Method and system for simulating vortex light transmission across sea surface based on electric field Monte Carlo method

Abstract

The present invention relates to a method and system for simulating vortex light transmission across sea surface based on an electric field Monte Carlo method. The method comprises the following steps: S10, loading photons and performing initialization settings; S20, calculating the position change of photons during random walk in a channel; S30, judging whether the photons have reached a detection surface based on the position change of the photons, if so, returning to step S10, otherwise, entering step S40; S40, calculating the absorptivity of the photons and local orthogonal coordinate conversion; S50, determining whether the photons have survived by survival wheel selection, if so, returning to step S20, otherwise, entering step S60; S60, judging whether all photons have been calculated, if so, entering step S70, otherwise, returning to step S10; S70, calculating the cumulative electric field under the influence of a sea surface light beam factor, obtaining the electric field intensity, and recording and saving the information. The present invention can more accurately simulate the vortex light transmission process across sea surface and obtain cumulative electric field information.

Description

Technical Field

[0001] The present invention relates to the field of optical communication technology, and in particular to a method and system for simulating vortex light transmission across sea surface based on an electric field Monte Carlo method. Background Art

[0002] The transmission characteristics of light beams in marine environments are of great significance to applications such as marine optical communications and marine lidar. The Monte Carlo method is a numerical calculation method based on random sampling and is widely used to simulate various complex physical processes, including the propagation and scattering of light. In the field of optics, especially the propagation of light in complex media (such as air and seawater), the Monte Carlo method simulates the absorption and scattering of photons in the medium by tracking the trajectories of a large number of photons. In this way, the Monte Carlo method can statistically accurately describe the transmission process of light and is particularly suitable for dealing with problems such as multiple scattering and light transmission in random media.

[0003] However, traditional Monte Carlo methods usually only care about the macroscopic state of photons, such as position, direction, energy, etc. For example, in the invention with publication number CN 114884599A, "Construction method of blue-green vortex light gas sea cross-medium collimated incidence single-pass transmission model", the coherence and interference effects of photons after multiple scattering are often ignored during the simulation process, resulting in inaccurate simulation of the vortex light transmission process. Summary of the Invention

[0004] The purpose of the present invention is to provide a method and system for simulating the transmission of vortex light across the sea surface based on the electric field Monte Carlo method, so as to improve the problem of insufficient accuracy in the simulation of the transmission of vortex light across the sea surface in the prior art.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] In a first aspect, the present invention provides a method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method, comprising the following steps:

[0007] S10, loading photons and performing initialization settings, including setting the initial coordinates of the photons, initial direction cosines, initial parallel components of the complex electric field and initial vertical components of the complex electric field. The initial parallel components of the complex electric field and initial vertical components of the complex electric field are set to and E2 = 0, where i represents the imaginary unit, l represents the topological charge of the vortex beam, is the azimuth;

[0008] S20, calculates the position change of the photon during its random walk in the channel;

[0009] S30, judging whether the photon reaches the detection surface according to the change in the position of the photon, if yes, returning to step S10, simulating the scattering process of the next photon; if not, proceeding to step S40;

[0010] S40, calculating the absorption rate of photons and local orthogonal coordinate transformation, and then proceeding to step S50;

[0011] S50, determining whether the photon survives by selecting the survival roulette wheel. If yes, return to step S20 and continue to simulate the subsequent behavior of the photon. If no, the photon no longer survives and proceed to step S60;

[0012] S60, determine whether all photons have been calculated, if yes, proceed to step S70, if not, return to step S10 to simulate the scattering process of the next photon;

[0013] S70, calculating the cumulative electric field under the influence of the sea surface light beam factor, obtaining the electric field intensity, and recording and saving it.

[0014] The above scheme is mainly aimed at the absorption and scattering effects of vortex light when it is transmitted in underwater channels in the ocean. It uses photons as the carrier of light information and records the electric field information, position and direction of photons after each Mie scattering, so as to more accurately calculate the propagation and scattering process of light underwater, which makes up for the shortcomings of existing simulation methods. In addition, combined with the influence of the undulating sea surface on the light beam, the electric field intensity E of the vortex light on the vortex light when it is transmitted across the sea surface is obtained. ins , providing new ideas and methods for the transmission of light beams across media.

[0015] In a second aspect, the present invention provides a system for simulating vortex light transmission across sea surface based on the electric field Monte Carlo method, comprising:

[0016] The initialization module is used to load photons and perform initialization settings, including setting the initial coordinates of the photons, initial direction cosines, initial parallel components of the complex electric field and initial vertical components of the complex electric field. The initial parallel components of the complex electric field and initial vertical components of the complex electric field are set to and E2 = 0, where i represents the imaginary unit, l represents the topological charge of the vortex beam, is the azimuth;

[0017] Position change detection module, used to calculate the position change of photons during random walk in the channel;

[0018] The first judgment module is used to judge whether the photon reaches the detection surface according to the change of the photon's position. If yes, it returns to the initialization module to simulate the scattering process of the next photon; if not, it enters the first calculation module;

[0019] The first calculation module is used to calculate the absorption rate of photons and local orthogonal coordinate transformation;

[0020] The second judgment module is used to determine whether the photon survives through the survival roulette selection. If yes, it returns to the position change detection module to continue simulating the subsequent behavior of the photon. If no, the photon no longer survives and enters the third judgment module;

[0021] The third judgment module is used to judge whether all photons have been calculated. If so, it enters the second calculation module. If not, it returns to the initialization module to simulate the scattering process of the next photon;

[0022] The second calculation module is used to calculate the cumulative electric field under the influence of the sea surface light beam factor, obtain the electric field intensity, and record and save it.

[0023] In a third aspect, the present invention provides a computer program product comprising computer-readable instructions, characterized in that when the computer-readable instructions are executed by a processor, the computer-readable instructions implement the steps of the method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method of the present invention.

[0024] In a fourth aspect, the present invention provides a computer-readable storage medium comprising computer-readable instructions, characterized in that when the computer-readable instructions are executed by a processor, the steps of the method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method of the present invention are implemented.

[0025] In a fifth aspect, the present invention provides an electronic device, comprising: a memory for storing program instructions; a processor connected to the memory for executing the program instructions in the memory to implement the steps of the method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method of the present invention.

[0026] Compared with the prior art, the present invention has the following significant technical advantages:

[0027] In particular, the present invention enhances the accuracy of light propagation calculations by combining the ocean-air interface to form a suitable system. By recording the photon's electric field information and position in detail, this method preserves the electric field information after each Mie scattering, accurately reflecting the changes in the light beam during propagation. This enables effective simulation of light transmission from underwater to the air interface and vice versa.

[0028] Furthermore, the present invention comprehensively considers the impact of sea surface fluctuations on the beam propagation path and intensity. This is particularly true in real-world ocean environments, where sea surface fluctuations significantly affect light propagation. Through comprehensive analysis of these factors, the present invention accurately predicts the electric field intensity of vortex light during cross-sea transmission, making the system suitable for bidirectional transmission between the ocean and air interfaces.

[0029] In order to more effectively handle complex scattering and absorption problems, the present invention has adopted the electric field Monte Carlo method, which can reflect the impact of multiple scattering effects on electric field intensity. In the initialization and updating process of the electric field, the formula adopted by the present invention has played an important role. The electric field initialization formula is used to set the electric field state before the photon enters the scattering medium. Its special effect is to provide a clear starting point for subsequent propagation and scattering process, so that the simulation of light field is more accurate. During initialization, the electric field distribution is affected by the incident beam type (such as plane wave or vortex beam), which ensures that the model can truly reflect the actual situation. This provides a basis for effective simulation and helps researchers better understand the propagation characteristics of light in the medium.

[0030] Secondly, the formula for updating the electric field of scattered photons updates the changes in the photon's electric field after each scattering, reflecting in real time the changes in electric field intensity after the photon interacts with the scattering medium. This formula takes into account factors such as the scattering angle and scattering amplitude, ensuring dynamic updating of electric field information. This dynamic update mechanism not only improves the accuracy of the model but also effectively simulates the effects of multiple scattering on light propagation, more realistically reflecting the attenuation characteristics and propagation path of the light beam, thereby achieving bidirectional applicability from the ocean-to-air interface and from the air-to-ocean interface.

[0031] In summary, the present invention combines the ocean and air interfaces to form a method and system suitable for two transmission scenarios, with the technical advantages of high efficiency, accuracy and reliability.

[0032] For other advantages of the present invention, please refer to the relevant description in the embodiment section. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0034] Figure 1 This is a flow chart of a method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method as an example in the embodiments.

[0035] Figure 2a 、 Figure 2b 、 Figure 2c The light field distribution diagrams of the changes in beam intensity when there is no wind, wind speed is 6m / s, and wind speed is 8m / s.

[0036] Figure 3 This is a block diagram of the composition of the vortex light cross-sea transmission simulation system based on the electric field Monte Carlo method as an example in the embodiments.

[0037] Figure 4 FIG. 4 is a block diagram of the electronic device in the embodiment. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0039] See also Figure 1 In this embodiment, a method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method is provided, which includes the following steps:

[0040] S10, loading photons and performing initialization settings, including setting the initial coordinates and initial direction cosines of the photons.

[0041] When using EMC simulation method to simulate the transmission of OAM (vortex light) beam in underwater scattering channel, one of the most important steps is to set the initial coordinates of photons. Assume that the initial axial coordinate of emission is z=0. In polar coordinate system, the coordinates of photons on the initial emission plane need to be set. For selection, ρ is related to the radial distribution characteristics of the OAM beam intensity, and the size of the intensity distribution with ρ determines the probability of extracting ρ.

[0042] The intensity distribution of the OAM beam on the emission surface is related to the radial basis function. For a Bessel-Gaussian beam, its radial basis function can be expressed as:

[0043]

[0044] Where E0 is a constant, ω0 is the beam waist radius, k ρ is the radial wave vector, l is the order of the Bessel-Gaussian beam, that is, the topological charge number, which can be any integer, and ρ is the initial radial coordinate, where E0, ω0, k ρ , l can be set directly. For the convenience of observation, the beam is set to a circular beam distribution pattern. J l (·) represents the first-kind Bessel function of order l, where “·” represents the parameter.

[0045] According to this radial basis function, the normalized light intensity density function can be obtained:

[0046]

[0047] This normalized intensity density function describes the radial intensity distribution of the OAM beam on the emission surface. In simulation, the initial radial coordinate ρ of each photon can be determined by sampling the intensity density function through a rejection algorithm.

[0048] The random sampling of the emitted photons ρ by the EMC method obeys the probability density distribution corresponding to the normalized light intensity density function. For the convenience of sampling, the cutoff radius of the incident OAM beam is set to R m , let ρ be [0,R m ] uniformly distributed within the range of . The more photons are emitted at the position ρ, the greater the probability of emission.

[0049] Therefore, the process of sampling ρ0 of the input OAM beam using the rejection algorithm is as follows:

[0050] (1) Generate a random number χ, satisfying χ~U(0,1), and calculate a radial coordinate ρ0=χR m .

[0051] (2) Generate a random number satisfy If satisfied Then accept this ρ0.

[0052] For azimuth For the sampling, since the OAM beam has radial symmetry in the polar coordinate system, a uniform distribution between 0 and 2π can be directly adopted.

[0053] In addition, in order to ensure the initial electric field component of the photon, according to the characteristics of the OAM beam, the initial complex electric field parallel component and the complex electric field vertical component are set to and E2 = 0, where i represents the imaginary unit and l represents the topological charge of the vortex beam.

[0054] Using the Cartesian coordinate system, the initial coordinates of the photon can be expressed as:

[0055]

[0056] The initial direction cosines can be expressed as:

[0057]

[0058] where θ0 and are the elevation and azimuth angles in the direction of photon emission, θ0 is obtained by the following formula:

[0059]

[0060] Where r3 and r4 represent random numbers between 0 and 1, which are uniformly distributed within the range of 0 to 1, and θ1 is the divergence angle of the light beam.

[0061] S20, calculate the position change of the photon during its random walk in the channel.

[0062] Define the position coordinates of the photon before scattering as (x, y, z), the position coordinates after scattering as (x′, y′, z′), the direction cosines before scattering as (u, v, w), and assume that the propagation distance of the photon after one scattering is l sct , according to Beer's Law, the photon scattering step is expressed as l sct =-ln(ζ) / Q sca , where Q sca is the scattering coefficient, and ζ is a random number that is uniformly distributed between 0 and 1. Thus, the photon travels a distance l from the position coordinates (x, y, z) before scattering. scc After that, the position coordinates (x′, y′, z′) can be expressed as:

[0063] x′=x+ul sct

[0064] y′=y+vl sct

[0065] z′=z+wl sct ;

[0066] The direction cosines can be updated after scattering by:

[0067]

[0068] θ、 are the scattering angle and azimuth angle, respectively.

[0069] As photons are continuously scattered, the scattering angle and azimuth will change, and the scattering angle and azimuth will be updated every time they are scattered.

[0070] Select the most appropriate phase function within different scattering angle ranges. The commonly used HG phase function has fewer parameters, so it is simple and easy to use. The expression of the HG phase function is:

[0071]

[0072] The scattering angle θ can be set by the phase function distribution law:

[0073]

[0074] θ is the scattering angle; g is the asymmetry factor, whose magnitude affects the ratio of forward scattering to backscattering. ζ is a random number uniformly distributed between 0 and 1. Given ζ and g, the scattering angle θ can be calculated.

[0075] The azimuth angle is uniformly distributed between 0-2π and can be expressed as Used in the scatter loop.

[0076] S30, judging whether the photon reaches the detection surface according to the change in the position of the photon, if so, returning to step S10 to simulate the scattering process of the next photon; if not, entering step S40.

[0077] For example, suppose a photon starts from the origin (0.1, 0.5, 0) and after several propagations, its position is updated to (1, 1, 6). In this case, because the z coordinate (6) is greater than the z-axis coordinate z of the detection surface, d (z d =5), so it is judged that the photon has reached the detection surface.

[0078] If the scattering angle is not zero, it is determined that scattering has occurred.

[0079] S40, calculate the absorption rate, local coordinates and other parameters of the photon, and then enter step S50.

[0080] When photons interact with spherical dielectric particles, part of the energy will be absorbed and scattered by the dielectric particles. The particle scattering coefficient, absorption coefficient, and extinction coefficient are Q sca , Q abs , Q ext , which is expressed as follows:

[0081]

[0082] Q ass =Q ext -Q sca .

[0083] a N with b N They are Mie coefficient, symbol Indicates taking the real part, x r Represents the relative size of scattering spherical particles. N represents terms of different orders, which are used to represent the contributions of spherical harmonics of different orders. By accumulating these terms of different orders, parameters such as scattering, absorption, and extinction can be more accurately described.

[0084] In order to represent the absorption of the light beam during propagation, the weight W of the photon after each scattering can be adjusted a To achieve this, the weight change can be expressed as W a =W(1-Q sca / Q ext ), Q sca / Q ext Represents the single scattering albedo, which represents the proportion of scattering in extinction, W is the initial weight of the photon, and the absorption rate is

[0085] The local orthogonal coordinate system of the photon before scattering is denoted as (m, n, s), and the coordinate system after interaction with the medium particles is denoted as (m', n', s'). m and n are the parallel and perpendicular components of the electric field before scattering, respectively, and are unit vectors relative to the scattering plane of the previous scattering. The electric field component is the real part of the complex electric field component. The electric field component describes the actual amplitude of the electric field at a specific location, a quantity that can be directly measured by physical measurement instruments. The complex electric field component provides complete amplitude and phase information. s is the direction of motion of the photon before scattering (also known as the incident direction), and s' is the direction of motion of the photon after scattering from the medium particles (also known as the scattering direction). The scattering direction s' and the incident direction s determine the scattering plane. The unit vectors m' and n' are the parallel and perpendicular components of the scattered light parallel to the scattering plane, respectively, and satisfy m' × n' = s'. E1, E1′, E2, and E2′ are the complex electric field components parallel to the electric field before scattering, parallel to the electric field after scattering, perpendicular to the electric field before scattering, and perpendicular to the electric field after scattering, respectively. The local coordinate transformation rules for photons before and after scattering can be abstracted through vector operations and expressed in matrix form. Each time a photon is scattered, the change in the local coordinate system satisfies the following relationship:

[0086]

[0087] where θ represents the scattering angle, Indicates the azimuth.

[0088] Similarly, the update of the complex electric field after the photon is scattered can be expressed as:

[0089]

[0090] Among them, S1 and S2 are the scattering amplitude functions with respect to the scattering angle θ, which are related to the scattering coefficient and the scattering angle function. According to Mie scattering theory, they can be expressed as:

[0091]

[0092]

[0093] where a N with b N are Mie coefficients, which are functions related to the actual size of the scattering medium particles, the wavelength of the incident light, and the complex refractive index of the scattering medium particles, but have nothing to do with the scattering angle θ. N With τ N is the scattering angle function and is only related to the scattering angle θ. They can be expressed as:

[0094]

[0095] Among them, x r =πd / λ, which represents the relative particle size of the scattering spherical particles, where d is the actual diameter of the particle in meters and λ is the wavelength. The complex refractive index of the scattering spherical particles is: n sct =n real +i*n imag , where the real part n real Related to the scattering effect of medium particles, the imaginary part n imag Related to the absorption of medium particles, n imag When it is not 0, it means that the photon will be absorbed by the medium particles and cause energy attenuation. N (x) and ξ N (x) are half-integer order Bessel function and second-order Hankel function respectively. N (cosθ) and P N ′(cosθ) are the Legendre function and the first-order associated Legendre function with respect to cosθ, respectively. Indicates along The intensity normalization factor of the scattered light propagating in the direction is expressed as:

[0096]

[0097] Among them, the symbol Indicates taking the real part, * indicates taking the conjugate, is the azimuth, and |E1| 2 +|E2| 2 =1.

[0098] S50, determine whether the photon survives by selecting the survival roulette wheel. If yes, return to step S20 and continue to simulate the subsequent behavior of the photon. If not, the photon no longer survives and enter step S60.

[0099] When a photon fails to reach the receiving surface during transmission, its weight decreases as it travels. When it falls below the set annihilation value, it indicates that the photon has annihilated during its motion and is not recorded on the receiving surface. This is because even when the photon reaches the receiving surface, its contribution to the beam intensity is negligible. Ignoring annihilated photons can speed up program execution, and therefore simulation efficiency. When a photon reaches the receiving surface and its weight exceeds the annihilation value, the photon ceases its motion and the accumulated electric field information is recorded.

[0100] S60, determine whether all photons have been calculated, if so, go to step S70, if not, return to step S10 to simulate the scattering process of the next photon.

[0101] S70, calculating the transmission coefficient and the sea surface beam influence factor and applying them to the accumulated electric field to obtain the electric field intensity, and recording and saving the obtained electric field intensity.

[0102] After the photon is scattered by the medium particles n times, its final local orthogonal coordinate system is (m (n) ,n (n) ,s (n) ), for the convenience of statistics, the final motion direction of all photons is limited to s (n) All (u d ,v d ,w d )=(0,0,1), that is, it propagates in the positive direction of the z axis and reaches the detection surface. (n) and n (n) The parallel and perpendicular electric field components in the direction are The corresponding electric field components in the x, y, and z directions can be according to Vector transformation is obtained. Taking into account the interaction between photons and scattering media and the phase delay caused by the propagation of photons in the scattering medium, the electric field components in the x, y, and z directions after photon superposition can be expressed as:

[0103]

[0104] Where G is the x, y, and z directions, k is the wave number, l (n) is the total path length traveled by a photon after being scattered n times.

[0105] In this embodiment, the detection surface is set at z=z d The actual photon reaches the final scattering position after n scatterings, and the coordinate in the z-axis direction is z (n) Generally speaking, the photon will not fall directly on the detection surface (the coordinate in the z-axis direction is z d ) is received, i.e. z (n) >z d or z (n) ≤z d In this case, the phase delay from the final scattering position of the photon to the detection surface needs to be considered, which can be expressed as In addition, there is an uncounted scattering process from the final scattering position to the detection position, which causes the attenuation of the photon energy. Therefore, a weight attenuation factor can be set as To equivalent the attenuation effect, the scattering cross section l sct is the scattering random step size.

[0106] Taking all the above factors into consideration, the electric field components of the photons received by the detection surface in the x, y, and z directions can be expressed as:

[0107]

[0108] w d represents the direction cosine of the photon arriving at the receiving plane.

[0109] According to the Fresnel formula, the total transmittance T of the light beam transmitted from underwater to the sea surface is up for:

[0110] T up =T wa1 T wa2 ;

[0111] Where T wa1 Indicates the transmittance of the air-sea interface itself, satisfying α represents the incident angle of the light beam from the sea-air interface, and β represents the refraction angle. According to the refraction theorem, the expression of the refraction angle is n1 and n2 represent the refractive index of seawater and air respectively. wa2 Indicates the transmittance caused by foam and other factors on the sea surface. When the wind speed p≤9m / s, T wa2 =1-1.2×10 -5 ×p 3.3 , when the wind speed is p>9m / s, T wa2 =1-1.2×10 -5 ×p 3.3 ×(0.225p-0.99).

[0112] The electric field components in the x, y, and z directions of the Bessel-Gaussian beam after it passes through the sea surface are:

[0113]

[0114] in represents the electric field of each component of the Bessel-Gaussian beam after the beam is scattered multiple times by the seawater. is the wave number of the Bessel-Gaussian beam, λ is the beam wavelength, z h represents the sea surface height fluctuation function, n1 is the refractive index of seawater, and T is the total transmittance. The total electric field intensity E ins The size can be expressed using the following formula:

[0115]

[0116] Among them E x 、E y 、E zare the electric field components in the x, y, and z directions, respectively.

[0117] We have previously discussed the upward transmission process of light propagating underwater and passing through the ocean interface. Now, when light propagates from air and transmits downward through the ocean interface, the transmission process is:

[0118] S100, loading photons and performing initialization settings, including setting the initial coordinates and initial direction cosines of the photons.

[0119] When using EMC simulation method to simulate the transmission of OAM (vortex light) beam in air scattering channel, one of the most important steps is to set the initial coordinates of photons. Assume that the initial emission axial coordinate is z = 0. In polar coordinate system, the emission coordinates on the initial emission plane of photons need to be set. For selection, ρ is related to the radial distribution characteristics of the OAM beam intensity, and the size of the intensity distribution with ρ determines the probability of extracting ρ.

[0120] The intensity distribution of the OAM beam on the emission surface is related to the radial basis function. For a Bessel-Gaussian beam, its radial basis function can be expressed as:

[0121]

[0122] Where E0 is a constant, ω0 is the beam waist radius, k ρ is the radial wave vector, l is the order of the Bessel-Gaussian beam, that is, the topological charge number, which can be any integer, and ρ is the initial radial coordinate, where E0, ω0, k ρ , l can be set directly. For the convenience of observation, the beam is set to a circular beam distribution pattern. J l (·) represents the first-kind Bessel function of order l, where “·” represents the parameter.

[0123] According to this radial basis function, the normalized light intensity density function can be obtained:

[0124]

[0125] This normalized intensity density function describes the radial intensity distribution of the OAM beam on the emission surface. In simulation, the initial radial coordinate ρ of each photon can be determined by sampling the intensity density function through a rejection algorithm.

[0126] The random sampling of the emitted photons ρ by the EMC method obeys the probability density distribution corresponding to the normalized light intensity density function. For the convenience of sampling, the cutoff radius of the incident OAM beam is set to R m , let ρ be [0,R m] uniformly distributed within the range of . The more photons are emitted at the position ρ, the greater the probability of emission.

[0127] Therefore, the process of sampling ρ0 of the input OAM beam using the rejection algorithm is as follows:

[0128] (1) Generate a random number χ, satisfying χ~U(0,1), and calculate a radial coordinate ρ0=χR m .

[0129] (2) Generate a random number satisfy If satisfied Then accept this ρ0.

[0130] For azimuth For the sampling, since the OAM beam has radial symmetry in the polar coordinate system, a uniform distribution between 0 and 2π can be directly adopted.

[0131] In addition, in order to ensure the initial electric field component of the photon, according to the characteristics of the OAM beam, the initial complex electric field parallel component and the complex electric field vertical component are set to and E2 = 0, where i represents the imaginary unit and l represents the topological charge of the vortex beam.

[0132] Using the Cartesian coordinate system, the initial coordinates of the photon can be expressed as:

[0133]

[0134] The initial direction cosines can be expressed as:

[0135]

[0136] where θ0 and are the elevation and azimuth angles in the direction of photon emission, θ0 is obtained by the following formula:

[0137]

[0138] Where r3 and r4 represent random numbers between 0 and 1, which are uniformly distributed within the range of 0 to 1, and θ1 is the divergence angle of the light beam.

[0139] S200, calculating the position change of the photon during its random walk in the channel.

[0140] Define the position coordinates of the photon before scattering as (x, y, z), the position coordinates after scattering as (x′, y′, z′), the direction cosines before scattering as (u, v, w), and assume that the propagation distance of the photon after one scattering is l sct, according to Beer's Law, the photon scattering step is expressed as l sct =-ln(ζ) / Q sca , where Q sca is the scattering coefficient, and ζ is a random number that is uniformly distributed between 0 and 1. Thus, the photon travels a distance l from the position coordinates (x, y, z) before scattering. scc After that, the position coordinates (x′, y′, z′) can be expressed as:

[0141] x′=x+ul sct

[0142] y′=y+vl sct

[0143] z′=z+wl sct ;

[0144] The direction cosines can be updated after scattering by:

[0145]

[0146] θ、 are the scattering angle and azimuth angle, respectively.

[0147] As photons are continuously scattered, the scattering angle and azimuth will change, and the scattering angle and azimuth will be updated every time they are scattered.

[0148] Select the most appropriate phase function within different scattering angle ranges. The commonly used HG phase function has fewer parameters, so it is simple and easy to use. The expression of the HG phase function is:

[0149]

[0150] The scattering angle θ can be set by the phase function distribution law:

[0151]

[0152] θ is the scattering angle; g is the asymmetry factor, whose magnitude affects the ratio of forward scattering to backscattering. ζ is a random number uniformly distributed between 0 and 1. Given ζ and g, the scattering angle θ can be calculated.

[0153] The azimuth angle is uniformly distributed between 0-2π and can be expressed as Used in the scatter loop.

[0154] S300, judging whether the photon reaches the detection surface according to the position change of the photon, if yes, returning to step S100, simulating the scattering process of the next photon; if not, entering step S400.

[0155] For example, suppose a photon starts from the origin (0.1, 0.5, 0) and after several propagations, its position is updated to (1, 1, 6). In this case, because the z coordinate (6) is greater than the z-axis coordinate z of the detection surface, d (z d =5), so it is judged that the photon has reached the detection surface.

[0156] If the scattering angle is not zero, it is determined that scattering has occurred.

[0157] S400, calculate the absorption rate, local coordinates and other parameters of the photon, and then enter step S500.

[0158] When photons interact with spherical dielectric particles, part of the energy will be absorbed and scattered by the dielectric particles. The particle scattering coefficient, absorption coefficient, and extinction coefficient are Q sca , Q abs , Q ext , which is expressed as follows:

[0159]

[0160] Q ass =Q ext -Q sca .

[0161] a N with b N They are Mie coefficient, symbol Indicates taking the real part, x r Represents the relative size of scattering spherical particles. N represents terms of different orders, which are used to represent the contributions of spherical harmonics of different orders. By accumulating these terms of different orders, parameters such as scattering, absorption, and extinction can be more accurately described.

[0162] In order to represent the absorption of the light beam during propagation, the weight W of the photon after each scattering can be adjusted a To achieve this, the weight change can be expressed as W a =W(1-Q sca / Q ext ), Q sca / Q ext Represents the single scattering albedo, which represents the proportion of scattering in extinction, W is the initial weight of the photon, and the absorption rate is

[0163] The local orthogonal coordinate system of the photon before scattering is denoted as (m, n, s), and the coordinate system after interaction with the medium particles is denoted as (m', n', s'). m and n are the parallel and perpendicular components of the electric field before scattering, respectively, and are unit vectors relative to the scattering plane of the previous scattering. The electric field component is the real part of the complex electric field component. The electric field component describes the actual amplitude of the electric field at a specific location, a quantity that can be directly measured by physical measurement instruments. The complex electric field component provides complete amplitude and phase information. s is the direction of motion of the photon before scattering (also known as the incident direction), and s' is the direction of motion of the photon after scattering from the medium particles (also known as the scattering direction). The scattering direction s' and the incident direction s determine the scattering plane. The unit vectors m' and n' are the parallel and perpendicular components of the scattered light parallel to the scattering plane, respectively, and satisfy m' × n' = s'. E1, E1′, E2, and E2′ are the complex electric field components parallel to the electric field before scattering, parallel to the electric field after scattering, perpendicular to the electric field before scattering, and perpendicular to the electric field after scattering, respectively. The local coordinate transformation rules for photons before and after scattering can be abstracted through vector operations and expressed in matrix form. Each time a photon is scattered, the change in the local coordinate system satisfies the following relationship:

[0164]

[0165] where θ represents the scattering angle, Indicates the azimuth.

[0166] Similarly, the update of the complex electric field after the photon is scattered can be expressed as:

[0167]

[0168] Among them, S1 and S2 are the scattering amplitude functions with respect to the scattering angle θ, which are related to the scattering coefficient and the scattering angle function. According to Mie scattering theory, they can be expressed as:

[0169]

[0170] where a N with b N are Mie coefficients, which are functions related to the actual size of the scattering medium particles, the wavelength of the incident light, and the complex refractive index of the scattering medium particles, but have nothing to do with the scattering angle θ. N With τ N is a function of the scattering angle and is only related to the scattering angle θ, and can be expressed as:

[0171]

[0172] Among them, x r=πd / λ, which represents the relative particle size of the scattering spherical particles, where d is the actual diameter of the particle in meters and λ is the wavelength. The complex refractive index of the scattering spherical particles is: n sct =n real +i*n imag , where the real part n real Related to the scattering effect of medium particles, the imaginary part n imag Related to the absorption of medium particles, n imag When it is not 0, it means that the photon will be absorbed by the medium particles and cause energy attenuation. N (x) and ξ N (x) are half-integer order Bessel function and second-order Hankel function respectively. N (cosθ) and P N ′(cosθ) are the Legendre function and the first-order associated Legendre function with respect to cosθ, respectively. Indicates along The intensity normalization factor of the scattered light propagating in the direction is expressed as:

[0173]

[0174] Among them, the symbol Indicates taking the real part, * indicates taking the conjugate, is the azimuth, and |E1| 2 +|E2| 2 =1.

[0175] S500, determine whether the photon survives by selecting the survival roulette wheel. If yes, return to step S200 and continue to simulate the subsequent behavior of the photon. If not, the photon no longer survives and enter step S600.

[0176] When a photon fails to reach the receiving surface during transmission, its weight decreases as it travels. When it falls below the set annihilation value, it indicates that the photon has annihilated during its motion and is not recorded on the receiving surface. This is because even when the photon reaches the receiving surface, its contribution to the beam intensity is negligible. Ignoring annihilated photons can speed up program execution, and therefore simulation efficiency. When a photon reaches the receiving surface and its weight exceeds the annihilation value, the photon ceases its motion and the accumulated electric field information is recorded.

[0177] S600, determine whether all photons have been calculated, if so, go to step S700, if not, return to step S100 to simulate the scattering process of the next photon.

[0178] S700: Calculate the transmission coefficient and the sea surface beam influence factor and apply them to the accumulated electric field to obtain the electric field intensity, and record and save it.

[0179] After the photon is scattered by the medium particles n times, its final local orthogonal coordinate system is (m (n) ,n (n) ,s (n) ), for the convenience of statistics, the final motion direction of all photons is limited to s (n) All (u d ,v d ,w d )=(0,0,1), that is, it propagates in the positive direction of the z axis and reaches the detection surface. (n) and n (n) The parallel and perpendicular electric field components in the direction are The corresponding electric field components in the x, y, and z directions can be according to Vector transformation is obtained. Taking into account the interaction between photons and scattering media and the phase delay caused by the propagation of photons in the scattering medium, the electric field components in the x, y, and z directions after photon superposition can be expressed as:

[0180]

[0181] Where G is the x, y, and z directions, k is the wave number, l (n) is the total path length traveled by a photon after being scattered n times.

[0182] In this embodiment, the detection surface is set at z=z d The actual photon reaches the final scattering position after n scatterings, and the coordinate in the z-axis direction is z (n) Generally speaking, the photon will not fall directly on the detection surface (the coordinate in the z-axis direction is z d ) is received, i.e. z (n) >z d or z (n) ≤z d In this case, the phase delay from the final scattering position of the photon to the detection surface needs to be considered, which can be expressed as In addition, there is an uncounted scattering process from the final scattering position to the detection position, which causes the attenuation of the photon energy. Therefore, a weight attenuation factor can be set as To equivalent the attenuation effect, the scattering cross section l sct is the random step size for scattering.

[0183] Taking all the above factors into consideration, the electric field components of the photons received by the detection surface in the x, y, and z directions can be expressed as:

[0184]

[0185] w d represents the direction cosine of the photon arriving at the receiving plane.

[0186] From the Fresnel formula, the total transmittance of a light beam passing through the sea surface is given by:

[0187] T down =T wa1 T wa2 ;

[0188] Where T wa1 Indicates the transmittance of the air-sea interface itself, satisfying α represents the incident angle of the light beam from the air-sea interface. According to the refraction theorem, the expression of the refraction angle is n1 and n2 represent the refractive index of seawater and air respectively. wa2 It represents the transmittance caused by sea surface materials (such as foam on the sea surface and other factors). When the wind speed p≤9m / s, T wa2 =1-1.2×10 -5 ×p 3.3 , when the wind speed is p>9m / s, T wa2 =1-1.2×10 -5 ×p 3.3 ×(0.225p-0.99). T down Expressed as the total transmittance of the light beam transmitted downward from air;

[0189] The electric field components in the x, y, and z directions of the Bessel-Gaussian beam after it passes through the sea surface are:

[0190]

[0191] in represents the electric field of each component of the Bessel-Gaussian beam after the beam is scattered multiple times through the air. is the wave number of the Bessel-Gaussian beam, λ is the beam wavelength, z h represents the sea surface height fluctuation function, n1 is the refractive index of seawater, and T is the total transmittance. The total electric field intensity E ins The size can be expressed using the following formula:

[0192]

[0193] Among them E x 、E y 、E z are the electric field components in the x, y, and z directions, respectively.

[0194] like Figure 2a 、 Figure 2b 、 Figure 2c As shown, Figure 2a 、 Figure 2b 、 Figure 2c The light field distribution of the beam intensity changes when there is no wind, at a wind speed of 6m / s, and at a wind speed of 8m / s. As the wind speed on the sea surface increases, the intensity distribution of the Bessel-Gaussian beam gradually becomes distorted. When the wind speed on the sea surface reaches 8m / s, the light intensity distribution becomes severely distorted. This is because the greater the wind speed on the sea surface, the lower the transmittance of the sea surface, and the transmitted light is also affected by the obstruction of the sea surface itself. As the wind speed increases, this obstruction becomes more significant. From the transmitted light intensity distribution diagram, the higher the wind speed on the sea surface, the more uneven the distribution of the laser transmitted light intensity. Especially when the relative height difference of the sea surface is large, the transmission of light is significantly obstructed, resulting in very little light being transmitted.

[0195] In an experimental example, the emission beam uses a Bessel-Gaussian beam that is common and easy to generate in the laboratory. To balance the code execution efficiency and simulation accuracy, the following parameters are used:

[0196]

[0197]

[0198] When a light beam is transmitted from underwater to the sea surface or from air to underwater, it will experience multiple scattering. Existing similar technologies have failed to effectively reflect this phenomenon. The present invention adopts the electric field Monte Carlo method to divide the light beam into multiple photons, simulating the multiple collisions of these photons with the scattering medium in the seawater during propagation, thereby truly reflecting the attenuation of the light beam intensity caused by multiple scattering when the light beam is transmitted from underwater to the sea surface.

[0199] See also Figure 3 Based on the same inventive concept, this embodiment also provides a vortex light cross-sea transmission simulation system based on the electric field Monte Carlo method, including:

[0200] The initialization module is used to load photons and perform initialization settings, including setting the initial coordinates of the photons, initial direction cosines, initial parallel components of the complex electric field and initial vertical components of the complex electric field. The initial parallel components of the complex electric field and initial vertical components of the complex electric field are set to and E2 = 0, where i represents the imaginary unit, l represents the topological charge of the vortex beam, is the azimuth;

[0201] Position change detection module, used to calculate the position change of photons during random walk in the channel;

[0202] The first judgment module is used to judge whether the photon reaches the detection surface according to the change of the photon's position. If yes, it returns to the initialization module to simulate the scattering process of the next photon; if not, it enters the first calculation module;

[0203] The first calculation module is used to calculate the absorption rate of photons and local orthogonal coordinate transformation;

[0204] The second judgment module is used to determine whether the photon survives through the survival roulette selection. If yes, it returns to the position change detection module to continue simulating the subsequent behavior of the photon. If no, the photon no longer survives and enters the third judgment module;

[0205] The third judgment module is used to judge whether all photons have been calculated. If so, it enters the second calculation module. If not, it returns to the initialization module to simulate the scattering process of the next photon;

[0206] The second calculation module is used to calculate the cumulative electric field under the influence of the sea surface light beam factor, obtain the electric field intensity, and record and save it.

[0207] The specific execution process of each component module in the above system can be found in the relevant description of the above method, which will not be repeated here.

[0208] like Figure 4 As shown, this embodiment also provides an electronic device, which may include a processor 41 and a memory 42, wherein the memory 42 is coupled to the processor 41. It is worth noting that this figure is exemplary, and other types of structures may be used to supplement or replace this structure to implement data extraction, report generation, communication or other functions.

[0209] like Figure 4 As shown, the electronic device may further include: an input unit 43, a display unit 44 and a power supply 45. It is worth noting that the electronic device does not necessarily have to include Figure 4 In addition, electronic devices may also include Figure 4 For components not shown, reference may be made to the prior art.

[0210] The processor 41 is sometimes also called a controller or an operation control, and may include a microprocessor or other processor devices and / or logic devices. The processor 41 receives inputs and controls the operations of various components of the electronic device.

[0211] The memory 42 may be, for example, one or more of a cache, flash memory, a hard drive, a removable medium, a volatile memory, a non-volatile memory, or other suitable devices, and may store information such as configuration information of the processor 41 and instructions executed by the processor 41. The processor 41 may execute programs stored in the memory 42 to implement information storage or processing. In one embodiment, the memory 42 also includes a buffer memory to store intermediate information.

[0212] An embodiment of the present invention further provides a computer program product, comprising computer-readable instructions. When the computer-readable instructions are executed in an electronic device, the program product enables the electronic device to perform the operating steps included in the method of the present invention.

[0213] An embodiment of the present invention further provides a storage medium storing computer-readable instructions, wherein the computer-readable instructions enable an electronic device to execute the operation steps included in the method of the present invention.

[0214] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the composition and steps of each example according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0215] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0216] The above-described embodiments are merely specific implementations of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications, substitutions, and improvements within the technical scope disclosed in the present invention, and such modifications, substitutions, and improvements are intended to be encompassed within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method, characterized in that: The following steps are involved: S10, loading photons and performing initialization settings, including setting the initial coordinates of the photons, initial direction cosines, initial parallel components of the complex electric field and initial vertical components of the complex electric field. The initial parallel components of the complex electric field and initial vertical components of the complex electric field are set to and E2 = 0, where i represents the imaginary unit, l represents the topological charge of the vortex beam, is the azimuth; S20, calculates the position change of the photon during its random walk in the channel; S30, judging whether the photon reaches the detection surface according to the change in the position of the photon, if yes, returning to step S10, simulating the scattering process of the next photon; if not, proceeding to step S40; S40, calculating the absorption rate of photons and local orthogonal coordinate transformation, and then proceeding to step S50; S50, determining whether the photon survives by selecting the survival roulette wheel. If yes, return to step S20 and continue to simulate the subsequent behavior of the photon. If no, the photon no longer survives and proceed to step S60; S60, determine whether all photons have been calculated, if yes, proceed to step S70, if not, return to step S10 to simulate the scattering process of the next photon; S70, calculating the cumulative electric field under the influence of the light beam on the sea surface, obtaining the electric field intensity, and recording and saving the information; In S10, the initial radial coordinate ρ0 is obtained by sampling, and then the Cartesian coordinate system is used. The initial coordinate of the photon is expressed as: The initial direction cosines are expressed as: where θ0 and are the elevation and azimuth angles in the direction of photon emission; θ0 is obtained by the following formula: Where r3 and r4 represent random numbers between 0 and 1, which are uniformly distributed within the range of 0 to 1, and θ1 is the divergence angle of the light beam; The process of sampling the initial radial coordinates of the input OAM beam using the rejection algorithm is as follows: (1) Generate a random number χ, satisfying χ~U(0,1), and calculate a radial coordinate ρ0=χR m ; R m is the cutoff radius of the incident OAM beam; (2) Generate a random number satisfy If satisfied Then accept this ρ0, where E0 is a constant, ω0 is the beam waist radius, k ρ is the radial wave vector, J l (·) represents the first-order Bessel function. The "·" in the function represents the parameters, E0, ω0, k ρ , l can be set directly.

2. The method for simulating vortex light transmission across sea surface based on the electric field Monte Carlo method according to claim 1, characterized in that: In S20, the position coordinates before photon scattering are defined as (x, y, z), the position coordinates after scattering are defined as (x′, y′, z′), and the direction cosines before photon scattering are defined as (u, v, w). Thus, we have: x′=x+ul sct y′=y+vl sct z′=z+wl sct ; The direction cosines are updated after scattering by: l sct is the propagation distance of the photon after one scattering, l sct =-ln(ζ) / Q sca , Q sca is the scattering coefficient, ζ is a random number uniformly distributed between 0 and 1; θ、 are the scattering angle and azimuth angle, respectively.

3. The method for simulating vortex light transmission across sea surface based on the electric field Monte Carlo method according to claim 2, characterized in that: In S40, the local orthogonal coordinate system of the photon before scattering is recorded as (m, n, s), and the coordinate system after interaction with the medium particle is recorded as (m', n', s'), m' × n' = s'; each time the photon is scattered, the change of the local coordinate system satisfies the following relationship: where θ represents the scattering angle, Indicates azimuth; The update of the complex electric field after the photon is scattered can be expressed as: Where E1, E1′, E2, and E2′ are the complex electric field components parallel to the electric field before scattering, parallel to the electric field after scattering, perpendicular to the electric field before scattering, and perpendicular to the electric field after scattering, respectively; S1 and S2 are the scattering amplitude functions with respect to the scattering angle θ. where a N with b N They are Mie coefficient, π N With τ N is the scattering angle function, Among them, x r =πd / λ, which represents the relative particle size of the scattering spherical particles, where d is the actual diameter of the particle in meters, and λ is the wavelength. The complex refractive index of the scattering spherical particles is: n sct =n real +i*n imag , where n real represents the real part, n imag represents the imaginary part; ψ N (x) and ξ N (x) are half-integer order Bessel function and Hankel function, P N (cosθ) and P N ′(cosθ) are the Legendre function and the first-order associated Legendre function about cosθ, Indicates along The intensity normalization factor of the scattered light propagating in the direction is expressed as: Among them, the symbol means taking the real part, * means taking the conjugate, |E1| 2 +|E2| 2 =1.

4. The method for simulating vortex light transmission across sea surface based on the electric field Monte Carlo method according to claim 3, characterized in that: In S70, the electric field components of the photons received by the detection surface in the x, y, and z directions can be expressed as: in, m (n) and n (n) The parallel electric field component and the perpendicular electric field component in the direction, i is an imaginary unit, is the wave number of the Bessel-Gaussian beam, λ is the beam wavelength, l (n) is the total path length traveled by the photon after being scattered n times, represents the phase extension from the final scattering position of the photon to the detection surface, represents the photon energy weight attenuation factor; z d is the z-axis coordinate, the scattering cross section w d represents the direction cosine of the photon arriving at the receiving plane, z (n) is the coordinate of the z-axis direction of the final scattering position after the photon is scattered n times; G is the three directions of x, y, and z. The final local orthogonal coordinate system after the photon is scattered by the medium particles n times is (m (n) ,n (n) ,s (n) ); When the light beam is transmitted from underwater to the sea surface, the electric field components in the x, y, and z directions of the Bessel-Gaussian beam after passing through the sea surface are: Where T wa1 Indicates the transmittance of the air-sea interface itself, satisfying α represents the incident angle of the light beam from the sea-air interface, β represents the refraction angle, T wa2 Indicates the transmittance caused by sea surface materials; z h represents the sea surface height fluctuation function, n1 and n2 represent the refractive index of seawater and air respectively, T up It represents the total transmittance of the light beam from underwater to the sea surface; When the light beam is transmitted from the air to the sea surface, the electric field components in the x, y, and z directions of the Bessel-Gaussian beam after passing through the sea surface are: T down =T wa1 T wa2 ; The total electric field strength E ins The size of is expressed using the following formula: Among them E x 、E y 、E z are the electric field components in the x, y, and z directions, respectively.

5. A vortex light cross-sea transmission simulation system based on the electric field Monte Carlo method, characterized in that: include: The initialization module is used to load photons and perform initialization settings, including setting the initial coordinates of the photons, initial direction cosines, initial parallel components of the complex electric field and initial vertical components of the complex electric field. The initial parallel components of the complex electric field and initial vertical components of the complex electric field are set to and E2 = 0, where i represents the imaginary unit, l represents the topological charge of the vortex beam, is the azimuth; Position change detection module, used to calculate the position change of photons during random walk in the channel; The first judgment module is used to judge whether the photon reaches the detection surface according to the change of the photon's position. If yes, it returns to the initialization module to simulate the scattering process of the next photon; if not, it enters the first calculation module; The first calculation module is used to calculate the absorption rate of photons and local orthogonal coordinate transformation; The second judgment module is used to determine whether the photon survives through the survival roulette selection. If yes, it returns to the position change detection module to continue simulating the subsequent behavior of the photon. If no, the photon no longer survives and enters the third judgment module; The third judgment module is used to judge whether all photons have been calculated. If so, it enters the second calculation module. If not, it returns to the initialization module to simulate the scattering process of the next photon; The second calculation module is used to calculate the cumulative electric field under the influence of the sea surface beam factor, obtain the electric field intensity, and record and save it; The initialization module performs the following operations when setting the initial coordinates and initial direction cosines of the photon: first, the initial radial coordinate ρ0 is obtained by sampling, and then the Cartesian coordinate system is used. The initial coordinates of the photon are expressed as: The initial direction cosines are expressed as: where θ0 and are the elevation and azimuth angles in the direction of photon emission; θ0 is obtained by the following formula: Where r3 and r4 represent random numbers between 0 and 1, which are uniformly distributed within the range of 0 to 1, and θ1 is the divergence angle of the light beam; The process of sampling the initial radial coordinate of the input OAM beam using the rejection algorithm is as follows: (1) Generate a random number χ, satisfying χ ~ U(0,1), and calculate a radial coordinate ρ0 = χR m ; (2) Generate a random number satisfy If satisfied Then accept this ρ0, where E0 is a constant, ω0 is the beam waist radius, k ρ is the radial wave vector, J l (·) represents the first-order Bessel function. The "·" in the function represents the parameters, E0, ω0, k ρ , l can be set directly.

6. A computer program product comprising computer-readable instructions, characterized in that When executed by a processor, the computer-readable instructions implement the steps of the method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method according to any one of claims 1 to 4.

7. A computer-readable storage medium comprising computer-readable instructions, characterized in that: When executed by a processor, the computer-readable instructions implement the steps of the method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method according to any one of claims 1 to 4.

8. An electronic device, characterized in that: include: Memory, which stores program instructions; A processor is connected to the memory and executes program instructions in the memory to implement the steps of the method for simulating vortex light transmission across the sea surface based on the electric field Monte Carlo method as described in any one of claims 1 to 4.

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