Method for analyzing femtosecond laser-induced damage behavior on surface of Zn-doped KDP crystal

Abstract

This invention provides a method for analyzing the femtosecond laser-induced damage behavior of Zn-doped KDP crystal surfaces, belonging to the field of engineering optics technology based on computer data processing. First, the effects of Zn doping concentration on the bandgap and electroacoustic coupling of the KDP crystal are analyzed using UV-Vis absorption spectroscopy and Brillouin scattering spectroscopy, respectively. Then, a one-dimensional model is constructed, and the time evolution of electron density, lattice temperature, and electron temperature on the Zn-doped KDP crystal surface under femtosecond laser irradiation is simulated using a rate equation for electron density accumulation and a two-temperature model. The influence of Zn doping concentration on the damage behavior of the KDP crystal surface is theoretically analyzed, and a theoretical model for calculating the femtosecond laser-induced damage threshold is established, thus non-destructively determining the optimal Zn doping concentration. This invention avoids contact with real samples, improving sample utilization; the simulation process is more stable and controllable with high data repeatability; it can also shorten the research cycle and accelerate the selection of the optimal doping concentration.

Description

Technical Field

[0001] This invention belongs to the field of engineering optics technology based on computer data processing, and particularly relates to a method for analyzing the femtosecond laser-induced damage behavior on the surface of Zn-doped KDP crystals. Background Technology

[0002] Potassium dihydrogen phosphate (KH₂PO₄, KDP) crystals possess excellent nonlinear optical properties and are widely used in laser frequency conversion and electro-optic modulation. In particular, the ability to grow large-sized single crystals makes it an irreplaceable optical element in inertial confinement fusion (ICF). During crystal growth, metal ions from the raw materials, solvent (water), or growth equipment inevitably enter the crystal structure. Furthermore, the presence of appropriate doping ions significantly optimizes the nonlinear optical properties of KDP crystals. Specifically, the presence of Zn ions increases the second harmonic generation (SHG) efficiency of KDP crystals by 1.55 times. However, the presence of Zn ions also affects the laser damage resistance of KDP crystals. Especially with the development of chirped-pulse amplification (CPA) technology, the surface of KDP crystals must withstand laser intensities far exceeding previous levels. Therefore, to enhance the optical properties of crystals while ensuring they have a sufficient damage threshold, it is necessary to thoroughly analyze and explore the optimal doping ratio of Zn ions.

[0003] Currently, to investigate the effect of doping concentration on the damage threshold, laser-induced damage experiments are required. However, traditional laser damage experiments are destructive tests. Once the sample reaches the damage threshold, the crystal structure undergoes irreversible damage, rendering it unusable for subsequent performance tests. This is disadvantageous for KDP crystals, which have long growth and processing cycles. Furthermore, traditional laser damage experiments have high hardware requirements, necessitating the construction of a dedicated platform including a high-power pulsed laser, a precision optical adjustment system, a real-time observation system, and an environmental control module. Such platforms are costly, complex to operate, and carry multiple potential experimental risks. In addition, traditional laser damage experiments also suffer from cumbersome procedures, long single-experiment cycles, and low efficiency in error and data processing.

[0004] Current research on the effects of Zn ions on the damage behavior of KDP crystals in femtosecond lasers mainly focuses on traditional laser damage experimental analysis, without involving a reliable model or calculation method. Summary of the Invention

[0005] To address the shortcomings of traditional laser damage experimental analysis, this invention provides a method for analyzing femtosecond laser-induced damage behavior on the surface of Zn-doped KDP crystals. The method simulates the interaction between the laser and the Zn-doped KDP crystal surface within a femtosecond timescale. The influence of Zn ions on the KDP crystal is analyzed using UV-Vis absorption spectroscopy and Brillouin scattering spectroscopy. The photoionization process is described using the multiphoton ionization formula in Keldysh theory, the collisional ionization process is described using the Drude formula, and the energy exchange between the electron-lattice system is described using a two-temperature equation.

[0006] To achieve the above objectives, this invention proposes a method for analyzing femtosecond laser-induced damage behavior on the surface of Zn-doped KDP crystals, comprising the following steps:

[0007] S1. Calculate the band gap and acoustic velocity of KDP crystals with different Zn doping amounts using ultraviolet-visible absorption spectroscopy and Brillouin light scattering spectroscopy, respectively.

[0008] S2. Establish a one-dimensional model of Zn-doped KDP crystal. The model is a line segment, and the two endpoints of the line segment represent the two sides of the crystal surface.

[0009] S3. Based on the band gap obtained in S1, calculate the photoionization, collisional ionization and relaxation decay terms of valence band electrons under femtosecond laser irradiation. These three terms constitute the rate equation describing the accumulation of free electrons in Zn-doped KDP crystals under femtosecond laser irradiation.

[0010] S4. Based on the acoustic velocity obtained in S1, calculate the electroacoustic coupling factor of different Zn-doped KDP crystals. Combine the energy absorption and diffusion process to construct a two-temperature equation describing the energy exchange between the electronic system and the lattice system of Zn-doped KDP crystals under femtosecond laser irradiation.

[0011] S5. Couple the rate equation and the two-temperature equation to form a self-consistent model for analyzing the femtosecond laser-induced damage behavior on the surface of Zn-doped KDP crystals.

[0012] S6. The self-consistent model is visualized at the one-dimensional model endpoint on the incident light side, and the femtosecond laser-induced damage behavior on the Zn-doped KDP crystal surface is analyzed by the time evolution of electron density, electron temperature and lattice temperature.

[0013] Furthermore, in S1, the KDP crystals with different Zn doping amounts, after being cut and polished, have a thickness of 1 mm and a band gap of... E g The calculation formula is:

[0014] ;

[0015] Where α is the linear absorption coefficient. Where is the energy of the incident photon, B is a constant related to the band tail range, and q is a coefficient controlling the electronic transition; the direct and indirect transition band gaps can correspond to 0.5 and 2, respectively. When calculating the optical band gap of a KDP crystal, the direct transition process (q=0.5) is appropriate.

[0016] Furthermore, in S1, the acoustic velocity v of the KDP crystal under different Zn doping amounts... s The calculation formula is:

[0017] ;

[0018] Among them, v p λ is the group velocity of the correlated phonon mode, λ is the incident laser wavelength, ƒ is the spectral position of the correlation peak, and n is the sample refractive index.

[0019] Furthermore, in S3, the rate equation for the accumulation of free electrons in the KDP crystal under different Zn doping concentrations is as follows:

[0020] ;

[0021] in, n e It is electron density. t It is time. I It is the intensity of the incident laser. W PI ( I ( t The term )) represents photoionization, and it employs the multiphoton ionization formula from Keldysh theory. W II ( I ( t ))· n e (t) It is the collisional ionization term, the collisional ionization rate. W II ( I ( t The Drude collisional ionization formula is used. W rel The relaxation decay term is represented as:

[0022] ;

[0023] in, n e It is electron density. τ r The relaxation time and the change in band gap directly affect the collisional ionization term, and also indirectly affect the photoionization term by affecting the effective ionization potential.

[0024] Furthermore, in S4, the electroacoustic coupling factor in the KDP crystal under different Zn doping concentrations... G Represented as:

[0025] ;

[0026] in, n e It is electron density. v s It is the acoustic speed of sound, k B It is Boltzmann's constant. k It refers to thermal conductivity.

[0027] Furthermore, in S4, the dual-temperature model is expressed as:

[0028] ;

[0029] in, n e It is electron density. t It is time. E g It is a band gap. I It is the intensity of the incident laser. G It is the electroacoustic coupling factor. W PI ( I ( t )) is a photoionization term, k e , C e and T e These represent the thermal conductivity, heat capacity, and temperature of free electrons, respectively. k l , C l and T l θ represents the thermal conductivity, heat capacity, and temperature of the crystal lattice, respectively; θ represents the free electron absorption coefficient; and m represents the number of photons absorbed by multiphotons. This represents the energy of the incident photon.

[0030] Furthermore, in S5, the self-consistent model is expressed as:

[0031] ;

[0032] in, n e It is electron density. t It is time. I It is the intensity of the incident laser. W PI ( I ( tThe term )) represents photoionization, and it employs the multiphoton ionization formula from Keldysh theory. W II ( I ( t ))· n e (t) It is the collisional ionization term, the collisional ionization rate. W II ( I ( t The Drude collisional ionization formula is used. E g It is a band gap. G It is the electroacoustic coupling factor. k e , C e and T e These represent the thermal conductivity, heat capacity, and temperature of free electrons, respectively. k l , C l and T l θ represents the thermal conductivity, heat capacity, and temperature of the crystal lattice, respectively; θ represents the free electron absorption coefficient; and m represents the number of photons absorbed by multiphotons. Represents the energy of the incident photon; W rel This is a relaxation decay term.

[0033] Furthermore, the damage criterion for KDP crystals is defined as the electron density reaching the critical electron density. n cr :

[0034] ;

[0035] Where e represents the electron charge; Represents the free space dielectric constant; Indicates the effective electron mass; ω This indicates the angular frequency of the incident laser.

[0036] Furthermore, the laser pulse width is on the order of femtoseconds, the laser parameters are defined in the global definition of the COMSOL simulation software, the model length of the Zn-doped KDP crystal is on the order of micrometers, and only the time evolution of the electron density, electron temperature and lattice temperature on the surface of the Zn-doped KDP crystal under a single pulse irradiation is calculated.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) This invention considers the effects of different Zn doping amounts on the band gap and sound velocity of KDP crystals;

[0039] (2) This invention provides a method for analyzing the femtosecond laser-induced damage behavior of Zn-doped KDP crystal surface. The method mathematically describes the time evolution of electron density, lattice temperature and electron temperature on the Zn-doped KDP crystal surface under femtosecond laser irradiation, and analyzes the influence of Zn doping amount on the damage behavior of KDP crystal surface.

[0040] (3) The establishment of the self-consistent model in this invention provides a theoretical basis for rapidly screening the optimal doping amount of Zn, and the method will not cause any damage to the crystal, thus greatly improving the sample utilization rate. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method for analyzing the femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal according to the present invention.

[0042] Figure 2 These are the UV-Vis absorption spectra and band gaps of different Zn-doped KDP crystals.

[0043] Figure 3 These are Brillouin light scattering spectra of KDP crystals with different Zn doping.

[0044] Figure 4 The photoionization efficiency W of different Zn-doped KDP crystals PI (I(t)) Schematic diagram.

[0045] Figure 5 This is a schematic diagram showing the damage size and damage threshold of different Zn-doped KDP crystals.

[0046] Figure 6 This is a schematic diagram showing the time evolution of electron density in different Zn-doped KDP crystals.

[0047] Figure 7 This is a time evolution diagram of electron density, electron temperature, and lattice temperature on the KDP crystal surface under femtosecond laser irradiation according to the present invention. Detailed Implementation

[0048] The invention will be further described below with reference to specific embodiments.

[0049] Simulation analysis avoids physical contact with real samples, preventing any damage to the physical structure or chemical composition of the crystal, thus significantly improving sample utilization. This is particularly suitable for studying KDP crystals, which have long growth cycles and complex processing. Furthermore, simulation analysis is conducted in a virtual computing environment, eliminating the risks associated with physical laser sources, high-voltage circuits, and high-temperature components, fundamentally avoiding the possibility of personnel injury or equipment damage. The experimental process is more stable and controllable. Based on deterministic physical models and mathematical equations, parameters (crystal parameters, laser parameters) can be precisely controlled. The simulation analysis process is fully automated, free from external environmental interference or human error, resulting in extremely high data repeatability. Simulation analysis can also shorten the research cycle and accelerate the selection of optimal doping levels. Therefore, this invention proposes a reliable model or calculation method based on simulation analysis to analyze the femtosecond laser damage behavior of Zn ions on KDP crystals.

[0050] like Figure 1 As shown, this invention provides a method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal, comprising the following steps:

[0051] Step 1: Calculate the band gap and acoustic velocity of KDP crystals with different Zn doping amounts using ultraviolet-visible absorption spectroscopy and Brillouin light scattering spectroscopy, respectively.

[0052] Step 2: Establish a one-dimensional model of the Zn-doped KDP crystal. The model is a 10 μm long line segment, with the two ends of the line segment representing the two sides of the crystal surface.

[0053] Step 3: Based on the band gap obtained in Step 1, calculate the photoionization term, collisional ionization term, and relaxation decay term of valence band electrons under femtosecond laser irradiation. These three terms constitute the rate equation describing the accumulation of free electrons in Zn-doped KDP crystals under femtosecond laser irradiation.

[0054] Step 4: Based on the acoustic velocity obtained in Step 1, calculate the electroacoustic coupling factor of different Zn-doped KDP crystals, and combine the energy absorption and diffusion processes to construct a two-temperature equation describing the energy exchange between the electronic system and the lattice system of Zn-doped KDP crystals under femtosecond laser irradiation.

[0055] Step 5: The rate equation and the two-temperature equation are coupled to form a self-consistent model for analyzing the femtosecond laser-induced damage behavior on the surface of Zn-doped KDP crystals;

[0056] Step 6: The self-consistent model is visualized at the endpoint of the one-dimensional model on the incident light side. The femtosecond laser-induced damage behavior on the Zn-doped KDP crystal surface is analyzed by the time evolution of electron density, electron temperature, and lattice temperature.

[0057] In step one, KDP crystals with different Zn doping concentrations were cut and polished to a thickness of 1 mm and a band gap of [missing information]. Eg The calculation formula is:

[0058] (1)

[0059] Where α is the linear absorption coefficient. is the energy of the incident photon, and B is a constant related to the band tail range. Additionally, q is a coefficient controlling electronic transitions. Direct and indirect transition band gaps can correspond to 0.5 and 2, respectively. When calculating the optical band gap of a KDP crystal, using the direct transition process (q=0.5) is appropriate.

[0060] Based on their Zn content, the samples were named KDP-0, KDP-1000, KDP-2000, and KDP-4000, respectively. Figure 2 As shown, different Zn doping amounts affect the band gap of KDP crystals, with KDP-0 having a band gap of 6.38 eV, KDP-1000 having a band gap of 6.49 eV, KDP-2000 having a band gap of 6.19 eV, and KDP-4000 having a band gap of 6.11 eV.

[0061] Furthermore, in step one, the acoustic velocity of the KDP crystal under different Zn doping concentrations... v s The calculation formula is:

[0062] (2)

[0063] in, v p λ is the group velocity of the correlated phonon mode, λ is the incident laser wavelength, ƒ is the spectral position of the correlation peak, and n is the sample refractive index.

[0064] like Figure 3 As shown, KDP crystals with different Zn doping amounts have the same spectral position and the same acoustic velocity.

[0065] In step three, the electron-photoionization phase in the KDP crystal under different Zn doping concentrations... W PI ( I (t) is calculated using the multiphoton ionization formula in Keldysh theory:

[0066] (3)

[0067] Where γ represents the adiabatic parameters (Keldysh parameters) of the solid material; Γ and ζ represent the equation parameters, which can be calculated from γ to obtain Γ=γ. 2 / (1+γ 2 ), ζ=1 / (1+γ 2 );< The ">" symbol represents the integer part within the parentheses, indicating the number of photons required to excite an electron from the valence band to the conduction band. Indicates the effective electron mass; ω Indicates the incident laser angular frequency. Ф(z) represents the reduced Planck constant; Ф(z) represents the Dawson equation; other abbreviations are as follows:

[0068] (4)

[0069] (5)

[0070] (6)

[0071] (7)

[0072] (8)

[0073] Where n represents the refractive index of the material; c represents the speed of light; I represents the incident laser intensity; K and E represent the first and second type complete elliptic integrals, respectively; and Δ represents the effective ionization potential.

[0074] As attached Figure 4 As shown, changes in the band gap indirectly affect the photoionization term by influencing the effective ionization potential. W PI ( I (t)).

[0075] In step three, the electron collisional ionization rate in the KDP crystal under different Zn doping concentrations is... W II ( I The formula for calculating (t) is:

[0076] (9)

[0077] in, E g Represents the band gap. t It is time. I It is the incident laser intensity, σ and τ c Representing the photon absorption cross section and the electron collision time, respectively, the mathematical expression is:

[0078] (10)

[0079] (11)

[0080] Where e represents the electron charge; Represents the free space dielectric constant; Indicates the effective electron mass; ω Indicates the incident laser angular frequency. E g Represents the band gap.

[0081] In step three, the electron decay term in the KDP crystal under different Zn doping concentrations is expressed as:

[0082] (12)

[0083] in, n e It is electron density. τ r It is the relaxation time.

[0084] In step three, the rate equation for the accumulation of free electrons in the KDP crystal under different Zn doping concentrations is as follows:

[0085] (13)

[0086] In step four, the electroacoustic coupling factor G in the KDP crystal under different Zn doping concentrations is expressed as:

[0087] (14)

[0088] in, n e It is electron density. v s It is the acoustic speed of sound, k B It is Boltzmann's constant. k It refers to thermal conductivity.

[0089] In step four, the two-temperature model is expressed as:

[0090] (15)

[0091] in, n e It is electron density. t It is time. E g It is a band gap. I It is the intensity of the incident laser. G It is the electroacoustic coupling factor. W PI ( I ( t )) is a photoionization term, k e , C e and T e These represent the thermal conductivity, heat capacity, and temperature of free electrons, respectively. kl , C l and T l θ represents the thermal conductivity, heat capacity, and temperature of the crystal lattice, respectively; θ represents the free electron absorption coefficient; and m represents the number of photons absorbed by multiphotons. This represents the energy of the incident photon.

[0092] In step five, the self-consistent model is represented as:

[0093] (16)

[0094] in, n e It is electron density. t It is time. I It is the intensity of the incident laser. W PI ( I ( t The term )) represents photoionization, and it employs the multiphoton ionization formula from Keldysh theory. W II ( I ( t The term )) represents the collisional ionization term, and the Drude collisional ionization formula is used. E g It is a band gap. G It is the electroacoustic coupling factor. k e , C e and T e These represent the thermal conductivity, heat capacity, and temperature of free electrons, respectively. k l , C l and T l θ represents the thermal conductivity, heat capacity, and temperature of the crystal lattice, respectively; θ represents the free electron absorption coefficient; and m represents the number of photons absorbed by multiphotons. This represents the energy of the incident photon.

[0095] Furthermore, the damage criterion for KDP crystals is defined as the electron density reaching the critical electron density n. cr :

[0096] (17)

[0097] Where e represents the electron charge; ε0 represents the free space permittivity; Indicates the effective electron mass; ω This indicates the angular frequency of the incident laser.

[0098] like Figure 5 As shown, under the same laser energy irradiation, the damage size of KDP crystal first decreases and then increases with the increase of Zn doping amount, while the damage threshold first increases and then decreases with the increase of Zn doping amount, and is 9.57 J / cm² for KDP-0, 10.51 J / cm² for KDP-1000, 8.63 J / cm² for KDP-2000, and 7.55 J / cm² for KDP-4000.

[0099] The laser pulse width is on the order of femtoseconds. The laser parameters are defined in the global definition of the COMSOL simulation software. The model length of the Zn-doped KDP crystal is on the order of micrometers. Only the simulation results after a single pulse irradiation are calculated.

[0100] like Figure 6 The figure shows the time evolution of electron density on the surface of different Zn-doped KDP crystals under femtosecond laser irradiation, with a pulse width of 300 fs and a pulse energy density of 8 J / cm². 2 Under single-pulse irradiation, the electron density of KDP crystals with different Zn doping amounts first decreases and then increases with the increase of Zn doping amount. Damage occurs when the electron density reaches the critical electron density. Therefore, the damage threshold first increases and then decreases with the increase of Zn doping amount. The self-consistent model reasonably explains the influence of Zn doping on the damage threshold of KDP crystal surface.

[0101] like Figure 7 As shown, the time evolution diagrams of electron density, electron temperature, and lattice temperature on the KDP crystal surface under femtosecond laser irradiation are presented. The self-consistent model completely simulates the femtosecond laser-induced damage behavior on the Zn-doped KDP crystal surface.

[0102] As can be seen from the above examples, this invention considers the influence of different Zn doping amounts on the band gap and sound velocity of KDP crystals; it provides a method for analyzing the femtosecond laser-induced damage behavior on the surface of Zn-doped KDP crystals, mathematically describing the time evolution of electron density, lattice temperature, and electron temperature on the surface of Zn-doped KDP crystals under femtosecond laser irradiation, and analyzing the influence of Zn doping amount on the damage behavior of KDP crystal surfaces; the establishment of a self-consistent model in this invention provides a theoretical basis for rapidly screening the optimal Zn doping amount, and this method does not cause any damage to the crystal, significantly improving sample utilization.

[0103] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0104] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal, characterized in that, Includes the following processes: S1. The band gap and acoustic velocity of KDP crystals with different Zn doping concentrations were calculated using UV-Vis absorption spectroscopy and Brillouin scattering spectroscopy, respectively. After cutting and polishing, the KDP crystals with different Zn doping concentrations had a thickness of 1 mm and the band gaps were... E g The calculation formula is: ； Where α is the linear absorption coefficient. is the energy of the incident photon; B is a constant related to the range of the band tail; q is the coefficient that controls the electron transition. Acoustic velocity v of KDP crystal under different Zn doping concentrations s The calculation formula is: ； Among them, v p is the group velocity of the correlated phonon mode, λ is the incident laser wavelength, ƒ is the spectral position of the correlation peak, and n is the sample refractive index; S2. Establish a one-dimensional model of Zn-doped KDP crystal. The model is a line segment, and the two endpoints of the line segment represent the two sides of the crystal surface. S3. Based on the band gap obtained in S1, calculate the photoionization, collisional ionization and relaxation decay terms of valence band electrons under femtosecond laser irradiation. These three terms constitute the rate equation describing the accumulation of free electrons in Zn-doped KDP crystals under femtosecond laser irradiation. S4. Based on the acoustic velocity obtained in S1, calculate the electroacoustic coupling factor of different Zn-doped KDP crystals. Combine the energy absorption and diffusion process to construct a two-temperature equation describing the energy exchange between the electronic system and the lattice system of Zn-doped KDP crystals under femtosecond laser irradiation. S5. Couple the rate equation and the two-temperature equation to form a self-consistent model for analyzing the femtosecond laser-induced damage behavior on the surface of Zn-doped KDP crystals. S6. The self-consistent model is visualized at the one-dimensional model endpoint on the incident light side, and the femtosecond laser-induced damage behavior on the Zn-doped KDP crystal surface is analyzed by the time evolution of electron density, electron temperature and lattice temperature.

2. The method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal as described in claim 1, characterized in that: In S3, the rate equation for the accumulation of free electrons in the KDP crystal under different Zn doping concentrations is as follows: ； in, n e It is electron density. t It is time. I It is the intensity of the incident laser. W PI ( I ( t The term )) represents photoionization, and it employs the multiphoton ionization formula from Keldysh theory. W II ( I ( t ))· n e (t) It is the collisional ionization term, the collisional ionization rate. W II ( I ( t The Drude collisional ionization formula is adopted. W rel The relaxation decay term is represented as: ； in, n e It is electron density. τ r It is the relaxation time.

3. The method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal as described in claim 2, characterized in that: In S4, the electroacoustic coupling factor in the KDP crystal under different Zn doping concentrations G Represented as: ； in, n e It is electron density. v s It is the acoustic speed of sound, k. B It is Boltzmann's constant. k It refers to thermal conductivity.

4. The method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal as described in claim 3, characterized in that: In S4, the dual-temperature model is expressed as: ； in, n e It is electron density. t It is time. E g It is a band gap. I It is the intensity of the incident laser. G It is the electroacoustic coupling factor. W PI ( I ( t )) is a photoionization term, k e , C e and T e These represent the thermal conductivity, heat capacity, and temperature of free electrons, respectively. k l , C l and T l θ represents the thermal conductivity, heat capacity, and temperature of the crystal lattice, respectively; θ represents the free electron absorption coefficient; and m represents the number of photons absorbed by multiphotons. This represents the energy of the incident photon.

5. The method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal as described in claim 4, characterized in that: In S5, the self-consistent model is expressed as: ； in, n e It is electron density. t It is time. I It is the intensity of the incident laser. W PI ( I ( t The term )) represents photoionization, and it employs the multiphoton ionization formula from Keldysh theory. W II ( I ( t ))· n e (t) It is the collisional ionization term, the collisional ionization rate. W II ( I ( t The Drude collisional ionization formula is adopted. E g It is a band gap. G It is the electroacoustic coupling factor. k e , C e and T e These represent the thermal conductivity, heat capacity, and temperature of free electrons, respectively. k l , C l and T l θ represents the thermal conductivity, heat capacity, and temperature of the crystal lattice, respectively; θ represents the free electron absorption coefficient; and m represents the number of photons absorbed by multiphotons. Represents the energy of the incident photon; W rel This is a relaxation decay term.

6. The method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal as described in claim 1, characterized in that: The damage criterion for KDP crystals is defined as the electron density reaching the critical electron density. n cr : ； Where e represents the electron charge; Represents the free space dielectric constant; Indicates the effective electron mass; ω This indicates the angular frequency of the incident laser.

7. The method for analyzing femtosecond laser-induced damage behavior on the surface of a Zn-doped KDP crystal as described in claim 1, characterized in that: The laser pulse width is on the order of femtoseconds. The laser parameters are defined in the global definition of the COMSOL simulation software. The model length of the Zn-doped KDP crystal is on the order of micrometers. Only the time evolution of the electron density, electron temperature and lattice temperature on the surface of the Zn-doped KDP crystal under a single pulse irradiation is calculated.

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