Numerical method and device for heat diffusion process of filamentation by femtosecond pulse laser transmission

Abstract

The present invention discloses a numerical method and device for heat diffusion process of femtosecond pulse laser transmission filamentation, which couples and solves the nonlinear Schrödinger equation, free electron density evolution equation and nonlinear energy loss density and heat transfer equation of femtosecond strong laser atmospheric transmission filamentation, and realizes quantitative calculation of laser filamentation plasma density, energy deposition density distribution and temperature field change. The technical scheme of the present invention can reveal the physical mechanism of femtosecond laser filamentation clearing to form optical transmission channel, inducing large disturbance of local airflow and inducing freezing of supercooled water droplets.

Description

Technical Field

[0001] The invention belongs to the technical field of high-intensity femtosecond laser atmospheric applications, and in particular relates to a numerical method and device for a heat diffusion process of high-repetition-rate femtosecond pulse laser transmission filamentation. Background Art

[0002] When a femtosecond laser pulse with an incident power several times higher than the self-focusing power is transmitted in the atmosphere, a long-distance plasma channel will be formed on the wake of the pulse transmission due to the competition between the Kerr self-focusing effect, plasma defocusing effect, and beam diffraction, which is called laser filaments. Laser atmospheric filaments have potential applications in remote atmospheric remote sensing, induced water vapor condensation, laser propulsion, laser drag reduction, and clearing to form optical transmission channels.

[0003] The basis of many applications of femtosecond laser filamentation is its long-distance transmission in the atmosphere. In particular, with the recombination of plasma filaments, a large part of the pulse energy is absorbed by the transmission medium in the form of heat in the laser irradiation filamentation area. The instantaneous heat deposition will produce thermal stress shock and subsequent heat diffusion process. This thermal effect is also considered to be an important reason for the generation of low air density structure, local airflow disturbance and the promotion of supercooled water freezing. At present, many methods for simulating the characteristics of femtosecond laser transmission filamentation have been proposed, such as a parallel simulation method for laser nonlinear transmission proposed by Southwest Jiaotong University [CN201410620686.4], a simulation method for Laguerre-Gaussian vortex femtosecond laser transmission in transparent media proposed by Jiangsu University [CN201610811919.8], and a method, medium and equipment for simulating long-distance transmission of filament laser proposed by Beijing Institute of Space Mechatronics [CN202010732692.4]. The above work is to simulate the characteristics of femtosecond laser transmission filamentation, which can obtain physical quantities such as the length and intensity of the filament, but cannot analyze more critical laser transmission effects such as the energy deposition density of the filament and subsequent heat diffusion. Therefore, it is impossible to provide sufficient data support to explain the physical mechanism of femtosecond laser filamentation to form optical transmission channels, induce large-scale disturbances in local airflow, and induce freezing of supercooled water droplets. Summary of the invention

[0004] The technical problem to be solved by the present invention is: the present invention provides a numerical method and device for the heat diffusion process of femtosecond pulse laser transmission filamentation, which can realize the quantitative description of the local temperature field changes induced by femtosecond laser atmospheric transmission filamentation, and provide technical support for revealing the mechanism of femtosecond laser cleaning to form optical transmission channels, induce large-scale airflow disturbances and induce freezing of supercooled water droplets, and promote the development of basic research and application exploration research related to femtosecond laser.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] A numerical method for heat diffusion process of femtosecond pulse laser transmission filamentation, comprising the following steps:

[0007] Step 1: Establish a femtosecond laser transmission simulation model, wherein the femtosecond laser transmission simulation model includes: a nonlinear propagation equation, an electron density evolution equation, and a nonlinear energy loss density equation;

[0008] Step 2: Solve the nonlinear propagation equation using a numerical method to obtain the electric field strength; solve the electron density evolution equation in the time domain in a coupled manner to obtain the free electron density; bring the free electron density and the electric field strength into the nonlinear energy loss density equation to obtain the energy deposition density distribution of a single femtosecond pulse at different transmission positions;

[0009] Step 3: According to the energy deposition density distribution of a single femtosecond pulse, the temperature field distribution after the influence of the filament energy deposition is obtained;

[0010] Step 4: Based on the temperature field distribution as the initial condition, the heat conduction equation is numerically solved to obtain the evolution process of the temperature field.

[0011] Preferably, in step 1, the nonlinear propagation equation is:

[0012]

[0013] Where E is the electric field intensity, k0 is the wave number, ω0 is the central angular frequency, k″ is the group velocity dispersion coefficient, τ is the delay time variable, n2 is the nonlinear refractive index, σ is the inverse bremsstrahlung cross section, τ c is the electron collision time, β K is the multiphoton absorption coefficient, K is the minimum number of photons required for multiphoton ionization, ρ is the free electron density, and ρ at is the number density of neutral gas molecules, r represents the radial coordinate of the beam cross section, and z represents the coordinate of the beam transmission direction;

[0014] Electron density evolution equation:

[0015]

[0016] Among them, U is the ionization energy, t is the time coordinate, is the reduced Planck constant;

[0017] The nonlinear energy loss density u(r,z,t) is expressed as:

[0018] u(r,z,t)=(σρ|E| 2 +β K |E| 2K)×(1-ρ / ρ at )

[0019] Preferably, in step 2, the method for solving the nonlinear propagation equation is: within each time step Δt; first, in the frequency domain, according to The linear part of the propagation equation is solved by the finite difference method; then the nonlinear part of the propagation equation is superimposed and solved in the time domain to obtain Complete the calculation of one time step; cycle in sequence until the calculation reaches in, m=0,1,……,N r ,n=0,1,……,N z ,k=0,1,……,N t , N r N represents the number of grid points in the radial r direction of the beam cross section. z represents the number of grid points in the transmission direction z, N t It represents the number of grid points in the time axis direction, Δr represents the grid spacing in the r direction, and Δz represents the grid spacing in the z direction.

[0020] Preferably, in step 2, the electron density evolution equation is solved in the time domain by coupling using the Runge-Kutta method to obtain the free electron density.

[0021] Preferably, in step 2, the free electron density and the electric field strength are introduced into the nonlinear energy loss density equation, and then integrated over time to obtain the energy deposition density distribution ΔU(r,z).

[0022] Preferably, in step 3, the method for obtaining the temperature field distribution after the influence of the light filament energy deposition is as follows: assuming that all the energy deposited by the light filament is absorbed by the gas in the form of heat, the temperature distribution of the gas after being heated is:

[0023] T(r,z,t)=ΔU(r,z) / κ+T e

[0024] Among them, T e is the gas environment temperature before the laser action, t = kΔτ, k = 1, 2, 3…, N, Δτ represents the pulse interval, T(r, z, t) represents the gas temperature at time t, and N represents the maximum number of grids in the calculation time direction.

[0025] Preferably, in step 4, the heat conduction equation is numerically solved using the finite difference method, the heating effect of each pulse is regarded as a delta function in time, and the energy deposition effect of each pulse is assumed to be the same; according to the emission frequency of the femtosecond laser pulse, the temperature field after the energy deposition of the second pulse is used as the initial temperature field for the next calculation, and the heating effect of the third, fourth, ..., and Nth pulses is repeatedly calculated in sequence, where N is the maximum calculation time length T max The total number of pulses included in the calculation, up to the maximum time length T max , and the evolution process of the temperature field is obtained.

[0026] The present invention also provides a numerical device for heat diffusion process of femtosecond pulse laser transmission filamentation, comprising:

[0027] An establishment module is used to establish a femtosecond laser transmission simulation model, wherein the femtosecond laser transmission simulation model includes: a nonlinear propagation equation, an electron density evolution equation and a nonlinear energy loss density equation;

[0028] The first calculation module is used to solve the nonlinear propagation equation using a numerical method to obtain the electric field strength; couple the electron density evolution equation in the time domain to obtain the free electron density; bring the free electron density and the electric field strength into the nonlinear energy loss density equation to obtain the energy deposition density distribution of a single beam femtosecond pulse at different transmission positions;

[0029] The second calculation module is used to obtain the temperature field distribution after the influence of the light filament energy deposition according to the single-beam femtosecond pulse energy deposition density distribution;

[0030] The third calculation module is used to numerically solve the heat conduction equation by the finite difference method based on the temperature field distribution as the initial condition to obtain the evolution process of the temperature field.

[0031] Preferably, the nonlinear propagation equation:

[0032]

[0033] Where E is the electric field intensity, k0 is the wave number, ω0 is the central angular frequency, k″ is the group velocity dispersion coefficient, τ is the delay time variable, n2 is the nonlinear refractive index, σ is the inverse bremsstrahlung cross section, τ c is the electron collision time, β K is the multiphoton absorption coefficient, K is the minimum number of photons required for multiphoton ionization, ρ is the free electron density, and ρ at is the number density of neutral gas molecules, r is the radial coordinate of the beam cross section, and z is the coordinate of the beam transmission direction.

[0034] Electron density evolution equation:

[0035]

[0036] Among them, U is the ionization energy, t is the time coordinate, is the reduced Planck constant;

[0037] The nonlinear energy loss density u(r,z,t) is expressed as:

[0038] u(r,z,t)=(σρ|E| 2 +β K |E| 2K )×(1-ρ / ρ at )

[0039] The present invention realizes the simulation of parameters such as light intensity, electron density, energy deposition density and filament-induced temperature field change in the filament laser transmission process by combining the technical means of numerically solving the femtosecond laser atmospheric transmission model and the heat transfer equation. It can reveal the mechanism of femtosecond laser cleaning to maintain the optical transmission channel, induce large-scale airflow disturbance and induce freezing of supercooled water droplets, and provide technical support for promoting the basic research and application exploration research and development related to femtosecond laser. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Implementation flow chart of the method of the present invention;

[0041] Figure 2 Schematic diagram of grid point processing of heat transfer equation;

[0042] FIG3(a) and FIG3(b) are schematic diagrams of the simulated electron density distribution and energy deposition density distribution in the rz plane, respectively. DETAILED DESCRIPTION

[0043] To make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0044] Embodiment 1:

[0045] like Figure 1 As shown, the present invention provides a numerical method for the heat diffusion process of femtosecond pulse laser transmission filamentation, comprising the following steps:

[0046] Step 1: Establish a femtosecond laser transmission simulation model, wherein the femtosecond laser transmission simulation model includes: a nonlinear propagation equation, an electron density evolution equation, and a nonlinear energy loss density equation;

[0047] Step 2: Solve the nonlinear propagation equation using a numerical method to obtain the electric field strength; solve the electron density evolution equation in the time domain in a coupled manner to obtain the free electron density; bring the free electron density and the electric field strength into the nonlinear energy loss density equation to obtain the energy deposition density distribution of a single femtosecond pulse at different transmission positions;

[0048] Step 3: According to the energy deposition density distribution of a single femtosecond pulse, the temperature field distribution after the influence of the filament energy deposition is obtained;

[0049] Step 4: Based on the temperature field distribution as the initial condition, the heat conduction equation is numerically solved to obtain the evolution process of the temperature field.

[0050] As an implementation method of an embodiment of the present invention, in step 1, the nonlinear propagation equation is:

[0051]

[0052] Where E is the electric field intensity, k0 is the wave number, ω0 is the central angular frequency, k″ is the group velocity dispersion coefficient, τ is the delay time variable, n2 is the nonlinear refractive index, σ is the inverse bremsstrahlung cross section, τ c is the electron collision time, β K is the multiphoton absorption coefficient, K is the minimum number of photons required for multiphoton ionization, ρ is the free electron density, and ρ at is the number density of neutral gas molecules, r is the radial coordinate of the beam cross section, and z is the coordinate of the beam transmission direction.

[0053] Electron density evolution equation:

[0054]

[0055] Among them, U is the ionization energy, t is the time coordinate, is the reduced Planck constant;

[0056] The nonlinear energy loss density u(r,z,t) can be expressed as:

[0057] u(r,z,t)=(σρE2+βK|E2K)×(1-ρ / ρat) (3)

[0058] As an implementation method of an embodiment of the present invention, in step 2, the method for solving the nonlinear propagation equation is: within each time step Δt; first, in the frequency domain, according to The linear part of the propagation equation is solved by the finite difference method; then the nonlinear part of the propagation equation is superimposed and solved in the time domain to obtain Complete the calculation of one time step; cycle in sequence until the calculation reaches in, m=0,1,……,N r ,n=0,1,……,N z ,k=0,1,……,N t , N r N represents the number of grid points in the radial r direction of the beam cross section. z represents the number of grid points in the transmission direction z, N t Indicates the number of grid points in the time axis direction, Δr indicates the grid spacing in the r direction, and Δz indicates the grid spacing in the z direction;

[0059] As an implementation method of an embodiment of the present invention, in step 2, the electron density evolution equation is solved in the time domain by coupling the Runge-Kutta method to obtain the free electron density.

[0060] As an implementation method of the present invention, in step 2, the free electron density and the electric field strength are introduced into the nonlinear energy loss density equation, and then integrated over time to obtain the energy deposition density distribution ΔU(r,z). ;

[0061] As an implementation method of an embodiment of the present invention, in step 3, the method for obtaining the temperature field distribution after the influence of the light filament energy deposition is: assuming that all the energy deposited by the light filament is absorbed by the gas in the form of heat, the temperature distribution of the gas after heating is: T(r,z,t)=ΔU(r,z) / κ+T e , where T e is the gas environment temperature before the laser action, t = kΔτ, k = 1, 2, 3…, N, Δτ represents the pulse interval, T(r, z, t) represents the gas temperature at time t, and N represents the maximum number of grids in the calculation time direction.

[0062] As an implementation method of the embodiment of the present invention, the heat conduction equation in step 4 is in the form of:

[0063]

[0064] Where κ is the thermal conductivity. The boundary conditions of this equation are:

[0065]

[0066] The finite difference method used for numerical solution of the heat conduction equation in step 4 is the decomposition technique, and the specific steps of this method are:

[0067] Step 41: Decompose equation (4) into two independent equations:

[0068] ① In radial direction

[0069]

[0070] ② In the direction of transmission

[0071]

[0072] Step 42: Construct a discretized grid, such as Figure 2 As shown, the variables are discretized and marked as follows:

[0073]

[0074] m=0,1,……,N r

[0075] n=0,1,……,N z

[0076] i=1,……,N t

[0077] Among them, Δr, Δz, Δt represent the calculation step size.

[0078] Step 43: Rewrite equations (6) and (7) into the difference operator form D 2 :

[0079]

[0080]

[0081] Among them, p represents the number of time steps in the current calculation, and the difference operator and The expression is:

[0082]

[0083]

[0084] Among them, c n =2(N r +n).

[0085] Step 44: Substitute (10) and (11) into (8) and (9) respectively, and then perform transposition processing to obtain:

[0086]

[0087]

[0088] in:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] Step 45: In each time step Δt, according to the known First, use (12) to establish a linear equation system, and use the pursuit method to obtain Then, use (13) to establish a linear equation system and use the pursuit method to obtain the next moment Repeat until the final t is found. max The final temperature field distribution value at time.

[0097] As shown in Figure 3(a) and Figure 3(b), the femtosecond laser parameters are set as follows during the simulation: the beam is a Gaussian beam, the wavelength λ = 800 m, and the incident pulse energy E in =7.1mJ, pulse width t p =30fs, beam waist radius w0=1mm.

[0098] Example 2

[0099] The present invention also provides a numerical device for heat diffusion process of femtosecond pulse laser transmission filamentation, comprising:

[0100] An establishment module is used to establish a femtosecond laser transmission simulation model, wherein the femtosecond laser transmission simulation model includes: a nonlinear propagation equation, an electron density evolution equation and a nonlinear energy loss density equation;

[0101] The first calculation module is used to solve the nonlinear propagation equation using a numerical method to obtain the electric field strength; couple the electron density evolution equation in the time domain to obtain the free electron density; bring the free electron density and the electric field strength into the nonlinear energy loss density equation to obtain the energy deposition density distribution of a single beam femtosecond pulse at different transmission positions;

[0102] The second calculation module is used to obtain the temperature field distribution after the influence of the light filament energy deposition according to the single-beam femtosecond pulse energy deposition density distribution;

[0103] The third calculation module is used to numerically solve the heat conduction equation by the finite difference method based on the temperature field distribution as the initial condition to obtain the evolution process of the temperature field.

[0104] As an implementation method of this embodiment, the nonlinear propagation equation is:

[0105]

[0106] Where E is the electric field intensity, k0 is the wave number, ω0 is the central angular frequency, k″ is the group velocity dispersion coefficient, τ is the delay time variable, n2 is the nonlinear refractive index, σ is the inverse bremsstrahlung cross section, τ c is the electron collision time, β K is the multiphoton absorption coefficient, K is the minimum number of photons required for multiphoton ionization, ρ is the free electron density, and ρ at is the number density of neutral gas molecules, r is the radial coordinate of the beam cross section, and z is the coordinate of the beam transmission direction.

[0107] Electron density evolution equation:

[0108]

[0109] Among them, U is the ionization energy, t is the time coordinate, is the reduced Planck constant;

[0110] The nonlinear energy loss density u(r,z,t) is expressed as:

[0111] u(r,z,t)=(σρ|E| 2 +β K |E| 2K )×(1-ρ / ρ at )

[0112] The present invention couples and solves the nonlinear Schrödinger equation, free electron density evolution equation, and nonlinear energy loss density and heat transfer equation for the atmospheric transmission of femtosecond laser filaments, and realizes the quantitative calculation of the plasma density, energy deposition density distribution, and temperature field changes of laser filaments. The technical solution of the present invention can reveal the physical mechanism of femtosecond laser filaments to clean up and form optical transmission channels, induce large-scale disturbances in local airflow, and induce freezing of supercooled water droplets.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A numerical method for heat diffusion process of femtosecond pulse laser transmission filamentation, characterized in that: The following steps are involved: Step 1: Establish a femtosecond laser transmission simulation model, wherein the femtosecond laser transmission simulation model includes: a nonlinear propagation equation, an electron density evolution equation, and a nonlinear energy loss density equation; Step 2: Solve the nonlinear propagation equation using a numerical method to obtain the electric field strength; solve the electron density evolution equation in the time domain in a coupled manner to obtain the free electron density; bring the free electron density and the electric field strength into the nonlinear energy loss density equation to obtain the energy deposition density distribution of a single femtosecond pulse at different transmission positions; Step 3: According to the energy deposition density distribution of a single femtosecond pulse, the temperature field distribution after the influence of the filament energy deposition is obtained; Step 4: Using the temperature field distribution as the initial condition, numerically solve the heat conduction equation to obtain the evolution process of the temperature field; In step 1, the nonlinear propagation equation is: Where E is the electric field intensity, k0 is the wave number, ω0 is the central angular frequency, k″ is the group velocity dispersion coefficient, τ is the delay time variable, n2 is the nonlinear refractive index, σ is the inverse bremsstrahlung cross section, τ c is the electron collision time, β K is the multiphoton absorption coefficient, K is the minimum number of photons required for multiphoton ionization, ρ is the free electron density, and ρ at is the number density of neutral gas molecules, r represents the radial coordinate of the beam cross section, and z represents the coordinate of the beam transmission direction; Electron density evolution equation: Among them, U is the ionization energy, t is the time coordinate, is the reduced Planck constant; The nonlinear energy loss density u(r,z,t) is expressed as: u(r,z,t)=(σρ|E| 2 +b K |E| 2K )×(1-r / r at ); In step 2, the method for solving the nonlinear propagation equation is: in each time step Δt; first, in the frequency domain, according to The linear part of the propagation equation is solved by the finite difference method; then the nonlinear part of the propagation equation is superimposed and solved in the time domain to obtain Complete the calculation of one time step; cycle in sequence until the calculation reaches in, m=0,1,……,N r ,n=0,1,……,N z ,k=0,1,……,N t , N r N represents the number of grid points in the radial r direction of the beam cross section. z represents the number of grid points in the transmission direction z, N t Indicates the number of grid points in the time axis direction, Δr indicates the grid spacing in the r direction, and Δz indicates the grid spacing in the z direction; In step 2, the electron density evolution equation is solved in the time domain by the Runge-Kutta method to obtain the free electron density; In step 2, the free electron density and electric field strength are substituted into the nonlinear energy loss density equation, and then integrated over time to obtain the energy deposition density distribution ΔU(r,z).

2. The numerical method for heat diffusion process of femtosecond pulse laser transmission filamentation as claimed in claim 1, characterized in that: The method for obtaining the temperature field distribution after the influence of the light filament energy deposition in step 3 is: assuming that all the energy deposited by the light filament is absorbed by the gas in the form of heat, the temperature distribution of the gas after being heated is: T(r,z,t)=ΔU(r,z) / κ+T e Among them, T e is the gas environment temperature before the laser action, t = kΔτ, k = 1, 2, 3…, Δτ represents the pulse interval, and T(r, z, t) represents the gas temperature at time t.

3. The numerical method for heat diffusion process of femtosecond pulse laser transmission filamentation as claimed in claim 2, characterized in that: In step 4, the heat conduction equation is numerically solved using the finite difference method, the heating effect of each pulse is considered as a delta function in time, and the energy deposition effect of each pulse is assumed to be the same; According to the frequency of femtosecond laser pulse emission, the temperature field after the second pulse energy deposition is used as the initial temperature field for the next calculation, and the third, fourth, ..., and Nth pulse heating effects are calculated repeatedly in sequence, where N is the maximum calculation time length T max The total number of pulses included in the calculation, up to the maximum time length T max , and the evolution process of the temperature field is obtained.

4. A numerical device for the heat diffusion process of femtosecond pulsed laser transmission filamentation that implements the numerical method for the heat diffusion process of femtosecond pulsed laser transmission filamentation according to any one of claims 1 to 3, characterized in that: include: An establishment module is used to establish a femtosecond laser transmission simulation model, wherein the femtosecond laser transmission simulation model includes: a nonlinear propagation equation, an electron density evolution equation and a nonlinear energy loss density equation; The first calculation module is used to solve the nonlinear propagation equation using a numerical method to obtain the electric field strength; couple the electron density evolution equation in the time domain to obtain the free electron density; bring the free electron density and the electric field strength into the nonlinear energy loss density equation to obtain the energy deposition density distribution of a single beam femtosecond pulse at different transmission positions; The second calculation module is used to obtain the temperature field distribution after the influence of the light filament energy deposition according to the single-beam femtosecond pulse energy deposition density distribution; The third calculation module is used to use the temperature field distribution as the initial condition, numerically solve the heat conduction equation through the finite difference method, and obtain the evolution process of the temperature field.

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