A method and system for analyzing high-order spatial mode coupling efficiency of few-mode fiber

Abstract

The application provides a method for analyzing high-order spatial mode coupling efficiency of a few-mode optical fiber, comprising constructing a structural model of a structure formed by fusing two sections of the few-mode optical fiber with matched parameters, and based on the structural model, using Laguerre-Gaussian modes to approximate linearly polarized modes to construct a mathematical model of field intensity distribution of the few-mode optical fiber under multiple spatial modes; wherein the multiple spatial modes comprise LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode; according to the mathematical model of field intensity distribution of the few-mode optical fiber under the multiple spatial modes, a mathematical model of coupling efficiency between the spatial modes under multiple fusion parameters and fiber parameters at a fusion point of the few-mode optical fiber is constructed, and power loss of the spatial modes at the fusion point is determined according to the mathematical model of coupling efficiency between the spatial modes. By implementing the application, accurate analysis of the coupling efficiency of each spatial mode of the few-mode optical fiber can be realized.

Description

Technical Field

[0001] This invention relates to the field of optical fiber detection technology, and in particular to a method and system for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers. Background Technology

[0002] With the continuous increase in communication services, the demand for transmission capacity in communication systems is growing, and various new technologies are constantly emerging. Currently, few-mode fiber (FMF) communication technology based on Mode Division Multiplexing (MDM) is highly favored. This technology can break through the capacity limit of traditional single-mode fiber communication and is the most competitive expansion solution to solve the "bandwidth crisis" of future communication networks, becoming the key to realizing future T bit / s or even P bit / s fiber communication. Therefore, in the face of the rapid development of FMF research and development, network construction and application, ensuring the reliable and efficient operation of long-distance, high-capacity FMF links, the analysis of FMF link splice fault characteristics has become extremely important.

[0003] In mode division multiplexing (MDM) systems based on few-mode fibers, fusion splicing between few-mode fibers is unavoidable. For few-mode fibers supporting multiple spatial modes, each with significantly different transmission loss characteristics, accurate analysis of the coupling loss characteristics of higher-order spatial modes in few-mode fiber fusion splice faults can provide a reliable basis for evaluating splice quality and improving the fault detection sensitivity of the localization system. Currently, there are numerous reports on the analysis of coupling loss characteristics in few-mode fiber fusion splice faults. For example, ATSUSHI NAKAMURA proposed an analysis of the fusion splice fault loss characteristics of LP01 and LP11 modes in few-mode fibers based on optical time-domain reflectometry (OTDR). By estimating the coupling efficiency matrix at the fusion crosstalk point using the backscattered Rayleigh waveforms of each spatial mode, and reconstructing the higher-order spatial mode waveforms using simple numerical processing, the high-purity fusion splice loss characteristics of different spatial modes in few-mode fibers can be obtained, thus optimizing the fault detection sensitivity of few-mode fiber links. For example, HIROSHI TAKAHASHI reported an OTDR dynamic crosstalk suppression method for high-purity measurement of LP11 mode fusion splice fault loss. This method addresses the degradation of LP11 mode fault loss measurement accuracy under mode crosstalk conditions by employing an efficient LP11 mode dynamic crosstalk suppression scheme based on the Brillouin loss mechanism. Similarly, Atsushi Nakamura approximates the field strength distributions of LP01 and LP11 modes in few-mode fibers using Gaussian and Hermitian-Gaussian distributions, respectively, and analyzes the fusion coupling efficiency characteristics between modes. Furthermore, previous work has explored in depth the influence mechanism of mode crosstalk on the LP01 and LP11 mode fusion splice fault loss and fault detection sensitivity characteristics under different fusion mismatch and rotation conditions.

[0004] However, the above reports only analyzed the fusion coupling efficiency of the fundamental modes LP01 and LP11 of few-mode fibers, but did not conduct a more in-depth study on the coupling loss characteristics of higher-order spatial modes in few-mode fibers. This makes it impossible to achieve an accurate analysis of the coupling efficiency of each spatial mode in few-mode fibers, resulting in a lack of corresponding theoretical basis for the fusion failure loss characteristics of higher-order spatial modes.

[0005] Therefore, it is necessary to propose a new method for analyzing the coupling efficiency of higher-order spatial modes in few-mode fibers. This method can achieve accurate analysis of the coupling efficiency of each spatial mode in few-mode fibers, which is of great significance for promoting the rapid development of few-mode fiber research and development, network construction and application. Summary of the Invention

[0006] The technical problem to be solved by the embodiments of the present invention is to provide a method and system for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers, which can realize the accurate analysis of the coupling efficiency of each spatial mode in few-mode optical fibers.

[0007] To address the aforementioned technical problems, embodiments of the present invention provide a method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers, the method comprising the following steps:

[0008] S1. Construct a structural model formed by splicing two segments of few-mode fiber with matched parameters, and based on the structural model, use the Laguerre Gaussian mode to approximate the linear polarization mode to construct a mathematical model of the field intensity distribution of the few-mode fiber in multiple spatial modes; wherein, the multiple spatial modes include LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode;

[0009] S2. Based on the mathematical model of field strength distribution of the few-mode fiber in multiple spatial modes, construct a mathematical model of coupling efficiency between spatial modes at the few-mode fiber fusion splice point under multiple fusion parameters and fiber parameters, and determine the power loss of each spatial mode fusion splice point based on the constructed mathematical model of coupling efficiency between spatial modes.

[0010] In step S1, the matching parameters include core radius, relative refractive index, normalized frequency, and profile shape.

[0011] In step S1, the solution of the Laguerre Gaussian modulus is expressed by the following formula (1):

[0012]

[0013] in, The normalization factor is l, and the azimuth component and radial component are the guiding azimuth component and the radial component, respectively. It is a Laguerre polynomial; Let be the Gaussian radius of the fundamental mode, k be the wavenumber, Δ be the relative refractive index, n1 be the core refractive index; θ be the offset azimuth angle; and r be the polar radius, where r 2 =x 2 +y 2 x and y are the coordinate axes of the few-mode fiber cross-section; a is the core radius.

[0014] In step S1, the mathematical model of field intensity distribution under each spatial mode is represented by the following formulas (2) to (7):

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] Among them, E 01 E 11a E 11b E 21a E 21b and E 02 The field strengths are for LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode, respectively.

[0022] In step S2, the mathematical model for the coupling efficiency between the various spatial modes can be uniformly expressed by formula (8):

[0023]

[0024] Where, η ij The coupling efficiency between the two modes at the fusion splice of the few-mode fiber reflects the power loss of the spatial mode at the splice; d is the axial offset; E i and E j In the LP01 mode, i,j = 1, 2, 3, ..., 6; i or j = 1 represents LP01 mode, i or j = 2 represents LP11a mode, i or j = 3 represents LP11b mode, i or j = 4 represents LP21a mode, i or j = 5 represents LP21b mode, and i or j = 6 represents LP02 mode.

[0025] In step S2, the mathematical model of coupling efficiency between LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode at the fusion point is expressed by the following formulas (9) to (19):

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Where, η ij =η jiη represents the coupling efficiency between LPi and LPj modes, i.e., the coupling efficiency between any two modes among LP01, LP11a, LP11b, LP21a, LP21b, and LP02; when i = j, η represents the coupling loss characteristics at the mode fusion point, and the coupling efficiency η is... ij The smaller the value, the greater the power loss at the spatial mode fusion point, and vice versa; when i≠j, η represents the energy at the mode fusion point where the LPi mode couples into the LPj mode. ij The larger the value, the greater the crosstalk at the weld joint, and vice versa.

[0048] This invention also provides a system for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers, comprising:

[0049] The field strength distribution mathematical model construction unit is used to construct a structural model formed by splicing two segments of parameter-matched few-mode optical fibers, and based on the structural model, the Laguerre Gaussian mode is used to approximate the linear polarization mode to construct a mathematical model of the field strength distribution of the few-mode optical fiber in multiple spatial modes; wherein, the multiple spatial modes include LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode;

[0050] The coupling efficiency mathematical model construction and analysis unit is used to construct a coupling efficiency mathematical model between spatial modes at the fusion splice point of the few-mode fiber under multiple fusion parameters and fiber parameters based on the field strength distribution mathematical model of the few-mode fiber in multiple spatial modes, and to determine the power loss of each spatial mode fusion splice point based on the constructed coupling efficiency mathematical model between each spatial mode.

[0051] The matching parameters include core radius, relative refractive index, normalized frequency, and profile shape.

[0052] The solution of the Laguerre Gaussian modulus is expressed by the following formula (1):

[0053]

[0054] in, The normalization factor is l, and the azimuth component and radial component are the guiding azimuth component and the radial component, respectively. It is a Laguerre polynomial; Let be the Gaussian radius of the fundamental mode, k be the wavenumber, Δ be the relative refractive index, n1 be the core refractive index; θ be the offset azimuth angle; and r be the polar radius, where r 2 =x 2 +y 2 x and y are the coordinate axes of the few-mode fiber cross-section; a is the core radius.

[0055] Implementing the embodiments of the present invention has the following beneficial effects:

[0056] This invention establishes a general mathematical model for analyzing the coupling efficiency of high-order spatial modes based on the Laguerre-Gaussian distribution. This model overcomes the limitations of existing theoretical models in analyzing the fusion coupling efficiency of high-order spatial modes. It can reveal the variation law of the coupling efficiency of different modes and the coupling efficiency between modes under the conditions of factors such as axial offset, rotation angle and fiber parameters in few-mode fiber fusion splices. This enables accurate analysis of the coupling efficiency of each spatial mode in few-mode fiber, and can provide a theoretical basis for high-sensitivity fault detection of few-mode fiber links and the field of few-mode fiber sensing. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, obtaining other drawings based on these drawings without creative effort still falls within the scope of the present invention.

[0058] Figure 1 A flowchart of a method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers, provided as an embodiment of the present invention;

[0059] Figure 2 This is a cross-sectional schematic diagram of the fusion structure formed by splicing two segments of few-mode fiber in a method for analyzing the coupling efficiency of higher-order spatial modes in few-mode fiber provided in an embodiment of the present invention.

[0060] Figure 3 The application scenario of the method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers provided in this embodiment of the invention is the self-coupling of the LP01 mode at the fusion splice of the few-mode optical fiber and its coupling efficiency curve with the higher-order mode.

[0061] Figure 4 The application scenario of the method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers provided in this embodiment of the invention is the self-coupling of the LP11a mode at the fusion splice of the few-mode optical fiber and its coupling efficiency curve with the higher-order mode.

[0062] Figure 5 The application scenario of the method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers provided in this embodiment of the invention is the self-coupling of LP11b mode at the fusion splice of few-mode optical fibers and its coupling efficiency curve with higher-order modes.

[0063] Figure 6 The application scenario of the method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers provided in this embodiment of the invention is the self-coupling of the LP21a mode at the fusion splice of the few-mode optical fiber and its coupling efficiency curve with the higher-order mode.

[0064] Figure 7 The application scenario of the method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers provided in this embodiment of the invention is the self-coupling of LP21b mode at the fusion splice of few-mode optical fibers and its coupling efficiency curve with higher-order modes.

[0065] Figure 8 The self-coupling efficiency curve of the LP02 mode at the fusion splice of a few-mode fiber is shown in the application scenario of a method for analyzing the coupling efficiency of higher-order spatial modes in a few-mode fiber, as provided in an embodiment of the present invention.

[0066] Figure 9 This is a schematic diagram of the structure of a system for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers, provided as an embodiment of the present invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0068] like Figure 1 As shown in the figure, this invention proposes a method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers. The method includes the following steps:

[0069] Step S1: Construct a structural model formed by splicing two segments of few-mode fiber with matched parameters, and based on the structural model, use the Laguerre Gaussian mode to approximate the linear polarization mode to construct a mathematical model of the field intensity distribution of the few-mode fiber in multiple spatial modes; wherein, the multiple spatial modes include LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode;

[0070] S2. Based on the mathematical model of field strength distribution of the few-mode fiber in multiple spatial modes, construct a mathematical model of coupling efficiency between spatial modes at the few-mode fiber fusion splice point under multiple fusion parameters and fiber parameters, and determine the power loss of each spatial mode fusion splice point based on the constructed mathematical model of coupling efficiency between spatial modes.

[0071] The specific process is as follows: In step S1, firstly, consider splicing two parameter-matched few-mode optical fibers, such as... Figure 2 As shown, it is assumed that the two few-mode fibers have, but are not limited to, the same core radius a, relative refractive index Δ, normalized frequency V, and profile shape.

[0072] When transmitting and receiving few-mode fibers are fused, there will be a fusion axial offset d and an offset azimuth angle θ. x and y are the coordinate axes of the few-mode fiber cross-section, z represents the axial direction of the few-mode fiber, and r is the polar coordinate system. 2 =x2 +y 2 .

[0073] Secondly, since few-mode step-index fibers possess cylindrical symmetry, this cylindrical symmetry can also be defined as a Laguerre Gaussian mode. Therefore, the Laguerre Gaussian mode LG is used to approximate the linear polarization mode LP. The solution of the Laguerre Gaussian mode LG is expressed by the following formula (1):

[0074]

[0075] in, The normalization factor is l, and the azimuth component and radial component are the guiding azimuth component and the radial component, respectively. It is a Laguerre polynomial; Let be the Gaussian radius of the fundamental mode, k be the wavenumber, Δ be the relative refractive index, n1 be the core refractive index; θ be the offset azimuth angle; and r be the polar radius, where r 2 =x 2 +y 2 x and y are the coordinate axes of the few-mode fiber cross-section; a is the core radius.

[0076] Finally, taking LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode as examples (but not limited to these modes), the mathematical models of field intensity distribution under each spatial mode are obtained as shown in the following formulas (2) to (7):

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] Among them, E 01 E 11a E 11b E 21a E 21b and E 02 The field strengths are for LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode, respectively.

[0084] In step S2, the mathematical model of coupling efficiency between various spatial modes (i.e., LPi mode and LPj mode at the few-mode fiber fusion splice under multiple splice parameters and fiber parameters) can be uniformly expressed by formula (8):

[0085]

[0086] Where, η ij The coupling efficiency between the two modes at the fusion splice of the few-mode fiber reflects the power loss of the spatial mode at the splice; d is the axial offset; E i and E j In the LP01 mode, i,j = 1, 2, 3, ..., 6; i or j = 1 represents LP01 mode, i or j = 2 represents LP11a mode, i or j = 3 represents LP11b mode, i or j = 4 represents LP21a mode, i or j = 5 represents LP21b mode, and i or j = 6 represents LP02 mode.

[0087] Substituting equations (2)-(7) into equation (8), we can obtain the mathematical model of the coupling efficiency between LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode at the fusion point, as shown in equations (9) to (19):

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] Where, η ij =η ji η represents the coupling efficiency between LPi and LPj modes, i.e., the coupling efficiency between any two modes among LP01, LP11a, LP11b, LP21a, LP21b, and LP02; when i = j, η represents the coupling loss characteristics at the mode fusion point, and the coupling efficiency η is... ij The smaller the value, the greater the power loss at the spatial mode fusion point, and vice versa; when i≠j, η represents the energy at the mode fusion point where the LPi mode couples into the LPj mode. ij The larger the value, the greater the crosstalk at the weld joint, and vice versa.

[0110] Therefore, the above theoretical model can be used to analyze the coupling loss and coupling efficiency between different spatial modes at the fusion splice point under different splice offsets d, offset azimuth angles θ and different fiber parameters.

[0111] like Figures 3 to 8 As shown, taking a six-mode FMF (containing LP01, LP11a, LP11b, LP21a, LP21b, and LP02 modes respectively) as an example, the application scenario of a method for analyzing the coupling efficiency of higher-order spatial modes in few-mode fibers provided in this embodiment of the invention is further explained. The specific process is as follows:

[0112] At this time, the core refractive index of the few-mode fiber is n1 = 1.44979, the cladding refractive index is n2 = 1.44402, the wavelength is λ = 1550nm, the core diameter of the few-mode fiber is a = 18.5μm, the axial offset distance is d = 0-3μm, the offset direction angle θ is 0°, 45° and 90°, and the fundamental mode Gaussian radius is ω0 = 4.2002μm;

[0113] (a) Analysis of self-coupling of LP01 mode at the fusion splice of few-mode fiber and its coupling efficiency with higher-order modes

[0114] According to the mathematical model of coupling efficiency using formulas (9)-(14), the coupling efficiency of the LP01 mode at the fusion point can be obtained, as well as the coupling efficiency of the LP01 mode with other higher-order modes at the fusion point. Figure 3 As shown in (a), the self-coupling efficiency of the LP01 mode in a few-mode fiber is as a function of the lateral offset d during excitation. The self-coupling efficiency of the LP01 mode decreases monotonically with the increase of fusion splice d. Meanwhile, since the mode field of the LP01 mode is axisymmetrically distributed, the coupling efficiency values ​​are consistent at different fusion splice rotation angles of 0°, 45° and 90°. Figure 3 Figures (b)-(f) show the coupling efficiency distribution between the fundamental mode and higher-order spatial modes of LP01 mode with LP11a, LP11b, LP21a, LP21b, and LP02, respectively, under axial offset distances d and offset angles of 0°, 45°, and 90°. The rhomboid, triangular, and hexagonal figures represent the coupling efficiency results between modes when the few-mode fiber fusion splice offset angle is 0°, 45°, and 90°, respectively. Figure 3 (b) It can be seen that, under the same welding offset condition, η 12 The coupling efficiency decreases as the welding rotation angle increases, and reaches zero at a rotation angle of 90°. Under welding rotation angles of 0° and 45°, the coupling efficiency increases with increasing welding offset. Similarly, a similar conclusion exists between LP01 and LP11b, the main difference being that the coupling efficiency is swapped between 0° and 90° conditions. Figure 3 As shown in (c), this is mainly because LP11a and LP11b are degenerate modes.

[0115] Depend on Figure 3 (d) It can be seen that under 0° and 90° rotation welding conditions, the coupling efficiency of modes LP01 and LP21a is the same, and it increases with the increase of welding offset; when the welding rotation angle is 45°, the coupling efficiency between the two modes is 0, while for the degenerate mode LP21b, as... Figure 3 As shown in (e), η 15 The efficiency increases with increasing weld offset; however, under both 0° and 90° rotational weld conditions, the coupling efficiency is 0. η 16 Since the mode fields of LP01 and LPL02 are axisymmetrically distributed, the coupling efficiency values ​​are consistent at different welding rotation angles of 0°, 45° and 90°, and the coupling efficiency between LP01 and LP02 increases with the increase of the offset.

[0116] (b) Analysis of LP11 mode self-coupling at few-mode fiber fusion splice and its coupling efficiency with higher-order modes

[0117] Similarly, according to formulas (15)-(23), when the LP11 mode is the excitation mode, the coupling efficiency of the mode itself at the fusion point is calculated, as well as the coupling efficiency between the LP11 mode and other higher-order modes at the fusion point. Figure 4 As shown in (a), the self-coupling efficiency of LP11a mode monotonically decreases with the increase of the weld offset d, and the coupling efficiency decreases with the increase of the weld rotation angle θ. In contrast, the degenerate mode LP11b is the opposite of LP11a. Figure 5 As shown in (a). By Figure 4 (b) It can be seen that under the 0° and 90° welding conditions, the mode coupling efficiency between LP11a and LP11b is the same and the coupling efficiency value is 0; when the welding rotation angle is 45°, the coupling efficiency increases with the increase of the welding offset.

[0118] like Figure 4 As shown in (c), under 0° and 45° welding conditions, η 24 The coupling efficiency increases with increasing weld offset, but at 0°, the coupling efficiency decreases as the offset reaches a certain level; the coupling efficiency is 0 when the weld rotation angle is 90°. The coupling efficiency between LP11b and LP21a, as... Figure 5 As shown in (b), at 90°, the coupling efficiency decreases as the offset reaches a certain level, and reaches zero when the welding rotation angle is 0°. The coupling efficiencies between LP11a, LP11b, and LP21b are respectively as follows: Figure 4 As shown in (d) and 5(c), under 45° fusion conditions, the coupling efficiency decreases as the offset reaches a certain level. Furthermore, due to the degeneracy mode, η at 0° and 90°... 25 Welding conditions η at 90° and 0° respectively 35 The values ​​are equal. The coupling efficiency between LP11a and LP02 modes, such as... Figure 4 As shown in (e), under 0° and 45° welding conditions, η 26 The coupling efficiency increases with the increase of the welding offset, and as the offset reaches a certain level, the coupling efficiency shows a decreasing trend; similarly, the same pattern exists between LP11b and LP02 under 45° and 90° rotation welding conditions.

[0119] (c) Analysis of LP21 mode self-coupling at few-mode fiber fusion splice and its coupling efficiency with higher-order modes

[0120] Similarly, according to formulas (24)-(28), when the LP21 mode is the excitation mode, the coupling efficiency of the mode itself at the fusion point is calculated, as well as the coupling efficiency of the LP21 mode with other higher-order modes at the fusion point. Figure 6 and Figure 7 The figures show the coupling efficiency distribution curves of LP21a and LP21b modes themselves, and their coupling efficiency distribution curves with other higher-order modes, respectively. Figure 6 As shown in (a), the self-coupling efficiency at the weld point of LP21a mode monotonically decreases with increasing d, and the trend is consistent under 0° and 90° weld conditions, while the coupling efficiency decreases more rapidly at 45°. For LP21b mode, the coupling efficiency is 0 when the weld rotation angle is 45°, as shown in (a). Figure 7 As shown in (a), the coupling efficiency between degenerate mode LP21a and LP21b is 0 under fusion conditions of 0°, 45°, and 90°, as... Figure 6 As shown in (b), the coupling efficiency between LP21a and LP02 modes is as follows. Figure 6 As shown in (c), under 0° and 90° welding conditions, η 46 The coupling efficiency increases with increasing weld offset, reaching 0 when the weld rotation angle is 45°. The coupling efficiency between LP21b and LP02 shows the opposite trend; under 0° and 90° weld conditions, η... 56 The efficiency is 0, while when the welding rotation angle is 45°, the coupling efficiency increases with the increase of the welding offset, such as... Figure 7 As shown in (b).

[0121] (d) Analysis of LP02 mode self-coupling efficiency at few-mode fiber fusion splice

[0122] Similarly, according to formula (29), when the LP02 mode is the excitation mode, the coupling efficiency of this mode at the fusion point is calculated, such as... Figure 8 As shown in the figure, the self-coupling efficiency varies with the weld offset. It can be seen from the figure that the coupling efficiency of the LP02 mode monotonically decreases with increasing d. Similar to the LP02 mode, due to the axisymmetric distribution of the mode field, the coupling efficiency values ​​are consistent at different weld rotation angles of 0°, 45°, and 90°.

[0123] like Figure 9 As shown in the figure, a system for analyzing the coupling efficiency of higher-order spatial modes in a few-mode fiber is provided in an embodiment of the present invention, comprising:

[0124] The field strength distribution mathematical model construction unit 110 is used to construct a structural model formed by splicing two segments of parameter-matched few-mode optical fibers, and based on the structural model, the Laguerre Gaussian mode is used to approximate the linear polarization mode to construct a mathematical model of field strength distribution of the few-mode optical fiber in multiple spatial modes; wherein, the multiple spatial modes include LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode;

[0125] The coupling efficiency mathematical model construction and analysis unit 120 is used to construct a coupling efficiency mathematical model between spatial modes at the fusion splice point of the few-mode fiber under multiple fusion parameters and fiber parameters based on the field strength distribution mathematical model of the few-mode fiber in multiple spatial modes, and to determine the power loss of each spatial mode fusion splice point based on the constructed coupling efficiency mathematical model between each spatial mode.

[0126] The matching parameters include core radius, relative refractive index, normalized frequency, and profile shape.

[0127] The solution of the Laguerre Gaussian modulus is expressed by the following formula (1):

[0128]

[0129] in, The normalization factor is l, and the azimuth component and radial component are the guiding azimuth component and the radial component, respectively. It is a Laguerre polynomial; Let be the Gaussian radius of the fundamental mode, k be the wavenumber, Δ be the relative refractive index, n1 be the core refractive index; θ be the offset azimuth angle; and r be the polar radius, where r 2 =x 2 +y 2 x and y are the coordinate axes of the few-mode fiber cross-section; a is the core radius.

[0130] Implementing the embodiments of the present invention has the following beneficial effects:

[0131] This invention establishes a general mathematical model for analyzing the coupling efficiency of high-order spatial modes based on the Laguerre-Gaussian distribution. This model overcomes the limitations of existing theoretical models in analyzing the fusion coupling efficiency of high-order spatial modes. It can reveal the variation law of the coupling efficiency of different modes and the coupling efficiency between modes under the conditions of factors such as axial offset, rotation angle and fiber parameters in few-mode fiber fusion splices. This enables accurate analysis of the coupling efficiency of each spatial mode in few-mode fiber, and can provide a theoretical basis for high-sensitivity fault detection of few-mode fiber links and the field of few-mode fiber sensing.

[0132] It is worth noting that the various units included in the above system embodiments are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0133] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as ROM / RAM, disk, optical disk, etc.

[0134] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers, characterized in that, The method includes the following steps: S1. Construct a structural model formed by splicing two segments of few-mode fiber with matched parameters, and based on the structural model, use the Laguerre Gaussian mode to approximate the linear polarization mode to construct a mathematical model of the field intensity distribution of the few-mode fiber in multiple spatial modes; wherein, the multiple spatial modes include LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode; S2. Based on the mathematical model of field strength distribution of the few-mode fiber in multiple spatial modes, construct a mathematical model of coupling efficiency between spatial modes at the fusion splice point of the few-mode fiber under multiple splicing parameters and fiber parameters, and determine the power loss of each spatial mode fusion splice point based on the constructed mathematical model of coupling efficiency between spatial modes. In step S2, the mathematical model of coupling efficiency between spatial modes can be uniformly expressed by formula (8): （8）； in, The coupling efficiency between the two modes at the fusion splice of the few-mode fiber reflects the power loss of the spatial mode at the fusion splice. This is the axial offset. and In ; The hourly average represents the LP01 mode. The time average represents the LP11a mode. The time average represents LP11b mode. The time average represents LP21a mode. The hourly average represents the LP21b mode. The hourly average represents LP 02 mode; In step S2, the mathematical model of coupling efficiency between LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode at the fusion point is expressed by the following formulas (9) to (19): （9）； （10）； （11）； （12）； （13）； （14）； （15）； （16）； （17）； （18）； （19）； （20）； （21）； （22）； （23）； （24）； （25）； （26）； （27）； （28）； （29）； in, , representing the coupling efficiency between LPi and LPj modes, that is, the coupling efficiency between any two modes among LP01, LP11a, LP11b, LP21a, LP21b, and LP02 modes; At this time, it represents the coupling loss characteristics at the mode fusion point, and the coupling efficiency. The smaller the value, the greater the power loss at the space mode fusion point, and vice versa; At this time, the energy at which the LPi mode couples into the LPj mode at the mode fusion point is represented. The larger the value, the greater the crosstalk at the weld joint, and vice versa.

2. The method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers as described in claim 1, characterized in that, In step S1, the matching parameters include core radius, relative refractive index, normalized frequency, and profile shape.

3. The method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers as described in claim 2, characterized in that, In step S1, the solution of the Laguerre Gaussian modulus is expressed by the following formula (1): （1）； in, As the normalization factor, and These are the azimuth component and the radial component, respectively; It is a Laguerre polynomial; The Gaussian radius of the fundamental mode. For wave number, The relative refractive index, The core refractive index; This is the offset azimuth angle; Let be the polar coordinate radius, and , and The coordinate axes represent the cross-section of few-mode optical fibers; The core radius is denoted as .

4. The method for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers as described in claim 3, characterized in that, In step S1, the mathematical model of field intensity distribution under each spatial mode is expressed by the following formulas (2) to (7): （2）； （3）； （4）； （5）； （6）； （7）； in, , , , , and The field strengths are for LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode, respectively.

5. A system for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers, characterized in that, include; The field strength distribution mathematical model construction unit is used to construct a structural model formed by splicing two segments of parameter-matched few-mode optical fibers, and based on the structural model, the Laguerre Gaussian mode is used to approximate the linear polarization mode to construct a mathematical model of the field strength distribution of the few-mode optical fiber in multiple spatial modes; wherein, the multiple spatial modes include LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode; The coupling efficiency mathematical model construction and analysis unit is used to construct a coupling efficiency mathematical model between spatial modes at the fusion splice point of the few-mode fiber under multiple fusion parameters and fiber parameters based on the field strength distribution mathematical model of the few-mode fiber in multiple spatial modes, and to determine the power loss of each spatial mode fusion splice point based on the constructed coupling efficiency mathematical model between each spatial mode. In step S2, the mathematical model of coupling efficiency between spatial modes can be uniformly expressed by formula (8): （8）； in, The coupling efficiency between the two modes at the fusion splice of the few-mode fiber reflects the power loss of the spatial mode at the fusion splice. This is the axial offset. and In ; The hourly average represents the LP01 mode. The time average represents the LP11a mode. The time average represents LP11b mode. The time average represents LP21a mode. The hourly average represents the LP21b mode. The hourly average represents LP 02 mode; In step S2, the mathematical model of coupling efficiency between LP01 mode, LP11a mode, LP11b mode, LP21a mode, LP21b mode and LP02 mode at the fusion point is expressed by the following formulas (9) to (19): （9）； （10）； （11）； （12）； （13）； （14）； （15）； （16）； （17）； （18）； （19）； （20）； （21）； （22）； （23）； （24）； （25）； （26）； （27）； （28）； （29）； in, , representing the coupling efficiency between LPi and LPj modes, that is, the coupling efficiency between any two modes among LP01, LP11a, LP11b, LP21a, LP21b, and LP02 modes; At this time, it represents the coupling loss characteristics at the mode fusion point, and the coupling efficiency. The smaller the value, the greater the power loss at the space mode fusion point, and vice versa; At this time, the energy at which the LPi mode couples into the LPj mode at the mode fusion point is represented. The larger the value, the greater the crosstalk at the weld joint, and vice versa.

6. The system for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers as described in claim 5, characterized in that, The matching parameters include core radius, relative refractive index, normalized frequency, and profile shape.

7. The system for analyzing the coupling efficiency of higher-order spatial modes in few-mode optical fibers as described in claim 6, characterized in that, The solution of the Laguerre Gaussian modulus is expressed by the following formula (1): （1）； in, As the normalization factor, and These are the azimuth component and the radial component, respectively; It is a Laguerre polynomial; The Gaussian radius of the fundamental mode. For wave number, The relative refractive index, The core refractive index; This is the offset azimuth angle; Let be the polar coordinate radius, and , and The coordinate axes represent the cross-section of few-mode optical fibers; The core radius is denoted as .

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