A method for predicting the laser damage threshold of pulse compression gratings taking into account the motion of surface electrons

Abstract

A method for predicting the laser damage threshold of a pulse compression grating taking into account the surface electron motion is provided. First, a sinusoidal grating geometric structure unit model is established, and the electromagnetic field and electromagnetic loss of the pulse compression grating surface are calculated using the Maxwell equations in the frequency domain; then, the electromagnetic loss is combined with the time function, and the double-temperature equation is used to calculate the electron temperature and lattice temperature of the pulse compression grating surface; finally, the electron temperature is introduced into the Fowler-DuBridge equation to establish the electron motion model of the grating surface under femtosecond pulses, and the residual electron density is introduced into the Poisson equation to calculate the residual electric field on the grating surface; the minimum value of the incident laser energy density when the grating surface equilibrium temperature reaches the metal melting point and the residual electric field reaches the Coulomb explosion threshold is taken as the laser damage threshold of the grating. The present invention can effectively improve the prediction accuracy of the laser damage threshold in the design and production process of the pulse compression grating, and is of great significance to the development of pulse compression gratings and the development of ultrafast optics based on chirped pulse amplification technology.

Description

Technical Field

[0001] The invention belongs to the technical field of laser damage assessment on the surface of engineering optical elements, and in particular relates to a method for predicting the anti-laser damage threshold of a femtosecond laser pulse compression grating taking into account the movement of surface electrons under the action of a femtosecond laser. Background Art

[0002] Ultrashort and ultra-intense pulses based on chirped pulse amplification technology can create unprecedented comprehensive extreme physical conditions in the laboratory, and are one of the major frontiers of current international scientific and technological competition. The specific implementation method of chirped pulse amplification technology is: (1) using a stretcher to stretch the seed pulse into a nanosecond pulse; (2) using a power amplifier to amplify the nanosecond pulse; (3) using a compressor to compress the amplified nanosecond pulse in time, and finally obtain ultrashort and ultra-intense laser pulses. Among them, the stretcher and the compressor are both composed of a pair of parallel large-aperture pulse compression gratings. The last grating in the pulse compression link carries the highest laser power and is most likely to cause laser-induced damage. Metal gratings have a wide working bandwidth and mature preparation process, and are currently the main grating type for large-size pulse compression gratings. Anti-laser damage ability is the most important parameter that directly affects the output energy and beam quality of metal pulse compression gratings. Once a large-aperture grating is damaged, it is likely to cause damage to downstream optical components. Therefore, it is very necessary to predict the anti-laser damage threshold of the grating before preparing a large-aperture grating.

[0003] The grating preparation process is often accompanied by repeated optimization of the grating structure. If only the method of preparing small-size grating samples and testing their damage threshold is adopted, a lot of time and money will be spent. Therefore, it is very necessary to save the testing cost by theoretically predicting the laser-induced damage on the surface of large-aperture gratings. The theoretical prediction of the damage threshold of metal pulse compression gratings is generally calculated by the finite element method, and the thermal stress model under the traditional Fourier model is mainly used. This model is used to calculate the electromagnetic field, temperature field and stress-strain field of the grating surface in the time domain, and then further analyzes the grating's laser damage threshold. However, under the radiation of femtosecond laser pulses, the pulse duration is much shorter than the relaxation time for the metal surface electrons and the lattice temperature to reach thermal equilibrium. The traditional Fourier prediction model only calculates the grating surface temperature and thermal stress damage, and does not consider the influence of the movement of electrons on the metal grating surface under femtosecond pulse radiation, resulting in the predicted grating laser damage threshold often having a certain deviation from the actual result.

[0004] Under femtosecond laser radiation, electrons on the metal surface absorb laser energy, and the kinetic energy of the electrons increases sharply. A part of them moves to the metal surface and overcomes the surface potential barrier to become emitted electrons. The electrons escape from the metal surface, breaking the electrical neutrality of the metal surface. The gradient distribution of the remaining electrons generates a residual electric field on the metal surface. If the residual electric field exceeds the threshold, a Coulomb explosion will occur to destroy the chemical bonds inside the metal, and the damage to the grating surface is direct and cannot be ignored. In 2020, Li Shanjun and others from Sichuan University published a method for predicting the laser damage threshold of materials by establishing an electron density model in patent CN 114324273 A. In 2021, Cheng Jian and others from Harbin Institute of Technology calculated the critical free electron density of fused quartz based on atomic transition theory in patent CN 110927125 A, and finally obtained the predicted value of the laser damage threshold of the component surface. Combining this type of prediction method with the theoretical calculation of the laser damage threshold of metal pulse compression gratings will effectively improve the accuracy of the prediction results. Summary of the invention

[0005] In view of the shortcomings of the existing theoretical prediction model, the present invention provides a method for predicting the laser damage threshold of metal pulse compression gratings. The method uses finite element analysis, introduces the electron motion field of the metal grating surface under femtosecond pulse radiation, and establishes a laser damage analysis and prediction model based on the multi-physical field of the grating surface, which effectively improves the prediction accuracy of the theoretical value of the grating laser damage threshold.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for predicting the laser damage threshold of metal pulse compression gratings. First, a sinusoidal grating geometric structure unit model is established, and the electromagnetic field and electromagnetic loss on the pulse compression grating surface are calculated using the Maxwell equations in the frequency domain; then, the electron temperature and lattice temperature on the pulse compression grating surface are calculated using the dual-temperature equation; finally, the electron temperature is substituted into the Fowler-DuBridge equation to establish an electron motion model on the grating surface under femtosecond pulses, and the residual electron density is substituted into the Poisson equation to calculate the residual electric field on the grating surface; the minimum value of the incident laser energy density when the grating surface equilibrium temperature reaches the metal melting point and the residual electric field reaches the Coulomb explosion threshold is taken as the grating anti-laser damage threshold. The specific steps of the method of the present invention are as follows:

[0008] The first step is to calculate the electromagnetic field and electromagnetic loss on the pulse compression grating surface

[0009] 1.1) Establish a sinusoidal grating geometric structure unit model, which consists of an air layer, a metal reflective film layer, a photoresist layer, and a substrate layer from top to bottom. The structural parameters of the metal pulse compression grating include: ridge height h, period p, duty ratio d, and top film thickness w. At the same time, according to the strict coupled wave vector theory, in order to ensure the diffraction efficiency and working bandwidth of the pulse compression grating, the grating period p and the incident pulse wavelength λ should satisfy the relationship: λ / 2<p<3λ / 2.

[0010] 1.2) Use Maxwell's equations to calculate the electromagnetic field distribution near the grating surface. Set the upper interface of the air layer to the port incidence condition, the incident angle of the femtosecond pulse to α, the incident laser energy density to J, and the pulse width to t p , incident laser power density I 0 =J / t p , the incident electric field Among them, ε 0 represents the vacuum dielectric constant. Due to the phase modulation effect of the grating on the electromagnetic field, the Floquet periodic boundary conditions are set on both sides of the sinusoidal grating geometric structure unit model. Select the frequency domain study and calculate the grating surface electromagnetic field E and the grating surface electromagnetic loss S according to formula (1):

[0011]

[0012] in, is the differential operator, E is the electromagnetic field intensity, k is the wave number in vacuum, μ r is the relative magnetic permeability, ε r is the relative dielectric constant, S is the electromagnetic loss, ε' is the imaginary part of the relative dielectric constant, ω is the frequency of the incident electromagnetic field, c 0 is the speed of light in a vacuum.

[0013] The second step is to calculate the surface electron temperature and lattice temperature of the pulse compression grating

[0014] The dual-temperature equation is used to describe the heat transfer process on the metal surface. The electromagnetic loss S calculated in equation (1) is substituted into equation (2) as the heat source. Using transient research, only the top metal of the grating is calculated, and the two sides are selected as periodic boundary conditions. The surface electron temperature T of the pulse compression grating is calculated according to equation (2): e and the lattice temperature T l distributed:

[0015]

[0016] Among them, C e is the electron heat capacity, T e is the electron temperature, t is the time, k e is the electronic thermal conductivity, G is the electron-lattice coupling coefficient, Cl is the lattice heat capacity, T l is the lattice temperature, k l is the lattice thermal conductivity.

[0017] Electron temperature T e and the lattice temperature T l The initial values ​​are all set to 300K. The femtosecond laser pulse irradiates the grating, and the grating surface electron temperature T e It rises rapidly to a maximum value within a few femtoseconds and then gradually decreases. During this period, the lattice temperature T l Slowly increases, and finally after a few picoseconds the electron temperature T e and lattice temperature T l The lattice temperature T l That is, the grating surface temperature T after laser pulse radiation. If the temperature T of the top metal film of the grating exceeds the melting point, thermal melting damage will occur.

[0018] The third step is to establish a model of electron motion on the grating surface under femtosecond pulses.

[0019] The Fowler-DuBridge theory is used to analyze the electron motion on the surface of a metal pulse compression grating under femtosecond pulse radiation.

[0020] 3.1) Set the surface of the top metal film of the grating as the source boundary condition, and the absorption source as the electron emission energy flux density J e Among them, J e Using formula (3), we can calculate:

[0021]

[0022] Among them, J 0 is the thermal electron emission energy flux density, J n is the multiphoton emission energy flux density.

[0023] Using J e The electron emission on the grating surface under femtosecond laser pulse radiation can be calculated. After the metal absorbs the laser pulse radiation, the surface electrons directly absorb the photon energy and may generate electrons with higher energy, some of which will move to the surface of the object and escape by overcoming the surface potential barrier, i.e. photoelectron emission. The photoelectron emission current density J on the metal surface is calculated according to formula (4): n :

[0024]

[0025] Among them, J n is the photoelectron emission current density, a n is the n-photon emission coefficient, e is the electron charge, hv is the photon energy, A is the theoretical Richardson constant, I0 is the incident laser power density, R is the metal surface reflectivity, is the metal work function, k B is the Boltzmann constant. n ) is the Fowler function, calculated according to formula (5):

[0026]

[0027] When the metal temperature rises above 1273.25K, the number of electrons with kinetic energy exceeding the work function increases sharply, and a large number of electrons escape from the metal surface, namely thermal electron emission. The thermal electron emission current density J on the metal surface is calculated according to formula (6): 0 :

[0028]

[0029] Among them, J 0 is the thermal electron emission current density, A is the theoretical Richardson constant, is the metal work function, k B is the Boltzmann constant.

[0030] 3.2) The grating metal surface emits electrons, and the surface and internal residual electrons will present a gradient distribution. At the same time, the internal electrons will move and diffuse near the grating surface to reduce the residual electron distribution gradient difference. The residual electron gradient distribution and diffusion trend of the grating top metal film are calculated according to formula (7):

[0031]

[0032] Among them, n e is the electron density emitted by the grating, e is the electron charge, J x is the electron energy density distribution on the grating surface, μ e is the electron mobility, D e is the electron diffusion coefficient, τ e is the electron relaxation time, m e is the mass of the electron, E c is the residual electric field strength generated by the residual electron density distribution gradient.

[0033] 3.3) Since the residual electron density of the metal film on the top of the grating is distributed in a gradient manner, a residual electric field E will be generated inside the grating. c , if the residual electric field E c If it is large enough, it will directly destroy the chemical bonds inside the grating and cause damage to the grating. c The Poisson equation is calculated by formula (8):

[0034]

[0035] Among them, ε 0 is the dielectric constant of vacuum, and ε is the relative dielectric constant of the material at the incident pulse frequency.

[0036] Step 4: Determine the grating anti-laser damage threshold F th Size

[0037] The maximum metal temperature T of the grating surface reflection layer max The melting point T of the metal on the pulse compression grating surface th For comparison, at the same time, the Coulomb electric field strength E c The maximum value E max The electric field strength threshold E of metal Coulomb explosion th If the maximum temperature of the metal reflective layer on the grating surface is T max >T th , and the maximum Coulomb electric field intensity E max <E th , will cause the grating surface temperature to be higher than its metal melting point, resulting in thermal melting damage; if the maximum temperature of the grating surface reflective layer metal T max <T th , and the maximum Coulomb electric field intensity E max >E th , which will cause the Coulomb force generated by the electric field inside the metal on the grating surface to be too large, directly destroying the chemical bonds inside the metal and causing Coulomb explosion damage; if the maximum temperature of the metal on the grating surface reflection layer is T max >T th , and the maximum value of the Coulomb electric field intensity E max >E th , will cause the metal layer on the grating surface to suffer from both thermal melting damage and Coulomb explosion damage; only when the maximum temperature of the metal on the grating surface reflection layer T max <T th At the same time, the maximum value of Coulomb electric field intensity E max <E th , the grating surface will not be damaged. Therefore, after the laser pulse irradiates the grating, the grating surface satisfies T max <T th And E max <E th The maximum incident laser energy density at this time is the laser damage threshold F of the grating. th .

[0038] Take the following metal pulse compression grating structure as an example: the grating ridge height h is 205-235nm, the grating period p is 530-560nm, the duty ratio d is 0.67-0.78, the grating metal film thickness is 200nm, and the average diffraction efficiency η in the 750-950nm band is eff>90% or more, highest diffraction efficiency η max 97%. For femtosecond laser pulses with a pulse width of 25fs-100fs, the traditional grating laser damage threshold prediction model calculates the 1-on-1 standard damage threshold to be 0.39J / cm 2 -0.66J / cm 2 The 1-on-1 standard damage threshold calculated by the model of the present invention is 0.36 J / cm 2 -0.65J / cm 2 According to experimental tests, the 1-on-1 standard laser damage threshold of this type of grating under 25fs-100fs pulse radiation is 0.33J / cm 2 -0.63J / cm 2 .

[0039] The beneficial effects of the present invention are:

[0040] The present invention uses a dual-temperature equation to describe the thermal coupling between the electrons on the top metal surface of the grating and the lattice temperature under femtosecond laser radiation, and uses the Fowler-DuBridge theory to describe the ultrafast electron motion and behavior on the metal surface irradiated by ultrashort and ultra-intense lasers. A complete multi-physics field model near the surface of the pulse compression grating under femtosecond laser radiation is established at the microscopic level. Compared with the laser damage resistance threshold obtained by existing experimental tests, the error is no more than 12%, which effectively improves the prediction accuracy of the laser damage resistance threshold in the design and production process of the pulse compression grating, and is of great significance to the development of pulse compression gratings and ultrafast optics based on chirped pulse amplification technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The geometric structure of the metal pulse compression grating, from top to bottom, is the air layer Ⅰ, the metal layer Ⅱ, the photoresist layer Ⅲ, and the substrate layer Ⅳ. Among them, p is the grating period, p 0 is the grating ridge width, duty ratio d = p 0 / p, h is the grating ridge height, w is the thickness of the top metal film, and α is the laser incident angle;

[0042] Figure 2 The incident laser energy density F is 0.59 J / cm 2 Schematic diagram of the change of the electron temperature and lattice temperature of the grating surface with time;

[0043] Figure 3 The incident laser energy density F is 0.49 J / cm 2 , 0.59J / cm 2 , 0.69J / cm 2 When the maximum grating surface lattice temperature T max Schematic diagram of changes over time;

[0044] Figure 4 The incident laser energy density F is 0.49 J / cm 2 , 0.59J / cm 2 , 0.69J / cm 2 When the electric field intensity on the grating surface reaches its maximum value E max Schematic diagram of changes over time. DETAILED DESCRIPTION

[0045] In order to better illustrate the present invention, the following detailed description of the implementation of the present invention is combined with the accompanying drawings and technical solutions, and the theoretical prediction method of the anti-laser damage threshold of the metal pulse compression grating used in the chirped pulse amplification system is described. This implementation description is implemented based on the technical solution of the present invention. The contents described below are all illustrative rather than restrictive, and should not be used to limit the scope of protection of the present invention.

[0046] The first step is to construct a surface electromagnetic field distribution model based on a metal pulse compression grating double-unit structure:

[0047] The geometric structure is air layer, gold film layer, photoresist layer, and substrate layer from top to bottom. The grating morphology is sin type, the grating line density is 1786 lines / mm, that is, the period p is 560nm, the ridge height h is 232nm, the duty ratio d is 0.75, and the metal film thickness is 200nm. The top boundary of the air layer and the bottom boundary of the substrate are set as port boundary conditions, the port type is set to periodic port, the top port is set to incident excitation on, the bottom port incident excitation is set to off, the incident laser is set to have a central wavelength λ of 800nm, and the pulse width t p The wavelength domain is 60fs, and it presents a Gaussian distribution in the time domain. The intensity peak is located at 120fs, and the incident angle α is 53°. The boundaries on both sides of the model are selected as periodic boundaries, the periodic type is selected as Floquet period, and the Floquet period k vector comes from the periodic port. Select wavelength domain analysis, and calculate the electromagnetic field distribution on the grating surface and the electromagnetic loss S distribution on the gold film surface of the top layer of the grating according to formula (1).

[0048] The second step is to establish the distribution model of the electron temperature and lattice temperature of the top gold film of the grating under femtosecond pulse radiation:

[0049] Based on the finite element analysis method, a two-temperature equation for the coupled state of the electron and lattice temperature in the gold film region on the top of the grating is created according to equation (2), where the gold film correlation coefficient involved in the two-temperature equation is obtained from the Metals Handbook published by the American Society for Metals or related papers. Then, the electromagnetic loss S obtained in the first step is brought into the calculation of equation (2), periodic boundary conditions are added on both sides of the gold film, transient analysis is selected, the time step is set to 0-15ps, and the time interval is 1fs, and the electron temperature T on the surface of the gold film on the top of the grating under a single pulse radiation is calculated. e and the lattice temperature T l Distributed over time.

[0050] The third step is to establish the electron emission model of the grating surface under femtosecond pulse radiation: Based on the finite element analysis method, the electron diffusion equation of the grating top gold film area is created according to equation (7), where the correlation coefficients involved in the equation are obtained in the same way as in the second step, and the electron temperature T e and the lattice temperature T l Substitute into the equation. The gold film surface on the top of the grating is set as the flux / source boundary condition, and the size is set to the total emitted electron current density flux J e Among them, J e The work function of gold is calculated by using equations (3), (4), (5), and (6): is 4.25 eV, while the laser photon energy with a central wavelength of 800 nm is 1.55 eV. Therefore, the photoelectron emission is two-photon emission and three-photon emission. To convert J under n = 2 and n = 3 n The sum is taken as the photoelectron emission current density. The initial value of the free electron number density of gold is n e0 5.9×10 28 m -3 . Calculate the electron emission rate of the top gold film surface of the grating and the residual electron distribution gradient of the gold film area under single pulse radiation. Then, use Poisson's equation to solve equation (8) to obtain the electric field E during the electron emission process on the entire gold film surface. c Select transient analysis, set the time step to 0-10ps, the time interval to 1fs, and select periodic boundary conditions on both sides of the top gold film of the grating.

[0051] The fourth step is to set different incident laser energy densities and repeatedly optimize and solve to obtain the grating anti-laser damage threshold:

[0052] In order to obtain more accurate results, the entire model is divided into free triangular meshes. Among them, the maximum mesh of the air layer, photoresist layer and substrate layer is λ / 8, and the minimum mesh is λ / 12. The gold film layer needs to calculate the coupling between electrons and the lattice, so the mesh needs to be divided finer, so the maximum mesh is λ / 12 and the minimum mesh is λ / 18. The laser spot radius is generally 0.2mm, and the equilibrium temperature T is calculated under different incident laser energy densities. c and the maximum value of the surface electric field strength E max :

[0053] 4.1) The incident laser energy density F is 0.49 J / cm 2 , the incident laser power density is 9.1667×10 16 W / cm 2 Substitute it into the first step to obtain the electromagnetic loss on the grating surface, and then substitute the electromagnetic loss into the second and third steps to obtain the maximum temperature T on the grating surface. max is 1141K, and the maximum electric field strength is E max is 8.439×10 9 V / m.

[0054] 4.2) The incident laser energy density F is 0.59 J / cm 2 , the incident laser power density is 9.8334×10 16 W / cm 2 Substitute it into the first step to obtain the electromagnetic loss on the grating surface, and then substitute the electromagnetic loss into the second and third steps to obtain the maximum temperature T on the grating surface. max is 1287.1K, and the maximum electric field strength is E max 9.840×10 9 V / m.

[0055] 4.2) The incident laser energy density F is 0.69 J / cm 2 , the incident laser power density is 1.05×10 17 W / cm 2 Substitute it into the first step to obtain the electromagnetic loss on the grating surface, and then substitute the electromagnetic loss into the second and third steps to obtain the maximum temperature T on the grating surface. max is 1541K, and the maximum electric field strength is E max 1.075×10 10 V / m.

[0056] Among them, the melting point of gold is T th is 1337K. The maximum grating surface temperature T max Changes over time such as Figure 3 As shown. The maximum electric field E on the grating surface max like Figure 4As shown, its variation trend is related to the electron temperature T e The incident laser energy density F is approximately the same, increasing to a maximum value within 200 fs and then slowly decreasing. 2 When T max With E max The incident laser energy density F is 0.69 J / cm 2 When T max With E max If the incident laser energy density F is 0.59 J / cm 2 When the electron temperature T e and lattice temperature T l Changes such as Figure 3 As shown, the electron temperature T e It rises rapidly to a maximum value of about 22000K within 200fs and then slowly decreases, while the lattice temperature T l The electron temperature T rises slowly during the entire coupling process. e and lattice temperature T l Reach thermal equilibrium 1335K, T max With E max are all smaller than the threshold and close to the threshold, so the final theoretical damage resistance threshold F of the grating is th Determined to be 0.59 J / cm 2 Previous experimental measurements have shown that the 1-on-1 standard laser damage threshold of the metal pulse compression grating structure is between 0.45 and 0.52 J / cm 2 The theoretical calculation result error is between 10.1% and 23.7%. Due to the limitations of the preparation process and splicing process, the theoretical calculation result error is within an acceptable range and has practical reference value.

[0057] The present invention realizes the establishment of multi-physical fields on the surface of a metal pulse compression grating under femtosecond laser irradiation, and provides a method for calculating the damage resistance threshold of a metal pulse compression grating under femtosecond laser pulse irradiation, with clear principles and high reliability of results.

[0058] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for predicting the laser damage threshold of a pulse compression grating taking into account the motion of surface electrons, characterized in that: Firstly, a sinusoidal grating geometric structure unit model is established, and the Maxwell equations are used in the frequency domain to calculate the electromagnetic field and electromagnetic loss on the pulse compression grating surface. Then, the double-temperature equation is used to calculate the electron temperature and lattice temperature on the pulse compression grating surface. Finally, the electron temperature is substituted into the Fowler-DuBridge equation to establish the electron motion model on the grating surface under femtosecond pulses, and the residual electron density is substituted into the Poisson equation to calculate the residual electric field on the grating surface. The minimum value of the incident laser energy density when the equilibrium temperature of the grating surface reaches the metal melting point and the residual electric field reaches the Coulomb explosion threshold is taken as the grating anti-laser damage threshold.

2. The method for predicting the laser damage threshold of a pulse compression grating taking into account the motion of surface electrons according to claim 1, characterized in that: The specific steps are as follows: The first step is to calculate the electromagnetic field and electromagnetic loss on the pulse compression grating surface 1.1) Establish a sinusoidal grating geometric structure unit model, which consists of an air layer, a metal reflective film layer, a photoresist layer and a substrate layer from top to bottom; the metal pulse compression grating structure parameters include: ridge height h, period p, duty ratio d, and top film thickness w; at the same time, according to the strict coupled wave vector theory, in order to ensure the diffraction efficiency and working bandwidth of the pulse compression grating, the grating period p and the incident pulse wavelength λ should satisfy the relationship: λ / 2<p<3λ / 2; 1.2) Use Maxwell's equations to calculate the electromagnetic field distribution near the grating surface; set the upper interface of the air layer as the port incidence condition, the incident angle of the femtosecond pulse to α, the incident laser energy density to J, and the pulse width to t p , incident laser power density I0 = J / t p , the incident electric field Where ε0 represents the dielectric constant of vacuum. Due to the phase modulation effect of the grating on the electromagnetic field, the Floquet periodic boundary conditions are set on both sides of the sinusoidal grating geometric structure unit model. The frequency domain is selected to calculate the electromagnetic field E and the electromagnetic loss S on the grating surface according to formula (1): in, is the differential operator, E is the electromagnetic field intensity, k is the wave number in vacuum, μ r is the relative magnetic permeability, ε r is the relative dielectric constant, S is the electromagnetic loss, ε' is the imaginary part of the relative dielectric constant, ω is the frequency of the incident electromagnetic field, and c0 is the speed of light in a vacuum; The second step is to calculate the surface electron temperature and lattice temperature of the pulse compression grating The double-temperature equation is used to describe the heat transfer process on the metal surface. The electromagnetic loss S calculated in equation (1) is substituted into equation (2) as the heat source. Using transient research, only the top metal of the grating is calculated, and the two sides are selected as periodic boundary conditions. The surface electron temperature T of the pulse compression grating is calculated according to equation (2): e and the lattice temperature T l distributed: Among them, C e is the electron heat capacity, T e is the electron temperature, t is the time, k e is the electronic thermal conductivity, G is the electron-lattice coupling coefficient, C l is the lattice heat capacity, T l is the lattice temperature, k l is the lattice thermal conductivity; Electron temperature T e and the lattice temperature T l The initial values ​​are all set to 300K. The femtosecond laser pulse irradiates the grating, and the grating surface electron temperature T e It rises rapidly to a maximum value within a few femtoseconds and then gradually decreases. During this period, the lattice temperature T l Slowly increases, and finally after a few picoseconds the electron temperature T e and lattice temperature T l The lattice temperature T l That is, the grating surface temperature T after laser pulse radiation. If the temperature T of the top metal film of the grating exceeds the melting point, thermal melting damage will occur; The third step is to establish a model of electron motion on the grating surface under femtosecond pulses. The Fowler-DuBridge theory is used to analyze the electron motion on the surface of a metal pulse compression grating under femtosecond pulse radiation. 3.1) Set the surface of the top metal film of the grating as the source boundary condition, and the absorption source as the electron emission energy flux density J e Among them, J e Using formula (3), we can calculate: Where J0 is the thermal electron emission energy flux density, J n is the multi-photon emission energy flux density; Using J e Calculate the electron emission on the grating surface under femtosecond laser pulse radiation; after the metal absorbs the laser pulse radiation, calculate the photoelectron emission current density J on the metal surface according to formula (4) n : Among them, J n is the photoelectron emission current density, a n is the n-photon emission coefficient, e is the electron charge, hv is the photon energy, A is the theoretical Richardson constant, I0 is the incident laser power density, R is the metal surface reflectivity, is the metal work function, k B is the Boltzmann constant; F(X n ) is the Fowler function, calculated according to formula (5): When the metal temperature rises above 1273.25K, the thermal electron emission current density J0 on the metal surface is calculated according to formula (6): Where, J0 is the thermal electron emission current density, A is the theoretical Richardson constant, is the metal work function, k B is the Boltzmann constant; 3.2) The grating metal surface emits electrons, and the surface and internal residual electrons will present a gradient distribution. At the same time, the internal electrons will move and diffuse near the grating surface to reduce the residual electron distribution gradient difference. The residual electron gradient distribution and diffusion trend of the grating top metal film are calculated according to formula (7): Among them, n e is the electron density emitted by the grating, e is the electron charge, J x is the electron energy density distribution on the grating surface, μ e is the electron mobility, D e is the electron diffusion coefficient, τ e is the electron relaxation time, m e is the mass of the electron, E c is the residual electric field strength generated by the residual electron density distribution gradient; 3.3) Since the residual electron density of the metal film on the top of the grating is distributed in a gradient manner, a residual electric field E will be generated inside the grating. c , if the residual electric field E c If it is large enough, it will directly destroy the chemical bonds inside the grating and cause damage to the grating; the residual electric field strength E c The Poisson equation is calculated by formula (8): Where ε0 is the dielectric constant of vacuum, ε is the relative dielectric constant of the material at the incident pulse frequency; Step 4: Determine the grating laser damage threshold F th Size The maximum metal temperature T of the grating surface reflection layer max The melting point T of the metal on the pulse compression grating surface th For comparison, at the same time, the Coulomb electric field strength E c The maximum value E max The electric field strength threshold E of metal Coulomb explosion th Contrast; if the maximum temperature of the metal reflecting layer on the grating surface is T max >T th , and the maximum Coulomb electric field intensity E max <E th , will cause the grating surface temperature to be higher than its metal melting point, resulting in thermal melting damage; if the maximum temperature of the grating surface reflective layer metal T max <T th , and the maximum Coulomb electric field intensity E max >E th , which will cause the Coulomb force generated by the electric field inside the metal on the grating surface to be too large, directly destroying the chemical bonds inside the metal and causing Coulomb explosion damage; if the maximum temperature of the metal on the grating surface reflection layer is T max >T th , and the maximum value of the Coulomb electric field intensity E max >E th , will cause the metal layer on the grating surface to suffer from both thermal melting damage and Coulomb explosion damage; only when the maximum temperature of the metal on the grating surface reflection layer T max <T th At the same time, the maximum value of the Coulomb electric field intensity E max <E th , the grating surface will not be damaged; therefore, after the laser pulse irradiates the grating, the grating surface satisfies T max <T th And E max <E th The maximum incident laser energy density at this time is the laser damage threshold F of the grating. th .

3. The method for predicting the laser damage threshold of a pulse compression grating taking into account the motion of surface electrons according to claim 2, characterized in that: The first step (1) is as follows: the grating ridge height h is 205-235nm, the grating period p is 530-560nm, the duty ratio d is 0.67-0.78, the grating metal film thickness is 200nm, and the average diffraction efficiency η is within the 750-950nm band. eff >90% or more, highest diffraction efficiency η max 97%.

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