Atmospheric disturbance analysis method and system based on bohmian mechanics and waveguide geometric optics

Abstract

The application discloses an atmospheric disturbance analysis method and system based on Bohm mechanics and waveguide geometric optics, and relates to the technical field of optical simulation and emulation.The application effectively solves the fundamental contradiction that traditional geometric optics cannot describe diffraction effect and wave optics lacks path traceability.By introducing the Bohm mechanics thought, the phase gradient of the light field is taken as a physical quantity for driving the evolution of the light rays, while the ability of the traditional ray tracing intuitive path analysis is reserved, and the wave effects such as interference and diffraction are naturally included, so that the simulation precision comparable to the wave optics is realized in the key scenes such as beam expansion and focusing limit, and a unified simulation tool which can perform physical mechanism backtracking and ensure numerical accuracy is provided for the precise optical design, micro-nano photonic device analysis and complex medium light transmission research, and the reliability, explanation and engineering practical value of the light field simulation are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of optical simulation technology, and in particular to an atmospheric disturbance analysis method and system based on Bohmian mechanics and waveguide geometric optics. Background Technology

[0002] The study of light transmission in gradient refractive index media is of crucial significance in many cutting-edge fields such as micro-nano photonic device design, laser atmospheric transmission, and optical imaging of biological tissues. Due to the complex refractive index distribution in these media, it is difficult to obtain analytical solutions to the propagation problem, and research heavily relies on high-fidelity numerical simulation techniques. Current mainstream simulation methods can be categorized into two types: geometric optics ray tracing and wave optics numerical simulation.

[0003] Traditional geometric optics ray tracing methods, based on Fermat's principle, characterize the propagation path of light energy by solving the differential equations of light rays. This method offers an intuitive physical picture and high computational efficiency, making it widely used in large-scale light transmission simulations. However, its theoretical framework fundamentally ignores the wave nature of light and cannot describe effects such as diffraction and interference. Therefore, it suffers from fundamental deviations when simulating beam expansion, focusing, and micro / nano-scale light fields, failing to meet the demands of modern precision optical design and analysis.

[0004] To accurately describe the wave properties of light fields, wave optics methods (such as solving the Helmholtz equations) offer another approach. While these methods can accurately obtain the complex amplitude distribution of the light field, they typically output the data in a "whole field" format, lacking an intuitive representation of local energy transfer paths. This makes it difficult to support diagnostic needs with clear physical orientations, such as optical path tracing and local interference analysis, and limits their application in system optimization and mechanism research.

[0005] To balance the intuitiveness of optical paths with the precision of wave fields, researchers have introduced Bohmian mechanics from quantum mechanics into optical simulation, proposing a new framework for waveguide geometric optics ray tracing. This method, through an optical-quantum analogy, utilizes the phase gradient of the optical field to drive the ray trajectory, naturally introducing wave effects into the traditional ray model. This achieves a unification of traceable "rays" and precise evolution of the "wavefront," demonstrating significant theoretical advantages.

[0006] However, transforming this framework into a stable and efficient practical simulation tool still faces a series of technical bottlenecks: First, its ray evolution depends on the global phase gradient obtained in real time from the full-wave simulation, which has huge computational overhead and is easily affected by numerical errors; Second, in strong gradient media or complex light fields, the stability of phase extraction and gradient calculation is poor, which restricts the robustness of the method; Third, the existing implementation lacks a systematic parameter optimization and verification process, resulting in insufficient engineering practicality. Summary of the Invention

[0007] The purpose of this invention is to provide an atmospheric disturbance analysis method and system based on Bohmian mechanics and waveguide geometric optics. This aims to improve the technical problems of insufficient accuracy of traditional ray models due to neglecting wave effects, which cannot simultaneously meet the requirements of physical accuracy and path intuition. Furthermore, the beam propagation curves obtained by traditional geometric optics methods only reflect geometric deflection and cannot reflect wave effects such as beam spread, intensity flicker, and wavefront distortion caused by atmospheric disturbances. This results in an inherent defect in the assessment of the impact of atmospheric disturbances and fails to meet the dual requirements of physical accuracy and path traceability in atmospheric optical transmission analysis.

[0008] To achieve the above-mentioned objectives, the embodiments of the present invention provide the following technical solutions:

[0009] An atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics, comprising:

[0010] Set up a light field simulation environment and simulate the propagation of the light field using a Gaussian laser beam. Calculate the initial complex amplitude distribution of the Gaussian laser beam based on a preset initial beam waist radius.

[0011] Based on Bohm's mechanical theory, an optical-quantum analogy is made between the Bohm guiding equation and the paraxial Helmholtz equation to construct the optical-Bohm trajectory equation.

[0012] Based on the initial complex amplitude distribution, the transverse rate of change of the ray trajectory of the Gaussian laser beam is calculated by using the distributed Fourier method and the optical-Bohm trajectory equation.

[0013] The position of the Gaussian laser beam is updated based on the lateral rate of change of the ray trajectory and iterated to generate Gaussian trajectory data during the simulation process.

[0014] Based on Gaussian trajectory data, a curve showing the variation of the waist radius is generated; atmospheric disturbance analysis is then performed based on the curve showing the variation of the waist radius, and atmospheric disturbance analysis results are generated.

[0015] Furthermore, the formula corresponding to the optical-Bohm trajectory equation is:

[0016] ;

[0017] in, This represents the transverse phase gradient of a Gaussian laser beam. Indicates wave number, This indicates the lateral position of a Gaussian laser beam. This represents the longitudinal propagation distance of a Gaussian laser beam. This represents the rate of lateral change of the light trail.

[0018] In the aforementioned process, this invention constructs an optical-Bohm trajectory equation driven by phase gradient by optical-quantum analogy between the Bohm guiding equation and the paraxial Helmholtz equation, fundamentally injecting phase information from wave optics into the ray evolution framework of geometric optics. This core feature allows the method to naturally encompass wave effects such as diffraction and interference while preserving the intuitiveness and traceability of ray paths, thus solving the fundamental technical problem of insufficient physical accuracy in traditional geometric optics ray tracing when describing beam propagation under atmospheric disturbances due to neglecting wave properties. Furthermore, by comparing the beam waist radius in the actual atmosphere with the theoretical curve under ideal undisturbed conditions, beam waist distortion is extracted. Combined with the statistical characteristics of ray trajectory offset, key parameters such as atmospheric turbulence intensity and atmospheric coherence length can be inverted. Further, by utilizing the phase distortion function extracted from the complex amplitude field, wavefront distortion can be quantified and its impact on light intensity scintillation and angle of arrival fluctuations can be evaluated. The resulting atmospheric disturbance analysis provides a physically accurate and path-traceable analytical tool for evaluating laser atmospheric transmission effects, designing adaptive optics systems, and applying atmospheric optical engineering, demonstrating significant advantages in the field of light transmission research in complex atmospheric environments.

[0019] Furthermore, when a Gaussian laser beam propagates in a vacuum, the calculation of the lateral rate of change of the trajectory of the Gaussian laser beam includes:

[0020] Based on the initial complex amplitude distribution, the propagation location of the Gaussian laser beam is calculated using the spectral method and the distributed Fourier method. Complex amplitude field at time;

[0021] The complex amplitude field is numerically differentiated using the central difference method to generate the corresponding transverse gradient field.

[0022] Based on the transverse gradient field, the corresponding light intensity is calculated, and the phase is calculated by combining the phase function;

[0023] Based on phase, the lateral variation rate of the ray trajectory of a Gaussian laser beam is calculated using the optical-Bohm trajectory equation.

[0024] Furthermore, the calculated Gaussian laser beam propagates to the position The complex amplitude field at time includes:

[0025] Based on the Helmholtz equation, paraxial conditions, and initial complex amplitude distribution, the paraxial Helmholtz equation is generated.

[0026] The propagation evolution of a Gaussian laser beam is performed using spectral methods, and the complex amplitude of the Gaussian laser beam propagating to any position is converted into the wavenumber domain through two-dimensional Fourier transform, generating the Helmholtz equation in the wavenumber domain.

[0027] Based on the Helmholtz equation in the wavenumber domain, the wavenumber domain is transformed back to the spatial domain through inverse Fourier transform to obtain the position. The complex amplitude field at that time.

[0028] Furthermore, when a Gaussian laser beam propagates in a gradient medium, the calculation of the lateral rate of change of the trajectory of the Gaussian laser beam includes:

[0029] Construct a Luneburg lens model and obtain the background refractive index;

[0030] Based on the background refractive index and initial complex amplitude distribution, the propagation location of the Gaussian laser beam is calculated using the spectral method, the Luneburg lens model, and the distributed Fourier method. The complex amplitude field in the first half of the refractive index step and the second half of the refractive index step;

[0031] The complex amplitude field is numerically differentiated using the central difference method to generate the corresponding transverse gradient field.

[0032] Based on the transverse gradient field, the corresponding light intensity is calculated, and the phase is calculated by combining the phase function;

[0033] Based on phase, the lateral variation rate of the ray trajectory of a Gaussian laser beam is calculated using the optical-Bohm trajectory equation.

[0034] In the above process, this invention achieves synchronous wave field calculation and ray tracing for light propagation under arbitrary refractive index distribution by using a unified optical-Bohm trajectory equation framework and combining it with an adaptive wave field solution strategy for different media. It can accurately quantify and visualize the impact of wave effects (such as diffraction and aberration) on the real light path, and solves the in-depth technical problem of inaccurate energy path prediction and lack of physical mechanism caused by completely ignoring wave properties when traditional geometric optics simulates light propagation in strong gradient and non-uniform media.

[0035] Furthermore, the generated atmospheric disturbance analysis results include:

[0036] Based on Gaussian trajectory data, the waist radius of the beam is calculated at different propagation distances, and the curve of the waist radius variation is plotted.

[0037] Plot the ideal waist radius variation curve, calculate the difference between the ideal waist radius variation curve and the waist radius variation curve, and generate the waist distortion curve;

[0038] The lateral position offset is calculated based on Gaussian trajectory data and inverted using the Kolmogorov turbulence theory model to generate turbulence parameter inversion results.

[0039] Based on the complex amplitude field, a phase distortion function is constructed and wave effect assessment is performed to generate wavefront distortion characteristics and wave effect assessment results.

[0040] By integrating the waist distortion curve, turbulence parameter inversion results, wavefront distortion characteristics, and wave effect assessment results, atmospheric disturbance analysis results are generated.

[0041] In the aforementioned process, this invention quantifies beam spread (beam waist distortion) and ray deflection statistics (turbulence parameter inversion) at the macroscopic level, and analyzes wavefront distortion and the resulting intensity scintillation and angle of arrival fluctuations at the microscopic level, achieving a full-chain analysis from "ray path" to "wave effect." This comprehensive diagnostic capability effectively solves the inherent contradiction that traditional geometric optics cannot describe wave effects such as diffraction and interference in atmospheric disturbances, while pure wave optics struggles to trace ray paths and local disturbance mechanisms. It provides an analytical tool for atmospheric light transmission research that combines physical accuracy and path traceability, significantly improving the depth of understanding and assessment capabilities of beam propagation behavior in complex atmospheric environments.

[0042] An atmospheric disturbance analysis system based on Bohmian mechanics and waveguide geometric optics includes:

[0043] The simulation module is used to set up the light field simulation environment and simulate the propagation of the light field through a Gaussian laser beam, and calculate the initial complex amplitude distribution of the Gaussian laser beam based on the preset initial beam waist radius.

[0044] A module is built to construct an optical-Bohm trajectory equation by making an optical-quantum analogy between the Bohm guiding equation and the paraxial Helmholtz equation based on Bohm's mechanical theory.

[0045] The calculation module is used to calculate the lateral rate of change of the ray trajectory of a Gaussian laser beam based on the initial complex amplitude distribution, using the distributed Fourier method and the optical-Bohm trajectory equation.

[0046] The iteration module is used to update the position of the Gaussian laser beam based on the lateral change rate of the ray trajectory and iterate to generate Gaussian trajectory data during the simulation process.

[0047] The analysis module is used to generate a beam waist radius variation curve based on Gaussian trajectory data; and to perform atmospheric disturbance analysis based on the beam waist radius variation curve to generate atmospheric disturbance analysis results. Attached Figure Description

[0048] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1This is a flowchart of the method for propagation in a vacuum in Embodiment 1 of the present invention;

[0050] Figure 2 This is a schematic diagram of the propagation ray distribution of 10,000 Gaussian laser beams in Embodiment 1 of the present invention;

[0051] Figure 3 This is a schematic diagram of the waist radius calculated by this method in Embodiment 1 of the present invention;

[0052] Figure 4 This is a schematic diagram of the waist radius calculated by this method in Embodiment 1 of the present invention;

[0053] Figure 5 The graph shows the variation curves of the beam waist radius in the geometric optics, wave optics methods, and the present invention in Embodiment 1.

[0054] Figure 6 This is a system structure diagram in Embodiment 1 of the present invention;

[0055] Figure 7(a) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.60 × 10 -4 The graph shows the change in the refractive index distribution of the Gaussian spot as it enters the Luneburg lens intact and the spot distribution as it exits;

[0056] Figure 7(b) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.57 × 10⁻⁶. -4 The graph shows the change in the refractive index distribution of the Gaussian spot as it enters the Luneburg lens intact and the spot distribution as it exits;

[0057] Figure 7(c) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.47 × 10⁻⁶. -4 The graph shows the change in the refractive index distribution of the Gaussian spot as it enters the Luneburg lens intact and the spot distribution as it exits;

[0058] Figure 7(d) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.29 × 10⁻⁶. -4 The graph shows the change in the refractive index distribution of the Gaussian spot as it enters the Luneburg lens intact and the spot distribution as it exits;

[0059] Figure 7(e) shows the change in the refractive index distribution of the Gaussian spot from its complete entry into the Luneburg lens to its exit when the beam waist radius is 0 in Embodiment 2 of the present invention.

[0060] Figure 7(f) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.40 × 10 -4 The graph shows the change in the refractive index distribution of the Gaussian spot as it enters the Luneburg lens intact and the spot distribution as it exits;

[0061] Figure 8This is a light distribution diagram of the Gaussian spot of the Luneburg lens in Embodiment 2 of the present invention;

[0062] Figure 9(a) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.60 × 10 -4 Distribution of Gaussian spot points in the xy plane at different propagation distances at time m;

[0063] Figure 9(b) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.24 × 10⁻⁶. -4 Distribution of Gaussian spot points in the xy plane at different propagation distances at time m;

[0064] Figure 9(c) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.05 × 10⁻⁶. -4 Distribution of Gaussian spot points in the xy plane at different propagation distances at time m;

[0065] Figure 9(d) shows the waist radius of the device in Embodiment 2 of the present invention, which is 0.30 × 10 -4 Distribution of Gaussian spot points in the xy plane at different propagation distances at time m;

[0066] Figure 10 This is a comparison graph showing the curves of the beam waist radius of the Gaussian spot changing with the propagation distance in the three methods of Embodiment 2 of the present invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0068] Example 1:

[0069] Please see Figure 1 This embodiment provides an atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics. Figure 1The execution entity of the method shown can be a software and / or hardware device. The execution entity of this application can include, but is not limited to, at least one of the following: user equipment, network equipment, etc. User equipment can include, but is not limited to, computers, smartphones, personal digital assistants (PDAs), and the aforementioned electronic devices. Network equipment can include, but is not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of computers or network servers. Cloud computing is a type of distributed computing, consisting of a super virtual computer composed of a group of loosely coupled computers. This embodiment does not impose any limitations on this.

[0070] When a Gaussian laser beam propagates in a vacuum, an atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics is employed, including:

[0071] S1. Set up the light field simulation environment and simulate the propagation of the light field using a Gaussian laser beam. Calculate the initial complex amplitude distribution of the Gaussian laser beam based on the preset initial beam waist radius.

[0072] Traditional ray tracing theory is achieved by solving the ray propagation equation in any general medium. The corresponding formula is:

[0073] ;

[0074] in, Represents the refractive index gradient of the medium. Represents the position vector (ray radius) of a point along the trajectory of a ray. Indicates the arc length along the propagation path. It represents the refractive index of the propagation medium.

[0075] make ,but:

[0076] ;

[0077] in, This represents the ray vector.

[0078] In traditional methods,

[0079] By simply substituting the initial conditions and refractive index distribution field into the above formula and continuously updating the step size, the spot distribution at any position can be obtained. However, traditional ray tracing does not consider the potential energy of the spot distribution, and its ray-traced spot always propagates in a straight line in a vacuum. Ray tracing based on Bohmian mechanics, due to diffraction effects, will continuously diverge even when propagating freely in a vacuum, and is more sensitive to wave optics effects. Therefore, the propagation of a scalar Gaussian laser beam is simulated, with a preset initial beam waist radius... (0.0608mm), given its initial complex amplitude distribution The corresponding formula is:

[0080] ;

[0081] ;

[0082] in, This represents the half-width of the initial beam waist radius of a Gaussian laser beam. It represents pi (π).

[0083] S2. Based on Bohm's mechanical theory, optical-quantum analogies are made between the Bohm guiding equation and the paraxial Helmholtz equation to construct the optical-Bohm trajectory equation.

[0084] Traditional ray tracing methods achieve good simulation results for large-scale light transmission, but suffer from significant errors at smaller scales. This is because traditional geometric optics ray tracing cannot account for the diffraction effect of wave optics, i.e., the interaction between light rays (the potential energy of the light spot distribution), and therefore cannot accurately describe the transmission of the light field. In Bohmian mechanics, the evolution of quantum systems can be understood through probability streamlines or trajectories. These streamlines or trajectories represent the paths of probability flow, equating probability density with electromagnetic energy density, and quantum density current or quantum flux with the Poynting vector. Thus, the trajectory equations constructed using Bohmian mechanics can describe the path of (electromagnetic) flow, adding wave effects while retaining the intuitiveness of geometric optics, making ray tracing more effective. Therefore, this embodiment chooses to analogize the Bohmian guiding equation to paraxial optics to obtain a new ray equation, i.e., constructing an optical-Bohmian trajectory equation.

[0085] In Bohmian mechanics, the evolution of a quantum system can be described by a "deterministic trajectory guided by a wave function," where the quantum wave function is... Decompose into modules and phase The particle velocity is determined by the phase gradient. The trajectory is determined to be a "probability streamline guided by the phase of the wave function." This is combined with probability flow. The definition is "probability per unit volume multiplied by particle velocity", that is... ( For particle velocity, (Probability density) and the relationship between probability flow and phase gradient ( (For mass), we can obtain Bohm's guiding equation:

[0086] ;

[0087] Since the form of the paraxial Helmholtz equation is equivalent to that of the Schrödinger equation, this idea from Bohmian mechanics can be extended to the propagation of light fields in wave optics. By mapping the probability density in Bohmian mechanics to the electromagnetic energy density in optics, and by analogy of the probability flow to the time-averaged Poynting vector describing the spatial flow of electromagnetic energy, the optical-Bohm trajectory equation can be obtained. The corresponding formula is:

[0088] ;

[0089] in, This represents the transverse phase gradient of a Gaussian laser beam. Indicates wave number, This indicates the lateral position of a Gaussian laser beam. This represents the longitudinal propagation distance of a Gaussian laser beam. This represents the rate of lateral change of the light trail.

[0090] In this process, the time derivative in Bohmian mechanics is... Analogous to the longitudinal distance derivative in optics Position vector Analogous to lateral position in optics Lateral phase gradient The phase gradient corresponding to the Bohm guiding equation , wave number Mass in Bohm's guiding equation Correspondingly, by solving this equation, the trajectories of each ray in the light spot can be obtained. The streamlines (rays) of electromagnetic energy are defined by the "phase gradient of optical complex amplitude," which retains the "ray intuition" of geometric optics and can also describe the diffraction, interference and other effects of wave optics.

[0091] S3. Based on the initial complex amplitude distribution, the transverse variation rate of the Gaussian laser beam trajectory is calculated using the distributed Fourier method and the optical-Bohm trajectory equation.

[0092] S3 includes:

[0093] S3-1. Based on the initial complex amplitude distribution, calculate the propagation position of the Gaussian laser beam using the spectral method and the distributed Fourier method. Complex amplitude field at time;

[0094] S3-2. The complex amplitude field is numerically differentiated using the central difference method to generate the corresponding transverse gradient field.

[0095] S3-2 includes:

[0096] S3-2-1. Based on the Helmholtz equation, paraxial conditions, and initial complex amplitude distribution, generate the paraxial Helmholtz equation;

[0097] Specifically, for monochromatic electromagnetic waves, the complex amplitude satisfies the Helmholtz equation, that is:

[0098] ;

[0099] in, Represents the gradient. It represents the spatial complex amplitude.

[0100] Assuming the beam propagates primarily along the positive z-axis, then let Substitute this into the Helmholtz equation and then use the paraxial condition: The paraxial Helmholtz equation is obtained:

[0101] ;

[0102] in, Represents the natural constant. Represents the imaginary unit. Represents partial derivatives, Indicates the horizontal Laplace operator. This represents the complex amplitude at position z in the wavenumber domain.

[0103] S3-2-2. The propagation evolution of the Gaussian laser beam is carried out using the spectral method, and the complex amplitude of the Gaussian laser beam propagating to any position is converted into the wavenumber domain through two-dimensional Fourier transform, generating the Helmholtz equation in the wavenumber domain.

[0104] Specifically, propagation evolution is performed using spectral methods, and a two-dimensional Fourier transform is applied to the transverse coordinates of the Gaussian laser beam to the wavenumber domain. The transformation formula is as follows:

[0105] ;

[0106] in, , Represents a two-dimensional Fourier transform. Indicates double integral, Represents the transverse wave vector. , These are two-dimensional vectors representing transverse wave vectors.

[0107] Based on the transformation formula, the paraxial Helmholtz equation is transformed to obtain the initial Helmholtz equation in the wavenumber domain, and the corresponding formula is:

[0108] ;

[0109] ;

[0110] in, This represents the square of the complex amplitude gradient.

[0111] By modifying the initial Helmholtz equation in the wavenumber domain, we obtain the Helmholtz equation in the wavenumber domain:

[0112] ;

[0113] ;

[0114] in, Indicates position The complex amplitude field at time. Initial complex amplitude distribution in the wavenumber domain. The corresponding formula is:

[0115] ;

[0116] S3-2-3. Based on the Helmholtz equation in the wavenumber domain, the wavenumber domain is transformed back to the spatial domain through the inverse Fourier transform to obtain the position. The complex amplitude field at time t is given by the following formula:

[0117] .

[0118] S3-3. Based on the transverse gradient field, calculate the corresponding light intensity, and combine it with the phase function to calculate the phase;

[0119] Specifically, the trajectory can be obtained by solving the phase gradient function. Since any complex amplitude can be written in the form of amplitude and phase, the position... The variant of the complex amplitude field at time is:

[0120] ;

[0121] in, Indicates the actual amplitude. Indicates the real phase.

[0122] And light intensity The corresponding formula is:

[0123] ;

[0124] ;

[0125] in, Represents the absolute value function. Represents the logarithmic function. Indicates the actual amplitude. It represents the conjugate of complex amplitude.

[0126] Based on:

[0127] ;

[0128] Calculate phase .

[0129] S3-4. Based on phase, the lateral variation rate of the Gaussian laser beam trajectory is calculated using the optical-Bohm trajectory equation.

[0130] Based on the formulas involved in S3-1 to S3-3, the optical-Bohm trajectory equation can be transformed into:

[0131] ;

[0132] Substituting the phase into a variant of the optical-Bohm trajectory equation, we obtain the transverse rate of change of the Gaussian laser beam's trajectory. .in, This indicates the operation of extracting the imaginary part.

[0133] S4. Update the position of the Gaussian laser beam based on the lateral change rate of the ray trajectory and iterate to generate Gaussian trajectory data during the simulation process;

[0134] Specifically, in each iteration (the number of steps the light field advances along the propagation direction), starting from the positions of 10,000 initial rays (Gaussian laser beams) randomly distributed in a Gaussian pattern, the current step number is updated by solving the Helmholtz equation, which incorporates diffraction effects and the refractive index distribution of the medium, during each propagation step. Complex amplitude field of (iteration) ,and It fully includes the effects of diffraction modulation and the refractive index distribution of gradient media (such as Luneburg lenses) in the propagation of light field.

[0135] Subsequently, the complex amplitude field Numerical processing is performed by first determining the real phase at the current step position using the phase calculation formula in S3-3, and then calculating the lateral phase gradient and its lateral rate of change using the central difference method and the optical-Bohm trajectory equation. That is, the lateral rate of change corresponding to 10,000 preset initial rays randomly distributed according to Gaussian is obtained using the same method as in S3. .

[0136] Current step number Horizontal position of light Using the initial value, according to the preset propagation step size And the lateral rate of change, using the Euler method formula:

[0137] ;

[0138] Update the ray position step by step to obtain the actual spatial position of the ray at the current step number. .

[0139] Finally, the actual spatial position of the ray at the current step is used as the new initial condition, and the entire process of "solving the Helmholtz equation to update the complex amplitude field → extracting the phase gradient and converting it into the lateral rate of change → updating the ray position using the Euler method" is repeated. The process continues to iterate along the longitudinal propagation direction (z-axis) of the light field until all steps of the preset propagation distance are calculated. Finally, the data such as the ray position, lateral rate of change, and complex amplitude field of each step in the iteration process are integrated to generate complete Gaussian trajectory data in the simulation process, realizing the generation of ray tracing trajectory based on the Bohmian mechanics.

[0140] S5. Based on Gaussian trajectory data, generate a curve showing the variation of the waist radius; based on the curve showing the variation of the waist radius, perform atmospheric disturbance analysis and generate atmospheric disturbance analysis results.

[0141] S5 includes:

[0142] S5-1. Based on Gaussian trajectory data, combined with the formula:

[0143] ;

[0144] Calculate the beam waist radius at different propagation distances and plot the beam waist radius variation curve under actual atmospheric conditions. .in, This represents the Rayleigh distance.

[0145] Simulation was performed using 10,000 Gaussian laser beams, such as... Figure 2 As shown, the Gaussian beam formed by these beams propagates along the positive z-axis and expands and diverges continuously with increasing propagation distance in a vacuum. The initial beam waist radius of the Gaussian beam is set to... .contrast Figure 3 and Figure 4 It can be seen that the waist radius has changed from the original Become It has been expanded tenfold, which is consistent with the results of theoretical calculations.

[0146] To facilitate comparison of the changes in the light spot throughout the propagation process and the differences between the results from traditional wave optics and geometric optics methods, the propagation changes of the Gaussian light spot simulated by wave optics, the results from geometric optics, and the beam waist radius of the light spot propagation in vacuum were compared. Figure 5 As shown, the improved ray tracing based on Bohm's mechanics can be seen to achieve good results in agreement with wave optics methods and analytical solutions. Moreover, compared with traditional ray tracing methods, this method can better represent the diffusion effect of a beam in a vacuum, which is something that traditional ray tracing methods cannot achieve.

[0147] S5-2. Plot the ideal waist radius variation curve, calculate the difference between the ideal waist radius variation curve and the waist radius variation curve, and generate the waist distortion curve.

[0148] Specifically, the beam waist radius under different propagation distances under ideal conditions is calculated using the analytical formula for Gaussian beam propagation, and the corresponding curves of ideal beam waist radius variation are plotted.

[0149] Calculate the difference between the ideal waist radius variation curve and the corresponding value of the waist radius variation curve at different propagation distances, and use this difference as the waist distortion for the corresponding propagation distance. Integrate the waist distortion for all propagation distances and plot the corresponding waist distortion curve.

[0150] S5-3. Calculate the lateral position offset based on Gaussian trajectory data, and perform inversion using the Kolmogorov turbulence theory model to generate turbulence parameter inversion results;

[0151] Specifically, the difference between each lateral position in the Gaussian trajectory data corresponding to each Gaussian laser beam and each lateral position in the ideal Gaussian trajectory data is calculated and used as the corresponding lateral position offset. An undisturbed ideal environment is set up, and the ideal Gaussian trajectory data is generated using the same method as in S1 to S3-1.

[0152] A spatial structure function is constructed based on the lateral position offsets, and inversion is performed using the Kolmogorov turbulence theory model to generate turbulence parameter inversion results. These results include atmospheric turbulence intensity and atmospheric coherence length. First, all Gaussian laser beams are positioned at a given propagation distance... The lateral position offset at a given location is considered as a spatial random field. The expected square of the difference in offset between any two lateral positions of the beam is calculated, which is the formula corresponding to the structure function:

[0153] ;

[0154] in, Indicates the lateral position of the beam The lateral position offset, Indicates the lateral position of the beam The lateral position offset, The spatial structure function value representing the lateral position offset (describes the difference in offset between two points in space as a function of intervals) (Statistical patterns of change) This represents the ensemble mean or statistical mean, which in actual calculations is achieved by applying the average of all values ​​that meet the same interval. This is achieved by averaging the light pairs. In actual calculations, this is done by traversing all light pairs and averaging them at intervals. By performing grouped statistical averaging, the curve of the structure function as a function of spatial interval is obtained, i.e., the structure function curve.

[0155] The calculated structure function curve is fitted with the theoretical model given by Kolmogorov turbulence theory using least squares. The distribution of atmospheric turbulence intensity is directly inverted through the fitting coefficients. Furthermore, the atmospheric coherence length is calculated by combining the classical relationship between atmospheric turbulence intensity and atmospheric coherence length (Kolmogorov turbulence theory).

[0156] S5-4. Based on the complex amplitude field generated in S3-1, construct the phase distortion function and evaluate the wave effect to generate wavefront distortion characteristics and wave effect evaluation results; the wave effect evaluation results include light intensity scintillation index and angle of arrival fluctuation.

[0157] It needs to be explained that the actual phase is extracted from the complex amplitude field generated in S3-1. and the ideal phase under undisturbed ideal conditions. By comparison, the corresponding phase distortion function is constructed, and the corresponding formula is:

[0158] ;

[0159] in, Indicates phase distortion. This represents the argument function.

[0160] The phase distortion function directly characterizes the spatial distribution of wavefront distortion caused by atmospheric disturbances. Based on the phase distortion function, the phase distortion values ​​corresponding to different spatial points are calculated, and then the transverse phase gradient is obtained by numerically differentiating the phase distortion values ​​using the central difference method. Then, based on the relationship between the lateral phase gradient and the angle of arrival:

[0161] ;

[0162] Generate the angle of arrival for each spatial point. ; This represents the wavenumber of light in the medium. The root mean square value of each angle of arrival is used to calculate the angle of arrival distribution, which is then used to quantify wavefront tilt and beam jitter. Simultaneously, the light intensity distribution is calculated based on the perturbed complex amplitude field (the complex amplitude field generated in S3-1). Then, according to the formula:

[0163] ;

[0164] The light intensity scintillation index is obtained by statistically averaging the light intensity distribution. This index is used to quantify the degree of random fluctuations in light intensity caused by atmospheric disturbances, thereby generating the evaluation results of wavefront distortion characteristics and wave effects. Indicates light intensity. Indicates light intensity distribution The second-order moment information (reflects the fluctuation range of the light intensity value). Indicates light intensity distribution The square of the average value (representing the DC component of the light intensity).

[0165] S5-5 integrates the waist distortion curve, turbulence parameter inversion results, wavefront distortion characteristics, and wave effect assessment results to generate atmospheric disturbance analysis results. That is, the atmospheric disturbance analysis results include the waist distortion curve, wavefront distortion characteristics, turbulence parameter inversion results, and wave effect assessment results.

[0166] In summary, this invention effectively resolves the fundamental contradiction that traditional geometrical optics cannot describe diffraction effects, while wave optics lacks path traceability. By introducing Bohmian mechanics and using the phase gradient of the optical field as the physical quantity driving ray evolution, it naturally incorporates wave effects such as interference and diffraction while retaining the intuitive path analysis capabilities of traditional ray tracing. This achieves simulation accuracy comparable to wave optics in key scenarios such as beam spread and focusing limits, providing a unified simulation tool for precision optical design, micro / nano photonic device analysis, and research on optical transmission in complex media. This tool enables both physical mechanism tracing and numerical accuracy, significantly improving the reliability, interpretability, and engineering practical value of optical field simulation.

[0167] like Figure 6 As shown, an atmospheric disturbance analysis system based on Bohmian mechanics and waveguide geometric optics includes:

[0168] The simulation module is used to set up the light field simulation environment and simulate the propagation of the light field through a Gaussian laser beam, and calculate the initial complex amplitude distribution of the Gaussian laser beam based on the preset initial beam waist radius.

[0169] A module is built to construct an optical-Bohm trajectory equation by making an optical-quantum analogy between the Bohm guiding equation and the paraxial Helmholtz equation based on Bohm's mechanical theory.

[0170] The calculation module is used to calculate the lateral rate of change of the ray trajectory of a Gaussian laser beam based on the initial complex amplitude distribution, using the distributed Fourier method and the optical-Bohm trajectory equation.

[0171] The iteration module is used to update the position of the Gaussian laser beam based on the lateral change rate of the ray trajectory and iterate to generate Gaussian trajectory data during the simulation process.

[0172] The analysis module is used to generate a beam waist radius variation curve based on Gaussian trajectory data; and to perform atmospheric disturbance analysis based on the beam waist radius variation curve to generate atmospheric disturbance analysis results.

[0173] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0174] Example 2:

[0175] When a Gaussian laser beam propagates in a gradient medium, an atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics is employed, including:

[0176] A1. Set up the light field simulation environment and simulate the propagation of the light field using a Gaussian laser beam. Calculate the initial complex amplitude distribution of the Gaussian laser beam based on the preset initial beam waist radius.

[0177] A2. Based on Bohm's mechanical theory, optical-quantum analogies are made between the Bohm guiding equation and the paraxial Helmholtz equation to construct the optical-Bohm trajectory equation.

[0178] A2 in this embodiment is the same as S2 in embodiment 1.

[0179] A3. Based on the initial complex amplitude distribution, the transverse rate of change of the ray trajectory of the Gaussian laser beam is calculated using the distributed Fourier method and the optical-Bohm trajectory equation.

[0180] A3 includes:

[0181] A3-1. Construct the Luneburg lens model and obtain the background refractive index;

[0182] The formula for the background refractive index of the Luneburg lens model is:

[0183] ;

[0184] in, This indicates the refractive index of the Luneburg lens. This represents the central refractive index of the Luneburg lens. This represents the radial distance from any point within the refractive index range to the center of the refractive index. This represents the radius of the Luneburg lens. In this embodiment, The value is 2. The value of is 1e-4, which gives the Luneburg lens model a specific characteristic that it can achieve sharp imaging, meaning that all light rays entering the lens will converge to a single point on the lens surface.

[0185] At this point, due to the refractive index gradient in the Luneburg lens model :

[0186] ;

[0187] The traditional ray tracing theory's ray transport equation changes, and the formula for the variant ray transport equation is as follows:

[0188] ;

[0189] ;

[0190] in, , , They represent position vectors, Represents partial derivatives, , , These represent direction vectors, respectively.

[0191] By solving the variant equation for ray propagation using the Runge-Kutta method, the variation of the light spot distribution with propagation distance can be obtained. The initial position of the Gaussian light spot is set as follows: The light spot propagates along the positive z-axis, and the center of the Luneburg lens is located at coordinate... As shown in Figures 7(a), 7(b), 7(c), 7(d), 7(e), and 7(f), the light spot exhibits a trend of first shrinking and then expanding, and when the position... for The light spot converges at this point, and the waist radius is close to 0.

[0192] A3-2. Based on the background refractive index and initial complex amplitude distribution, the propagation position of the Gaussian laser beam is calculated using the spectral method, the Luneburg lens model, and the distributed Fourier method. The complex amplitude field in the first half of the refractive index step and the second half of the refractive index step;

[0193] Specifically, based on the content of A3-1 and following the same approach as S3 in Example 1, the Helmholtz equation for propagation in the gradient medium is generated, and the corresponding formula is:

[0194] ;

[0195] ;

[0196] ;

[0197] ;

[0198] ;

[0199] in, Represents the squared gradient value. Represents position vector The corresponding square value of the background refractive index, Represents the spatial complex amplitude. This represents the square of the phase gradient. Represents the diffraction operator. express, Represents the refractive index operator. Represents the square of the wave number. This represents the square of the reference refractive index.

[0200] When considering the exact solution form under non-paraxial conditions, we first process the first half of the refractive index change in the spatial domain to obtain the complex amplitude field in the first half of the refractive index step. The corresponding formula is:

[0201] ;

[0202] in, This represents the increment of the propagation distance in the z-direction.

[0203] The complex amplitude field of the first half-refractive index step is obtained through Fourier transform. When converted to the wavenumber domain, the corresponding formula is:

[0204] ;

[0205] in, Represents the transverse component of the wave vector. This represents the wave domain-complex amplitude field in the first half of the refractive index step.

[0206] Considering the diffraction effect, the formula corresponding to the Helmholtz equation under the exact result is:

[0207] ;

[0208] in, This represents the square of the phase gradient in the wavenumber domain.

[0209] Since the diffraction effect takes into account a uniform refractive index space, i.e. Then the solution to the Helmholtz equation under the exact result is:

[0210] ;

[0211] ;

[0212] in, This represents the wave domain-complex amplitude field in the second half of the refractive index step. This represents the component of the wave vector in the z-direction.

[0213] Then, by using the inverse Fourier transform, the wave domain-complex amplitude field of the second half of the refractive index step will be obtained. Transforming back to the spatial domain, the corresponding formula is:

[0214] ;

[0215] ;

[0216] in, This represents the intermediate variable complex amplitude field in the second half of the refractive index step. This represents the complex amplitude field in the second half of the refractive index step.

[0217] A3-3. The complex amplitude field is numerically differentiated using the central difference method to generate the corresponding transverse gradient field.

[0218] A3-4. Based on the transverse gradient field, calculate the corresponding light intensity, and combine it with the phase function to calculate the phase;

[0219] A3-5. Based on phase, calculate the lateral variation rate of the ray trajectory of a Gaussian laser beam using the optical-Bohm trajectory equation.

[0220] Specifically, firstly, according to the formula:

[0221] ;

[0222] ;

[0223] Generate the component form of the propagation trajectory equation.

[0224] Substituting the complex amplitude corresponding to A3-2, the potential energy field of the complex amplitude can be simply understood as the potential energy between light rays, which drives the propagation of light rays, thereby realizing the evolution of the light ray trajectory based on Bohm's mechanics, and obtaining the lateral change rate of the light ray trajectory when the Gaussian laser beam propagates in the gradient medium.

[0225] In this embodiment, a Gaussian light spot composed of 10,000 rays is also set to propagate along the positive z-axis from the initial position. Through the center A Luneburg lens with radius propagates to position The trajectory, such as Figure 8 As shown, the red circle represents the initial beam waist radius of the distributed light spot. It can be seen that the Gaussian light spot... The beam converges in the vicinity, and inside the lens, the beam waist radius continuously decreases with propagation. After passing through the center of the lens, the beam diverges rapidly. The figure below shows the planar point distribution of this Gaussian beam at different propagation distances.

[0226] At this point, the distribution of Gaussian spot points in the xy plane at different propagation distances is shown in Figures 9(a), 9(b), 9(c), and 9(d). By comparing with the results from geometric optics, it can be found that the spot results at different propagation distances... The results show a clear difference, but the reason lies partly in the grid settings and partly in the diffraction limit of wave optics, which results in a minimum beam waist radius for the light spot. The beam waist appears large at the convergence point because the number of edge points in the image is actually small compared to the total number of rays (edge ​​ray points correspond to background sampling points on the periphery of the wave optics, while most rays are actually closer to the center). By observing the radial distribution at this location, we can see that the light spot does indeed converge at that point.

[0227] To better explain the beneficial effects of this embodiment, a comparison is made of the beam waist radius of the Gaussian spot as a function of propagation distance using three methods (traditional geometrical optics, the method of this embodiment, and wave optics). The horizontal axis represents the propagation distance (position). The vertical axis represents the position. The values ​​for the waist radius are shown; the green line represents the result of traditional geometrical optics, the yellow line represents the result of wave optics, and the blue line represents the method of this embodiment. For example... Figure 10 As shown, the results of the three beam waist variation curves are basically consistent within the lens range, and the improved ray tracing method is closer to the result of geometric optics within the lens range. This is because both methods calculate the beam waist radius using point distribution, while wave optics directly calculates the beam waist radius at that position through phase, indicating that the initial propagation error of the three methods is very small. Only near the beam convergence point do the calculated results of the beam waist radius begin to differ. The Gaussian beam of the method in this embodiment and wave optics both have the minimum beam width. The calculation result of wave optics and the improved ray tracing result are different (the difference between the two results is due to the generation and calculation method of the beam waist radius), rather than the traditional geometric optics beam waist radius directly converging to near zero and failing to consider the influence of diffraction effects. However, it is precisely because of this difference that the result is unique to considering diffraction effects. From the perspective of the overall beam waist radius variation, the improved ray tracing result of the beam waist radius variation is closer to that of wave optics, and the result is more accurate. This is the superiority of the method in this embodiment. It should be noted that in small-scale simulations (where the beam waist radius is close to the wavelength), the effects of wave optics are amplified, and the errors in geometric optics calculations become increasingly larger, making traditional geometric optics methods unsuitable.

[0228] A4. Update the position of the Gaussian laser beam based on the lateral change rate of the ray trajectory and iterate to generate Gaussian trajectory data during the simulation process;

[0229] A5. Based on Gaussian trajectory data, generate a curve showing the variation of the waist radius; based on the curve showing the variation of the waist radius, perform atmospheric disturbance analysis and generate atmospheric disturbance analysis results.

[0230] A4 and A5 in this embodiment are the same as S4 and S5 in embodiment 1.

[0231] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0232] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for analyzing atmospheric disturbances based on Bohmian mechanics and waveguide geometric optics, characterized in that, include: Set up a light field simulation environment and simulate the propagation of the light field using a Gaussian laser beam. Calculate the initial complex amplitude distribution of the Gaussian laser beam based on a preset initial beam waist radius. Based on Bohm's mechanical theory, an optical-quantum analogy is made between the Bohm guiding equation and the paraxial Helmholtz equation to construct the optical-Bohm trajectory equation. Based on the initial complex amplitude distribution, the transverse rate of change of the ray trajectory of the Gaussian laser beam is calculated by using the distributed Fourier method and the optical-Bohm trajectory equation. The position of the Gaussian laser beam is updated based on the lateral rate of change of the ray trajectory and iterated to generate Gaussian trajectory data during the simulation process. Based on Gaussian trajectory data, a curve showing the variation of the waist radius is generated; atmospheric disturbance analysis is then performed based on the curve showing the variation of the waist radius, and atmospheric disturbance analysis results are generated.

2. The atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics according to claim 1, characterized in that, The formula corresponding to the optical-Bohm trajectory equation is: ； in, This represents the transverse phase gradient of a Gaussian laser beam. Indicates wave number, This indicates the lateral position of a Gaussian laser beam. This represents the longitudinal propagation distance of a Gaussian laser beam. This represents the rate of lateral change of the light trail.

3. The atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics according to claim 1, characterized in that, When a Gaussian laser beam propagates in a vacuum, the calculation of the lateral rate of change of the beam's trajectory includes: Based on the initial complex amplitude distribution, the propagation location of the Gaussian laser beam is calculated using the spectral method and the distributed Fourier method. Complex amplitude field at time; The complex amplitude field is numerically differentiated using the central difference method to generate the corresponding transverse gradient field. Based on the transverse gradient field, the corresponding light intensity is calculated, and the phase is calculated by combining the phase function; Based on phase, the lateral variation rate of the ray trajectory of a Gaussian laser beam is calculated using the optical-Bohm trajectory equation.

4. The atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics according to claim 3, characterized in that, The calculation of the propagation of the Gaussian laser beam to the location The complex amplitude field at time includes: Based on the Helmholtz equation, paraxial conditions, and initial complex amplitude distribution, the paraxial Helmholtz equation is generated. The propagation evolution of a Gaussian laser beam is performed using spectral methods, and the complex amplitude of the Gaussian laser beam propagating to any position is converted into the wavenumber domain through two-dimensional Fourier transform, generating the Helmholtz equation in the wavenumber domain. Based on the Helmholtz equation in the wavenumber domain, the wavenumber domain is transformed back to the spatial domain through inverse Fourier transform to obtain the position. The complex amplitude field at that time.

5. The atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics according to claim 1, characterized in that, When a Gaussian laser beam propagates in a gradient medium, the calculation of the lateral rate of change of the beam's trajectory includes: Construct a Luneburg lens model and obtain the background refractive index; Based on the background refractive index and initial complex amplitude distribution, the propagation location of the Gaussian laser beam is calculated using the spectral method, the Luneburg lens model, and the distributed Fourier method. The complex amplitude field in the first half of the refractive index step and the second half of the refractive index step; The complex amplitude field is numerically differentiated using the central difference method to generate the corresponding transverse gradient field. Based on the transverse gradient field, the corresponding light intensity is calculated, and the phase is calculated by combining the phase function; Based on phase, the lateral variation rate of the ray trajectory of a Gaussian laser beam is calculated using the optical-Bohm trajectory equation.

6. The atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics according to claim 3, characterized in that, The generated atmospheric disturbance analysis results include: Based on Gaussian trajectory data, the waist radius of the beam is calculated at different propagation distances, and the curve of the waist radius variation is plotted. Plot the ideal waist radius variation curve, calculate the difference between the ideal waist radius variation curve and the waist radius variation curve, and generate the waist distortion curve; The lateral position offset is calculated based on Gaussian trajectory data and inverted using the Kolmogorov turbulence theory model to generate turbulence parameter inversion results. Based on the complex amplitude field, a phase distortion function is constructed and wave effect assessment is performed to generate wavefront distortion characteristics and wave effect assessment results. By integrating the waist distortion curve, turbulence parameter inversion results, wavefront distortion characteristics, and wave effect assessment results, atmospheric disturbance analysis results are generated.

7. An atmospheric disturbance analysis system based on Bohmian mechanics and waveguide geometric optics, used to implement the atmospheric disturbance analysis method based on Bohmian mechanics and waveguide geometric optics as described in any one of claims 1 to 6, characterized in that, include: The simulation module is used to set up the light field simulation environment and simulate the propagation of the light field through a Gaussian laser beam, and calculate the initial complex amplitude distribution of the Gaussian laser beam based on the preset initial beam waist radius. A module is built to construct an optical-Bohm trajectory equation by making an optical-quantum analogy between the Bohm guiding equation and the paraxial Helmholtz equation based on Bohm's mechanical theory. The calculation module is used to calculate the lateral rate of change of the ray trajectory of a Gaussian laser beam based on the initial complex amplitude distribution, using the distributed Fourier method and the optical-Bohm trajectory equation. The iteration module is used to update the position of the Gaussian laser beam based on the lateral change rate of the ray trajectory and iterate to generate Gaussian trajectory data during the simulation process. The analysis module is used to generate curves showing the variation of the waist radius based on Gaussian trajectory data; Atmospheric disturbance analysis is performed based on the waist radius variation curve, and atmospheric disturbance analysis results are generated.

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