multi-core few-mode optical fiber;

[0058] Figure 2 is a flowchart of a method for detecting inter-modal crosstalk in a weakly coupled few-mode multi-core optical fiber provided in an embodiment of the present invention;

[0059] Figure 3 is LP in an embodiment of the present invention 01 mode, LP 11 mode, LP 21 mode and LP 31 mode of the light intensity distribution diagram;

[0060] Figure 4 is LP in an embodiment of the present invention 01 mode, LP 11 mode, LP 21 mode and LP 31 mode of the simulation results of crosstalk varying with the distance parameter;

[0061] Figure 5 is LP in an embodiment of the present invention 01 mode, LP 11 mode, LP 21 mode and LP 31 mode of the simulation results of inter-modal crosstalk varying with the core pitch;

[0062] Figure 6 is LP in an embodiment of the present invention 01 mode, LP 11 mode, LP 21 mode and LP 31 mode of the simulation results of inter-modal crosstalk varying with the optical wavelength;

[0063] Figure 7(a) shows the relationship between inter - mode crosstalk and core bending radius in the LP 01 mode, LP 11 mode, LP 21 mode, and LP 31 mode of an ideal homogeneous multi - core few - mode optical fiber;

[0064] Figure 7(b) shows the relationship between inter - mode crosstalk and core bending radius in the LP 01 mode, LP 11 mode, LP 21 mode, and LP 31 mode of an actual homogeneous multi - core optical fiber;

[0065] Figure 8 Figure [[]] shows the relationship between inter - mode crosstalk and core bending radius in the LP 01 mode, LP 11 mode, LP 21 mode, and LP 31 mode of a heterogeneous multi - core few - mode optical fiber;

[0066] Figure 9 Figure [[]] is a structural diagram of a weak - coupling few - mode multi - core optical fiber inter - mode crosstalk detection system provided in an embodiment of the present invention;

[0067] Description of the reference numerals in the accompanying drawings: 100, optical fiber parameter and injection power acquisition module; 200, electric field strength calculation module for core region and cladding region; 300, inter - mode coupling mode coefficient calculation module; 400, optical fiber inter - mode crosstalk value acquisition module. Detailed implementation manners

[0068] 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 be able to implement it, but the specific embodiments given are not intended to limit the present invention.

[0069] Embodiment 1

[0070] The principle of a step - type multi - core few - mode optical fiber is to change the angle of light incident on the core, so that each mode transmits along different broken - line trajectories in the core, and its principle is as Figure 1 shown;

[0071] For the crosstalk between LP modes, we adopt the segmented idea, that is, it is assumed that within a small length segment, crosstalk occurs only once, and within each small segment, the mode coupling coefficient is closely related to the electric field distribution of the mode.

[0072] Referring to Figure 2 shown, this embodiment takes a step - type multi - core few - mode optical fiber as the object and provides a method for detecting the inter - mode crosstalk of a weak - coupling few - mode multi - core optical fiber. The specific steps are as follows:

[0073] S1: Obtain fiber parameters and injection power, where the fiber parameters include core refractive index, cladding refractive index, core radius, core propagation constant, and optical wavelength;

[0074] S2: Based on the fiber parameters, calculate the electric field strength in the core region of the fiber and the electric field strength in the cladding region of the fiber;

[0075] S3: Based on the electric field strength in the core region, the electric field strength in the cladding region, and the injection power, calculate the inter-mode coupling mode coefficient;

[0076] S4: According to the inter-mode coupling mode coefficient, construct an inter-modal crosstalk calculation equation for the fiber to obtain the inter-modal crosstalk value of the fiber;

[0077] Among them, the calculation method of the inter-mode coupling mode coefficient is: divide the fiber into multiple small segments to obtain the relationship between the inter-mode coupling mode coefficient and the electric field distribution of the linearly polarized mode in each small segment, and calculate the initial inter-mode coupling mode coefficient k' according to the relationship mn :

[0078]

[0079] Among them, ω is the angular frequency, ε0 is the vacuum permittivity, E m and H m respectively represent the electric field strength and magnetic field strength in the core region, E n represents the electric field strength within the cladding range, e z represents the unit vector in the z direction, n1 and n2 respectively represent the refractive index of the core and the refractive index of the cladding, and the symbol * represents the conjugate operation of the matrix;

[0080] According to the electric field strength in the core region and the electric field strength in the cladding region, obtain the electric field strength of the linearly polarized mode LP mn ;

[0081] Based on the electric field strength of the linearly polarized mode LP mn optimize the initial inter-mode coupling mode coefficient k' mn to obtain the final inter-mode coupling mode coefficient k mn ;

[0082] In S2, the calculation methods of the electric field strength in the core region and the electric field strength in the cladding region include:

[0083] Since the fiber is a cylindrical structure, for LP mnThe mode electric field is expanded into a cylindrical polar coordinate form, so that the electric field vector is represented as a superposition of three dimensions. According to the longitudinal electric field component in the core region and the transverse electric field component in the core region, the electric field strength E in the core region is obtained m :

[0084]

[0085] According to the longitudinal electric field component in the cladding region and the transverse electric field component in the core region, the electric field strength E in the cladding region is obtained n :

[0086]

[0087] where, e r represents the unit vector in the r direction, represents the unit vector in the z direction, e z1 and E z2 respectively represent the longitudinal electric field component in the core region and the longitudinal electric field component in the cladding region; E r1 and both represent the transverse electric field component in the core region, E r2 and both represent the transverse electric field component in the cladding region.

[0088] where, the calculation method for calculating the longitudinal electric field components in the core region and the cladding region includes:

[0089] Using the homogeneous Helmholtz equation to calculate the longitudinal electric field components in the core region and the cladding region:

[0090]

[0091] where, E z1 and E z2 respectively represent the longitudinal electric field component in the core region and the longitudinal electric field component in the cladding region, A = jUC / aβ, j is the imaginary unit, C is a system constant, n1 is the core refractive index, β is the core propagation constant, a is the core radius, k = λ / 2π is the wave number, λ represents the optical wavelength, J m (x) represents the m-th order Bessel function of the first kind, K m (x) represents the m-th order modified Bessel function of the second kind, n2 is the cladding refractive index, r represents the radial direction in the cylindrical coordinate system, represents the circumferential direction in the cylindrical coordinate system.

[0092] Substitute the longitudinal electric field components in the core region and the cladding region into Maxwell's equations to obtain the transverse electric field components in the core region and the cladding region:

[0093]

[0094]

[0095] where, E r1 and both represent the transverse electric field components in the core region, and E r2 and both represent the transverse electric field components in the cladding region; J' m (x) is the m-th derivative of J m (x); K' m (x) is the m-th derivative of K m (x).

[0096] According to the electric field intensity in the core region and the electric field intensity in the cladding region, obtain the electric field intensity I mn of the linearly polarized mode LP m , and its calculation method is:

[0097]

[0098] where, represents the conjugate of the longitudinal electric field component E z1 in the core region; E z2 represents the longitudinal electric field component in the cladding region; represents the conjugate of the transverse electric field component E r1 in the core region; E r2 represents the transverse electric field component in the cladding region; represents the conjugate of the transverse electric field component in the core region; represents the transverse electric field component in the cladding region; A = jUC / aβ, j is the imaginary unit, C is a system constant, n1 is the core refractive index, β is the core propagation constant, a is the core radius, k = λ / 2π is the wave number, λ represents the optical wavelength; J m (x) represents the m-th order Bessel function of the first kind; K m (x) represents the m-th order modified Bessel function of the second kind, n2 is the cladding refractive index, r represents the radial direction in the cylindrical coordinate system, represents the circumferential direction in the cylindrical coordinate system; J' m (x) is the derivative of J m(x) derivative of order m; K' m (x) is K m (x) derivative of order m.

[0099] The final inter-mode coupling mode coefficient k mn is obtained as follows:

[0100] Normalize the denominator in Equation (1), expressed as:

[0101]

[0102] where P represents the injection power;

[0103] Substitute the electric field intensity I of the linear polarization mode LP mn into the numerator of Equation (1) to obtain m Substitute Equation (12) into Equation (1) to obtain the final inter-mode coupling mode coefficient k

[0104]

[0105] : mn :

[0106]

[0107] In this embodiment, the method for obtaining the fiber mode crosstalk value IMXT includes:

[0108]

[0109] where N represents the number of segments after the fiber is segmented, d represents the segment length after the fiber is segmented, Δβ mn,i represents the equivalent phase mismatch of the i-th segment, g mn,i represents the corrected coupling mode coefficient of the i-th segment, k mn,i represents the coupling mode coefficient of the i-th segment between core m and core n.

[0110] Based on the above embodiments, the accuracy of the above method is verified by simulation in this embodiment, specifically as follows:

[0111] In a step-index fiber, the normalized frequency V value of the fiber is a very important parameter, and the V value satisfies the following expression:

[0112]

[0113] For a given fiber structure parameter and operating wavelength, the mode type, mode number, and effective refractive index of each mode in the fiber are all determined. As the normalized frequency V value increases, the number of modes supported in the fiber gradually increases. Therefore, in order to satisfy the existence of LP 01 and LP11 , LP 21 and LP 31 mode, the given structural parameters and operating wavelength are as follows:

[0114] Parameter Symbol Size Core radius a 8μm Cladding refractive index <![CDATA[n1]]> 1.444 Core refractive index <![CDATA[n2]]> 1.4530 Core pitch <![CDATA[D mn > 30μm Bending radius <![CDATA[R b > 200mm Optical wavelength λ 1550nm Relative refractive index difference between core and cladding Δ 0.62％

[0115] Given a core radius a = 8 μm, a cladding refractive index n1 = 1.444, a core refractive index of approximately n2 = 1.4530, a core spacing of D mn = 30 μm, an optical pulse wavelength of λ = 1550 nm, a normalized frequency V = 5.2364, satisfying a two-core four-LP mode fiber, studying the relationship between different fiber parameters and intermodal crosstalk under the LP 01 mode, LP 11 mode, LP 21 mode and LP 31 mode (whose optical intensity distribution is as shown in Figure 3 ), the experimental results are as shown in Figures 4 - 8 .

[0116] Figure 4 It reflects the result of the change of intermodal crosstalk with the distance parameter. It can be seen that for LP 01 , the intermodal crosstalk reaches about -39 dB at 1 km. For LP mn , the effective refractive index of the low-order mode is slightly higher than that of the high-order mode, which affects the magnitude of the propagation constant β. The slight change in the propagation constant greatly affects the mode coupling coefficient, thus affecting the intermodal crosstalk. Therefore, the intermodal crosstalk of the high-order mode is greater than that of the low-order mode. The intermodal crosstalk of the LP 31 mode is about -22 dB.

[0117] Figure 5 It shows the process of the change of intermodal crosstalk with the core spacing. The radius of the core is 8 μm. When the core spacing gradually increases, it can be seen that the intermodal crosstalk gradually decreases, which indicates that appropriately increasing the core spacing is one of the effective methods to reduce intermodal crosstalk.

[0118] Figure 6 It shows the change of intermodal crosstalk with the optical wavelength. First, it is necessary to satisfy the propagation of LP 01 , LP 11 , LP 21 and LP 31 modes in the fiber. Therefore, the normalized frequency V value of the fiber should be greater than 5.136. Therefore, the optical wavelength λ of the fiber transmission system is set to vary in the range of 1500 nm - 1550 nm. It can be seen from the figure that when the optical wavelength increases, the coupled mode coefficient will increase accordingly, and the intermodal crosstalk will also increase.

[0119] Figures 7(a) and 7(b) show the relationship between the inter - mode crosstalk and the core bending radius of an ideal homogeneous multi - core few - mode fiber and an actual homogeneous multi - core fiber. As can be seen from Figure 7(a), for an ideal homogeneous multi - core few - mode fiber, the inter - mode crosstalk is linearly proportional to the core bending radius, and the inter - mode crosstalk increases with the increase of the bending radius. For an actual homogeneous multi - core fiber, there is a critical bending radius, which is about 150 mm. As shown in Figure 7(b), when the bending radius of the core is less than the critical bending radius, the inter - mode crosstalk increases with the increase of the bending radius; when the bending radius of the core is greater than the critical bending radius, the inter - mode crosstalk decreases with the increase of the bending radius and tends to a stable value as the bending radius increases.

[0120] Figure 8 shows the relationship between the heterogeneous multi - core few - mode fiber and the core bending radius, and its corresponding critical bending radius is about 65 mm. It can be seen that Figure 8 when the bending radius of the core is less than the critical bending radius, the inter - mode crosstalk increases with the increase of the bending radius; when the bending radius of the core is greater than the critical bending radius, as the bending radius increases, the inter - mode crosstalk oscillates and continuously decreases, and finally tends to a stable value.

[0121] Embodiment 2

[0122] Based on the same inventive concept as the method described in Embodiment 1, the present invention also provides a detection system for inter - mode crosstalk of weakly - coupled few - mode multi - core fibers. As Figure 9 shown, the system includes the following modules:

[0123] An optical fiber parameter and injection power acquisition module 100, which is used to acquire optical fiber parameters and injection power. The optical fiber parameters include core refractive index, cladding refractive index, core radius, core propagation constant, and optical wavelength;

[0124] An electric field strength calculation module 200 for the core region and the cladding region, which is used to calculate the electric field strength in the core region of the optical fiber and the electric field strength in the cladding region of the optical fiber based on the optical fiber parameters;

[0125] An inter - mode coupling mode coefficient calculation module 300, which is used to calculate the inter - mode coupling mode coefficient based on the electric field strength in the core region, the electric field strength in the cladding region, and the injection power;

[0126] An optical fiber inter - mode crosstalk value acquisition module 400, which is used to construct an optical fiber inter - mode crosstalk calculation equation according to the inter - mode coupling mode coefficient and obtain the optical fiber inter - mode crosstalk value.

[0127] A weak-coupling few-mode multi-core fiber inter-modal crosstalk detection system proposed in this embodiment is used to implement the aforementioned weak-coupling few-mode multi-core fiber inter-modal crosstalk detection method. Therefore, the specific implementation manners in the weak-coupling few-mode multi-core fiber inter-modal crosstalk detection system can be seen in the embodiment part of the aforementioned weak-coupling few-mode multi-core fiber inter-modal crosstalk detection method. For example, the optical fiber parameter and injection power acquisition module 100, the electric field strength calculation module 200 for the core region and the cladding region, the inter-mode coupling mode coefficient calculation module 300, and the optical fiber inter-modal crosstalk value acquisition module 400 are respectively used to correspondingly implement steps S1, S2, S3, and S4 in the weak-coupling few-mode multi-core fiber inter-modal crosstalk detection method in Embodiment 1. Therefore, the specific implementation manners can refer to the descriptions of the corresponding individual part embodiments. To avoid redundancy, they will not be elaborated here.

[0128] Embodiment 3

[0129] The present invention also provides a weak-coupling few-mode multi-core fiber inter-modal crosstalk detection device, which calculates the optical fiber inter-modal crosstalk value by using the weak-coupling few-mode multi-core fiber inter-modal crosstalk detection system described in Embodiment 2.

[0130] In this embodiment, the weak-coupling few-mode multi-core fiber inter-modal crosstalk detection device is applied to homogeneous few-mode multi-core fibers or heterogeneous few-mode multi-core fibers.

[0131] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0132] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the processes and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0133] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction device that implements the functions specified in one or more of the processes and / or blocks Figure 1 one or more of the processes and / or blocks Figure 1 specified in the block or blocks.

[0134] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one or more of the processes and / or blocks Figure 1 one or more of the processes and / or blocks Figure 1 specified in the block or blocks.

[0135] Obviously, the above embodiments are only examples for clear illustration and are not limitations on the implementation. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers, characterized in that: The following steps are involved: S1: Obtaining optical fiber parameters and injection power, wherein the optical fiber parameters include core refractive index, cladding refractive index, core radius, core propagation constant and light wavelength; S2: Based on the optical fiber parameters, calculating the electric field intensity in the core region of the optical fiber and the electric field intensity in the cladding region of the optical fiber; S3: calculating the inter-mode coupling mode coefficient based on the electric field intensity in the core region, the electric field intensity in the cladding region and the injection power; S4: constructing an optical fiber inter-mode crosstalk calculation equation according to the inter-mode coupling mode coefficient to obtain an optical fiber inter-mode crosstalk value; The method for calculating the inter-mode coupling mode coefficient is as follows: dividing the optical fiber into multiple small segments, obtaining the relationship between the inter-mode coupling mode coefficient and the electric field distribution of the linear polarization mode in each small segment, and calculating the initial inter-mode coupling mode coefficient k' according to the relationship. mn : Where ω is the angular frequency, ε0 ​​is the dielectric constant of vacuum, and E m and H m They represent the electric field intensity and magnetic field intensity in the core region, E n represents the electric field strength within the envelope, e z represents the unit vector in the z direction, n1 and n2 represent the refractive index of the core and the refractive index of the cladding respectively, the symbol * represents the conjugate operation of the matrix, m represents the core m, and n represents the core n; According to the electric field intensity in the core region and the electric field intensity in the cladding region, a linear polarization mode LP is obtained. mn The electric field strength; Based on the linear polarization mode LP mn The electric field strength of the initial mode coupling coefficient k' mn Optimize and obtain the final inter-mode coupling coefficient k mn .

2. The method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers according to claim 1, characterized in that: The method for calculating the electric field intensity in the core region of the optical fiber and the electric field intensity in the cladding region of the optical fiber includes: Since the optical fiber is a cylindrical structure, the LP mn The mode electric field is expanded into cylindrical polar coordinates, so that the electric field vector is represented as a superposition of three dimensions. According to the longitudinal electric field component in the core region and the transverse electric field component in the core region, the electric field intensity E in the core region is obtained. m : According to the longitudinal electric field component in the cladding region and the transverse electric field component in the core region, the electric field intensity E in the cladding region is obtained. n : In the cylindrical polar coordinate system, e r represents the unit vector in the r direction, express Unit vector in the direction, e z represents the unit vector in the z direction; E z1 and E z2 They represent the longitudinal electric field component in the core region and the longitudinal electric field component in the cladding region respectively; E r1 and Both represent the transverse electric field component in the core region, E r2 and Both represent the components of the transverse electric field in the cladding region.

3. The method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers according to claim 2, characterized in that: The method for calculating the longitudinal electric field components in the core region and the cladding region includes: The homogeneous Helmholtz equation is used to calculate the longitudinal electric field components in the core region and in the cladding region: Among them, E z1 and E z2 They represent the longitudinal electric field component in the core region and the longitudinal electric field component in the cladding region, respectively. A=jUC / aβ, j is an imaginary unit, C is a system constant, n1 is the core refractive index, β is the core propagation constant, a is the core radius, k = λ / 2π is the wave number, λ represents the wavelength of light, J m (x) represents the first kind m-order Bessel function, K m (x) represents the m-th order modified Bessel function of the second kind, n2 is the cladding refractive index, r represents the radial direction in the cylindrical coordinate system, Represents the circumferential direction in the cylindrical coordinate system.

4. The method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers according to claim 3, characterized in that: Substituting the longitudinal electric field components in the core region and the cladding region into Maxwell's equations, the transverse electric field components in the core region and the cladding region are obtained: Among them, E r1 and Both represent the transverse electric field component in the core region, E r2 and Both represent the components of the transverse electric field in the cladding region; J' m (x) is J m The m-th derivative of (x); K' m (x) is K m The m-th derivative of (x).

5. The method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers according to any one of claims 1 to 4, characterized in that: The linear polarization mode LP mn The electric field strength I m The calculation method is: in, The component E representing the longitudinal electric field in the core region z1 conjugation of E z2 represents the component of the longitudinal electric field in the cladding region; The component E representing the transverse electric field in the core region r1 conjugation of E r2 represents the component of the transverse electric field in the cladding region; The component of the transverse electric field in the core region conjugation of; represents the component of the transverse electric field in the cladding region; A = jUC / aβ, j is an imaginary unit, C is a system constant, n1 is the core refractive index, β is the core propagation constant, a is the core radius, k = λ / 2π is the wave number, λ represents the wavelength of light; J m (x) represents the first kind m-order Bessel function; K m (x) represents the m-th order modified Bessel function of the second kind, n2 is the cladding refractive index, r represents the radial direction in the cylindrical coordinate system, represents the circumferential direction in the cylindrical coordinate system; J' m (x) is J m The m-th derivative of (x); K' m (x) is K m The m-th derivative of (x).

6. The method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers according to claim 5, characterized in that: The final inter-mode coupling coefficient k mn The method to obtain is: The denominator in formula (1) is normalized and expressed as: Where P represents the injected power; The linear polarization mode LP mn The electric field strength I m Substituting into the numerator of formula (1), we get Substituting equation (12) into equation (1), we get the final inter-mode coupling coefficient k mn :

7. The method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers according to claim 1, characterized in that: The method for obtaining the optical fiber inter-mode crosstalk value IMXT includes: Where N represents the number of segments after the optical fiber is segmented, d represents the segment length after the optical fiber is segmented, and Δβ mn,i represents the equivalent phase mismatch of the i-th segment, g mn,i represents the corrected coupling mode coefficient of the i-th segment, k mn,i It represents the coupling mode coefficient of the i-th segment between the fiber core m and the fiber core n.

8. A weakly coupled few-mode multi-core optical fiber inter-mode crosstalk detection system, characterized in that: The method for detecting inter-mode crosstalk of weakly coupled few-mode multi-core optical fibers according to any one of claims 1 to 7 comprises the following modules: An optical fiber parameter and injection power acquisition module is used to acquire optical fiber parameters and injection power, wherein the optical fiber parameters include core refractive index, cladding refractive index, core radius, core propagation constant and optical wavelength; A core region and cladding region electric field strength calculation module, used to calculate the electric field strength in the core region of the optical fiber and the electric field strength in the cladding region of the optical fiber based on the optical fiber parameters; An inter-mode coupling mode coefficient calculation module, used to calculate the inter-mode coupling mode coefficient based on the electric field strength in the core region, the electric field strength in the cladding region and the injection power; The optical fiber inter-mode crosstalk value acquisition module is used to construct an optical fiber inter-mode crosstalk calculation equation according to the inter-mode coupling mode coefficient to obtain the optical fiber inter-mode crosstalk value.

9. A weakly coupled few-mode multi-core optical fiber inter-mode crosstalk detection device, characterized in that: The optical fiber inter-mode crosstalk value is calculated using the weakly coupled few-mode multi-core optical fiber inter-mode crosstalk detection system as described in claim 8.

10. The weakly coupled few-mode multi-core optical fiber inter-mode crosstalk detection device according to claim 9, characterized in that: Applicable to homogeneous few-mode multi-core optical fiber or heterogeneous few-mode multi-core optical fiber.

Images