Optical Information Encoding Method for a Three-Ring Composite Vortex Beam with Intermittent Orbital Angular Momentum

Abstract

The optical information encoding method of a three-ring composite vortex beam with interval orbital angular momentum disclosed by the present invention specifically includes the following steps: Step 1: Derive the complex amplitude expression of the optical field when each order of LG beam propagates along the Z-axis; Step 2: Write the light intensity distribution formula of the superimposed composite vortex beam according to Step 1; Step 3: Determine the mode values of the LG beams that are convenient for decoding and recognition; Step 4: Simulate the light intensity distribution diagram of the composite vortex beam after superimposing the selected mode values and normalize the light intensity distribution diagram; Step 5: Encode the light intensity diagram simulated for the three-ring vortex beam. This method solves the problems of small channel capacity, low transmission efficiency, high bit error rate, etc. in existing communications.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical communication coding, and particularly relates to an optical information coding method for a three-ring composite vortex beam with spaced orbital angular momentum. Background Technique

[0002] In 1992, Allen et al. found that vortex beams have a new type of phase space distribution, that is, a spiral wavefront structure. Due to its unique optical field structure, the orthogonality between different OAM modes, and the diversity of OAM state values, vortex beams have been widely used in the fields of quantum information processing, biomedicine, optical micro-manipulation, quantum coding, etc., and have particularly potential application value in the field of space optical communication.

[0003] Encoding digital signals using the dimension of light is an important basis for optical communication. Traditional encoding relies on dimensions such as the amplitude, frequency, and phase of light to achieve high-capacity communication. This method has disadvantages such as low information transmission rate and wide occupied frequency band. As the amount of information transmitted continues to increase, traditional encoding methods can no longer meet people's needs for communication systems with larger channel capacities. Therefore, it is necessary to find new optical coding dimensions to achieve larger-capacity information transmission. As a new optical dimension, the OAM of vortex beams has the advantages of large channel capacity and high transmission rate, and can solve the problem of transmission capacity contraction in optical coding. As a special type of vortex beam, Laguerre-Gaussian (LG) vortex beams have attracted extensive attention from scholars at home and abroad. The beam carrying OAM has been relatively maturely applied in multiplexing communication systems, which has laid a foundation for OAM coding communication systems. Currently, the research on the coding of double-ring composite vortex beams formed by the coaxial superposition of two LG beams is relatively mature, and the coding of three-ring composite vortex beams formed by the coaxial superposition of three LG beams has not been studied. Moreover, in the previous coding methods, adjacent two composite vortex beams are prone to confusion during decoding at the receiving end, resulting in an increase in the bit error rate. In order to reduce the bit error rate and improve the reliability of transmission, a method for encoding optical information of a three-ring composite vortex beam with spaced OAM is proposed, in which the OAM of three LG beams is sampled at intervals and then superposed and encoded. The three-ring composite vortex beam coding improves the coding ability of stronger coding information, which is particularly important for space optical communication. Summary of the Invention

[0004] The purpose of the present invention is to provide an optical information coding method for a three-ring composite vortex beam with spaced orbital angular momentum, which solves the problems of small channel capacity, low transmission efficiency, and high bit error rate in existing communications.

[0005] The technical solution adopted by the present invention is an optical information coding method for a three-ring composite vortex beam with spaced orbital angular momentum, which specifically includes the following steps:

[0006] Step 1: Derive the expression of the complex amplitude of the optical field when Laguerre-Gaussian (LG) beams of all orders propagate along the Z-axis;

[0007] Step 2: According to Step 1, write out the formula for the intensity distribution of the superposed composite vortex beam;

[0008] Step 3: Determine the combination of mode values of LG beams that is convenient for decoding and recognition;

[0009] Step 4: Simulate the intensity distribution diagram of the composite vortex beam after superposition of the selected mode values, and normalize the intensity distribution diagram;

[0010] Step 5: Encode the intensity diagram simulated for the three-ring vortex beam.

[0011] The features of the present invention also lie in that,

[0012] Step 1 is specifically implemented according to the following steps:

[0013] The mathematical function describing the Laguerre-Gaussian beam is a paraxial approximate solution of the Helmholtz equation. Under the paraxial approximation, the Helmholtz equation is expressed as:

[0014]

[0015] According to the existing expression of the optical field of the Laguerre-Gaussian beam propagating along the Z-axis direction, the expression is as follows:

[0016]

[0017] where z is the propagation distance, is the spot size, where ω0 is the beam waist radius at z = 0, is the associated Laguerre polynomial, κ = 2π / λ is the wave vector, and λ is the wavelength, is the Rayleigh length, (2p + |l| + 1)tan -1 (Z / Z R ) is the Gouy phase;

[0018] Derive the optical field expressions for radial exponent p = 0 and p ≠ 0. When p = 0, At this time, the expression of the complex amplitude of the optical field of the LG beam at Z is:

[0019]

[0020] When p ≠ 0, from Equation (2), the expression of the complex amplitude of the optical field of the LG beam at Z can be obtained as:

[0021]

[0022] Step 2 is specifically implemented according to the following steps:

[0023] Superpose two LG beams and to obtain the expression of the complex amplitude after superposition as follows:

[0024]

[0025] Then the expression of the light intensity distribution of the composite vortex beam is:

[0026]

[0027] Based on the superposition principle of two LG beams, the expression of the complex amplitude after superposing three LG beams and is derived as follows:

[0028]

[0029] Similarly, the expression of the light intensity distribution of the composite vortex beam is:

[0030]

[0031] Step 3 is specifically implemented according to the following steps:

[0032] All three LG beams use the method of the same interval OAM, that is, adopt and Coaxially superpose to obtain 32 groups of three-ring composite vortex beams.

[0033] Step 4 is specifically implemented according to the following steps:

[0034] All three LG beams use a He-Ne laser to generate LG beams with a wavelength of λ = 632.8 nm. According to formulas (3) to (8), for the mode combinations selected in step 3 and Perform MATLAB coaxial superposition simulation to obtain the light intensity diagrams of 32 groups of three-ring composite vortex beams and normalize them.

[0035] Step 5 is specifically implemented according to the following steps:

[0036] Perform 5-bit binary coding on the light intensity distribution of each three-ring composite vortex beam, and correspondingly obtain 32 groups of 5-bit binary sequences, that is, 00000 to 11111.

[0037] The beneficial effects of the present invention are as follows: In optical communication, spatial mode coding technology can utilize different orthogonal electromagnetic modes in parallel to increase the channel capacity. The OAM mode is one of the modes in spatial mode coding. According to the orthogonality of different OAM modes, the channel capacity can be increased. For the three-ring composite vortex beam of the method of the present invention, when taking the mode values, the OAM all adopts interval sampling. One is to reduce the number of encoded information bits and improve the information transmission rate. The other is to solve the problem that when decoding the three-ring composite vortex beam with continuous OAM at the receiving end, the light intensity patterns of adjacent beams are prone to confusion. Therefore, the OAM interval sampling also reduces the bit error rate during decoding. Brief Description of the Drawings

[0038] Figure 1 is the light intensity distribution diagram of a double-ring composite vortex beam after the superposition of two LG beams with the same radial exponent and different topological charge numbers;

[0039] Figure 2 is the light intensity distribution diagram of a double-ring composite vortex beam after the superposition of two LG beams with the same topological charge number and different radial exponents;

[0040] Figure 3 is the light intensity distribution diagram of 32 groups of double-ring composite vortex beams after the superposition of two LG beams;

[0041] Figure 4 is the light intensity distribution diagram of 32 groups of three-ring composite vortex beams after the superposition of three LG beams. Detailed Embodiment

[0042] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0043] The present invention provides a light information coding method for a three-ring composite vortex beam with interval orbital angular momentum. A He-Ne laser is selected to generate a laser beam with a wavelength of λ = 632.8 nm, and three LG beams with different OAMs are generated and superimposed, and the three-ring composite vortex beam after the superposition of the three LG beams is encoded. The specific steps are as follows:

[0044] Step 1: Derive the complex amplitude expression of the light field when each order of LG beam propagates along the Z axis;

[0045] Step 1 is specifically implemented according to the following steps:

[0046] The mathematical function describing the Laguerre-Gaussian beam is a paraxial approximation solution of the Helmholtz equation. Under the paraxial approximation, the Helmholtz equation is expressed as:

[0047]

[0048] According to the existing light field expression of the Laguerre-Gaussian beam propagating along the Z axis, the expression is as follows:

[0049]

[0050] where \(z\) is the transmission distance, is the spot size, where \(\omega_0\) is the beam waist radius at \(z = 0\), is the associated Laguerre polynomial, \(\kappa=2\pi / \lambda\) is the wave vector, and \(\lambda\) is the wavelength, is the Rayleigh length, \((2p + |l|+1)\tan -1 (Z / Z R ) is the Gouy phase;

[0051] The optical field expressions for radial index \(p = 0\) and \(p\neq0\) are derived. When \(p = 0\), At this time, the complex amplitude expression of the optical field of the LG beam at \(Z\) is:

[0052]

[0053] When \(p\neq0\), from Equation (2), the complex amplitude expression of the optical field of the LG beam at \(Z\) is:

[0054]

[0055] Step 2: According to Step 1, write the light intensity distribution formula of the superimposed composite vortex beam;

[0056] Step 2 is specifically implemented according to the following steps:

[0057] Superimpose two LG beams and to obtain the superimposed complex amplitude expression as:

[0058]

[0059] Then the light intensity distribution expression of the composite vortex beam is:

[0060]

[0061] Based on Equations (2)-(6), for two LG beams with the same radial index and different topological charges and coaxially superimposed, the light intensity distribution diagram of the double-ring composite vortex beam as shown in Figure 1 is simulated; It can be seen from Figure 1 that the light intensity distribution presents bright annular spots, the number of rings is \(p + 1\), and the number of spots in each layer is \(|l_2 - l_1|\).

[0062] Based on Equations (2)-(6), for two LG beams with the same topological charge and different radial indices and Coaxial superposition is carried out, and the intensity distribution diagram of the double-ring composite vortex beam as shown in Figure 2 is obtained through simulation; it can be seen from Figure 2 that the intensity distribution presents bright multi-rings. For each row, as the topological charge number l = |l1| = |l2| increases, the radius of each ring gradually increases; for each column, as the radial index increases, the number of rings also gradually increases, and the number of rings is p = max(p1, p2) + 1.

[0063] Based on formulas (2) to (6), the intensity distribution diagrams of the double-ring composite vortex beam after the superposition of 32 groups of two LG beams are simulated; respectively take and for coaxial superposition. It can be seen from Figure 3 that the intensity distribution after superposition presents bright annular light spots, the number of light spots is |l2 - l1|, and the number of rings p = max(p1, p2) + 1. The composite vortex beam can be described as 1-ring 6-light spots, 2-ring 12-light spots, 4-ring 8-light spots.

[0064] Based on the superposition principle of two LG beams, the complex amplitude expression after the superposition of three LG beams and is deduced as:

[0065]

[0066] Similarly, the intensity distribution expression of the composite vortex beam is:

[0067]

[0068] Step 3: Determine the mode value combinations (topological charge number and radial index values) of the LG beam that are convenient for decoding and recognition;

[0069] Step 3 is specifically implemented according to the following steps:

[0070] In order to ensure the effectiveness and reliability of encoding at the same time, the three LG beams all use the OAM with the same interval method, that is, adopt and for coaxial superposition to obtain a three-ring composite vortex beam.

[0071] Step 4: Simulate the intensity distribution diagram of the composite vortex beam after the superposition of the selected mode values, and normalize the intensity distribution diagram;

[0072] Step 4 is specifically implemented according to the following steps:

[0073] All three LG beams use a He-Ne laser to generate LG beams with a wavelength of λ = 632.8 nm. According to formulas (2)-(4) and formulas (7)-(8), for the mode combinations selected in step 3 and {24, 28, 32} are simulated for coaxial superposition in MATLAB, and 32 groups of intensity diagrams of the three-ring composite vortex beams can be obtained, and they are normalized. The results are as Figure 4 shown. It can be seen from Figure 4 that the intensity distribution after superposition presents bright annular light spots. The number of rings p = max(p1, p2, p3)+1. From the inside to the outside, the number of light spots in each layer is |l2 - l1| and |l3 – l2| in turn, and the rest are envelope rings. The three-ring composite vortex beam can be described as having 2 rings, 5 light spots in the inner layer, and 6 light spots in the outer layer; it is described as having 3 rings, 11 light spots in the inner layer, 12 light spots in the middle layer, and the outer layer is an envelope ring.

[0074] Step 5: Encode the intensity diagrams of the three-ring vortex beams simulated.

[0075] Step 5 is specifically implemented according to the following steps:

[0076] As can be seen from step 4, 32 groups of different intensity diagrams of the three-ring composite vortex beams will be obtained. The intensity distribution of each three-ring composite vortex beam is encoded in 5-bit binary, and 32 groups of 5-bit binary sequences can be correspondingly obtained, that is, 00000 - 11111, as shown in Table 1. For example: The corresponding code is "00010", The corresponding code is "10101".

[0077] Table 1 Codes corresponding to 32 groups of three-ring composite vortex beams

[0078]

Claims

1. A method for optical information encoding of a three-ring composite vortex beam with orbital angular momentum intervals, characterized in that Specifically, it includes the following steps: Step 1: Deduce the expression of the complex amplitude of the optical field when LG beams of each order propagate along the Z-axis; Step 1 is specifically implemented according to the following steps: The mathematical function describing the Laguerre-Gaussian beam is a paraxial approximate solution of the Helmholtz equation. Under the paraxial approximation, the Helmholtz equation is expressed as: According to the existing expression of the optical field of the Laguerre-Gaussian beam propagating along the Z-axis, the expression is as follows: where z is the transmission distance, is the spot size, where ω0 is the beam waist radius at z = 0, is the associated Laguerre polynomial, κ = 2π / λ is the wave vector, and λ is the wavelength, is the Rayleigh length, (2p + |l| + 1)tan -1 (Z / Z R ) is the Gouy phase; Derive the optical field expressions for radial indices p = 0 and p ≠ 0. When p = 0, At this time, the complex amplitude expression of the optical field of the LG beam at Z is: When p≠0, from Equation (2), the expression of the complex amplitude of the optical field of the LG beam at Z is: Step 2: Based on Step 1, write the formula for the intensity distribution of the superimposed composite vortex beam; Step 2 is specifically implemented according to the following steps: Superpose two LG beams and to obtain the expression of the complex amplitude after superposition as follows: Then the expression for the intensity distribution of the composite vortex beam is: Based on the superposition principle of two LG beams, the complex amplitude expression after the superposition of three LG beams and is derived as follows: Similarly, the expression for the intensity distribution of the composite vortex beam is: Step 3: Determine the combination of mode values of the LG beam that is convenient for decoding and recognition; Step 3 is specifically implemented according to the following steps: All three LG beams use the same-spacing OAM method, that is, adopt and 32 groups of three-ring composite vortex beams are obtained by coaxial superposition; Step 4: Simulate the intensity distribution diagram of the composite vortex beam after superimposing the selected mode values, and normalize the intensity distribution diagram; Step 4 is specifically implemented according to the following steps: All three LG beams use a He-Ne laser to generate LG beams with a wavelength of λ = 632.8 nm. According to formulas (3) to (8), for the mode combinations selected in step 3 and perform MATLAB coaxial superposition simulation to obtain 32 groups of intensity diagrams of triple-ring composite vortex beams and normalize them; Step 5: Encode the intensity diagram simulated for the three-ring vortex beam; Step 5 is specifically implemented according to the following steps: Perform 5-bit binary encoding on the intensity distribution of each three-ring composite vortex beam, and correspondingly, 32 groups of 5-bit binary sequences can be obtained, namely 00000~11111.

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