A method for high-precision non-destructive evaluation of laser damage threshold of crystals

Abstract

This invention relates to a method for high-precision non-destructive evaluation of the laser damage threshold of crystals. The method includes: characterizing the defect states of the crystal under test using a photoluminescence testing system to obtain internal defect state information; testing the surface absorption characteristics of the crystal under test using a photothermal weak absorption testing system to obtain an absorption coefficient correction factor; inputting the defect state information and the absorption coefficient correction factor into a free electron density analysis model containing defect state terms to calculate the free electron density under laser irradiation conditions; calculating the temperature field distribution and thermal stress distribution of the crystal using an optical-thermal-mechanical multiphysics coupling analysis model based on the free electron density; and determining the laser damage threshold of the crystal under test based on the comparison results of the free electron density, temperature field distribution, and thermal stress distribution with a preset damage threshold. This invention achieves high-precision non-destructive evaluation of the laser damage threshold of crystals, significantly reducing testing costs and improving evaluation accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of laser damage threshold evaluation test, in particular to a method for evaluating the laser damage threshold of a crystal with high precision and non-destructively. BACKGROUND

[0002] In high-power laser driving devices and photolithography systems, the damage of optical elements has always been a bottleneck problem affecting the safe operation of the system. Especially for crystal materials, due to the complexity of the growth and preparation process, the price of large crystals is relatively high, and the laser damage of the crystal cannot be effectively repaired after the laser damage, so the laser damage of the crystal is the key to the overall system operation cost. For the laser damage resistance test of the element, the laser damage threshold test is often used for evaluation, but the traditional laser damage threshold test often destructively damages the structure of the crystal to realize the corresponding laser damage threshold test, which brings great waste to the crystal element, and also cannot effectively test the laser damage of all positions of the element.

[0003] Therefore, there is an urgent need to invent a method for evaluating the laser damage threshold of a crystal with high precision and non-destructively, which is of great significance to improve the crystal damage mechanism cognition and improve the corresponding crystal growth and preparation process. In the prior art, although there are some non-destructive detection methods based on photothermal weak absorption, these methods can only establish a simple empirical relationship, lack of in-depth analysis of the internal defect state of the crystal, and cannot accurately reflect the physical mechanism of the deviation of the laser damage threshold of the crystal from the intrinsic damage threshold of the crystal caused by various defects of the crystal, resulting in limited evaluation precision. SUMMARY

[0004] In view of the above-mentioned shortcomings of the prior art, the purpose of the present application is to provide a method for evaluating the laser damage threshold of a crystal with high precision and non-destructively, which realizes the high-precision non-destructive evaluation of the laser damage threshold of the crystal by establishing a quantitative physical model between the internal defect state of the crystal and the laser damage threshold, and can significantly reduce the test cost and improve the evaluation accuracy.

[0005] To achieve the above-mentioned purpose, the present application adopts the following technical solutions.

[0006] A method for evaluating the laser damage threshold of a crystal with high precision and non-destructively, comprising:

[0007] characterizing the defect state of the to-be-tested crystal by using a photoluminescence test system to obtain the internal defect state information of the crystal;

[0008] testing the surface absorption characteristics of the to-be-tested crystal by using a photothermal weak absorption test system to obtain an absorption coefficient correction factor;

[0009] inputting the defect state information and the absorption coefficient correction factor into a free electron density analysis model containing a defect state term, and calculating a free electron density under laser irradiation conditions;

[0010] calculating a temperature field distribution and a thermal stress distribution of the crystal based on the free electron density through an optical-thermal-mechanical multi-physical field coupling analysis model; and

[0011] determining a laser damage threshold of the to-be-tested crystal according to a comparison result of the free electron density, the temperature field distribution and the thermal stress distribution with a preset damage threshold.

[0012] Further, in the method, the defect state characterization of the to-be-tested crystal by the photoluminescence test system comprises:

[0013] emitting excitation light to induce the to-be-tested crystal to generate photoluminescence;

[0014] recording a position of a photoluminescence peak and a corresponding integral intensity;

[0015] combining a central wavelength position of the excitation light and a corresponding integral light intensity to calculate a position of a corresponding defect state in a band gap and a corresponding defect state electron density; and

[0016] inputting the defect state information into a free electron density joint analysis model with a defect state term.

[0017] Further, in the method, the wavelength range of the excitation light is any wavelength laser in a deep ultraviolet to ultraviolet band.

[0018] Further, in the method, a calculation formula of the free electron density analysis model containing the defect state term is expressed as: a free electron density change rate is equal to a free electron density term of valence band electrons formed by multi-photon absorption, tunneling ionization and avalanche ionization minus a conduction band electron relaxation term, plus a defect state electron photoluminescence ionization term minus a defect state electron density relaxation term.

[0019] Further, in the method, the multi-photon absorption, tunneling ionization and avalanche ionization terms all contain a product of the absorption coefficient correction factor and an incident laser intensity.

[0020] Further, in the method, the optical-thermal-mechanical multi-physical field coupling analysis model comprises:

[0021] calculating a temperature field distribution of the crystal based on a Fourier conduction differential equation; and

[0022] calculating a thermal stress distribution of the crystal based on a thermal elastic theory.

[0023] Further, in the method, when the temperature field distribution of the crystal is calculated based on the Fourier conduction differential equation, the calculation of the temperature change involves the parameters of the absorption coefficient, the reflectivity, the incident light intensity, the incident light spot radius, the time domain function of the incident light spot, and the thermal diffusion coefficient.

[0024] Further, in the method, the method further comprises:

[0025] acquiring the material physical property parameters of the to-be-tested crystal; and

[0026] determining the free electron density damage threshold, the temperature damage threshold, and the thermal stress damage threshold based on the material physical property parameters.

[0027] Further, in the method, the material physical property parameters include at least one of the thermal expansion coefficient, the Poisson's ratio, the Young's modulus, the melting point temperature, and the mechanical breaking strength.

[0028] Further, in the method, the method is applicable to testing any wavelength in the wavelength range from deep ultraviolet to mid-infrared, any pulse width in the pulse width range from femtosecond pulse laser to nanosecond pulse laser, and any organic or inorganic non-metallic crystal as the test sample.

[0029] In summary, compared with the prior art, the present application has at least one of the following beneficial technical effects:

[0030] The present application obtains the defect state information and the absorption characteristics in the crystal by combining the photoluminescence test and the photothermal weak absorption test, and establishes a free electron density analysis model containing a defect state term and an optical-thermal-mechanical multi-physical field coupling analysis model, so that the laser damage threshold of the crystal can be accurately predicted without causing destructive damage to the crystal, the test cost is significantly reduced compared with the traditional destructive test method, the waste of the crystal material is avoided, the evaluation accuracy is improved through in-depth analysis of the influence mechanism of the defect state in the crystal on the damage threshold, and an effective technical means is provided for the crystal damage mechanism research and the preparation process optimization. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0032] Figure 1 A flowchart of a method for high-precision non-destructive evaluation of the laser damage threshold of a crystal is shown.

[0033] Figure 2 A flowchart of a photoluminescence test method is shown.

[0034] Figure 3 Photoluminescence spectra of calcium fluoride crystals and corresponding defect state energy level diagrams are shown.

[0035] Figure 4 A photo of a round calcium fluoride crystal sample is shown.

[0036] Figure 5 A flow chart of a free electron density calculation method is shown.

[0037] Figure 6 Calculation results obtained from a free electron density analysis model and an optical-thermal-mechanical multi-physics coupling analysis model under certain laser irradiation conditions are shown, wherein, Figure 6 (a) is a graph of the time variation of the conduction band electron density under different defect state conditions, Figure 6 (b) is a graph of the time variation of the crystal temperature gradient, Figure 6 (c) is a graph of the hoop tensile and compressive stress distribution at the radial position of the crystal.

[0038] Figure 7 A flow chart of a multi-physics coupling analysis method for high-precision non-destructive evaluation of the laser damage threshold of a crystal is shown. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative work fall within the scope of protection of the present application. In addition, it should be understood that the specific embodiments described herein are only used to illustrate and explain the present application, and are not used to limit the present application.

[0040] It should be noted that the description order of the following embodiments is not used to limit the preferred order of the embodiments of the present application. Moreover, the description of each embodiment in the following embodiments has its own focus, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.

[0041] The execution order of the method steps described in the embodiments of the present application can be executed in the order described in the specific embodiments, or the execution order of each step can be adjusted on the premise of solving the technical problems according to actual needs, which is not listed one by one here.

[0042] The present application will be further described in detail below with reference to the drawings.

[0043] Reference Figure 1The method 100 for evaluating the laser damage threshold of a crystal with high precision and without damage is provided, which combines various characterization techniques and theoretical analysis models to accurately evaluate the laser damage threshold of the crystal without causing structural damage to the test sample.

[0044] The method 100 includes five main steps to form a complete evaluation process. In step 102, a photoluminescence test system is used to characterize the defect state of the crystal to be tested to obtain the defect state information inside the crystal. In some embodiments, step 102 induces the photoluminescence phenomenon of the crystal to be tested by emitting excitation light, records the position and corresponding integral intensity of the photoluminescence peak, and identifies the intrinsic defects existing inside the crystal.

[0045] In step 104, a photothermal weak absorption test system is used to test the surface absorption characteristics of the crystal to be tested to obtain the absorption coefficient correction factor. Step 104 tests the weak absorption distribution and specific value of the crystal surface, and obtains the corresponding absorption coefficient correction factor through comparison and analysis with the calibration sample. In some embodiments, the photothermal weak absorption test system uses the same laser wavelength as the laser damage threshold test to ensure the consistency and accuracy of the test results.

[0046] In step 106, the defect state information and the absorption coefficient correction factor are input into a free electron density analysis model containing a defect state term to calculate the free electron density under laser irradiation. Step 106 combines the defect state information obtained in step 102 and the absorption coefficient correction factor obtained in step 104, and analyzes the electron density change in the laser irradiation process through a theoretical calculation model.

[0047] In step 108, the temperature field distribution and thermal stress distribution of the crystal are calculated based on the free electron density through an optical-thermal-mechanical multi-physical field coupling analysis model. Step 108 takes the free electron density calculated in step 106 as an input parameter, combines the Fourier conduction differential equation to calculate the temperature field distribution of the crystal, and calculates the thermal stress distribution of the crystal based on the thermal elastic theory. In some embodiments, the multi-physical field coupling analysis model includes the interaction between optical absorption, heat conduction and mechanical stress in the laser irradiation process.

[0048] In step 110, the laser damage threshold of the crystal to be tested is determined according to the comparison results of the free electron density, the temperature field distribution and the thermal stress distribution with the preset damage threshold. Step 110 compares the calculated physical parameters with the corresponding damage threshold conditions to determine whether the crystal is damaged under a specific laser irradiation condition. When any one of the free electron density, the temperature or the thermal stress exceeds its damage threshold condition, it is determined that the laser irradiation condition will induce the crystal to be damaged.

[0049] There is a logical progression between the steps of the method 100. The steps 102 and 104 respectively characterize the crystal from two dimensions of internal defects and surface properties, providing basic data for subsequent theoretical analysis. The step 106 converts the characterization results into electron density information, the step 108 further calculates the temperature and stress distribution, and the step 110 judges the damage by synthesizing multiple physical parameters. This multi-dimensional and multi-physical field analysis method improves the accuracy and reliability of damage threshold evaluation.

[0050] With reference to Figure 2 The embodiment of the present application provides a photoluminescence test method 200 for defect state characterization of a to-be-tested crystal, which realizes accurate identification and quantitative characterization of intrinsic defects in the crystal through photoluminescence detection and analysis.

[0051] The method 200 starts from step 202, and emits excitation light to induce photoluminescence of the to-be-tested crystal. In step 202, the excitation light irradiates the surface of the to-be-tested crystal, excites the electrons in the crystal from the valence band to the conduction band or the defect state energy level, and then the photoluminescence phenomenon is generated in the process of electron relaxation. In some embodiments, the photoluminescence test system can use a 200 nm optical parametric amplification pulse laser as an excitation light source, which has sufficient photon energy to excite the defect states in the crystal.

[0052] The method 200 continues to step 204, and judges whether the wavelength of the excitation light is in the deep ultraviolet to ultraviolet band. Step 204 is a decision node, which ensures that the wavelength of the excitation light is in the appropriate range to obtain the best defect state detection effect. When the wavelength of the excitation light meets the requirements, the method 200 directly enters step 206; when the wavelength of the excitation light does not meet the requirements, the method 200 turns to step 208 for wavelength adjustment.

[0053] In step 208, the wavelength of the excitation light is adjusted to the deep ultraviolet to ultraviolet band, and then the method 200 returns to step 206. Step 208 ensures that the excitation light has appropriate photon energy and can effectively excite various defect states in the crystal, thereby obtaining complete defect state information.

[0054] Step 206 records the position of the photoluminescence peak and the corresponding integral intensity. Step 206 captures the photoluminescence signal emitted by the crystal through a spectral detection device, and accurately measures the wavelength position and intensity information of each photoluminescence peak. In some embodiments, the photoluminescence spectrum shows multiple characteristic peaks, each peak corresponding to a specific defect state energy level in the crystal.

[0055] With reference to Figure 3 The photoluminescence spectrum of the calcium fluoride crystal shows two photoluminescence peaks at 425 nm and 537 nm. Figure 3The upper part shows the photoluminescence intensity spectrum as a function of wavelength, where the photoluminescence peak intensity at 425 nm is higher than that at 537 nm. These two characteristic peaks indicate the presence of two different energy level positions of defect states inside the calcium fluoride crystal.

[0056] Figure 3 The lower part shows the corresponding defect state energy level position diagram, including the conduction band, valence band, and two defect state energy levels Defect band 1 and Defect band 2 located in the forbidden band. The vertical arrows in the energy level diagram represent various electron transition processes, including multi-photon ionization from the valence band to the conduction band, photoin ionization from the defect state to the conduction band, and relaxation from the conduction band back to the defect state. The photon energy corresponding to the 193 nm excitation wavelength is 6.4 eV, while the forbidden band width of the calcium fluoride crystal is 12.1 eV.

[0057] Method 200 enters step 210, combining the central wavelength position of the excitation light and the corresponding integrated light intensity to calculate the corresponding defect state position in the forbidden band and the corresponding defect state electron density. Step 210 determines the specific energy level position of the defect state in the forbidden band by analyzing the energy position and intensity information of the photoluminescence peak, and calculates the electron density of each defect state. For example, in some embodiments, by detecting specific photoluminescence peaks at 425 nm and 537 nm, it is determined that there are two energy level positions of defect states in the forbidden band.

[0058] Method 200 is completed in step 212, and the defect state information is input into the free electron density joint analysis model with defect state terms. Step 212 takes the defect state position and electron density information calculated in step 210 as input parameters, providing basic data for subsequent laser damage threshold theoretical calculation. In some embodiments, the defect state information includes the energy level position, electron density and related physical parameters of each defect state.

[0059] Method 200 ensures the optimization of test conditions through a feedback mechanism. The judgment mechanism of step 204 and the adjustment function of step 208 form a closed loop control, ensuring that the excitation light wavelength is always in the deep ultraviolet to ultraviolet wavelength range most suitable for defect state detection. This adaptive adjustment mechanism improves the accuracy and repeatability of defect state characterization.

[0060] Reference Figure 4 The calcium fluoride crystal is used as a specific test object for the verification and demonstration of the method described in this embodiment. Figure 4 The actual morphology of a circular calcium fluoride crystal sample is shown, which presents a transparent ring structure with a flat polished surface feature.

[0061] The diameter of the calcium fluoride crystal sample is 38.1 mm, and the excitation light is incident on the sample surface at an angle of 45°. Figure 4The horizontal bidirectional arrow notation in the middle precisely indicates the sample size. The crystal sample is placed on a measurement background with grid lines, which form a square pattern of thin lines with alternating white and light pink grid lines, providing a reference scale for size evaluation.

[0062] The calcium fluoride crystal sample exhibits a clear and transparent appearance, with smooth edges, characteristic of a precisely polished optical element. The circular geometry of the crystal shows a uniform thickness distribution around its perimeter, with a slightly brighter central portion due to light transmission through the material. In some embodiments, the uniform thickness and smooth surface of the calcium fluoride crystal sample ensure the accuracy of photoluminescence tests and photothermal weak absorption tests.

[0063] The calcium fluoride crystal as a representative test sample has optical and physical properties. The bandgap of this material is 12.1 eV, showing good transparency in the deep ultraviolet to mid-infrared wavelength range, suitable for laser damage threshold evaluation research. In some embodiments, the lattice structure and defect characteristics of the calcium fluoride crystal provide an ideal test platform for verifying the effectiveness of non-destructive evaluation methods.

[0064] The fine scale function of the grid background allows the geometric characteristics and size parameters of the crystal sample to be accurately visually verified. The measurement notation is located in the central position of the crystal diameter, clearly indicating the size specification of the sample. Accurate size control and surface quality play an important role in ensuring the repeatability and accuracy of test results.

[0065] Referring Figure 5 The embodiments of the present application also provide a free electron density calculation method 300 for describing the detailed calculation process of the free electron density analysis model of the defect state term. The method 300 is based on the traditional Keldysh & Drude free electron density joint analysis model and adds a defect state term to realize accurate calculation of the change of free electron density inside the crystal under laser irradiation conditions.

[0066] The method 300 starts from step 302, calculating the free electron density term formed by the multi-photon absorption, tunneling ionization and avalanche ionization of the valence band electrons. Step 302 analyzes the ionization process of the valence band electrons under laser irradiation, in which the multi-photon absorption is based on the Keldysh theory and the avalanche ionization is based on the Drude ionization model. For example, in some embodiments, for the case of 355 nm ultraviolet pulse laser induced damage of calcium fluoride crystal, multi-photon absorption ionization dominates due to the large photon energy of 355 nm ultraviolet laser.

[0067] Method 300 proceeds to step 304, calculating the conduction band electron relaxation term. Step 304 analyzes the process of free electrons in the conduction band returning to the valence band or defect states through various relaxation mechanisms, which represents the decreasing part of the free electron density. In some embodiments, the conduction band electron relaxation term is related to the relaxation time constant quantitative characterization.

[0068] Step 306 calculates the defect state electron photoionization term. Step 306 analyzes the process of electrons in the defect states being excited to the conduction band under laser irradiation, which represents the increasing part of the free electron density contributed by the defect states. In some embodiments, the defect state electron photoionization term is related to the defect state electron density , the photoionization cross section σ, and the laser photon flux.

[0069] Method 300 proceeds to step 308, calculating the defect state electron density relaxation term. Step 308 analyzes the process of free electrons in the conduction band relaxing back to the defect states, which represents the recovery of the defect state electron density. In some embodiments, the defect state electron density relaxation term takes into account the maximum electron capacity of the defect states and the relaxation time constant .

[0070] Method 300 reaches decision point step 310, determining whether to include the absorption coefficient correction factor. Step 310 serves as a conditional branching node, determining whether the absorption coefficient correction factor q obtained from the photothermal weak absorption test needs to be applied according to the test conditions. When the influence of the surface absorption characteristics needs to be considered, method 300 proceeds to step 312; when no correction is needed, method 300 proceeds to step 314.

[0071] In step 312, the product of the absorption coefficient correction factor and the incident laser intensity is applied to the multi-photon absorption, tunneling ionization, and avalanche ionization terms. Step 312 determines the photothermal weak absorption coefficient correction factor relationship by calibrating the sample, compares the photothermal weak absorption value of the actual test sample with the value of the calibration sample, and obtains the corresponding correction factor q, which reflects the influence of the crystal surface non-intrinsic defects on the laser absorption characteristics.

[0072] Step 314 directly uses the incident laser intensity for calculation without applying the absorption coefficient correction factor. Step 314 is suitable for cases where the influence of the surface absorption characteristics is small or negligible, and directly uses the incident laser intensity I(t) for free electron density calculation.

[0073] Steps 312 and 314 converge to step 316, calculating the free electron density change rate. Step 316 synthesizes the calculation results of the aforementioned terms to obtain the complete expression of the free electron density change rate. In some embodiments, the calculation formula of the free electron density analysis model is represented as:

[0074] ;

[0075] wherein, represents the free electron density, represents the free electron density formed by multi-photon absorption, tunneling ionization, and avalanche ionization of valence band electrons; represents the conduction band electron relaxation term; represents the defect state electron photoionization term; represents the defect state electron density relaxation term.

[0076] The multi-photon absorption, tunneling ionization, and avalanche ionization terms all contain an absorption coefficient correction factor q multiplied by the incident laser intensity I(t). This design ensures the uniform influence of surface absorption characteristics on various ionization processes, improving the physical consistency and calculation accuracy of the model.

[0077] Referring to Figure 6 (a), the conduction band electron density curves under different defect state conditions demonstrate the diversity of free electron density evolution processes. Figure 6 (a) shows the conduction band electron density time evolution under four different conditions: no defect state, (M1, M2): 1e18, (M1, M2): 5e18, and (M1, M2): 1e19.

[0078] Figure 6 The black curve in (a) represents the conduction band electron density change under the condition of no defect state, showing the lowest electron density level, reaching about . The red curve marked as "(M1, M2): 1e18" shows a medium level of electron density, also reaching about . The brown curve marked as "(M1, M2): 5e18" shows a slightly higher electron density level, reaching about .

[0079] The green curve marked as "(M1, M2): 1e19" shows the highest electron density level, reaching about . All curves exhibit a rapid initial growth within the first few nanoseconds, followed by a plateau state or gradual change in the remaining period. The green curve exhibits the most significant initial upward trend and maintains the highest electron density level throughout the time range.

[0080] Figure 6 The time axis in (a) ranges from 0 to 20 nanoseconds, and the vertical axis represents the conduction band electron density, with units of , ranging from 0 to about The difference in the evolution of electron density under different defect state density conditions indicates that defect states have a significant impact on the laser damage process. In some embodiments, a higher defect state electron density results in a higher conduction band electron density, thereby increasing the likelihood of laser damage.

[0081] Referring to Figure 6 (b), the crystal temperature gradient ΔT under the laser irradiation condition rapidly increases with time and reaches a peak value in a short time, and then gradually decays with time, which reflects the transient response characteristics of the temperature field of the crystal under the action of the pulsed laser. Referring to Figure 6 (c), the hoop stress distribution curve at the radial position R of the crystal under the action of the temperature field shows that the region near the center of the crystal is a compressive stress region, and the outer region is a tensile stress region. The thermal stress gradually decreases after reaching a peak value near a certain radial position. Figure 6 (b) and Figure 6 (c) respectively give typical results of the temperature field and thermal stress distribution calculated by the multi-physical field coupling analysis model, which together with the electron density evolution results shown in Figure 6 (a) reflect the internal relationship between defect states, temperature rise and thermal stress.

[0082] The method 300 realizes adaptive processing of different test conditions through a conditional branching mechanism. The judgment function of step 310 and the respective processing of steps 312 and 314 form a flexible calculation framework, which takes into account the influence of surface absorption characteristics and maintains the generality of the model. This design enables the free electron density analysis model to be applicable to various different crystal materials and test conditions.

[0083] Referring to Figure 7 , the embodiment of the present application also provides an optical-thermal-mechanical multi-physical field coupling analysis method 400, which realizes accurate evaluation of the laser damage threshold of the crystal through steps of material property parameter acquisition, temperature field calculation, thermal stress analysis and damage threshold determination.

[0084] The method 400 starts from step 402, acquiring the material physical property parameters of the crystal to be tested. Step 402 collects the basic physical property data of the crystal, providing a material parameter basis for subsequent multi-physical field coupling calculation. In some embodiments, the material physical property parameters include at least one of the thermal expansion coefficient, the Poisson's ratio, the Young's modulus, the melting point temperature and the mechanical breaking strength. For calcium fluoride crystals, these parameters provide material-specific input data for the multi-physical field analysis model.

[0085] Method 400 proceeds to step 404, calculating the temperature field distribution of the crystal based on Fourier conduction differential equation. Step 404 analyzes the heat conduction phenomenon inside the crystal during laser irradiation, and obtains the spatio-temporal distribution of the temperature field by solving the Fourier conduction differential equation. In some embodiments, the calculation of temperature change involves the absorption coefficient A, reflectivity , incident light intensity , incident light spot radius R, time domain function of the incident light spot, and thermal diffusion coefficient a parameters.

[0086] The calculation formula of the Fourier conduction differential equation expresses the quantitative relationship between the temperature change and each physical parameter. The temperature change is calculated by integral form, specifically,

[0087]

[0088] wherein, represents the absorption coefficient; represents the reflectivity; represents the incident light intensity; represents the incident light spot radius; represents the time domain function of the incident light spot; represents the thermal diffusion coefficient.

[0089] Method 400 proceeds to step 406, calculating the thermal stress distribution of the crystal based on the thermoelastic theory. Step 406 analyzes the thermal expansion effect caused by temperature change and the corresponding mechanical stress distribution, and establishes the coupling relationship between the temperature field and the stress field by the thermoelastic theory. In some embodiments, the calculation formula of the thermoelastic theory involves the thermal expansion coefficient β, Poisson's ratio and Young's modulus and other parameters.

[0090] The calculation formula of the thermoelastic theory expresses the relationship between the thermal stress and the temperature distribution and the material characteristic parameters.

[0091] Specifically, the calculation formula of the thermoelastic calculation theory is as follows:

[0092]

[0093] wherein, represents the thermal expansion coefficient, representing the volume change characteristic of the material under temperature change; represents the Poisson's ratio, describing the transverse deformation characteristic of the material under the action of uniaxial stress; represents the Young's modulus, reflecting the elastic stiffness of the material. The combination of these parameters ​​These constitute the material constants for thermal stress calculation.

[0094] Method 400 continues to step 408, determining the free electron density damage threshold, temperature damage threshold, and thermal stress damage threshold based on the material's physical property parameters. Step 408 establishes the critical condition relationship between each physical parameter and damage occurrence, taking into account the crystal's material properties. In some embodiments, for calcium fluoride crystals, the free electron density damage threshold is set to 2 × 10⁻⁶. 21 / cm 2 This threshold represents the critical electron density level that leads to the destruction of the crystal structure.

[0095] Temperature damage thresholds are determined based on the melting point temperature of the crystal; thermal damage occurs when the crystal temperature rises above the melting point. Thermal stress damage thresholds are determined based on the material's mechanical fracture strength; mechanical peeling damage occurs when thermal stress exceeds the fracture strength. In some implementations, these damage thresholds provide quantitative comparison criteria for subsequent damage assessment.

[0096] Method 400 reaches decision point step 410, which determines whether the test conditions are applicable to the deep ultraviolet to mid-infrared wavelength range and the femtosecond to nanosecond pulse width range. Step 410 serves as a condition check node, ensuring that the test parameters are within the applicable range of method 400. When the test conditions meet the requirements, method 400 directly proceeds to step 412 for damage threshold assessment; when the test conditions do not meet the requirements, method 400 proceeds to step 414 for parameter adjustment.

[0097] In step 412, a laser damage threshold assessment of the crystal is performed. Step 412 combines the calculated results of free electron density, temperature field distribution, and thermal stress distribution with the corresponding damage thresholds for comparison and analysis. In some embodiments, when any one of the physical parameters—free electron density, temperature, or thermal stress—exceeds its damage critical condition, it is determined that the laser irradiation condition will induce laser damage in the crystal.

[0098] Step 414 adjusts the test parameters to the applicable range. Step 414 ensures that the test parameters are within the effective operating range of Method 400 by modifying the laser wavelength, pulse width, or other test conditions. After adjustment, Method 400 returns to Step 412 to continue the damage threshold assessment.

[0099] In some implementations, a 355 nm wavelength laser is used for photothermal weak absorption testing. This wavelength falls within the ultraviolet range and is suitable for detecting the surface absorption characteristics of calcium fluoride crystals. The 355 nm laser has appropriate photon energy, which can effectively excite intrinsic defects on the crystal surface, thereby obtaining an accurate absorption coefficient correction factor.

[0100] For the specific laser irradiation condition (wavelength 355 nm, pulse width 7.6 ns, fluence 10.63 J / cm 2 ), the calculated free electron density of calcium fluoride crystal is 1.8×10 9 / cm 2 , which is much lower than the damage threshold 2×10 21 / cm 2 . The maximum temperature rise is 30 °C, which is much lower than the melting temperature of calcium fluoride crystal. The corresponding thermal stress distribution includes tensile stress and compressive stress, both of which are much smaller than the mechanical breaking strength of calcium fluoride crystal.

[0101] Based on these calculation results, under the current laser irradiation condition, calcium fluoride crystal will not be damaged by electron ionization, excessive temperature or excessive thermal stress. To verify the accuracy of the theoretical calculation, a 50x magnification optical microscope is used to observe the material damage at the irradiation position. The microscope observation results show that the calcium fluoride crystal does not appear laser damage, which verifies the accuracy of the non-destructive evaluation method.

[0102] The multi-physics coupling analysis of method 400 is reflected in the correlation between each calculation step. The temperature field distribution calculated in step 404 provides input for the thermal stress calculation in step 406, and the material parameters obtained in step 402 are used throughout the entire calculation process. This coupling analysis method takes into account the interaction between optical absorption, heat conduction and mechanical stress during laser irradiation, improving the physical accuracy of damage threshold evaluation.

[0103] Method 400 forms an adaptive control mechanism through the condition judgment in step 410 and the parameter adjustment in step 414. This mechanism ensures that the test conditions are always within the effective working range of the method, and is suitable for various combinations of laser parameters in the deep ultraviolet to mid-infrared wavelength range and femtosecond to nanosecond pulse width range. This flexibility enables method 400 to be applicable to different types of crystal materials and a variety of laser test conditions.

[0104] This high-precision non-destructive evaluation method of crystal laser damage threshold has a wide range of applications and excellent flexibility, and can meet the testing needs of different laser parameter conditions and various crystal materials. The applicability of the method is reflected in multiple dimensions such as laser wavelength range, pulse width range and sample type.

[0105] In terms of laser wavelength applicability, the method is applicable to test laser wavelengths ranging from deep ultraviolet to mid-infrared at any wavelength. The deep ultraviolet band covers 193 nm, 248 nm, and other excimer laser wavelengths, which have important applications in semiconductor lithography and precision machining. The ultraviolet band includes 355 nm, 266 nm, and other commonly used solid laser frequency-doubled output wavelengths, widely used in material processing and scientific research. The visible light band covers 532 nm, 1064 nm fundamental frequency and its frequency-doubled wavelength, suitable for various laser processing and testing applications.

[0106] The near-infrared to mid-infrared band includes 1064 nm, 2940 nm, 10600 nm, and other wavelengths, which have wide applications in laser medicine, material processing, and spectral analysis. The method can adapt to the evaluation requirements of crystal damage threshold under different wavelength conditions by adjusting the laser wavelength of the photoluminescence test system and the photothermal weak absorption test system. In some embodiments, lasers of different wavelengths have different photon energies and penetration depths, and the method adapts to these differences through corresponding theoretical model parameter adjustments.

[0107] In terms of laser pulse width applicability, the method is applicable to test laser pulse widths ranging from femtosecond pulse laser to nanosecond pulse laser at any pulse width. The pulse width of femtosecond pulse laser is usually in the range of tens to hundreds of femtoseconds. In this ultra-short pulse laser, the main manifestations are nonlinear optical effects and multi-photon absorption processes.

[0108] The pulse width of picosecond pulse laser ranges from several picoseconds to several tens of picoseconds. In this time scale, thermal diffusion effects begin to appear but are still limited.

[0109] The pulse width of nanosecond pulse laser ranges from several nanoseconds to several tens of nanoseconds. In this time scale, thermal conduction effects become significant, and the calculation of temperature field distribution and thermal stress distribution becomes more important. The method can accurately handle physical processes under different pulse width conditions by adjusting time-dependent parameters in the free electron density analysis model, time-domain functions in the Fourier conduction differential equation, and time evolution terms in the thermoelastic theory.

[0110] In terms of the scope of test samples, the method is applicable to testing samples of any organic or inorganic non-metallic crystal. Organic crystals include various organic optical crystals such as urea crystals, L-arginine phosphate crystals, benzoic acid crystals, etc., which have important value in nonlinear optical and laser frequency conversion applications. Organic crystals usually have lower laser damage threshold and complex molecular structure, and the method can effectively identify molecular defects and structural incompleteness in organic crystals through photoluminescence testing.

[0111] Inorganic non-metallic crystals cover a wide range of material types, including oxide crystals, fluoride crystals, sulfide crystals, phosphate crystals, etc. Oxide crystals such as quartz crystals, sapphire crystals, barium titanate crystals, etc. are widely used in laser technology and optoelectronics. Fluoride crystals such as calcium fluoride, magnesium fluoride, lithium fluoride, etc. have excellent transparency in deep ultraviolet laser applications. Sulfide crystals and phosphate crystals play an important role in infrared laser and nonlinear optical applications.

[0112] The applicability of the method to different types of crystals is reflected in the universality of the theoretical model and the adjustability of the parameters. The photoluminescence test system can detect intrinsic defects in various crystal materials, including point defects, line defects, surface defects, and other types of lattice incompleteness. The photothermal weak absorption test system can characterize non-intrinsic defects on the surface of different crystals, including processing damage, contaminant residues, micro-cracks, and other surface defects.

[0113] The free electron density analysis model can adapt to the electronic structure characteristics of different crystal materials by adjusting material-specific physical parameters such as bandgap width, electron effective mass, and phonon coupling strength. The Fourier conduction differential equation can accurately describe the thermal conduction characteristics of different crystal materials by adjusting thermal conductivity, specific heat capacity, and density. The thermal elastic theory can accurately calculate the thermal stress distribution of different crystal materials by adjusting the thermal expansion coefficient, elastic modulus, and Poisson's ratio.

[0114] The wide applicability of the method is also reflected in the adaptability to different crystal growth methods and processing techniques. Whether the crystal is prepared by the Czochralski method, the Bridgman method, the solution growth method, or the vapor deposition method, the method can identify intrinsic defects introduced during the growth process through photoluminescence testing. Whether the crystal surface is processed by mechanical polishing, chemical polishing, or ion beam polishing, the method can characterize non-intrinsic defects introduced during the processing process through photothermal weak absorption testing.

[0115] The flexibility of the method is also reflected in the adjustability of test conditions and the scalability of test results. By adjusting the excitation light wavelength and intensity of the photoluminescence test system, the defect state detection effect of different crystal materials can be optimized. By adjusting the detection laser parameters of the photothermal weak absorption test system, the laser damage test conditions in actual application can be matched. By adjusting the parameters in the theoretical calculation model, different physical conditions and material properties can be adapted.

[0116] The applicability of the method is reflected in the compatibility of emerging crystal materials and advanced laser technologies. With the continuous development of new optical crystal materials, such as perovskite crystals, two-dimensional material crystals, and superlattice structures, the method can adapt to the damage threshold evaluation needs of these new materials by updating the material parameter database and optimizing the theoretical model. With the continuous progress of laser technology, such as ultrafast lasers, high-power lasers, and special wavelength lasers, the method can meet the testing requirements of these advanced laser technologies by expanding the scope of application of the theoretical model and improving the calculation accuracy.

[0117] Any process or method described in flowcharts of the present application or otherwise described herein can be understood as representing modules, segments, or portions of code that include one or more executable instructions for implementing specific logic functions or steps, and the scope of preferred embodiments of the present application includes additional implementation in which functions may be performed in different orders, in substantially simultaneous fashion, or in reverse order, according to the functions involved, as will be understood by those skilled in the art of the embodiments of the present application.

[0118] The logic and / or steps represented in flowcharts or otherwise described herein, for example, can be considered as a list of executable instructions for implementing logic functions, which can be embodied in any computer-readable medium for use by or in conjunction with an instruction execution system, device, or apparatus, such as a computer-based system, a system including a processing module, or other system that can fetch and execute instructions from the instruction execution system, device, or apparatus.

[0119] The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for high precision non-destructive evaluation of the damage threshold of a crystalline laser, characterized in that, The method comprises the following steps: characterizing a defect state of a to-be-tested crystal by using a photoluminescence test system to obtain defect state information inside the crystal; testing surface absorption characteristics of the to-be-tested crystal by using a photothermal weak absorption test system to obtain an absorption coefficient correction factor; inputting the defect state information and the absorption coefficient correction factor into a free electron density analysis model containing a defect state term to calculate a free electron density under laser irradiation, wherein a calculation formula of the free electron density analysis model containing the defect state term is expressed as: a free electron density change rate is equal to a free electron density term formed by valence band electrons through multi-photon absorption, tunneling ionization and avalanche ionization minus a conduction band electron relaxation term, plus a defect state electron photionization term minus a defect state electron density relaxation term, and the multi-photon absorption, tunneling ionization and avalanche ionization terms all contain a product of the absorption coefficient correction factor and an incident laser intensity; calculating a temperature field distribution and a thermal stress distribution of the crystal by using an optical-thermal-mechanical multi-physics field coupling analysis model based on the free electron density; and determining a laser damage threshold of the to-be-tested crystal according to a comparison result of the free electron density, the temperature field distribution and the thermal stress distribution with a preset damage threshold.

2. The method of claim 1, wherein, The characterization of the defect state of the to-be-tested crystal by using the photoluminescence test system comprises the following steps: emitting excitation light to induce the to-be-tested crystal to generate photoluminescence; recording positions of photoluminescence peaks and corresponding integral intensities; combining a central wavelength position of the excitation light and a corresponding integral light intensity to calculate positions of corresponding defect states in a forbidden band and corresponding defect state electron densities; and inputting the defect state information into a free electron density joint analysis model with a defect state term.

3. The method of claim 2, wherein, The wavelength range of the excitation light is any wavelength laser in a deep ultraviolet to ultraviolet band.

4. The method of claim 1, wherein, The optical-thermal-mechanical multi-physics field coupling analysis model comprises the following steps: calculating a temperature field distribution of the crystal based on a Fourier conduction differential equation; and calculating a thermal stress distribution of the crystal based on a thermal elastic theory.

5. The method of claim 4, wherein, When the temperature field distribution of the crystal is calculated based on the Fourier conduction differential equation, the calculation of temperature change involves absorption coefficient, reflectivity, incident light intensity, incident spot radius, time domain function of the incident spot and thermal diffusion coefficient parameters.

6. The method of claim 1, wherein, The method further comprises the following steps: obtaining material physical characteristic parameters of the to-be-tested crystal; and determining a free electron density damage threshold, a temperature damage threshold and a thermal stress damage threshold based on the material physical characteristic parameters.

7. The method of claim 6, wherein, The material physical characteristic parameters include at least one of a thermal expansion coefficient, a Poisson's ratio, a Young's modulus, a melting point temperature and a mechanical breaking strength.

8. The method of claim 1, wherein, The method is suitable for testing any wavelength in a deep ultraviolet to mid-infrared wavelength range, any pulse width in a femtosecond pulse laser to nanosecond pulse laser range, and any organic or inorganic non-metallic crystal.

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