A method for mode decomposition of few-mode fiber by extracting angular characteristic parameters from the output optical intensity distribution of optical fiber

Abstract

The present invention discloses a method for decomposing few-mode fiber modes by extracting angular characteristic parameters from the optical intensity distribution output by an optical fiber. First, calculate the mode field distributions and corresponding orders of all spatial modes supported by the few-mode fiber to be measured. Secondly, refine the angular characteristic parameters that connect the optical intensity distribution output by the optical fiber and the complex amplitude of each spatial mode. Thirdly, establish a system of equations that maps the angular characteristic parameters to the complex amplitude of the spatial mode, and design a mode recovery algorithm to solve for the complex amplitude of the spatial mode. Then, build an optical device for detecting the mode field output by the optical fiber, and accurately calibrate the mode field distributions of each order of spatial modes detected by the spatial image detector. In the measured optical intensity distribution image at any moment, applying the above-mentioned algorithm can achieve the recovery of the complex amplitude of each spatial mode, that is, mode decomposition. The present invention can accurately recover the complex amplitude of each spatial mode only from the optical intensity distribution output by the optical fiber, and has strong applicability.

Description

Technical Field

[0001] The present invention relates to a method for decomposing few-mode fiber modes by extracting angular characteristic parameters from the optical intensity distribution output by an optical fiber, and belongs to the fields of space-division multiplexing optical fiber communication systems and integrated optics. Background Art

[0002] Spatial modes are specific spatial optical field distributions that can stably exist in multimode fibers or few-mode fibers, and are divided into different angular orders and radial orders. Each different order of spatial mode is orthogonal to each other and can be used as an independent transmission channel to increase the multiplexing dimension, thereby further improving the capacity of optical communication transmission. In addition, spatial modes also have extensive application potential in the fields of optical sensing, optical imaging, etc. Compared with multimode fibers, few-mode fibers support a limited number of stable and controllable spatial modes and have attracted much attention in recent research. In many studies and applications using few-mode fibers, a basic problem is to simply and accurately characterize the optical field output by the fiber. In few-mode fibers, multiple spatial modes are often excited simultaneously. Even if a relatively pure mode is excited, mode coupling during transmission is inevitable, so the fiber output end is usually a mixed optical field. The accurate description of each spatial mode contained in the fiber output mixed optical field is not only crucial for characterizing the performance of few-mode fibers and their related devices, but also crucial for developing other applications based on few-mode fibers. This problem is called the mode decomposition of few-mode fibers. In the past two decades, a variety of mode decomposition techniques have been proposed and are usually demonstrated in traditional step-index few-mode fibers. The basic theory of all these techniques is that the optical field in the fiber can be expressed as a coherent superposition of spatial modes, and each spatial mode is represented by a complex coefficient to represent the weight, that is, the complex mode coefficient or complex amplitude. Currently, there are mainly two types of mode decomposition methods that can recover the complete complex amplitude of each spatial mode in the fiber, including amplitude and phase, which means the most accurate characterization of the spatial mode in the few-mode fiber. The first type of mode decomposition method requires a reference beam. For example, digital holography and fiber point diffraction interferometers, etc., obtain the electric field distribution at the fiber output end through wavefront (phase) measurement, and calculate all mode complex amplitudes using the orthonormal characteristics of the modes. However, introducing a reference beam will limit its potential applicability because a more complex and stable optical system is required for on-site measurement.

[0003] The second type of methods can recover the modal complex amplitudes only from the optical intensity distribution output from the optical fiber without introducing a reference beam. Such methods usually include Gerchberg-Saxton, stochastic parallel gradient descent, and neural networks, etc. The neural network method has developed rapidly, but it requires a high-performance computer and a long training process. Recently, a mode decomposition method that only measures the intensity of the optical field output from the optical fiber without any training process (E.S. Manuylovich, V.V. Dvoyrin, and S.K. Turitsyn, "Fast mode decomposition in few-mode fibers," Nat. Commun. 11, 5507 (2020).) and its technical variants (E. Manuylovich, E. Manuylovich, A. Donodin, S. Turitsyn, and S. Turitsyn, "Intensity-only-measurement mode decomposition in few-mode fibers," Opt. Express, OE 29, 36769–36783 (2021).) have attracted attention. This method shows excellent performance in terms of both decomposition time and the number of resolvable modes under noise-free conditions. Its mathematical idea is to list an equation with a matrix about the eigenmode structure to relate the intensity distribution and the mode coefficients. The recovery of the modal complex amplitudes can be simply achieved by performing the Moore-Penrose pseudo-inverse transformation on the matrix. However, the usability of the proposed equation highly depends on the accuracy of the input optical intensity distribution information. Therefore, the number of modes that this method can resolve is severely limited by the signal-to-noise ratio of the input optical intensity distribution. If the optical fiber supports more than 6 modes in one polarization, then the modal complex amplitudes can only be recovered when the signal-to-noise ratio (SNR) is better than 32 dB. This is a very harsh condition. In fact, due to the inherent limitations of existing spatial image detectors (such as infrared charge-coupled devices), in the previously reported work, the experimental signal-to-noise ratio was often around 20 dB. Therefore, it is very difficult for this method to resolve the spatial modes of few-mode fibers that support more modes. Thus, it can be seen that the mode decomposition technology for recovering the complex amplitude of each spatial mode only from intensity measurement still needs to be further studied and developed. Summary of the Invention

[0004] The object of the present invention is to solve the problem that the existing mode decomposition method based only on light intensity measurement is limited by the signal-to-noise ratio and has poor applicability, and to propose a few-mode fiber mode decomposition method based on extracting angular characteristic parameters from the light intensity distribution of the fiber output. This novel method only needs to measure the light intensity distribution of the few-mode fiber output and solve the equations to restore the complex amplitude of each spatial mode. It has the characteristics of low computational complexity, clear physical meaning, wide application range, fast calculation speed, and accurate calculation results. This simple and accurate method can become a powerful tool for few-mode fibers applied in the fields of communication, sensing, imaging, etc., and has strong application value.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A few-mode fiber mode decomposition method based on extracting angular characteristic parameters from the light intensity distribution of the fiber output, the method comprising:

[0007] Step 1: Calculate the mode field distribution and propagation constant of all spatial modes of the few-mode fiber to be measured by using numerical calculation or analytical solution methods; the specific process is as follows:

[0008] For the few-mode fiber to be measured, first determine its geometric parameters (including the shape and size of the few-mode fiber) and optical characteristic parameters (including refractive index distribution and other physical parameters that will affect its optical properties). For simple fibers for which analytical solutions can be obtained, the analytical expression of the mode field distribution of the spatial mode is obtained by using the analytical solution; for complex fibers for which it is difficult to obtain analytical solutions, numerical simulation methods such as the finite element method or the finite difference method are used for calculation to obtain the numerical solution of the mode field distribution of the spatial eigenmode and the corresponding mode order.

[0009] Step 2: Represent the spatial mode field in the few-mode fiber to be measured as a coherent superposition of all spatial modes that can be supported in the fiber with arbitrary complex amplitudes, and extract the characteristic parameters that can reflect the complex amplitude of the spatial mode in the real physical image, that is, the angular Fourier coefficients;

[0010] Step 3: Theoretically derive the equations between the complex amplitude of the spatial mode of the few-mode fiber to be measured and the characteristic parameters, design an algorithm to solve the equations to obtain the complex amplitude of each spatial mode, and obtain the complex amplitude of each spatial mode; the specific process is as follows:

[0011] Use the fiber mode theory to derive the bond equations between the complex amplitude of the spatial mode of the few-mode fiber and the characteristic parameters, and substitute the measured characteristic parameters into the equations to solve to restore the complex amplitude of each spatial mode. Since numerical solution of the equations is often required when the number of fiber modes increases, if there is more than one numerical solution, the corresponding light intensity distribution maps need to be reconstructed respectively by using each set of complex amplitudes of the spatial modes corresponding to these numerical solutions, and compared with the actually measured light intensity distribution, and the one closest is the correct solution.

[0012] Step 4: Set up an optical device for amplifying and imaging to detect the mode field emerging from the optical fiber, accurately calibrate the mode field distributions of each spatial mode on the spatial image detector, and record the light field intensity distribution at any moment using the spatial image detector. The specific process is as follows:

[0013] The following method (not the only one) can be used for the accurate calibration of the spatial mode electric field distribution, that is, the light generated by a monochromatic laser source is converted into a pure spatial mode using optical elements such as a spatial light modulator and coupled into the multimode fiber to be measured through a focusing coupling system. Then, a polarizer and a lens magnification imaging system are placed at the output end of the multimode fiber to collect the light intensity distribution of the pure spatial mode, thereby achieving the accurate calibration of the spatial mode electric field distribution. Thereafter, record the light intensity distribution output from the end face of the multimode fiber at any moment.

[0014] Step 5: Extract the corresponding characteristic parameters from the measured light intensity distribution image, substitute them into the mode recovery algorithm in Step 3 to obtain the complex amplitudes of each spatial mode, and based on the complex amplitude results, simulate and calculate the corresponding recovered light intensity distribution.

[0015] The multimode fiber includes both common step-index fibers and ring-core fibers, as well as any multimode fiber with an axisymmetric refractive index characteristic, no geometric feature change in the transmission direction, and capable of conducting electromagnetic waves, and there is no restriction on the material used for the fiber.

[0016] The spatial mode should be a collective term for a series of spatial modes that are mutually orthogonal, power-normalized, and obtained by numerical calculation, analytical solution, or actual measurement.

[0017] The angular Fourier coefficient refers to the Fourier coefficient of any angular annular sampling sequence extracted from the light intensity distribution; the system of equations refers to a system of equations represented in any form with the information from the light intensity distribution and the spatial mode electric field structure information as known quantities and the amplitude and phase of the spatial mode as unknown quantities.

[0018] The nonlinear equation solving algorithm includes both analytical solution solving methods and numerical solving algorithms; it includes common nonlinear least squares algorithms (such as the Levenberg-Marquardt and trust region methods, etc.), stochastic parallel gradient descent algorithms, machine learning algorithms, as well as any numerical solving algorithm that can achieve the solution of nonlinear equations; it includes numerical calculation methods implemented using computer programming languages and numerical calculation methods utilized in commercial software.

[0019] The spatial image detector refers to various detectors that can record the spatial mode field output from the optical fiber.

[0020] The precise calibration of the spatial mode mentioned above refers to the calibration carried out by any method, including the electric field structure of the spatial mode and its location. It includes, but is not limited to, exciting a pure spatial mode and capturing the intensity distribution of the outgoing light for calibration; using an incoherent light source to determine the position of the fiber core imaged on the spatial image detector, and using numerical calculation or analytical solution methods to calculate the electric field structure of the spatial mode to achieve calibration, etc.

[0021] The advantages and positive effects of the present invention are:

[0022] The mode decomposition method proposed by the present invention has potential applications in broad fields such as communication, sensing, imaging, etc. based on few-mode fiber spatial modes. Starting from the basic definition of spatial modes, the method of the present invention inversely solves the complex amplitude from the characteristics of their light field intensity distribution, avoiding the introduction of a reference beam, and having high precision and high noise robustness, which makes it have universal application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a brief flow chart of the few-mode fiber mode decomposition method for extracting angular characteristic parameters from the light intensity distribution output by an optical fiber proposed by the present invention.

[0024] Figure 2 It is the refractive index profile of the ring-core optical fiber in the specific embodiment, the orbital angular momentum (OAM) modes supported by the ring-core optical fiber, and the radial field functions of these OAM modes. (a) The relative refractive index difference (Δn) between the core and cladding of the ring-core optical fiber. (b) The intensity distribution and phase distribution of each OAM mode, and the image size is 401×401 pixels. (c) The radial field functions of OAM modes with different angular orders.

[0025] Figure 3 It is a schematic flow chart of the complete mode decomposition algorithm in the specific embodiment. (a) The flow chart of the angular Fourier transform algorithm. (b) The real light intensity distribution. (c1) The intensity values of the angular sampling sequence in the real light intensity distribution. (c2-c3) The real part and imaginary part of the Fourier coefficients. (d1-d2) The amplitude and phase of the spatial mode. (e) The restored light intensity distribution.

[0026] Figure 4 It is the experimental setup in the specific embodiment. Among them: SMF, single-mode fiber; PC, polarization controller; SLM, spatial light modulator; RCF, ring-core fiber; Pol., polarizing mirror; OL, objective lens.

[0027] Figure 5 It is several examples of measured and reconstructed light intensity distributions and their correlations in the specific embodiment. SPECIFIC EMBODIMENT

[0028] The present invention will be further described below in conjunction with the accompanying drawings, taking the mode decomposition of a few-mode ring-core fiber supporting four modules as an example. The accompanying drawings are only for illustrative purposes and do not limit the scope of application of the present invention.

[0029] A few-mode fiber mode decomposition method for extracting angular feature parameters based on the output optical intensity distribution of the fiber. The brief process is shown in Figure 1 . First, start from the upper branch of the flow chart. For a few-mode fiber based on given geometric parameters (including the shape and size of the few-mode fiber) and optical characteristic parameters (including the refractive index distribution and other physical parameters that affect its optical properties), calculate the number of modes it can support, and obtain the mode field distributions and corresponding orders of these spatial modes. For simple fibers for which analytical solutions can be obtained, use the analytical solutions to find the analytical expressions of the mode field distributions of the spatial eigenmodes; for complex fibers for which it is difficult to obtain analytical solutions, use numerical simulation methods such as the finite element method or the finite difference method to calculate. The spatial modes in the fiber can be represented by different mode bases, and one of the bases is the orbital angular momentum mode (OAM) basis, and the situation described in the present invention is more convenient to characterize in this basis.

[0030] In this example, the refractive index profile of the few-mode ring-core fiber is cylindrically symmetric, and the relative refractive index difference (Δn) between the core and the cladding near the core center is as shown in Figure 2 (a). The diameter of the fiber cladding is 125 μm, and the inner and outer radii of the ring core are 3.75 μm and 8.25 μm respectively. The maximum value of Δn in the refractive index profile is 0.008. In order to reduce the coupling between modules caused by micro-perturbations, two notches are introduced in the refractive index profile. The first notch ranges from 3.75 μm to 4.6 μm, and Δn is 0.0065; the second notch ranges from 5.4 μm to 6.8 μm, and Δn is 0.0053. The intensity and phase distributions of each OAM mode supported by the fiber at 1550 nm are calculated by COMSOL using the finite element method, as shown in Figure 2 (b). The angular order of each OAM mode can be seen from the number of times of alternating bright and dark changes in the angular direction of the phase distribution. Therefore, this fiber supports four angular order modules, namely the 0th order (OAM 0 ), the 1st order (OAM ±1 ), the 2nd order (OAM ±2 ), and the 3rd order (OAM ±3 ). Figure 2 Each fiber mode shown in (b) also has two orthogonal polarization states (x polarization state and y polarization state). Each mode in the same module has the same intensity distribution and the same radial field function. Figure 2 (c) shows the normalized radial field function Fr |l| (r) of different order fiber modes.

[0031] Any optical field in a few-mode fiber is a linear superposition of all the spatial modes it can support. Therefore, describing the optical field in a fiber is equivalent to describing the optical field formed by superposing each spatial mode with an arbitrary complex amplitude. Once such an optical field is captured by a spatial image detector at the output end, an intensity distribution map can be obtained. Through a certain degree of mathematical analysis, physical quantities related to the complex amplitude of the spatial modes in the fiber can be extracted from the intensity distribution map, thereby realizing the restoration of the mode complex amplitude.

[0032] The following will theoretically analyze the relationship between the amplitudes and phases of each spatial mode in the OAM mode basis and the physically measurable quantities in the intensity distribution without restricting the angular order of the fiber modes. Without loss of generality, a polarization (x or y polarization) is selected, and then the optical field in the fiber can be expressed as

[0033]

[0034] where r and θ are the radial and angular coordinates, is the electric field distribution of the OAM mode, l is the angular order (L is the highest angular order), is the complex amplitude representing the amplitude and phase of the corresponding mode, Fr |l| is the radial field function of the corresponding mode.

[0035] The intensity distribution can be measured experimentally, and its expression is

[0036]

[0037] The mode decomposition problem essentially uses the intensity distribution I L (r, θ) at the output of the fiber to determine the complex amplitude ρ l ={A l , α l}. Since adding a constant phase shift to each phase coefficient does not affect the output intensity, it is assumed in this example that α 0 =0. For a fiber supporting 2L + 1 modes, 2L + 1 amplitudes and 2L phases need to be determined.

[0038] It is necessary to simplify the form of I L (r, θ). Through theoretical derivation, I L (r, θ) can be condensed into the following formula.

[0039]

[0040] Select a definite radius r = r 0 , then I L (r, θ) is simplified to a one-dimensional sequence of angular sampling.

[0041]

[0042] Next, rewrite I L (r 0 , θ) into a suitable form to expand it into a Fourier series.

[0043]

[0044] According to the simple correspondence with the standard expansion of the Fourier series, the real and imaginary parts of the first 2L + 1 Fourier coefficients can be expressed as a system of equations

[0045]

[0046] Thus, we have determined a deterministic relationship between the amplitudes and phases of the individual spatial modes and the physically measurable quantities in the light intensity distribution, namely Equation (6). The physically measurable quantities are the Fourier coefficients of the angular sampling points. Applying the fast Fourier transform (FFT) algorithm to I L (r 0 , θ), the required Fourier coefficients can be easily obtained. At the same time, as the prior knowledge of the eigenmode field distribution, Fr |l| (r 0 ) is known. With the help of this deterministic relationship, the mode decomposition problem is transformed into solving the system of equations (6), which can be completed by different algorithms for solving nonlinear systems of equations.

[0047] The above is the general expression without restricting the angular order of the fiber modes. For the few-mode ring-core fiber described in this example, the highest angular order is 3. Then, the system of equations described in Equation (6) contains 14 equations and 14 unknowns to be measured (the amplitudes and phases of 7 modes respectively). If the fiber modes are extended to more than the 3rd order, then only the highest order L needs to be determined (for any fiber to be measured, it can be determined in the first step of this method), and then it is possible to determine how many equations need to be solved in the system of equations (6) at this time.

[0048] Although the mode decomposition problem has been transformed into solving the system of equations determined by Equation (6), in practice, when using existing methods for solving nonlinear systems of equations, such as the nonlinear least squares algorithm (Levenberg - Marquardt and trust region methods, etc.) to solve the said system of equations, there are usually multiple numerical solutions. However, it should be noted that we only use the information of a single angular annular sampling point in the light intensity distribution to obtain these solutions, and this is not a full utilization of it. To use all the information provided by the light intensity distribution, we further designed an algorithm to solve this system of equations and then obtain the complex amplitudes of the individual spatial modes. The complete algorithm flow is summarized in Figure 3 (a), which is described in detail below.

[0049] First, Figure 3 (b) is an intensity distribution diagram of any light field for which the complex amplitude of each spatial mode needs to be determined. The angular dashed lines represent angular annular sampling points, and their intensity values are extracted and expanded into a one-dimensional sequence (c1). Applying the fast Fourier transform algorithm to this one-dimensional sequence gives the real and imaginary part values of each Fourier coefficient, as shown in (c2 - c3). Substitute these extracted Fourier coefficient values into the system of equations determined by Equation (6) (in this example, the highest order of the spatial mode is 3, so the system of equations contains 14 equations). Since Fr |l| (r 0 ) is known (while in the experiment, the electric field distributions of each spatial mode on the spatial image detector need to be calibrated to obtain these values), the only unknowns in the system of equations are the complex amplitudes of each spatial mode. By solving such a system of equations, multiple sets of numerical solutions may be obtained, corresponding to several different sets of complex amplitudes of the spatial modes. At this time, we need to separately simulate the intensity distribution diagrams corresponding to these sets of complex amplitudes and use the correlation coefficient to measure the degree of closeness between them and the intensity distribution diagram to be measured. The set of complex amplitudes with the highest correlation coefficient is regarded as the finally recovered complex amplitude. The true and recovered spatial mode amplitudes and phases under simulation conditions are shown in (d1 - d2), and the finally recovered intensity distribution is shown in Figure (e).

[0050] Then comes the lower branch of the flow chart, that is, the experimental level. In this part, an optical device for detecting the mode field emerging from the optical fiber needs to be built, and the electric field distributions of each order of spatial mode on the spatial image detector need to be accurately calibrated. The experimental device is as Figure 4As shown. In this example, we propose a method for calibrating the spatial mode electric field distribution. Although this method is demonstrated in a few-mode ring-core fiber used for demonstration, it is a general scheme. Due to problems in the existing fiber manufacturing process, there are some differences between the actual fiber refractive index profile and the designed one, which will cause the electric field distributions of each spatial mode imaged onto the spatial image detector to be different from the theoretical calculations. Therefore, we choose to inject pure modes into the fiber to achieve the calibration of the electric field distributions of each spatial mode. The experimental setup can be divided into a coupling part and an imaging part. In the coupling part, we generate pure modes and couple them into the ring-core fiber. First, we use a tunable laser (KEYSIGHT 81600B, 1460nm - 1640nm) to generate the fundamental mode light at 1550nm. A polarization controller is used to change the polarization of the beam to match the axis of the spatial light modulator (SLM, Holoeye Pluto2.1), which only responds to linearly polarized states. The light is collimated into a Gaussian beam by a lens (Lens 1) and modulated by the SLM. Two mirrors and a three-axis displacement platform are used for precise alignment of the optical path. The Gaussian beam is coupled into the ring-core fiber through an objective lens (OL) and excites the fundamental mode. Then, by loading a spiral phase plate with different fork gratings on the phase surface of the SLM, the Gaussian beam is converted into pure OAM modes with different azimuthal orders (1 / 2 / 3), and the corresponding modes are excited in the ring-core fiber. In the imaging part, the output light field of the ring-core fiber is collimated and expanded by two lenses (Lens 2, Lens 3). A polarization state is selected by a polarizer. And the light field is finally captured by a camera (FIND-RSCOPE 85706, 400 - 1800nm). By changing the phase surface of the SLM, we obtained a series of light intensity distributions of approximately pure modes in the experiment, and then determined the intensity and phase distributions of each OAM mode experimentally from these pure modes, just like Figure 2 the form of each spatial mode shown in (b), and then achieved the precise calibration of the electric field distribution of each mode.

[0051] Finally, from any measured light intensity distribution map whose complex amplitudes of each spatial mode need to be determined, the corresponding azimuthal Fourier coefficient characteristic parameters are extracted and substituted into the mode decomposition algorithm designed by Figure (3), and the complex amplitudes of each spatial mode can be obtained. Based on this complex amplitude result, the corresponding restored light intensity distribution is simulated and calculated. Several measured and reconstructed light intensity distributions, and their correlation coefficients are as Figure 5 shown. Taking the fourth column of images as an example, its correlation is as low as 0.98094, but the measured image and the reconstructed image still show a high degree of similarity.

[0052] The example described herein is only one example of the usage of the present invention, and does not limit the type of few-mode optical fiber, refractive index distribution, manufacturing material, working wavelength band, etc., nor is it limited to the method for solving the nonlinear equation and the specific method for accurately calibrating the spatial mode, etc. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for decomposing few-mode fiber modes by extracting angular characteristic parameters from the output optical intensity distribution of an optical fiber, characterized in that it includes the following steps: Step 1: According to the structural parameters of the fiber to be measured, use numerical calculation or analytical solution methods to calculate the mode field distributions and corresponding orders of all spatial modes supported by the few-mode fiber to be measured; Step 2: Represent the spatial mode field in the few-mode fiber to be measured as a coherent superposition of all spatial modes that the fiber can support with arbitrary complex amplitudes, and extract the characteristic parameters that can reflect the complex amplitude of the spatial mode in the real physical image, that is, the angular Fourier coefficients; Step 3: Theoretically derive a non-linear equation set between the complex amplitude of the spatial mode of the few-mode fiber to be measured and the angular characteristic parameters, design a solution algorithm for this non-linear equation set, and obtain the complex amplitudes of each spatial mode; Step 4: Experimentally build a set of amplified imaging optical devices for detecting the output mode field of the optical fiber, accurately calibrate the mode field distributions of each order of spatial modes on the spatial image detector, and use the spatial image detector to record the light field intensity distribution at any time; Step 5: Extract the corresponding angular characteristic parameters from the measured light intensity distribution image, substitute them together with the mode field distributions of each order of spatial modes measured in Step 4 into the mode recovery algorithm in Step 3 to obtain the complex amplitudes of each order of spatial modes, and based on the complex amplitude results, simulate and calculate the corresponding recovered light intensity distribution.

2. The method for decomposing few-mode fiber modes by extracting angular characteristic parameters from the output optical intensity distribution of an optical fiber according to claim 1, characterized in that: The few-mode fiber includes both common step-index fibers and ring-core fibers, and also any few-mode fiber with an axisymmetric refractive index characteristic, no geometric feature change in the transmission direction, and capable of conducting electromagnetic waves.

3. The method for decomposing few-mode fiber modes by extracting angular characteristic parameters from the output optical intensity distribution of an optical fiber according to claim 1, characterized in that: In Step 1, for the few-mode fiber to be measured, first determine its geometric parameters and optical characteristic parameters. For a simple fiber for which an analytical solution can be obtained, use the analytical solution to find the analytical expression of the mode field distribution of the spatial mode. For a complex fiber for which it is difficult to obtain an analytical solution, use numerical simulation methods to obtain the numerical solution of the mode field distribution of the spatial eigenmode and the corresponding mode order; The spatial mode is a general term for a series of spatial modes that are mutually orthogonal, power-normalized, and obtained by numerical calculation, analytical solution, or actual measurement.

4. The method for decomposing few-mode fiber modes by extracting angular characteristic parameters from the output optical intensity distribution of an optical fiber according to claim 1, characterized in that: The angular Fourier coefficients in Step 2 refer to the Fourier coefficients of any angular annular sampling sequence extracted from the light intensity distribution; the equation set refers to an equation set expressed in any form with the information from the light intensity distribution and the electric field structure information of the spatial mode as known quantities and the amplitude and phase of the spatial mode as unknown quantities.

5. The method for decomposing few-mode fiber modes by extracting angular characteristic parameters from the output optical intensity distribution of an optical fiber according to claim 1, characterized in that: In Step 3, the coupled equations between the spatial mode complex amplitudes and the characteristic parameters of the few-mode fiber are deduced using the fiber mode theory. The measured characteristic parameters are substituted into the equations to solve for the complex amplitudes of each spatial mode. If there are more than one numerical solutions, the corresponding light intensity distribution maps are reconstructed respectively using each set of complex amplitudes of the spatial modes corresponding to these numerical solutions, and then compared with the actually measured light intensity distribution. The one with the closest match is the correct solution. The solution algorithms for the non-linear equations include both analytical solution methods and numerical solution algorithms; they include non-linear least squares algorithms, stochastic parallel gradient descent algorithms, machine learning algorithms, and any numerical solution algorithms for solving non-linear equations; they include numerical calculation methods implemented using computer programming languages and numerical calculation methods used in commercial software.

6. The few-mode fiber mode decomposition method for extracting angular characteristic parameters from the fiber output light intensity distribution according to claim 1, characterized in that: In Step 4, the accurate calibration of the spatial mode electric field distribution includes, but is not limited to, the following methods: converting the light generated by a monochromatic laser source into a pure spatial mode using optical elements such as a spatial light modulator and coupling it into the few-mode fiber to be measured through a focusing coupling system, then placing a polarizer and a lens magnification imaging system at the output end of the few-mode fiber to collect the light intensity distribution of the pure spatial mode to achieve the accurate calibration of the spatial mode electric field distribution. Thereafter, the light intensity distribution output from the few-mode fiber end face at any time is recorded. The spatial image detector refers to any detector capable of recording the spatial mode field output from the fiber.

7. The few-mode fiber mode decomposition method for extracting angular characteristic parameters from the fiber output light intensity distribution according to claim 1, characterized in that: The accurate calibration of the spatial mode refers to the calibration using any method including the spatial mode electric field structure and its position, including but not limited to exciting a pure spatial mode and capturing the output light intensity distribution for calibration; using an incoherent light source to determine the position of the fiber core imaged on the spatial image detector and using numerical calculation or analytical solution methods to calculate the spatial mode electric field structure for calibration; using a determined 4F system to achieve calibration through the calculation of the light field transmission.

8. An apparatus for implementing the few-mode fiber mode decomposition method for extracting angular characteristic parameters from the fiber output light intensity distribution according to any one of claims 1-7, characterized in that: The apparatus consists of a tunable laser, a polarization controller PC, a lens 1, a spatial light modulator SLM, a mirror 1, a mirror 2, a three-axis displacement platform, a ring fiber RCF, a lens 2, a lens 3, a polarizer Pol, and a camera CCD in sequence. The apparatus includes a coupling part and an imaging part, where: The coupling part is used to generate a pure mode and couple it into the ring-core fiber. The tunable laser generates the fundamental mode light at 1550 nm. The polarization controller is used to change the polarization of the light beam to match the axis of the spatial light modulator, which only responds to the linearly polarized state. Lens 1 collimates the light into a Gaussian beam, which is modulated by the SLM. The mirrors 1, 2 and a three-axis displacement platform are used for the precise alignment of the optical path. The Gaussian beam is coupled into the ring-core fiber through the objective lens OL and excites the fundamental mode. Then, by loading a spiral phase plate with different forked gratings on the phase surface of the SLM, the Gaussian beam is converted into pure OAM modes with different angular orders of 1 / 2 / 3, and the corresponding modes are excited in the ring-core fiber. In the imaging part, the output optical field of the ring-core fiber is collimated and expanded by lens 2 and lens 3. A polarization state is selected by the polarizer, and the optical field is finally captured by the camera. By changing the phase surface of the SLM, a series of light intensity distributions of approximately pure modes are obtained. Furthermore, the intensity and phase distributions of each OAM mode are determined experimentally from these pure modes, and the precise calibration of the electric field distribution of each mode is achieved. Finally, by extracting the corresponding angular Fourier coefficient characteristic parameters, the complex amplitudes of each order of spatial mode are obtained, and based on the results of this complex amplitude, the corresponding restored light intensity distribution is simulated and calculated.

9. The device for the few-mode fiber mode decomposition method of extracting angular characteristic parameters based on the optical fiber output light intensity distribution according to claim 8, characterized in that: the device is the device described in step 4 of claim 1.

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