Method for determining transmission characteristics of double-vortex light beam in ocean turbulence

Abstract

The invention belongs to the technical field of optical communication, and particularly relates to a method for determining transmission characteristics of a double-vortex light beam in ocean turbulence, and the method comprises the steps: constructing a double-vortex light beam source field through coaxially superposing two Laguerre Gaussian light beams; simulating the influence of ocean turbulence based on a random phase screen theory and a power spectrum inversion method, and calculating the light intensity and phase distribution of a receiving end in combination with an angular spectrum transmission theory; finally, orbital angular momentum mode distribution is analyzed through spiral harmonic expansion, and a relation model of light beam broadening and transmission distance is established. The characteristic that the orbital angular momentum energy retention rate of a double-vortex light beam in ocean turbulence is higher than that of a single-vortex light beam is revealed for the first time, it is found that when the topological charge difference v is smaller than or equal to 3, the transmission stability is optimal, and meanwhile the influence rule of parameters such as the turbulent flow energy dissipation rate and the temperature variance dissipation rate on light beam broadening is quantified; and the optical communication quality and the target detection precision in the marine environment can be obviously improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical communication, and particularly relates to a method for determining the transmission characteristics of a double-vortex beam in ocean turbulence. Background Art

[0002] Underwater optical communication, as a high-speed and high-bandwidth communication technology, has received extensive attention and applications in the fields of marine science, information transmission, and communication in recent years. In the marine environment, the transmission characteristics of a light beam are affected by various factors such as seawater absorption, scattering, and ocean turbulence. At present, significant progress has been made in the research on the transmission characteristics of a light beam in ocean turbulence, mainly focusing on the transmission characteristics of a single-vortex beam or a common beam. Due to its unique helical phase structure, the vortex beam shows great potential in the fields of optical communication, remote sensing, and super-resolution imaging. In particular, the vortex beam carrying orbital angular momentum (OAM) can achieve high-density encoding and transmission of information due to the orthogonality of its spatial modes.

[0003] Although there have been many studies on the transmission characteristics of a single-vortex beam in ocean turbulence, the research on double-vortex beams is relatively scarce. As a special form of the vortex beam, the double-vortex beam is formed by superimposing two vortex beams with different topological charge numbers, and has a more complex phase and intensity distribution. However, there are few reports in the prior art on the method for determining the transmission characteristics of a double-vortex beam in ocean turbulence. This limits our understanding of the transmission behavior of a double-vortex beam in the marine environment. In particular, under the conditions of ocean turbulence, the research on its light intensity scintillation, beam drift, phase fluctuation, and OAM mode distribution is still insufficient. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for determining the transmission characteristics of a double-vortex beam in ocean turbulence, aiming to accurately quantify the transmission characteristics of a double-vortex beam in ocean turbulence, so as to overcome the problems of insufficient anti-turbulence performance and poor transmission stability of the traditional single-vortex beam.

[0005] The present invention achieves the above purpose through the following technical solutions:

[0006] The present invention proposes a method for determining the transmission characteristics of a double-vortex beam in ocean turbulence, and the method includes the following steps:

[0007] S1. Obtain two Laguerre-Gaussian beams at the source field L = 0 and perform coaxial superposition to synthesize a double-vortex beam at the source field;

[0008] S2. Based on the random phase screen theory and the power spectrum inversion method, construct a transmission calculation model of the double-vortex beam under ocean turbulence and perform numerical simulation;

[0009] S3. Determine the propagation characteristics of the double-vortex beam in ocean turbulence according to the numerical simulation results, including the phase distribution, intensity distribution, corresponding orbital angular momentum mode distribution at the receiving end, and the relationship between the beam broadening and propagation distance under different topological charge differences and different ocean turbulence parameters.

[0010] Preferably, step S1 includes:

[0011] S101. Determine the expression of the Laguerre-Gaussian beam at the source field where L = 0 as:

[0012]

[0013] where A is a constant, w0 is the beam waist radius of the beam source plane, is the azimuth angle of the beam, m is the topological charge number as the arcwise mode index, and r represents the radial distance;

[0014] S102. Coaxially superimpose two different Laguerre-Gaussian beams to synthesize the double-vortex beam at the source field, and the source field expression is:

[0015]

[0016] where δ is the phase difference of one of the vortex beams, δ = Nπ / 2, N takes any integer, m1 and m2 are the topological charge numbers of the two superimposed vortex beams, and v = |m1 - m2| represents the topological charge difference between the two beams.

[0017] Preferably, in step S2, the calculation model for the propagation of the double-vortex beam under ocean turbulence is constructed based on the random phase screen theory and the power spectrum inversion method, including:

[0018] S201. Generate the random phase screen of ocean turbulence using the power spectrum inversion method based on the random phase screen theory The calculation formula is:

[0019]

[0020] where h(k x , k y ) is the complex Gaussian random matrix, which is the standard normal distribution function in the frequency domain, where k x and k y are the dimensions of the complex Gaussian random matrix, represents the inverse Fourier transform;

[0021] S202. Combine the angular spectrum propagation theory to obtain the optical field after passing through an ocean turbulence phase screen The calculation formula is:

[0022]

[0023] wherein is the initial beam field of the double-vortex beam, and U prop (k x , k y ) is the transmission function when the beam propagates in free space, expressed as:

[0024] U prop (k x , k y ) = exp(ikl).exp[iπλl(k x 2 +k y 2 )]

[0025] The optical field expression of the double-vortex beam after passing through the nth oceanic turbulence phase screen is:

[0026]

[0027] where L is the propagation distance of the beam in seawater.

[0028] Preferably, in step S3, according to the numerical simulation results, determining the phase distribution and intensity distribution at the receiving end of the double-vortex beam in oceanic turbulence includes:

[0029] S301. Based on the source field expression and transmission calculation model of the double-vortex beam, set the initial beam parameters and oceanic turbulence phase screen parameters;

[0030] S302. Numerically simulate and calculate the complex amplitude distribution of the double-vortex beam after propagating in oceanic turbulence, and extract the intensity distribution and phase distribution of the receiving plane.

[0031] Preferably, in step S3, the steps of determining the distribution of the orbital angular momentum modes corresponding to the double-vortex beam according to the numerical simulation results are specifically:

[0032] Perform OAM mode helical harmonic expansion on the optical field of the double-vortex beam at the receiving end to obtain the helical phase spectrum vector of the beam, and the expression is:

[0033]

[0034] Determine the weights and energy distributions of the OAM modes corresponding to the double-vortex beam according to the helical phase spectrum vector.

[0035] Preferably, in step S3, the steps of determining the relationship between the beam broadening and the propagation distance under different topological charge differences and different oceanic turbulence parameters according to the numerical simulation results are specifically:

[0036] Set different topological charge differences v, turbulent kinetic energy dissipation rate ε, temperature variance dissipation rate χ T , temperature-salinity fluctuation equilibrium parameter ω, and transmission distance L;

[0037] Based on the transmission calculation model, perform numerical simulations to calculate the relationship distribution curve between beam broadening and transmission distance under different parameter combinations;

[0038] Beam broadening W e Is described by the following formula:

[0039]

[0040] Where I represents the light intensity after passing through the turbulence; it can be expressed by the formula:

[0041]

[0042] The beneficial effects of the present invention are as follows:

[0043] 1. Through the innovative coaxial superposition design of double beams, this method effectively improves the transmission stability of vortex beams in ocean turbulence. By using the random phase screen theory and the power spectrum inversion method, it can accurately simulate the influence of ocean turbulence on beam transmission, and combine the angular spectrum transmission theory to completely characterize the light intensity and phase distribution characteristics at the receiving end. Through the spiral harmonic expansion technology, the quantitative analysis of the orbital angular momentum mode distribution of double vortex beams is realized for the first time, providing a new technical means for evaluating the anti-interference performance of beams.

[0044] 2. This method establishes a complete beam broadening calculation model. By introducing key parameters such as topological charge difference and turbulent kinetic energy dissipation rate, it realizes the multi-dimensional evaluation of transmission characteristics. Compared with the traditional single-beam analysis method, this scheme can more comprehensively reflect the transmission performance of beams under ocean turbulence conditions, providing a reliable theoretical support for the design and optimization of underwater optical communication systems. This method has high calculation efficiency and strong applicability, and can be widely applied to fields such as ocean environmental monitoring and underwater wireless communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Is the execution flow chart of the determination method steps in the present invention;

[0046] Figure 2 Is the schematic diagram of the optical field transmission calculation model of the beam passing through the ocean turbulence phase screen based on the random phase screen theory in the present invention;

[0047] Figure 3 Is the simulation of free space in the present invention, with the turbulent kinetic energy dissipation rate ε being 1×10 -2 m 2 s -3 、1×10 -7 m 2s -3 and 1×10 -9 m 2 s -3 Distribution diagrams of the light intensity and phase of the double-vortex beam at the receiving end under four modes;

[0048] Figure 4 is the simulation of the free space and temperature variance dissipation rate χ of the present invention T is 1×10 -8 K 2 s -1 、1×10 -6 K 2 s -1 and 1×10 -5 K 2 s -1 Distribution diagrams of the light intensity and phase of the double-vortex beam at the receiving end under four modes;

[0049] Figure 5 is the simulation of the free space and the balance parameter ω of temperature and salinity fluctuations of the present invention being -5, -3, and -1, and the distribution diagrams of the light intensity and phase of the double-vortex beam at the receiving end under four modes;

[0050] Figure 6 is the distribution diagram of the angular momentum of the double-vortex beam after passing through ocean turbulence on the receiving surface under four modes of the topological charge difference v = 0, v = 1, v = 3, and v = 5 of the present invention;

[0051] Figure 7 is the simulation of the free space and the turbulent kinetic energy dissipation rate ε of the present invention being 1×10 -2 m 2 s -3 、1×10 -5 m 2 s -3 and 1×10 -7 m 2 s -3 Distribution diagrams of the angular momentum of the double-vortex beam after passing through ocean turbulence on the receiving surface under four modes;

[0052] Figure 8 is the simulation of the free space and temperature variance dissipation rate χ of the present invention T is 1×10 -8 K 2 s -1 、1×10 -7 K 2 s -1 and 1×10 -6 K 2 s -1 Distribution diagrams of the angular momentum of the double-vortex beam after passing through ocean turbulence on the receiving surface under four modes;

[0053] Figure 9 It is the angular momentum distribution diagram of the double vortex light beam on the receiving surface after passing through the ocean turbulence in four modes of simulating free space and temperature-salinity fluctuation balance parameters ω of -5, -3 and -1 according to the present invention;

[0054] Figure 10 It is a curve diagram showing the relationship between beam broadening and transmission distance under four modes of simulated topological charge difference v=0, v=1, v=3, and v=5 according to the present invention;

[0055] Figure 11 It is a beam broadening distribution curve diagram when the topological charge difference v is different in the simulation of the present invention;

[0056] Figure 12 The present invention simulates free space, and the turbulent kinetic energy dissipation rate ε is 1×10- S m 2 s -3 , 1×10 -7 m 2 s -3 and 1×10 -9 m 2 s -3 The relationship between beam broadening and transmission distance in four modes;

[0057] Figure 13 is the simulated free space, temperature variance dissipation rate χ T 1×10 -8 K 2 s -1 , 1×10 -6 K 2 s -1 and 1×10 -5 K 2 s -1 The relationship between beam broadening and transmission distance in four modes;

[0058] Figure 14 The present invention simulates the relationship between beam broadening and transmission distance in four modes of free space, temperature and salinity fluctuation balance parameter ω being -5, -3 and -1;

[0059] Figure 15 It is an overall flow chart for the implementation of the determination method in the present invention. DETAILED DESCRIPTION

[0060] The following description provides specific application scenarios and requirements of this specification, aiming to enable those skilled in the art to manufacture and use the content in this specification. For those skilled in the art, various local modifications to the disclosed embodiments are obvious, and the general principles defined here can be applied to other embodiments and applications without departing from the spirit and scope of this specification. Therefore, this specification is not limited to the shown embodiments, but rather the broadest scope consistent with the claims.

[0061] The terms used herein are for the purpose of describing particular example embodiments only and are not restrictive. For example, unless the context clearly dictates otherwise, as used herein, the singular forms "a", "an" and "the" may also include the plural forms. When used in this specification, the terms "comprises", "comprising" and / or "having" mean that the associated integers, steps, operations, elements and / or components exist, but do not preclude the existence or addition of one or more other features, integers, steps, operations, elements, components and / or groups.

[0062] In view of the following description, these features of this specification and other features, as well as the operations and functions of the related elements of the structure, and the economy of the combination and manufacture of the components can be significantly improved. Referring to the accompanying drawings, all of which form a part of this specification. However, it should be clearly understood that the drawings are for illustrative and descriptive purposes only and are not intended to limit the scope of this specification. It should also be understood that the drawings are not drawn to scale.

[0063] The flowcharts used in this specification illustrate the operations implemented by the system according to some embodiments in this specification. It should be clearly understood that the operations of the flowchart may not be implemented in sequence. On the contrary, the operations may be implemented in reverse order or simultaneously. In addition, one or more other operations may be added to the flowchart. One or more operations may be removed from the flowchart.

[0064] Please refer to Figure 1 and Figure 15 , this embodiment proposes a method for determining the transmission characteristics of a double-vortex beam in ocean turbulence, and the method includes the following steps:

[0065] S1. Obtain two Laguerre-Gaussian beams at the source field L = 0 and perform coaxial superposition to synthesize the double-vortex beam at the source field; wherein, the Laguerre-Gaussian beam is a vortex beam with a radial mode n of 0 and a topological charge number m, and the value of which is constantly 1.

[0066] S2. Based on the random phase screen theory and the power spectrum inversion method, construct a calculation model for the transmission of the double-vortex beam under ocean turbulence and perform numerical simulation;

[0067] S3. Determine the propagation characteristics of the double-vortex beam in oceanic turbulence according to the numerical simulation results, including the phase distribution, intensity distribution, corresponding orbital angular momentum mode distribution at the receiving end, and the relationship between the beam broadening and propagation distance under different topological charge differences and different oceanic turbulence parameters.

[0068] Optionally, the present application uses a classical propagation calculation model for numerical simulation, and combines the angular spectrum propagation theory to establish a propagation calculation model of the double-vortex Laguerre-Gaussian beam in oceanic turbulence. The Nikishov spectral model (a classical theoretical model describing the refractive index fluctuations in oceanic turbulence, proposed by the Russian scholar Nikishov) is used to describe the refractive index fluctuations in oceanic turbulence.

[0069] In a specific embodiment, for the refractive index fluctuation characteristics of oceanic turbulence, based on the random phase screen theory, the power spectrum inversion method is used to generate the oceanic turbulence random phase screen. The calculation formula is:

[0070]

[0071] where h(k x , k y ) is to generate a complex Gaussian random matrix, which is a standard normal distribution function in the frequency domain, where k x and k y are the dimensions of the complex Gaussian random matrix, represents the inverse Fourier transform.

[0072] Combined with the angular spectrum propagation theory, the optical field after passing through an oceanic turbulence phase screen is obtained. The calculation formula is:

[0073]

[0074] where is the initial beam field of the double-vortex beam (DLGVB), and U prop (k x , k y ) is the propagation function when the beam propagates in free space, which is expressed as:

[0075] U prop (k x , k y ) = exp(ikl).exp[iπλl(k x 2 + k y 2 )]

[0076] Similarly, the optical field of the DLGVB beam after passing through the nth oceanic turbulence phase screen can be expressed as:

[0077]

[0078] When the DLGVB beam propagates in ocean turbulence, in addition to the influence of ocean turbulence on the beam, the scattering and absorption of the beam in pure seawater also need to be further considered. Further modification is required. The relationship between the extinction coefficient of pure seawater and the beam wavelength can be given by the formula:

[0079] τ(λ) = A ω (λ) + B ω (λ)

[0080] where A ω (λ) is the absorption coefficient of seawater molecules. This absorption coefficient is the smallest in the blue-green band of 450 nm to 580 nm, about 0.02 m -1 ~0.05 m -1 , and B ω (λ) is the scattering coefficient of seawater molecules, which can be calculated by Rayleigh scattering, about 1.9×10 -3 .

[0081] Since the direct transmission of the beam follows an exponential decay form, the final expression of the light field when the DLGVB beam propagates in seawater can be written as:

[0082]

[0083] where L is the propagation distance of the beam in seawater.

[0084] According to the propagation calculation model, simulate the intensity and phase distributions of the double-vortex beam at the receiving end of ocean turbulence, and expand the light field after passing through ocean turbulence with different modes of helical harmonics in sequence to obtain the weights of the corresponding OAM modes in the beam. The normalized energy spectrum function can be expressed as:

[0085]

[0086] The Laguerre-Gaussian beam in step S1 is a high-order Gaussian beam. When it propagates along the L direction, it is described by the combination of the Laguerre polynomial and the Gaussian distribution function:

[0087]

[0088] where r represents the radial distance, w0 is the beam waist radius of the beam source plane, is the azimuth angle of the beam, m is the topological charge number as the azimuthal mode index, p is the order, and w(L) is the radius of the beam at L, expressed as: z Ris the confocal parameter, also known as the Rayleigh radius, where Φ is expressed as: Φ = (n + 2m + 1)arctan(L / z R ) - k(L + r 2 / R),

[0089] In a specific embodiment, step S1 includes:

[0090] S101. Determine the expression of the Laguerre-Gaussian beam at the source field L = 0 as:

[0091]

[0092] where A is a constant, w0 is the waist radius of the beam source plane, is the azimuth angle of the beam, m is the topological charge number as the azimuthal mode index, and r represents the radial distance;

[0093] S102. Coaxially superimpose two different Laguerre-Gaussian beams to synthesize a double-vortex beam at the source field. The source field expression is:

[0094]

[0095] where δ is the phase difference of one of the vortex beams, δ = Nπ / 2, N takes any integer, m1 and m2 are the topological charge numbers of the two superimposed vortex beams, and v = |m1 - m2| represents the difference in topological charge numbers of the two beams.

[0096] In step S2, based on the random phase screen theory and the power spectrum inversion method, its fluctuating power spectrum density function is:

[0097]

[0098] where σ = 8.284(κη) 4 / 3 + 12.978(κη) 2 , and the meanings and typical values of the rest are shown in the following table:

[0099] Parameter Symbol Name Typical Value ε Kinetic Energy Dissipation Rate <![CDATA[10 -10 m 2 / s 3 ~10 -1 m 2 / s 3 > <![CDATA[χ T > Temperature Variance Dissipation Rate <![CDATA[10 -10 K 2 / s~10 -4 K 2 / s]]> ω Temperature-Salinity Fluctuation Equilibrium Parameter -5～0 η Kolmogorov Scale <![CDATA[6×10 -5 m~0.01m]]> <![CDATA[A T > Constant <![CDATA[1.863×10 -2 > As Constant <![CDATA[1.9×10 -4 > <![CDATA[A TS > Constant <![CDATA[9.41×10 -3 >

[0100] In step S2, based on the random phase screen theory and the power spectrum inversion method, construct a calculation model for the transmission of a double-vortex beam under ocean turbulence, including:

[0101] S201. Generate an ocean turbulence random phase screen using the power spectrum inversion method based on the random phase screen theory The calculation formula is:

[0102]

[0103] where h(k x , ky ) To generate a complex Gaussian random matrix, which is a standard normal distribution function in the frequency domain, where k x and k y are the dimensions of the complex Gaussian random matrix, denotes the inverse Fourier transform;

[0104] S202. Combining the angular spectrum transmission theory, obtain the optical field after transmission through an oceanic turbulence phase screen The calculation formula is:

[0105]

[0106] where is the initial beam field of the double-vortex beam, U prop (k x , k y ) is the transmission function when the beam propagates in free space, expressed as:

[0107] U prop (k x , k y ) = exp(ikl).exp[iπλl(k x 2 +k y 2 )]

[0108] The expression of the optical field of the double-vortex beam after transmission through the nth oceanic turbulence phase screen is:

[0109]

[0110] where L is the transmission distance of the beam in seawater.

[0111] In step S3, according to the numerical simulation results, determine the phase distribution and intensity distribution at the receiving end of the double-vortex beam in oceanic turbulence, including:

[0112] S301. Based on the source field expression and transmission calculation model of the double-vortex beam, set the initial beam parameters and oceanic turbulence phase screen parameters. The beam parameters are set as the initial wavelength λ = 532 nm, the waist radius w0 = 0.003 m, the topological charge difference v = 3, the transmission distance L = 60 m, the phase screen model parameter is set as the number of grids N = 200, and the interval of the oceanic turbulence phase screen l = 5 m;

[0113] S302. Numerically simulate and calculate the complex amplitude distribution of the double-vortex beam after transmission in oceanic turbulence, extract the intensity distribution and phase distribution of the receiving plane, and set different turbulent kinetic energy dissipation rates ε and temperature variance dissipation rates χ T, the temperature-salinity fluctuation equilibrium parameter ω is used to determine the light intensity and phase distributions at the receiving end after free-space transmission and transmission through ocean turbulence.

[0114] In step S3, according to the numerical simulation results, the steps to determine the orbital angular momentum mode distribution corresponding to the double-vortex beam are specifically as follows:

[0115] DLGVB optical field The expansion of mode m is expressed as follows:

[0116]

[0117] Among them, for the expansion coefficient a m (r, L) is:

[0118]

[0119] From this, the energy on the m-th order helical harmonic can be obtained as:

[0120]

[0121] The normalized energy spectrum function can be obtained as:

[0122]

[0123] By analogy, the helical phase spectrum vector of the optical field is expanded in the OAM mode helical harmonics within a certain range, and the weights and energy distributions corresponding to the OAM modes in the double-vortex beam are determined.

[0124] In step S3, according to the numerical simulation results, the steps to determine the relationship between beam broadening and transmission distance under different topological charge differences and different ocean turbulence parameters are specifically as follows:

[0125] Set different topological charge differences v, turbulent kinetic energy dissipation rate ε, temperature variance dissipation rate χ T , the temperature-salinity fluctuation equilibrium parameter ω, and the transmission distance L;

[0126] Based on the transmission calculation model, numerical simulations are carried out to calculate the relationship distribution curve between beam broadening and transmission distance under different parameter combinations;

[0127] Beam broadening W e is described by the following formula:

[0128]

[0129] Among them, I represents the light intensity after passing through the turbulence; it can be expressed by the formula:

[0130]

[0131] In this embodiment, the above determination method is further implemented in the following manner: Based on the wavelength λ, wave number k, turbulent kinetic energy dissipation rate ε, temperature variance dissipation rate χ T 、temperature-salinity fluctuation equilibrium parameter ω, beam waist radius w0, total transmission distance L, width D of the ocean turbulence random phase screen, and spacing l between the ocean turbulence random phase screens, a simulation model is constructed to simulate the light intensity and phase distributions of the double-vortex beam after passing through ocean turbulence; Based on the topological charge difference v, turbulent kinetic energy dissipation rate ε, temperature variance dissipation rate χ T 、temperature-salinity fluctuation equilibrium parameter ω, and transmission distance L, a simulation model is constructed to obtain the orbital angular momentum mode distribution image of the double-vortex beam after passing through ocean turbulence and the relationship distribution curve between beam broadening and transmission distance under different topological charge differences and different ocean turbulence parameters.

[0132] The above determination method will be further elaborated and analyzed in combination with simulation experiments below.

[0133] Simulation Experiment 1: The present invention is used to simulate the light intensity and phase distributions of the double-vortex beam after passing through ocean turbulence.

[0134] The results are as shown in Figure 3 、 4 、and 5. It can be seen from the figure that the double-vortex beam will produce spot splitting, and the number of split light fields is the same as the difference v in the topological charges of the superimposed vortex beams. As the turbulent kinetic energy dissipation rate decreases and the temperature variance dissipation rate and temperature-salinity fluctuation equilibrium parameter increase, the light intensity distortion received on the receiving plane becomes more serious, and at the same time, the phase distribution becomes more and more blurred.

[0135] This phenomenon indicates that the increase in ocean turbulence intensity leads to a more intense influence of ocean turbulence on the beam transmission process, and the more serious the light intensity dissipation.

[0136] Simulation Experiment 2: The present invention is used to simulate the orbital angular momentum mode distribution of the light field. The results are as shown in Figure 6 、 7 、8, and 9; Figure 6 (a) where v = 0 represents a traditional single-ring vortex beam, (b), (c), and (d) where v = 1, v = 3, and v = 5 represent double-vortex beams. It can be obtained from (a) that the energy retention ratio of the single-ring vortex beam after passing through ocean turbulence is 71.04%. Compared with the double-vortex beams in (b), (c), and (d), the retention rate is lower. The results show that the retention ratio of the intensity of the source field mode energy of the traditional single-ring vortex beam is lower than that of the double-vortex beam. From the results in the figure, it is also obtained that v = 1 corresponds to a retention ratio of 92.6%, v = 3 corresponds to a retention ratio of 86.3%, and v = 5 corresponds to a retention ratio of 78.8%, indicating that the retention ratio will decrease as the topological charge difference increases. Figure 7 、 8, the (a) figure in Fig. 9 represents the energy retention ratio during transmission in free space, and (b), (c), and (d) respectively represent the energy retention ratios during transmission in ocean turbulence under different turbulent kinetic energy dissipation rates, different temperature variance dissipation rates, and different temperature-salinity fluctuation equilibrium parameters. It can be seen from the figure that as the turbulent kinetic energy dissipation rate gradually decreases from 1×10 -2 m 2 s -3 to 1×10 -7 m 2 s -3 , and the temperature variance dissipation rate increases gradually from 1×10 -8 K 2 s -1 to 1×10 -6 K 2 s -1 , and at the same time, as the temperature-salinity fluctuation equilibrium parameter increases gradually from -3 to -1, the energy retention ratio shows a gradually decreasing trend.

[0137] This phenomenon indicates that for a double-vortex beam with two orbital angular momentum modes carried by the source field, the influence of ocean turbulence is dispersed into different angular momentum modes, resulting in a relatively high energy retention ratio; as the difference in topological charge numbers increases, more split light spots are generated during transmission, leading to the dispersion of the beam energy during the process, and further resulting in an increased influence of ocean turbulence and a decrease in the energy residue ratio; and the corresponding parameter change trends will all lead to an intensification of the ocean turbulence intensity, further causing a more severe influence on the beam transmission in the ocean, thus broadening the orbital angular momentum spectrum and reducing the information retention performance.

[0138] In simulation experiment three, the beam broadening under different topological charge number differences and different ocean turbulence parameters was simulated and calculated using the present invention.

[0139] The results are as shown in Figure 10 , 11 , 12, 13, and 14. It can be seen from Figure 10 that the double-vortex beam with v = 1 has the smallest beam broadening under the same conditions, meaning that the double-vortex beam with v = 1 is more conducive to transmission in ocean turbulence, and the beam broadening of the double-vortex beam increases with the increase in the difference in topological charge numbers at the same transmission distance. It can be seen from Figure 11 that when v changes from 0 to 1 under the same ocean turbulence parameter conditions, the beam broadening decreases significantly, but as the difference in topological charge numbers continues to increase, the beam broadening will gradually increase. When v = 3, the beam broadening will increase to be close to that at the beginning when v = 0. The results show that compared with the traditional single-ring vortex beam, when the difference in topological charge numbers is less than 3, the detection performance of the double-vortex beam in ocean turbulence is better than that in other modes, and the beam broadening caused by the influence of ocean turbulence is smaller. It can be seen from Figure 12 , 13, it can be seen from 14 that under the same transmission distance, for the DLGVB beam in ocean turbulence, as the turbulent kinetic energy dissipation rate decreases and the salinity-temperature fluctuation equilibrium constant and the temperature variance dissipation rate increase, the beam broadening gradually increases.

[0140] This phenomenon indicates that different topological charge differences and different ocean turbulence parameters have a significant impact on the beam broadening.

[0141] The above description is only a preferred embodiment of the present disclosure and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of disclosure involved in the present disclosure is not limited to the technical solutions formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosure concept. For example, the technical solutions formed by mutually replacing the above features with the technical features (but not limited to) having similar functions disclosed in the present disclosure.

[0142] In addition, although the operations are depicted in a specific order, this should not be construed as requiring that the operations be performed in the specific order shown or in a sequential order. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of the present disclosure. Certain features described in the context of a single embodiment can also be implemented in combination in a single embodiment. Conversely, the various features described in the context of a single embodiment can also be implemented separately or in any suitable sub-combination in multiple embodiments.

[0143] The above-described embodiments merely represent several implementation manners of the present invention, and the description thereof is relatively specific and detailed, but should not be construed as limiting the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can be made, and these all belong to the protection scope of the present invention.

Claims

1. A method for determining the propagation characteristics of a double-vortex beam in oceanic turbulence, characterized in that The method includes the following steps: S1. Obtain two Laguerre-Gaussian beams at the source field where L = 0 and perform coaxial superposition to synthesize a double-vortex beam at the source field; S2. Based on the random phase screen theory and the power spectrum inversion method, construct a transmission calculation model for the double-vortex beam under ocean turbulence and perform numerical simulation; S3. According to the numerical simulation results, determine the transmission characteristics of the double-vortex beam in ocean turbulence, including the phase distribution, intensity distribution, corresponding orbital angular momentum mode distribution at the receiving end, and the relationship between beam broadening and transmission distance under different topological charge differences and different ocean turbulence parameters.

2. The method for determining the propagation characteristics of a double-vortex beam in oceanic turbulence according to claim 1, wherein Step S1 includes: S101. Determine the expression of the Laguerre-Gaussian beam at the source field where L = 0 as: where A is a constant, w0 is the waist radius of the beam source plane, is the azimuth angle of the beam, m is the topological charge number as the azimuthal mode index, and r represents the radial distance; S102. Coaxially superpose two different Laguerre-Gaussian beams to synthesize a double-vortex beam at the source field, and the source field expression is: where δ is the phase difference of one of the vortex beams, δ = Nπ / 2, N takes any integer, m1 and m2 are the topological charges of the two superposed vortex beams, and v = |m1 - m2| represents the topological charge difference between the two beams.

3. The method for determining the transmission characteristics of a double-vortex beam in oceanic turbulence according to claim 1, wherein In step S2, the construction of the transmission calculation model for the double-vortex beam under ocean turbulence based on the random phase screen theory and the power spectrum inversion method includes: S201. Generate an ocean turbulence random phase screen using the power spectrum inversion method based on the random phase screen theory The calculation formula is as follows: Among them, h(k x , k y ) is a complex Gaussian random matrix, which is a standard normal distribution function in the frequency domain, where k x and k y are the dimensions of the complex Gaussian random matrix, represents the inverse Fourier transform; S202. Combine the angular spectrum transfer theory to obtain the optical field after transmission through an oceanic turbulence phase screen The calculation formula is as follows: Among them is the initial beam field of the double-vortex beam, U prop (k x , k y ) is the propagation function of the beam when propagating in free space, expressed as: U prop (k x ,k y ) = exp(ikl).exp[iπλl(k x 2 + k y 2 )] The optical field expression of the double-vortex beam after passing through the nth ocean turbulence phase screen is: where L is the distance that the beam travels in seawater.

4. The method for determining the propagation characteristics of a double-vortex beam in oceanic turbulence according to claim 3, wherein In step S3, according to the numerical simulation results, determining the phase distribution and intensity distribution at the receiving end of the double-vortex beam in ocean turbulence includes: S301. Based on the source field expression and the transmission calculation model of the double-vortex beam, set the initial parameters of the beam and the parameters of the ocean turbulence phase screen; S302. Numerically simulate to calculate the complex amplitude distribution of the double-vortex beam after transmission in ocean turbulence, and extract the intensity distribution and phase distribution of the receiving plane.

5. A method for determining the transmission characteristics of a double-vortex beam in oceanic turbulence according to claim 1, characterized in that In step S3, the steps for determining the corresponding orbital angular momentum mode distribution in the double-vortex beam according to the numerical simulation results are specifically: The optical field of the double-vortex beam at the receiving end is subjected to OAM mode helical harmonic expansion to obtain the helical phase spectrum vector of the beam, and the expression is: Determine the weights and energy distributions of the corresponding OAM modes in the double-vortex beam according to the helical phase spectrum vector.

6. The method for determining the transmission characteristics of a double-vortex beam in oceanic turbulence according to claim 1, wherein In step S3, the steps for determining the relationship between beam broadening and transmission distance under different topological charge differences and different ocean turbulence parameters according to the numerical simulation results are specifically: Set different topological charge differences v, turbulent kinetic energy dissipation rate ε, temperature variance dissipation rate χ T , temperature-salinity fluctuation equilibrium parameter ω, and transmission distance L; Perform numerical simulation based on the transmission calculation model to calculate the relationship distribution curve between beam broadening and transmission distance under different parameter combinations; Beam broadening W e is described by the following formula: where I represents the intensity after passing through the turbulence; it can be expressed by the formula:

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