Multi-core OAM mode demultiplexing device and method based on spiral transformation reverse design

Abstract

The invention provides a multi-core OAM mode demultiplexing device and method based on spiral transformation reverse design, and the method comprises the steps: initially setting spiral coordinate transformation phase plates for reverse design optimization, namely an optical transformation phase plate, a phase correction phase plate and an elliptical lens phase plate; an input vortex mode is propagated and evolved into an output spatially separated Gaussian-like mode through the three phase plates in sequence, phase distribution of the three phase plates is optimized through a wavefront matching method, an average overlapping integral of the output Gaussian-like mode and an ideal Gaussian mode is used as a target function, iteration is carried out until convergence, and the output Gaussian-like mode is obtained. According to the photon orbital angular momentum mode demultiplexing device, the number of modes supported by the photon orbital angular momentum mode demultiplexing device after reverse design optimization is nearly doubled, and the quality of an output light beam is improved; compatibility of 19-core OAM optical fiber communication is facilitated, and great significance is achieved for development of the ultra-large-capacity dense OAM space division multiplexing field.

Description

Technical Field

[0001] The present invention relates to the field of optical communication technology, and in particular to a multi-core OAM mode demultiplexing device and method based on spiral transformation inverse design. Background Art

[0002] With the rapid development of information technology with the Internet as the core, including mobile Internet, Internet of Things, cloud computing, big data, etc., the amount of information has expanded rapidly, putting higher requirements on the transmission capacity of optical communication systems.

[0003] At present, the space for improving communication capacity of traditional channel multiplexing technologies, such as wavelength division multiplexing, time division multiplexing and polarization multiplexing, has reached its limit. In order to further significantly improve the communication capacity, space division multiplexing technology has become an important research direction in the current communication field. Since vortex beams have characteristics such as phase singularities and theoretically infinite orthogonal OAM mode space, they have shown broad application prospects in many fields such as optical communication, optical micromanipulation, optical imaging and quantum information. In particular, OAM space division multiplexing technology has become a promising technology to cope with the growing communication capacity. Among them, an optical vortex mode sorter that supports multiple modes, multiple cores and large bandwidth, that is, an OAM mode demultiplexer, is needed to achieve precise optical coupling between multi-core OAM fibers and single-mode fiber arrays. Several types of schemes for OAM mode demultiplexing have been proposed, such as Dammann gratings, photonic lanterns, 3D direct writing waveguides, optical coordinate transformation, etc.

[0004] Compared with other OAM demultiplexing technologies, the vortex beam coordinate transformation technology based on the ray model is an efficient and high-resolution solution for dense OAM space division multiplexing. However, the performance of vortex mode demultiplexing is limited by the paraxial approximation and plane wave approximation. The high-order vortex mode has a large divergence angle, gradually deviates from the approximate conditions, and causes phase distortion. This limits the number of supported modes and reduces the quality of the transformed beam. Although this problem can be alleviated by increasing the size of the phase plate and compensating for the phase distortion through non-paraxial phase correction, increasing the size of the phase plate is not suitable for integration and arraying, and non-paraxial phase correction cannot flexibly adjust the configuration of the input and output beam sizes, and is not suitable for the mutual matching between multi-core multimode optical fiber and single-mode optical fiber arrays. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a multi-core OAM mode demultiplexing device and method based on spiral transformation inverse design, which can be extended to high-resolution spatial separation of a larger number of vortex modes.

[0006] The technical solution of the present invention is: a multi-core OAM mode demultiplexing method based on spiral transformation inverse design, comprising the following steps:

[0007] S1), using the spiral transformation phase plate obtained by analytical solution based on the ray model as the initial input of the wavefront matching method;

[0008] S2), taking the perfect vortex mode whose central bright ring radius does not change with the change of topological charge as the incident vortex beam; and constructing the mode field distribution PV of the incident vortex beam and the mode field distribution of the output beam;

[0009] S3), using the wavefront matching method to calculate the mode field distribution of the perfect vortex beams with different incident topological charges propagating forward to the mth phase plate and the mode field distribution of the output ideal Gaussian mode propagating backward to the position of the mth phase plate;

[0010] S4), when the phases on both sides of the mth phase plate do not match, calculate the phase error of each spatial coordinate point on the mth phase plate; and use the average value of the phase error of each set of input and output modes as the phase distribution that needs to be updated for the mth phase plate;

[0011] S5), traversing all phase plates is regarded as one wavefront matching method iteration, and then the overlap integral of each input and output mode is calculated to obtain the average mode conversion efficiency of this generation, and the difference σ0 of the average mode conversion efficiency between two adjacent generations is used as the condition for judging whether the iteration converges;

[0012] S6), using reverse design optimization to obtain three phase plates;

[0013] S7), the incident perfect vortex beams with different topological charges are phase modulated and propagated in sequence, and the light field profile gradually propagates and evolves into a Gaussian-like mode, and the center of the vortex beam of each core is aligned with the center position of the transformation phase plate; the input vortex beams with different topological charges are correspondingly converted into Gaussian beams at different positions on the output plane to achieve spatial separation of different vortex modes.

[0014] Preferably, in step S1), the initially input phase plates are optically variable phase plates, phase correction phase plates, and elliptical lens phase plates.

[0015] Preferably, in step S1), the transformation relationship of the spiral coordinate transformation from the (r, θ) coordinate plane to the (u, v) coordinate plane is:

[0016]

[0017] Among them, a, r0, β are all helix parameters, (r, θ) represents the polar coordinates of the vortex beam, and (u, v) is the position coordinates of the phase correction phase plate.

[0018] Preferably, in step S1), the phase distribution of the optical transformation phase plate and the phase correction phase plate corresponding to the spiral transformation is obtained by solving the following partial differential equations based on the ray model:

[0019]

[0020]

[0021] Wherein, P1 and P2 represent the phases of the optical transformation phase plate and the phase correction phase plate respectively, k = 2π / λ is the wave number; (x, y) is the position coordinate of the optical transformation phase plate; (u, v) is the position coordinate of the phase correction phase plate; d represents the distance between the optical transformation phase plate and the phase correction phase plate;

[0022] Preferably, in step S1), the elliptical lens phase plate corresponding to the spiral transformation is denoted as P3, and its phase distribution is expressed as:

[0023]

[0024] Where f is the focal length of the elliptical lens; (x, y) is the position coordinate of the elliptical lens phase plate.

[0025] Preferably, in step S2), the mode field distribution PV(r,θ) of the incident vortex beam is expressed as:

[0026]

[0027] Where (r,θ) represents the polar coordinates of the vortex beam; r max represents the maximum radius of the central bright ring; w0 represents the beam ring width; l is the topological charge number; i represents the imaginary unit.

[0028] Preferably, in step S2), the output beam is a Gaussian beam, and the mode field distribution G(r,θ) of the output beam is:

[0029]

[0030] Where w is the waist radius of the Gaussian beam; (r,θ) represents the polar coordinates of the vortex beam.

[0031] Preferably, in step S3), the mode field distribution of the incident vortex beam with topological charge number l propagates forward to the mth phase plate It is expressed as:

[0032]

[0033] The mode field distribution of the output ideal Gaussian beam corresponding to the input mode and propagating back to the mth phase plate It is expressed as:

[0034]

[0035] in, is the Fourier transform, and represents the forward phase modulation of the mth phase plate and the reverse phase modulation of the m+1th phase plate, respectively, and H is the beam transmission function; (x, y, z m ) represents the three-dimensional rectangular coordinate system in physical space; k x ,k y ,z represent the wave number components of the light wave in the transverse x and y directions and the coordinates of the light wave along the propagation direction respectively.

[0036] Preferably, step S4) specifically includes the following steps:

[0037] S41), assuming that the input and output beam powers are normalized, the complex amplitude distribution of the input vortex mode forward propagating to the mth phase plane is for:

[0038]

[0039] In the formula, A f represents the amplitude distribution of the input light field propagating forward to the phase plane of the mth block; i represents the imaginary unit, φ f represents the phase distribution of the input light field propagating forward to the phase plane of the mth block;

[0040] S42), output the complex amplitude distribution of the ideal Gaussian mode back-propagating to the phase plane of the mth block for:

[0041]

[0042] In the formula, A b represents the amplitude distribution of the output ideal light field propagating back to the phase plane of the mth block; φ b represents the phase distribution of the output ideal light field propagating back to the phase plane of the mth block;

[0043] S43), the phase distribution that can perfectly compensate the phase mismatch between the two is calculated to be φ = -φ f +φ b ;

[0044] S44), calculating the average phase error of each group of input and output modes as the phase distribution that needs to be updated for the mth phase plate.

[0045] Preferably, in step S5), the input mode is propagated to the output plane through a series of phase plane modulations, and the corresponding output mode complex amplitude distribution is u1(x, y), and the ideal output mode complex amplitude distribution is u2(x, y). The overlap integral I of the two is:

[0046]

[0047] In the formula, represents the conjugated output mode complex amplitude distribution;

[0048] Calculate the overlap integral between each output mode and the ideal output mode, find the average value, and record it as the average mode conversion efficiency of this generation.

[0049] Preferably, in step S5), when the average mode conversion efficiency difference σ0 between two adjacent generations is less than a set threshold, it is determined whether the iterative optimization has converged.

[0050] Preferably, in step S6), three phase plates are obtained by inverse design optimization, as follows:

[0051] The optical transformation phase plate, phase correction phase plate and elliptical lens phase plate obtained by analytically solving the partial differential equation are used as the initial input phase distribution. The wavefront matching method is iterated until the set number of iterations is met or the convergence condition is reached, and the optical transformation phase plate, phase correction phase plate and elliptical lens phase plate after inverse optimization and reconstruction are obtained.

[0052] Preferably, in step S7), spatial separation of different vortex modes is achieved, which specifically includes the following steps: the vortex mode with donut-shaped intensity distribution is modulated by the optical transformation phase plate after reverse reconstruction and propagated, gradually unfolded into a long light spot, and then modulated by the phase correction phase plate and the elliptical lens phase plate after reverse reconstruction in turn and propagated to the output plane, and the long light spot gradually propagates and evolves into Gaussian-like spots at different positions separated in space.

[0053] Preferably, the present invention further provides a multi-core OAM mode demultiplexing device based on a spiral transformation inverse design, comprising a double-sided diffractive optical element, a single-sided diffractive optical element, and an optical transformation phase plate, a phase correction phase plate, and an elliptical lens phase plate;

[0054] The optical transformation phase plate and the phase correction phase plate are respectively located on the front and back sides of the double-sided diffractive optical element; the elliptical lens phase plate is integrated on one side of the single-sided diffractive optical element.

[0055] Preferably, the optical transformation phase plate, phase correction phase plate, and elliptical lens phase plate are each arranged in a hexagonal array of 19 cores. After the incident 19-core array vortex beam is modulated and propagated and evolved by the arrayed optical transformation phase plate, phase correction phase plate, and elliptical lens phase plate in sequence, it is converted into a spatially separated Gaussian-like beam in the output plane to achieve vortex mode sorting.

[0056] Preferably, the double-sided diffractive optical element and the single-sided diffractive optical element are quartz plates with different thicknesses, wherein the thickness of the double-sided diffractive optical element is 5 mm; the thickness of the single-sided diffractive optical element is 1 mm.

[0057] The beneficial effects of the present invention are:

[0058] 1. The present invention utilizes inverse design wavefront matching to iteratively optimize the phase distribution of spiral transformation, breaking through the limitations of the previous optical coordinate transformation based on the ray model to calculate the phase distribution for paraxial approximation and plane wave approximation;

[0059] 2. Compared with the previous spiral transformation, the optimized optical transformation of the present invention can be extended to high-resolution spatial separation of more vortex modes, that is, OAM mode demultiplexing;

[0060] 3. Compared with the previous spiral transformation whose input and output beam configurations are unadjustable, the 19-core photon orbital angular momentum mode demultiplexing device provided by the present invention based on the reverse design of spiral transformation can be compatible with 19-core OAM optical fiber communication, which is of great significance for the development of ultra-large capacity dense OAM space division multiplexing field. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 1 is a comparison diagram of three phase plates in the embodiment of the present invention, wherein (a) is a schematic diagram of a spiral transformation phase plate; (b) is a schematic diagram of a reverse design optimized phase plate; phase plates 1-3 are respectively an optical transformation phase plate, a phase correction phase plate, and an elliptical lens phase plate;

[0062] Figure 2 The figures are comparison diagrams of demultiplexed light spots and light intensity profiles in the embodiments of the present invention, wherein (a) is a diagram of demultiplexed light spots and light intensity profiles of spiral transformation; (b) is a diagram of demultiplexed light spots and light intensity profiles of optical transformation optimized by reverse design;

[0063] Figure 3 Schematic diagram of the structure of a 19-core photon orbital angular momentum demultiplexer optimized based on the inverse design of spiral transformation in an embodiment of the present invention;

[0064] Figure 4 Demultiplexing spot diagram of a 19-core photon orbital angular momentum demultiplexing device optimized based on the inverse design of spiral transformation in an embodiment of the present invention;

[0065] In the figure, 1-double-sided diffractive optical element; 2-single-sided diffractive optical element; 3-optical transformation phase plate; 4-phase correction phase plate; 5-elliptical lens phase plate. DETAILED DESCRIPTION

[0066] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings:

[0067] Example 1

[0068] This embodiment provides a multi-core OAM mode demultiplexing method based on spiral transformation inverse design, comprising the following steps:

[0069] S1), using the spiral transformation phase plate obtained by analytical solution based on the ray model as the initial input of the wavefront matching method; Figure 1 (a) As shown; in this embodiment, the initial input phase plates are respectively an optical transformation phase plate 3, a phase correction phase plate 4, and an elliptical lens phase plate 5.

[0070] Among them, the transformation relationship of the spiral coordinate transformation from the (r,θ) coordinate plane to the (u,v) coordinate plane is:

[0071]

[0072] Among them, a, r0, β are all helix parameters, (r, θ) represents the polar coordinates of the vortex beam, and (u, v) is the position coordinates of the phase correction phase plate.

[0073] The phase distribution of the optical transformation phase plate and the phase correction phase plate corresponding to the spiral transformation is obtained by solving the following partial differential equations based on the ray model:

[0074]

[0075]

[0076] Wherein, P1 and P2 represent the phases of the optical transformation phase plate and the phase correction phase plate respectively, k = 2π / λ is the wave number; (x, y) is the position coordinate of the optical transformation phase plate; (u, v) is the position coordinate of the phase correction phase plate; d represents the spacing between the optical transformation phase plate and the phase correction phase plate.

[0077] The elliptical lens phase plate corresponding to the spiral transformation is denoted as P3, and its phase distribution is expressed as:

[0078]

[0079] Where f is the focal length of the elliptical lens; (x, y) is the position coordinate of the elliptical lens phase plate.

[0080] S2), taking the perfect vortex mode whose central bright ring radius does not change with the change of topological charge as the incident vortex beam; and constructing the mode field distribution PV of the incident vortex beam and the mode field distribution G(r,θ) of the output beam;

[0081] Wherein, the expression of the mode field distribution PV(r,θ) of the incident vortex beam is:

[0082]

[0083] Where (r,θ) represents the polar coordinates of the vortex beam; r max represents the maximum radius of the central bright ring; w0 represents the beam ring width; l is the topological charge number; i represents the imaginary unit.

[0084] The output beam is a Gaussian beam, and the mode field distribution G(r,θ) of the output beam is:

[0085]

[0086] Where w is the waist radius of the Gaussian beam; (r,θ) represents the polar coordinates of the vortex beam.

[0087] S3), using the wavefront matching method to calculate the mode field distribution of the perfect vortex beams with different incident topological charges propagating forward to the mth phase plate and the mode field distribution of the output ideal Gaussian mode propagating backward to the position of the mth phase plate;

[0088] In this embodiment, the mode field distribution of the incident vortex beam with topological charge number l propagating forward to the mth phase plate is It is expressed as:

[0089]

[0090] The mode field distribution of the output ideal Gaussian beam corresponding to the input mode and propagating back to the mth phase plate It is expressed as:

[0091]

[0092] in, is the Fourier transform, and represents the forward phase modulation of the mth phase plate and the reverse phase modulation of the m+1th phase plate, respectively, and H is the beam transmission function; (x, y, z m ) represents the three-dimensional rectangular coordinate system in physical space; k x ,k y ,z represent the wave number components of the light wave in the transverse x and y directions and the coordinates of the light wave along the propagation direction respectively.

[0093] S4), when the phases on both sides of the mth phase plate do not match, calculate the phase error of each spatial coordinate point on the mth phase plate; and use the average value of the phase error of each set of input and output modes as the phase distribution that needs to be updated for the mth phase plate; specifically comprising the following steps:

[0094] S41), assuming that the input and output beam powers are normalized, the complex amplitude distribution of the input vortex mode forward propagating to the mth phase plane is for:

[0095]

[0096] In the formula, A f represents the amplitude distribution of the input light field propagating forward to the phase plane of the mth block; i represents the imaginary unit, φ f represents the phase distribution of the input light field propagating forward to the phase plane of the mth block;

[0097] S42), output the complex amplitude distribution of the ideal Gaussian mode back-propagating to the phase plane of the mth block for:

[0098]

[0099] In the formula, A b represents the amplitude distribution of the output ideal light field propagating back to the phase plane of the mth block; φ b represents the phase distribution of the output ideal light field propagating back to the phase plane of the mth block;

[0100] S43), the phase distribution that can perfectly compensate the phase mismatch between the two is calculated to be φ = -φ f +φ b ;

[0101] S44), calculating the average phase error of each group of input and output modes as the phase distribution that needs to be updated for the mth phase plate.

[0102] S5), traversing all phase plates is regarded as one wavefront matching method iteration, and then the overlap integral of each input and output mode is calculated to obtain the average mode conversion efficiency of this generation, and the difference σ0 of the average mode conversion efficiency between two adjacent generations is used as the condition for judging whether the iteration converges; specifically:

[0103] The input mode is propagated to the output plane through a series of phase plane modulations, and the corresponding output mode complex amplitude distribution is u1(x, y). The ideal output mode complex amplitude distribution is u2(x, y). The overlap integral I of the two is:

[0104]

[0105] In the formula, represents the conjugated output mode complex amplitude distribution.

[0106] Calculate the overlap integral between each output mode and the ideal output mode, find the average value, and record it as the average mode conversion efficiency of this generation.

[0107] When the difference σ0 of the average mode conversion efficiency between two adjacent generations is less than the set threshold, it is determined whether this iterative optimization has converged.

[0108] S6), three phase plates are obtained by inverse design optimization, such as Figure 1 As shown in (b), this embodiment uses the optical transformation phase plate, phase correction phase plate, and elliptical lens phase plate obtained by analytically solving the partial differential equation as the initial input phase distribution, and iterates the wavefront matching method until the set number of iterations is met or the convergence condition is reached, thereby obtaining the optical transformation phase plate, phase correction phase plate, and elliptical lens phase plate after inverse optimization and reconstruction.

[0109] S7), the incident perfect vortex beams with different topological charges are phase modulated and propagated in sequence, and the light field profile gradually propagates and evolves into a Gaussian-like mode, and the center of the vortex beam of each core is aligned with the center position of the transformation phase plate; the input vortex beams with different topological charges are correspondingly converted into Gaussian beams at different positions on the output plane to achieve spatial separation of different vortex modes.

[0110] In this embodiment, the vortex pattern of the donut-shaped intensity distribution is modulated by the optical transformation phase plate after reverse reconstruction and propagates, gradually unfolding into a long light spot, and then modulated by the phase correction phase plate and the elliptical lens phase plate after reverse reconstruction and propagating to the output plane. The long light spot gradually propagates and evolves into Gaussian-like light spots at different positions separated in space. Figure 2 (a) and Figure 2 (b) shows a comparison between the OAM mode demultiplexing effect achieved with the original spiral transformation. The optical transformation after reverse design optimization can support high-resolution spatial sorting of more vortex modes (-10 to +10 order OAM modes, a total of 21). Compared with the spiral transformation, the number of supported modes has nearly doubled.

[0111] This embodiment uses the phase distribution based on spiral transformation as the initial input, uses the transformation between the input perfect vortex beam and the output ideal Gaussian vortex mode, and utilizes the inversely designed wavefront matching algorithm to iteratively optimize the conversion between arrays supporting -10 to +10 order perfect vortex beams and spatially separated Gaussian modes, and provides an arrayed 19-core photon orbital angular momentum demultiplexing device prepared as a diffractive optical element. Compared with the spiral transformation, the number of modes supported by the final sorting is nearly doubled, which effectively reduces the crosstalk between adjacent demultiplexed light spots, improves the final sorting effect, and is expected to be compatible with 19-core OAM fiber communications.

[0112] Example 2

[0113] like Figure 3 As shown, this embodiment provides a multi-core OAM mode demultiplexing device based on the spiral transformation inverse design, including a double-sided diffractive optical element 1, a single-sided diffractive optical element 2, and an optical transformation phase plate 3, a phase correction phase plate 4, and an elliptical lens phase plate 5;

[0114] The optical transformation phase plate 3 and the phase correction phase plate 4 are respectively located on the front and back sides of the double-sided diffractive optical element 1 ; the elliptical lens phase plate 5 is integrated on one side of the single-sided diffractive optical element 2 .

[0115] In this embodiment, the optical transformation phase plate 3, the phase correction phase plate 4, and the elliptical lens phase plate 5 are each arranged in a hexagonal array of 19 cores. After the incident 19-core array vortex beam is modulated and propagated and evolved by the arrayed optical transformation phase plate 3, the phase correction phase plate 4, and the elliptical lens phase plate 5 in sequence, it is converted into a spatially separated Gaussian-like beam in the output plane to achieve the sorting of vortex modes.

[0116] In this embodiment, the double-sided diffractive optical element 1 and the single-sided diffractive optical element 2 are quartz plates of different thicknesses, wherein the thickness of the double-sided diffractive optical element 1 is 5 mm; the thickness of the single-sided diffractive optical element 2 is 1 mm. The demultiplexed light spots output by 21 vortex beams with different topological charges after passing through each core of the device are as follows: Figure 4 shown.

[0117] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

Claims

1. A multi-core OAM mode demultiplexing method based on spiral transformation inverse design, characterized in that: The steps include: S1), using the spiral transformation phase plate obtained by analytical solution based on the ray model as the initial input of the wavefront matching method; S2), taking the perfect vortex mode whose central bright ring radius does not change with the change of topological charge as the incident vortex beam; and calculating the mode field distribution of the incident vortex beam and the mode field distribution of the output beam; S3), using the wavefront matching method to calculate the mode field distribution of the perfect vortex beams with different incident topological charges propagating forward to the mth phase plate and the mode field distribution of the output ideal Gaussian mode propagating backward to the position of the mth phase plate; S4), when the phases on both sides of the mth phase plate do not match, calculate the phase error of each spatial coordinate point on the mth phase plate; and use the average value of the phase error of each set of input and output modes as the phase distribution that needs to be updated for the mth phase plate; S5), traversing all phase plates is regarded as one wavefront matching method iteration, and then the overlap integral of each input and output mode is calculated to obtain the average mode conversion efficiency of this generation, and the difference σ0 of the average mode conversion efficiency between two adjacent generations is used as the condition for judging whether the iteration converges; S6), using reverse design optimization to obtain three phase plates; S7), the incident perfect vortex beams with different topological charges are phase modulated and propagated in sequence, and the light field profile gradually propagates and evolves into a Gaussian-like mode, and the center of the vortex beam of each core is aligned with the center position of the transformation phase plate; the input vortex beams with different topological charges are correspondingly converted into Gaussian beams at different positions on the output plane to achieve spatial separation of different vortex modes.

2. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 1, characterized in that: In step S1), the phase plates initially input are respectively an optical transformation phase plate (3), a phase correction phase plate (4), and an elliptical lens phase plate (5).

3. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 2, characterized in that: In step S1), the spiral transformation phase plate obtained by analytical solution based on the ray model specifically includes the following steps: S11), the transformation relationship of the spiral coordinate transformation from the (r,θ) coordinate plane to the (u,v) coordinate plane is: Among them, a, r0, β are all helix parameters, (r, θ) represents the polar coordinates of the vortex beam, and (u, v) is the position coordinates of the phase correction phase plate; S12), the phase distribution of the optical transformation phase plate (3) and the phase correction phase plate (4) corresponding to the spiral transformation is obtained by solving the following partial differential equations based on the ray model: In the formula, P1 and P2 represent the phases of the optical transformation phase plate (3) and the phase correction phase plate (4) respectively, k=2π / λ is the wave number; (x, y) are the position coordinates of the optical transformation phase plate (3); (u, v) are the position coordinates of the phase correction phase plate (4); d represents the distance between the optical transformation phase plate (3) and the phase correction phase plate (4); S13), the elliptical lens phase plate (5) corresponding to the spiral transformation is denoted as P3, and its phase distribution is expressed as: Wherein, f is the focal length of the elliptical lens; (x, y) is the position coordinate of the elliptical lens phase plate (5).

4. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 1, characterized in that: In step S2), the mode field distribution PV(r,θ) of the incident vortex beam is expressed as: Where (r,θ) represents the polar coordinates of the vortex beam; r max represents the maximum radius of the central bright ring; w0 represents the beam ring width; l is the topological charge number; i represents the imaginary unit; The output beam is a Gaussian beam, and the mode field distribution G(r,θ) of the output beam is: Where w is the waist radius of the Gaussian beam; (r,θ) represents the polar coordinates of the vortex beam.

5. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 1, characterized in that: In step S3), the mode field distribution of the incident vortex beam with topological charge number l propagates forward to the mth phase plate It is expressed as: The mode field distribution of the output ideal Gaussian beam corresponding to the input mode and propagating back to the mth phase plate It is expressed as: in, is the Fourier transform, and represents the forward phase modulation of the mth phase plate and the reverse phase modulation of the m+1th phase plate, respectively, and H is the beam transmission function; (x, y, z m ) represents the three-dimensional rectangular coordinate system in physical space; k x ,k y ,z represent the wave number components of the light wave in the transverse x and y directions and the coordinates of the light wave along the propagation direction respectively.

6. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 1, characterized in that: Step S4) specifically includes the following steps: S41), assuming that the input and output beam powers are normalized, the complex amplitude distribution of the input vortex mode forward propagating to the mth phase plane is for: In the formula, A f represents the amplitude distribution of the input light field propagating forward to the phase plane of the mth block; i represents the imaginary unit, φ f represents the phase distribution of the input light field propagating forward to the phase plane of the mth block; S42), output the complex amplitude distribution of the ideal Gaussian mode back-propagating to the phase plane of the mth block for: In the formula, A b represents the amplitude distribution of the output ideal light field propagating back to the phase plane of the mth block; φ b represents the phase distribution of the output ideal light field propagating back to the phase plane of the mth block; S43), the phase distribution that can perfectly compensate the phase mismatch between the two is calculated to be φ = -φ f +φ b ; S44), calculating the average phase error of each group of input and output modes as the phase distribution that needs to be updated for the mth phase plate.

7. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 1, characterized in that: In step S5), the input mode is propagated to the output plane through a series of phase plane modulations, and the corresponding output mode complex amplitude distribution is u1(x, y), and the ideal output mode complex amplitude distribution is u2(x, y). The overlap integral I of the two is: In the formula, represents the conjugated output mode complex amplitude distribution; The overlap integral between each output mode and the ideal output mode is calculated, and the average value is obtained, which is recorded as the average mode conversion efficiency of this generation. When the difference σ0 of the average mode conversion efficiency between two adjacent generations is less than the set threshold, it is determined whether this iterative optimization has converged.

8. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 1, characterized in that: Step S6), three phase plates are obtained by inverse design optimization, as follows: The optical transformation phase plate (3), phase correction phase plate (4), and elliptical lens phase plate (5) obtained by analytically solving the partial differential equation are used as the initial input phase distribution, and the wavefront matching method is iterated until the set number of iterations is met or the convergence condition is reached, so as to obtain the optical transformation phase plate (3), phase correction phase plate (4), and elliptical lens phase plate (5) after inverse optimization and reconstruction.

9. The multi-core OAM mode demultiplexing method based on spiral transformation inverse design according to claim 1, characterized in that: In step S7), the spatial separation of different vortex modes is achieved, which specifically includes the following steps: the vortex mode with donut-shaped intensity distribution is modulated by the optical transformation phase plate after reverse reconstruction and propagated, gradually unfolded into a long light spot, and then modulated by the phase correction phase plate and the elliptical lens phase plate after reverse reconstruction and propagated to the output plane in turn, and the long light spot gradually propagates and evolves into Gaussian-like spots at different positions separated in space.

10. A multi-core OAM mode demultiplexing device based on spiral transformation reverse design, characterized in that the device is used for the method described in any one of claims 1 to 9, and the device comprises a double-sided diffractive optical element (1), a single-sided diffractive optical element (2), and an optical transformation phase plate (3), a phase correction phase plate (4), and an elliptical lens phase plate (5); the optical transformation phase plate (3) and the phase correction phase plate (4) are respectively located on the front and back sides of the double-sided diffractive optical element (1); the elliptical lens phase plate (5) is integrated on one side of the single-sided diffractive optical element (2); and the optical transformation phase plate (3), the phase correction phase plate (4), and the elliptical lens phase plate (5) are each arranged in a hexagonal array of 19 cores, and the incident 19-core array vortex beam is modulated and propagated by the arrayed optical transformation phase plate (3), the phase correction phase plate (4), and the elliptical lens phase plate (5) in turn, and then converted into a spatially separated Gaussian-like beam on the output plane to achieve vortex mode sorting.

Images