CN111211843B - Reverse design method of photon orbital angular momentum mode multiplexer/demultiplexer - Google Patents
Reverse design method of photon orbital angular momentum mode multiplexer/demultiplexer Download PDFInfo
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Abstract
The invention discloses a reverse design method of a photon orbital angular momentum mode multiplexer/demultiplexer, which comprises the following steps: arranging a plurality of phase plates separated by free space, and marking one phase plate as L e And fixing it as an equivalent form of an elliptical lens; computation output Gaussian pattern backpropagation to L e And through L e A tilted plane wave mode formed during phase modulation for the first phase plate to L e Optimizing by using a wave front matching method from an OAM mode to an inclined plane wave mode until convergence; releasing the limitation on the phase plates fixed as the elliptical lenses, and optimizing all the phase plates by using a wave front matching method from an OAM mode to a Gaussian mode until convergence; with the phase shift value phi of each pixel of all phase plates i As a parameter, a weighted average of the adjacent order crosstalk
As an objective function, minimizing the objective function by the steepest descent method
And minimizing, namely iterating the steepest descent method until the maximum crosstalk of the adjacent order is less than or equal to the maximum crosstalk of the non-adjacent order, and stopping.
Description
Technical Field
The invention relates to the technical field of optical communication, in particular to a reverse design method of a photon orbital angular momentum mode multiplexer/demultiplexer.
Background
With the increasing demand for communication capacity in modern society and the approaching of the utilization of traditional multiplexing dimensions such as amplitude, wavelength and polarization to the limit, how to utilize space, which is an underutilized multiplexing dimension, i.e., space division multiplexing technology, has been receiving attention from more and more researchers in recent years. Among them, multiplexing vortex modes carrying photon Orbital Angular Momentum (OAM) is one of important research directions.
The mode multiplexing/demultiplexing device is a core device in a mode division multiplexing communication system. Studies have demonstrated that a series of phase plates separated by free space can achieve arbitrary unitary transformations, so that the phase plates can simply and efficiently implement mode multiplexing/demultiplexing. Either analytical methods or inverse design methods can be used to design the phase plate. The analytic method is to design a phase plate with coordinate transformation function according to logarithm-polar coordinate transformation or spiral transformation theory. The reverse design method optimizes the phase distribution of the phase plate by adopting numerical algorithms such as a wavefront matching method or a steepest descent method.
The reverse design based on the wave front matching method is to correct the input mode f of forward propagation in the plane of each phase plate i And a counter-propagating output mode b i Phase mismatch between them, maximizing the degree of mode overlap. The optimization process is repeated one by one plane until convergence. The modification to each plane can be obtained by the overlap function of each set of input/output patterns, and the overlap function of the ith set of input/output patterns on the kth plane is defined as:
wherein phi k The phase distribution of the k-th plane. The correction term of the phase plate is the argument of the mean overlap function of all modes in the plane, i.e.
Wherein phi i Is an overlap function o ki The average phase of (2).
The wavefront matching method can only match the input and output modes as much as possible, i.e. maximize the overlapping integral of the input and output modes, without the presence of an objective function.
The reverse design based on the steepest descent method is to set the mode overlapping degree of the obtained mode and the target mode as an objective functionThe phase shift distribution of the phase plate is iterated along the gradient direction. The pattern overlap is defined as the overlap integral of the resulting pattern and the target pattern. Let the resulting light field be u z The target light field is u g The pattern overlap y in the discretization case is represented as:
for the discretization case in numerical calculation, the independent variable of the mode overlap is the phase shift value per pixel on each phase plate, i.e.
Wherein N is the number of phase plates, and N is the number of pixels of a single phase plate.
And representing the phase shift value of the q-th pixel point on the p-th plane.
In order to apply the steepest descent method, an analytical expression of the objective function with respect to the argument needs to be found. The propagation of the optical field throughout the device can be decomposed into the effects of several phase plates and free-space propagation. The effect of the phase plate on the optical field is calculated by angular spectrum decomposition method for free space propagation
And propagation of optical fields in free space
Can be respectively represented as
Wherein φ is the phase distribution of the phase plate;
hadamard product (matrix-to-element product) of a matrix; f and F -1 Respectively representing a two-dimensional discrete fourier transform and an inverse transform; h (z) is a matrix discretized by a transfer function, z representing the propagation distance. The propagation of the optical field throughout the device can be expressed as:
as can be seen from the above equation, the overlap integral is a differentiable function of the phase shift value, and reverse design using the steepest descent method is feasible. However, the reverse design process has great freedom degree, and the iteration process is easy to fall into the local optimal solution, so that parameters such as initial conditions, phase plate spacing and the like and the iteration mode need to be carefully selected.
Disclosure of Invention
The invention provides an inverse design method of a photon orbital angular momentum mode multiplexer/demultiplexer, which aims to solve the problem that a general inverse design algorithm is easy to fall into local optimization under the condition of extremely high degree of freedom, effectively overcomes the defect that an iterative process falls into local optimization, and obtains the OAM mode multiplexer/demultiplexer with high performance and large bandwidth.
In order to achieve the purpose of the invention, the technical scheme is as follows: an inverse design method of a photon orbital angular momentum mode multiplexer/demultiplexer comprises the following steps:
s1: arranging a plurality of phase plates separated by free space, and marking one phase plate as L e And fix it as an equivalent form of an elliptical lens, i.e.
Wherein: k is the wave vector of the incident light wave, f x To representMajor axis focal length of elliptical lens, f y Represents the minor axis focal length of the elliptical lens;
s2: compute output Gaussian mode counter-propagating to L e And through L e The inclined plane wave mode formed during phase modulation is denoted L for the first phase plate 1 To L e Optimizing by using a wave front matching method from an OAM mode to an inclined plane wave mode, and adopting the wave front matching method to iterate until the difference of the conversion efficiency of the average mode of two adjacent iterations is less than epsilon 1 Stopping the operation;
s3: releasing the limitation on the phase plates fixed as the elliptical lenses, optimizing all the phase plates by using a wave front matching method from an OAM mode to a Gaussian mode, and adopting the wave front matching method to iterate until the difference of the conversion efficiency of the average mode of two adjacent iterations is less than epsilon 2 Stopping the operation;
s4: with the phase shift value phi of each pixel of all phase plates i As a parameter, a weighted average of the adjacent order crosstalk
As an objective function, minimizing the objective function by the steepest descent method
And minimizing, namely stopping iterating the steepest descent method until the maximum crosstalk of the adjacent order is less than or equal to the maximum crosstalk of the non-adjacent order.
Preferably, the number of the phase plates is 4, and the first phase plate, the second phase plate, the third phase plate and the fourth phase plate are respectively arranged from left to right, wherein the third phase plate is fixed to the equivalent form of the elliptic lens in the step S1.
Further, the beam waist radius of the gaussian mode described in step S3 is 5 μm, and the gaussian mode pitch obtained by demultiplexing different-order OAM modes is 127 μm, so as to match a standard one-dimensional single-mode fiber array.
Still further, the distance between two adjacent phase plates is set to be less than 5 mm.
Still further, the phase plate is composed of a diffractive optical element, or the phase plate is composed of a phase modulation element with a super-structured surface.
Still further, said epsilon 1 Is 0.00001,. epsilon 2 Is 0.00001.
The invention has the following beneficial effects:
the invention optimizes the phase distribution of the phase plate step by step according to the spiral transformation theory, firstly optimizes the transformation from a vortex mode to an inclined plane wave mode, further optimizes the transformation to a Gaussian mode, and further reduces the crosstalk by adopting a steepest descent method. The invention can effectively overcome the defect that the iterative process falls into local optimization, and obtain the OAM mode multiplexer/demultiplexer with high performance and large bandwidth.
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FIG. 1 is a flow chart of the steps of the reverse design method described in example 1.
Fig. 2 is a schematic diagram of the propagation of the beam in the phase plate of example 1.
Fig. 3 shows the structure of a device obtained by the reverse design method for 4 phase plates described in example 1.
Wherein the shade of the pixel in fig. 3 represents the phase shift value.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
Example 1
As shown in fig. 1, an inverse design method of a photonic orbital angular momentum mode multiplexer/demultiplexer includes the following steps:
s1: arranging a plurality of phase plates separated by free space, and marking one of the phase plates as L e And fix it as an equivalent form of an elliptical lens, i.e.
Wherein: k is the wave vector of the incident light wave, f x Denotes the major-axis focal length of the elliptical lens, f y Represents the minor axis focal length of the elliptical lens; initializing the phase distribution of the phase plate to
In the form of a uniform distribution.
S2: compute output Gaussian mode counter-propagating to L e And through L e The inclined plane wave mode formed during phase modulation is denoted L for the first phase plate 1 To L e Optimization using wavefront matching from OAM mode to inclined plane wave mode, i.e. L 1 To L e And iterating one phase plate by one phase plate, and matching the phases of the forward OAM mode and the backward inclined plane wave mode on each phase plate. Adopting wave front matching method to iterate to the difference of the average mode conversion efficiency of two adjacent iterations is less than epsilon 1 Stop when equal to 0.00001;
one phase plate is fixed into an equivalent form of an elliptic lens, and the phase distribution of the other phase plates is optimized by adopting a wave front matching method until convergence.
S3: releasing the limitation on the phase plates fixed as the elliptical lenses, optimizing all the phase plates by using a wave front matching method from an OAM mode to a Gaussian mode, namely iterating the phase plates one by one to match the phases of the OAM mode propagating in the forward direction and the Gaussian mode propagating in the reverse direction on each phase plate, and iterating to an average mode conversion efficiency difference of two adjacent iterations by adopting the wave front matching method to be smaller than epsilon 2 Stop when equal to 0.00001;
and on the basis of the phase distributions obtained in the steps S1 and S2, optimizing the phase distributions of all the phase plates by adopting a wavefront matching method until convergence.
S4: with the phase shift value phi of each pixel of all phase plates i As a parameter, a weighted average of the adjacent order crosstalk
As an objective function, minimizing the objective function by the steepest descent method
Minimizing, and iterating the steepest descent method until the maximum crosstalk of adjacent orders is less than or equal to non-adjacentAnd stops when the order is maximum crosstalk.
In a specific embodiment, the number of the phase plates is 4, and the first phase plate, the second phase plate, the third phase plate and the fourth phase plate are respectively arranged from left to right, wherein the third phase plate is fixed as an equivalent form of an elliptic lens in the step S1.
In a specific embodiment, the beam waist radius of the gaussian mode described in step S3 is 5 μm, and the gaussian mode pitch obtained by demultiplexing different-order OAM modes is 127 μm, so as to match a standard one-dimensional single-mode fiber array.
In a specific embodiment, the distance between two adjacent phase plates is set to be less than 5mm so as to adapt to a double-sided micro-machining process.
In a specific embodiment, said phase plate is constituted by a diffractive optical element or said phase plate is constituted by a phase modulating element of a super structured surface.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention and are not intended to limit the embodiments of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (6)
1. A reverse design method of a photon orbital angular momentum mode multiplexer/demultiplexer is characterized in that: the reverse design method comprises the following steps:
s1: arranging a plurality of phase plates separated by free space, and marking one of the phase plates as L e And fix it as an equivalent form of an elliptical lens, i.e.
Wherein: k is the wave vector of the incident light wave, f x Denotes the major-axis focal length of the elliptical lens, f y Represents the minor axis focal length of the elliptical lens;
S2：compute output Gaussian mode counter-propagating to L e And through L e The inclined plane wave mode formed during phase modulation is denoted L for the first phase plate 1 To L e Optimizing by using a wave front matching method from an OAM mode to an inclined plane wave mode, and adopting the wave front matching method to iterate until the difference of the conversion efficiency of the average mode of two adjacent iterations is less than epsilon 1 Stopping the operation;
s3: releasing the limitation on the phase plates fixed as the elliptical lenses, optimizing all the phase plates by using a wave front matching method from an OAM mode to a Gaussian mode, and adopting the wave front matching method to iterate until the difference of the conversion efficiency of the average mode of two adjacent iterations is less than epsilon 2 Stopping the operation;
s4: with the phase shift value phi of each pixel of all phase plates i Weighted average of adjacent order crosstalk as a parameter
As an objective function, minimizing the objective function by the steepest descent method
And minimizing, namely stopping iterating the steepest descent method until the maximum crosstalk of the adjacent order is less than or equal to the maximum crosstalk of the non-adjacent order.
2. The inverse design method of a photonic orbital angular momentum mode multiplexer/demultiplexer of claim 1, wherein: the number of the phase plates is 4, and the first phase plate, the second phase plate, the third phase plate and the fourth phase plate are respectively arranged from left to right, wherein the third phase plate is fixed to be an equivalent form of an elliptic lens in the step S1.
3. The inverse design method of the photonic orbital angular momentum mode multiplexer/demultiplexer according to claim 2, wherein: the beam waist radius of the gaussian mode in step S3 is 5 μm, and the gaussian mode pitch obtained by demultiplexing different-order OAM modes is 127 μm, so as to match a standard one-dimensional single-mode fiber array.
4. The inverse design method of a photonic orbital angular momentum mode multiplexer/demultiplexer of claim 2, wherein: and setting the distance between two adjacent phase plates to be less than 5 mm.
5. The inverse design method of the photonic orbital angular momentum mode multiplexer/demultiplexer according to claim 4, wherein: the phase plate is composed of a diffractive optical element or a phase modulation element with a super-structured surface.
6. The inverse design method of the photonic orbital angular momentum mode multiplexer/demultiplexer of any one of claims 2 to 5, wherein: e is of 1 0.00001,. epsilon 2 Is 0.00001.
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| CN108923880A (en) * | 2018-04-23 | 2018-11-30 | 中山大学 | A kind of photon trajectory angular momentum mode measurement method and system based on Screw transformation |
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