Steady-state simulation method, device and storage medium for solid-state laser

Abstract

The application belongs to the technical field of laser, and discloses a steady-state simulation method, equipment and storage medium of a solid laser. A pump source model is constructed to calculate pump light intensity and photon flux; a crystal heat source distribution is solved based on the pump light intensity, a three-dimensional temperature field and a thermal lens focal length are obtained by using a step-by-step Fourier solving method; the stability is analyzed by dynamically updating the equivalent g parameter and the curvature radius of the resonant cavity by using the thermal lens focal length; the pump absorption and gain distribution are calculated in combination with the pump light intensity, the photon flux and the crystal boundary reflection characteristics; the pump-laser mode overlap factor is calculated based on the beam parameter calculated according to the equivalent g parameter, the pump light intensity and the laser light intensity; the laser threshold power is calculated, and the output power is calculated in combination with the threshold power and the input pump power; the steady-state laser field is iteratively solved based on the equivalent g parameter, the thermal lens focal length and the gain distribution, and finally the simulation result is output, the dynamic coupling feedback of the thermal lens focal length and the resonant cavity parameter is realized, and the simulation precision is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of laser technology, and in particular to a steady-state simulation method, device and storage medium for solid-state lasers. Background Technology

[0002] Solid-state lasers, as one of the core laser types widely used in industrial production within the field of optical engineering, have demonstrated an irreplaceable technical support role in several key areas such as industrial precision cutting, laser remote sensing, and biomedical treatment. In recent years, with the continuous iteration and increasing maturity of technologies related to solid-state laser material preparation, pumping techniques, and resonant cavity design, the industry has placed increasingly stringent requirements on their manufacturing precision, output beam quality, and long-term operational stability. Against this backdrop, conducting refined simulation research on solid-state lasers can not only provide a scientific basis for structural optimization and performance prediction, but also effectively reduce R&D costs and shorten product iteration cycles, thus possessing indispensable theoretical value and engineering practical significance.

[0003] However, in traditional numerical simulations of solid-state lasers, researchers often focus on the transmission characteristics of the laser beam, generally neglecting a series of key physical changes caused by the thermal effects within the gain crystal. During solid-state laser operation, the gain crystal generates a significant temperature gradient due to the absorption of pump light energy. This uneven temperature distribution not only induces elastic deformation of the crystal through thermal stress but also directly distorts the spatial distribution of the crystal's refractive index. Based on this, nonlinear optical phenomena such as thermally induced birefringence and thermal lensing occur successively within the crystal. Thermal lensing alters the equivalent focal length of the resonant cavity, disrupting beam mode stability and affecting laser output power; thermally induced birefringence disrupts the polarization state consistency of the incident light, significantly reducing the laser's polarization purity, ultimately having a significant negative impact on the overall performance of the laser.

[0004] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] The main objective of this invention is to provide a steady-state simulation method, device, and storage medium for solid-state lasers, aiming to solve the technical problem that existing laser simulation methods neglect the dynamic coupling feedback between thermal lensing effects and resonant cavity parameters, resulting in simulation results that cannot accurately reflect the actual operating characteristics of the laser.

[0006] To achieve the above objectives, the present invention provides a steady-state simulation method for a solid-state laser, the method comprising the following steps: A pump source model is constructed, and the pump light intensity and pump photon flux are calculated using the pump source model. The distribution of heat sources inside the crystal is calculated based on the pump light intensity. The three-dimensional temperature field of the crystal is obtained by iterative calculation of the distribution of heat sources inside the crystal. The focal length of the thermal lens is obtained based on the solution of the three-dimensional temperature field of the crystal. Based on the focal length of the thermal lens, the effective g-parameter and radius of curvature of the resonant cavity are dynamically updated, and the stability analysis of the resonant cavity is performed based on the updated effective g-parameter and radius of curvature. Here, the g-parameter is the core parameter describing the stability of the resonant cavity's geometric structure. The beam parameters are calculated based on the effective g-parameters, including the laser beam waist radius and the center spot size of the gain medium; The pump absorption and gain distribution are calculated based on the pump intensity, pump photon flux, and crystal boundary reflection characteristics. The pump-laser mode overlap factor is calculated using the laser beam waist radius, the center spot size of the gain medium, the pump intensity, and the spatial distribution of the laser intensity. The laser threshold power including thermal lens feedback is calculated based on the gain distribution and the pump-laser mode overlap factor combined with the total cavity loss. The laser output power is calculated based on the laser threshold power and the input pump power. Based on the effective g-parameter, the focal length of the thermal lens, and the gain distribution, the steady-state laser field modulated by the thermal lens is solved by iterative round trip. The simulation results are output, including at least the resonant cavity stability analysis results, beam parameters, laser threshold power, laser output power, pump-laser mode overlap factor, and steady-state laser field distribution data.

[0007] In one embodiment, the crystal boundary reflection characteristics are used to determine whether total internal reflection occurs based on Snell's law, taking into account the incident angle of light incident on the side boundary. If total internal reflection does not occur, the average reflectivity of s-polarization and p-polarization is calculated using Fresnel's formula as the side Fresnel reflectivity. The side Fresnel reflectivity is used to correct the transmission and absorption distribution of pump light within the crystal.

[0008] In one embodiment, the effective g-parameter of the dynamically updated resonant cavity is calculated based on the focal length of the thermal lens to obtain the optical power. Based on the position of the thermal lens within the cavity (center of the medium), update the effective g-parameters of the laser cavity: , ,in, For the original g parameters, These represent the distances from the left and right endoscopes to the thermal lens, respectively.

[0009] In one embodiment, the formula for determining the stability of the resonant cavity is g1g2. If 0 < g1g2 < 1, then the resonant cavity is determined to be in a stable state. L is the cavity length. The radius of curvature of the endoscope is denoted as .

[0010] In one embodiment, the laser beam waist radius calculation process is as follows: based on the effective g-parameter of the resonant cavity, the cavity length, and the laser wavelength, combined with the formula:

[0011] in, Where L is the wavelength, L is the cavity length, and g1 and g2 are the effective g parameters; The size of the central spot in the gain medium is calculated based on the laser beam waist radius and Rayleigh distance, using the following formula:

[0012] Where z is the distance from the gain center to the beam waist. This is the Rayleigh distance.

[0013] In one embodiment, the laser threshold power is the pump power scaled by the desired gain / average gain, where the average gain is obtained by combining the total loss with the gain integral and the pump-laser mode overlap factor, and the desired gain is... , For the length of the gain medium, Total loss.

[0014] In one embodiment, the calculation rule for the laser output power is as follows: when the input pump power is less than the threshold power, the output power is 0; when the input pump power is greater than or equal to the threshold power, the output power = slope efficiency × (input pump power - threshold power), wherein the slope efficiency combines quantum efficiency, mode extraction efficiency, output coupling coefficient and intrinsic loss correction, the quantum efficiency is solved based on the ratio of pump photon energy to laser photon energy and the quantum efficiency coefficient, and the mode extraction efficiency is solved based on the ratio of the steady-state field mode weight to the global gain.

[0015] Furthermore, to achieve the above objectives, the present invention also proposes a steady-state simulation device for a solid-state laser, the steady-state simulation device for a solid-state laser comprising: a memory, a processor, and a steady-state simulation program for a solid-state laser stored in the memory and executable on the processor, the steady-state simulation program for the solid-state laser being configured to implement the steps of the steady-state simulation method for a solid-state laser as described above.

[0016] Furthermore, to achieve the above objectives, the present invention also proposes a storage medium storing a steady-state simulation program for a solid-state laser, wherein when the steady-state simulation program for the solid-state laser is executed by a processor, the steps of the steady-state simulation method for the solid-state laser as described above are implemented.

[0017] Furthermore, to achieve the above objectives, the present invention also proposes a computer program product, wherein the computer program product stores a steady-state simulation program for a solid-state laser, and when the steady-state simulation program for the solid-state laser is executed by a processor, it implements the steps of the steady-state simulation method for the solid-state laser as described above.

[0018] This invention constructs a pump source model to calculate pump intensity and photon flux; solves for crystal heat source distribution based on pump intensity, and obtains the three-dimensional temperature field and thermal lens focal length using a step-by-step Fourier transform method; dynamically updates the equivalent g-parameters and radius of curvature of the resonant cavity using the thermal lens focal length for stability analysis; calculates pump absorption and gain distribution by combining pump intensity, photon flux, and crystal boundary reflection characteristics; calculates the pump-laser mode overlap factor based on beam parameters calculated from the equivalent g-parameters, pump intensity, and laser intensity; calculates the laser threshold power and combines the threshold power with the input pump power to calculate the output power; iteratively solves the steady-state laser field based on the equivalent g-parameters, thermal lens focal length, and gain distribution, and finally outputs the simulation results. This achieves dynamic coupling feedback between the thermal lens focal length and resonant cavity parameters, significantly improving simulation accuracy. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the first embodiment of the steady-state simulation method for solid-state lasers of the present invention; Figure 2 This is a diagram of the laser structure in the steady-state simulation method for solid-state lasers of the present invention; Figure 3 This is a crystal temperature distribution diagram in the steady-state simulation method of the solid-state laser of the present invention; Figure 4 This is a diagram showing the circumferential stress distribution of the crystal in the steady-state simulation method for the solid-state laser of this invention. Figure 5 This is a diagram showing the distribution of tangential refractive index variation in the crystal during the steady-state simulation method of the solid-state laser of this invention.

[0020] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0021] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0022] This invention provides a steady-state simulation method for solid-state lasers, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of a steady-state simulation method for a solid-state laser according to the present invention.

[0023] In this embodiment, the steady-state simulation method for the solid-state laser includes the following steps: Step S10: Construct a pump source model and use the pump source model to calculate the pump light intensity and pump photon flux.

[0024] In this embodiment, the execution subject is a steady-state simulation device for a solid-state laser. This device has functions such as data processing, data communication, and program execution. The steady-state simulation device for the solid-state laser can be a computer terminal device or other network device, or other devices with similar functions. This embodiment does not limit the scope of the simulation device.

[0025] It is important to note that in traditional numerical simulations of solid-state lasers, researchers often focus on the transmission characteristics of the laser beam, while generally neglecting a series of key physical changes caused by the thermal effects within the gain crystal. During solid-state laser operation, the gain crystal generates a significant temperature gradient due to the absorption of pump light energy. This uneven temperature distribution not only induces elastic deformation of the crystal through thermal stress but also directly distorts the spatial distribution of the crystal's refractive index. Based on this, nonlinear optical phenomena such as thermally induced birefringence and thermal lensing effects appear within the crystal. Thermal lensing alters the equivalent focal length of the resonant cavity, disrupting beam mode stability and affecting laser output power; thermally induced birefringence disrupts the polarization state consistency of the incident light, significantly reducing the laser's polarization purity, ultimately having a significant negative impact on the overall performance of the laser. Traditional simulation methods typically use static parameter approximations when dealing with thermal lensing effects, i.e., pre-setting a fixed thermal lens focal length value for calculation, failing to achieve dynamic coupling and real-time feedback between the thermal lens focal length and resonant cavity parameters. This static processing method cannot truly reflect the physical process of the dynamic evolution of thermal effects with changes in pump power during the actual operation of the laser. This leads to inaccurate analysis of resonant cavity stability, large deviations in beam parameter calculation, and difficulty in accurately predicting the threshold power and output power characteristics of the laser.

[0026] To address the aforementioned technical issues, this embodiment constructs a pump source model to calculate the pump intensity and photon flux; based on the pump intensity, it solves for the crystal heat source distribution, and uses the step-by-step Fourier transform to obtain the three-dimensional temperature field and the focal length of the thermal lens; it uses the thermal lens focal length to dynamically update the equivalent g-parameters and radius of curvature of the resonant cavity for stability analysis; it combines the pump intensity, photon flux, and crystal boundary reflection characteristics to calculate the pump absorption and gain distribution; it calculates the pump-laser mode overlap factor based on the beam parameters calculated according to the equivalent g-parameters, the pump intensity, and the laser intensity; it calculates the laser threshold power and combines the threshold power and the input pump power to calculate the output power; it iteratively solves for the steady-state laser field based on the equivalent g-parameters, the thermal lens focal length, and the gain distribution, and finally outputs the simulation results. This achieves dynamic coupling feedback between the thermal lens focal length and the resonant cavity parameters, significantly improving the simulation accuracy.

[0027] In the specific implementation, first refer to Figure 2 As shown, a thermo-optical coupling simulation structure for a single-sided end-pumped Nd:YAG plano-concave laser is proposed. The cavity is a dedicated plano-concave resonant cavity for Nd:YAG solid-state lasers. Its core components include: a pump source 1, a plane mirror 2, a solid-state gain medium 3, and a concave mirror 4. The pump source 1 is a semiconductor pump source with a wavelength of 808 nm and a power of 40 W. The pump light emitted has an initial spot radius of 0.09 mm. The pump light passes through the plane mirror 2, through the Nd:YAG solid-state gain medium 3, and then enters the concave mirror 4. After being reflected by the concave mirror 4, it is refracted back along the original optical path to form a closed resonant cavity optical path.

[0028] It should be noted that the pump source model is constructed by defining the PumpSource class as the pump input unit of the laser cavity. The core calculation of the offset-free Gaussian intensity distribution and photon flux is as follows: based on fundamental physical quantities such as Planck's constant and the speed of light, combined with parameters such as pump wavelength, spot radius, power, and divergence angle, the Rayleigh distance is derived to distinguish the spot size of natural broadening and divergence broadening. Finally, the pump intensity and photon flux are output to provide input for subsequent gain calculation.

[0029] In one embodiment, the calculation process for the offset-free Gaussian intensity distribution is as follows: The pump spot radius w is calculated based on the Rayleigh distance and divergence angle of the pump source, and then... (The sentence is incomplete and requires further context to be fully translated.) Calculate the pump light intensity, where P is the pump power, x and y are the lateral coordinates, and the beam waist is... , To allow the Gaussian beam to broaden naturally, , The beam divergence angle is denoted as . The pump photon flux is obtained by dividing the pump intensity by the single-photon energy, where the single-photon energy is determined by the product of Planck's constant and the pump frequency. Furthermore, the equation for calculating the Rayleigh distance based on the spot radius and pump wavelength is:

[0030] in, For the pump wavelength, Let be the radius of the light spot.

[0031] Furthermore, this embodiment also involves the initialization of the laser cavity simulation system: the core is to complete the initialization and verification of multi-dimensional parameters and meshes: first, define core optical parameters such as cavity length, gain medium size, optical loss, and output coupling ratio, and verify the rationality of the parameters; associate a PumpSource class instance as a pump input unit and assign the basic physical parameters of Nd:YAG; initialize the optical three-dimensional mesh and mark the crystal region mask, define the frequency domain mesh of the laser field, and pre-initialize the radial / axial mesh required for thermal calculations; finally, print the pre-configured parameters to complete the basic configuration before simulation.

[0032] Medium Dispersive Refractive Index Calculation: To improve the accuracy of optical simulation, a fixed refractive index setting is abandoned. The dispersive refractive index calculation of Nd:YAG crystals is implemented based on the Sellmeier equation: First, the incident light wavelength is converted to μm, and the standard Sellmeier coefficients of Nd:YAG at room temperature are substituted into the formula: The square of the refractive index is calculated, and then the square root is taken to obtain the accurate refractive index at the corresponding wavelength. This provides the fundamental optical parameters after dispersion correction for subsequent calculations such as wavenumber and phase modulation. The incident light wavelength, denoted as the standard Sellmeier coefficient for Nd:YAG crystals, where n is the refractive index at the corresponding wavelength.

[0033] Step S20: Calculate the heat source distribution inside the crystal based on the pump light intensity, calculate the three-dimensional temperature field of the crystal obtained by iterative calculation of the heat source distribution inside the crystal, and obtain the focal length of the thermal lens based on the solution of the three-dimensional temperature field of the crystal.

[0034] It should be noted that the comprehensive calculation of the thermal properties of crystals consists of three core parts: First, the calculation of heat source distribution, which involves correlating with pump light intensity and deriving the heat source term of pump absorption conversion based on parameters such as pump absorption coefficient, slope efficiency, and energy ratio, and verifying the total heat generation power and the peak value of the heat source; second, the solution of the temperature field, which uses an iterative method to solve the three-dimensional temperature field of the crystal, combining parameters such as thermal conductivity and convective heat transfer coefficient, and iterating until the convergence condition is met; and third, the calculation of thermal derivation effect parameters, which, based on the temperature field results and combined with the coefficient of thermal expansion, elastic modulus, and photoelastic coefficient, calculates the refractive index change caused by thermal stress and photoelastic effect, and at the same time, provides a basis for calculating the focal length of the thermal lens by correlating temperature change and refractive index change through the thermo-optic coefficient.

[0035] In one embodiment, such as Figure 3 As shown, this embodiment of the invention provides a crystal temperature distribution map, wherein the temperature distribution is calculated based on the finite difference iterative solution of the steady-state heat conduction equation, covering heat source driving, governing equations, numerical discretization, boundary conditions, and convergence criteria. The formula for calculating the heat source term is:

[0036] in, The volumetric heat source density at radial and axial z-points; The absorption coefficient of Nd:YAG for 808 nm pump light; The pump light intensity is calculated using a Gaussian pump source model; Nd:YAG is a cylindrical crystal. Ignoring circumferential temperature changes, a two-dimensional steady-state heat conduction equation based on the radial-axial (rz) direction is adopted:

[0037] Where T is temperature; k is the thermal conductivity of Nd:YAG; the continuity equation is discretized into a grid algebraic equation using the finite difference method, facilitating iterative calculation. The water-cooled convection boundary conditions are:

[0038] Where h is the water-cooled convective heat transfer coefficient; Take the coolant temperature ; The discrete equations were then solved using an iterative method, with the convergence criterion being that the overall average temperature error was less than a threshold. For example... Figure 4 As shown, this embodiment of the invention provides a circumferential stress distribution diagram for a crystal. The thermal stress distribution of the Nd:YAG crystal in the code is based on thermoelasticity theory, and is applied to cylindrical crystals (radial r, circumferential). (Axial direction z), neglecting the circumferential temperature gradient, only considering the free thermal expansion strain caused by the thermal stress resulting from the two-dimensional temperature field rz:

[0039] in, Given the thermal expansion coefficient of Nd:YAG, the circumferential stress distribution of the crystal was calculated using the generalized Hooke's law combined with a discretization method.

[0040] Where E is the elastic modulus of Nd:YAG crystal, which is fixed at 280×10⁹ Pa in the code; ν is Poisson's ratio, which is fixed at 0.28 in the code; For actual circumferential strain, For the actual radial strain, The actual axial strain is represented by all three values, which are derived from the crystal displacement field through the strain-displacement geometric equation.

[0041] like Figure 5 As shown in the figure, an embodiment of the present invention provides a tangential refractive index variation distribution diagram of a crystal. Targeting the thermo-optical coupling characteristics of Nd:YAG cylindrical crystals, it combines the coupling effect of thermo-optical and elasto-optical effects to achieve tangential (… This module numerically solves for the refractive index change. Taking the solved two-dimensional (radial r - axial z) temperature and thermal stress fields of the crystal as input, it calculates the tangential refractive index change at each grid point of the crystal based on the thermo-optical and elastic-optical coupling theory of isotropic media. The total tangential refractive index change is the algebraic sum of the refractive index changes caused by the thermo-optical effect and those caused by the elastic-optical effect. The specific calculation logic is as follows: First, the contribution of the thermo-optical effect is calculated based on the thermo-optical coefficient of the Nd:YAG crystal. The thermo-optical coefficient of Nd:YAG at room temperature is used. Combined with the temperature change at the (r,z) position of the crystal The change in tangential refractive index caused by the thermo-optic effect was obtained. Since Nd:YAG is an optically isotropic medium in the stress-free state, the refractive index change caused by the thermo-optical effect has no directional difference. Therefore, the tangential thermo-optical refractive index change is consistent with the radial and axial changes. Secondly, the contribution of the thermo-optical effect is calculated based on the thermo-optical tensor properties of the isotropic medium, taking the ground-state refractive index of Nd:YAG at a laser wavelength of 1064 nm. Elastic coefficient Combined with the already solved tangential stress Radial stress Axial stress First calculate the tangential stress combination term. Then, the tangential elasto-optical refractive index change is obtained through the coupling relationship between the elasto-optical effect and the refractive index. The negative sign originates from the inherent coupling relationship between stress and refractive index change in the elasto-optical effect, determining the proportion of stress conversion to refractive index change; finally, the contributions of the thermo-optical effect and the elasto-optical effect are superimposed to obtain the total change in the tangential refractive index of the crystal:

[0042] Step S30: Based on the focal length of the thermal lens, dynamically update the effective g-parameter and radius of curvature of the resonant cavity, and perform resonant cavity stability analysis based on the updated effective g-parameter and radius of curvature.

[0043] In the specific implementation, the effective g-parameter of the resonant cavity is dynamically updated by calculating the optical power based on the focal length of the thermal lens. Based on the position of the thermal lens within the cavity (center of the medium), update the effective g-parameters of the laser cavity: , ,in, For the original g parameters, These represent the distances from the left and right cavity mirrors to the thermal lens, respectively. The g-parameter is a core parameter describing the stability of the resonant cavity's geometry. Based on the updated effective g-parameters of the resonant cavity, the effective radius of curvature is calculated, for example, L / (1-g). 1eff L is the sum of z1 and z2; finally, the corrected effective g parameters, radius of curvature, optical power, etc. are printed to complete the thermal lens feedback update of the cavity parameters.

[0044] Furthermore, the formula for determining the stability of the resonant cavity is g1g2. If 0 < g1g2 < 1, then the resonant cavity is determined to be in a stable state. L is the cavity length. This represents the radius of curvature of the endoscope. Otherwise, it is determined to be in an unstable state.

[0045] Step S40: Calculate the beam parameters based on the effective g-parameters.

[0046] It should be noted that the beam parameters in this embodiment include the laser beam waist radius and the center spot size of the gain medium.

[0047] In specific implementation, the laser beam waist radius calculation process is as follows: based on the effective g-parameter of the resonant cavity, the cavity length, and the laser wavelength, combined with the formula:

[0048] in, Where L is the wavelength, L is the cavity length, and g1 and g2 are the effective g parameters; The size of the central spot in the gain medium is calculated based on the laser beam waist radius and Rayleigh distance, using the following formula:

[0049] Where z is the distance from the gain center to the beam waist. This is the Rayleigh distance.

[0050] Step S50: Calculate the pump absorption and gain distribution based on the pump light intensity, pump photon flux, and crystal boundary reflection characteristics.

[0051] In practical implementation, the calculation process for the crystal boundary reflection characteristics involves calculating the incident angle of light rays hitting the side boundary, determining whether total internal reflection occurs based on Snell's law, and if not, using Fresnel's formula to calculate the average reflectivity of s-polarization and p-polarization as the side Fresnel reflectivity. For example, the refraction angle of the side boundary of a gain crystal is calculated using Snell's law. ,when When total internal reflection occurs, it is determined to be total internal reflection. When it is not total internal reflection, Fresnel's formula is used for calculation. In the case of unpolarized light, the average value of the s-polarized and p-polarized reflectivities is taken as the final Fresnel reflectivity of the side boundary.

[0052] Furthermore, a specific implementation involves combining the four-level rate equation to calculate the interaction characteristics between the pump light and the gain medium. The core optimization incorporates Fresnel reflection from the crystal side boundaries: First, the total pump intensity is calculated; based on the steady-state solution of the four-level rate equation, the population distribution of the pump level, upper level, and lower level is solved; then, the gain grid is calculated using the population inversion distribution combined with quantum efficiency; simultaneously, the absorption coefficient and absorption grid are calculated to quantify the degree of pump light absorption within the crystal, providing basic gain / absorption data for subsequent threshold power and output power calculations. The total pump intensity is obtained by combining the crystal end-face reflection intensity and the side-boundary Fresnel reflection intensity. The level population is then solved based on the four-level system rate equation to obtain the gain distribution. The process of solving the level population using the four-level system rate equation is as follows: the pump level population is solved based on the pump photon flux, absorption cross-section, and level lifetime. Upper energy level population Lower energy level population The ground state population is obtained through particle number conservation. Gain distribution based on population inversion number stimulated radiation cross section Solving for quantum efficiency.

[0053] Step S60: Calculate the pump-laser mode overlap factor using the laser beam waist radius, the center spot size of the gain medium, the pump intensity, and the spatial distribution of the laser intensity.

[0054] In practical implementation, the pump-laser mode overlap factor, which is the degree of overlap between the pump light and the laser mode, is calculated using the following formula:

[0055] in, For pump light intensity, The intensity of the laser mode light. As a volume unit, The theoretical mode distribution is constructed by combining the laser beam waist radius and the center spot size of the gain medium with the propagation equation of the Gaussian beam.

[0056] Step S70: Calculate the laser threshold power with thermal lens feedback based on the gain distribution and the pump-laser mode overlap factor combined with the total cavity loss.

[0057] In a specific implementation, the laser threshold power is the pump power scaled by the desired gain / average gain. The average gain is obtained by combining the total loss with the gain integral and the pump-laser mode overlap factor. The desired gain is... , For the length of the gain medium, Total loss, total loss It is the linear sum of output loss and intrinsic loss.

[0058] Step S80: Calculate the laser output power based on the laser threshold power and the input pump power.

[0059] In the specific implementation, the calculation rule for laser output power is as follows: when the input pump power is less than the threshold power, the output power is 0; when the input pump power is greater than or equal to the threshold power, the output power = slope efficiency × (input pump power - threshold power). Here, the slope efficiency combines quantum efficiency, mode extraction efficiency, output coupling coefficient and intrinsic loss correction. The quantum efficiency is solved based on the ratio of pump photon energy to laser photon energy and the quantum efficiency coefficient. The mode extraction efficiency is solved based on the ratio of the steady-state field mode weight to the global gain.

[0060] Step S90: Based on the effective g parameter, the focal length of the thermal lens, and the gain distribution, the steady-state laser field modulated by the thermal lens is solved by iterative round trip.

[0061] It should be noted that the steady-state laser field with thermal lens is solved by the round-trip iterative method: First, the initial beam waist radius is calculated based on the effective g parameter to initialize the Gaussian laser field; the free space propagation kernel, cavity mirror reflection phase modulation, and thermal lens phase modulation logic are defined to complete the single-pass propagation from left to right and from right to left; during the iteration process, the round-trip loss and gain self-consistency calibration are combined to calculate the iteration error, and the iteration stops when the convergence threshold is met. The convergence state and the number of iterations are output, and finally the steady-state laser field distribution is obtained.

[0062] In one embodiment, the steady-state laser field modulated by the thermal lens is solved using the Fast Fourier Transform method, and the frequency domain transfer function is:

[0063] in, Let d be the angular spectral component, d be the propagation distance, and k0 be the wavenumber. The propagation process utilizes Fourier transform to realize the propagation of the optical field in free space and within the gain medium. Step S100: Output simulation results.

[0064] It should be noted that the simulation results in this embodiment include at least the resonant cavity stability analysis results, beam parameters, laser threshold power, laser output power, pump-laser mode overlap factor, and steady-state laser field distribution data. Specifically, the implementation integrates the entire simulation results and outputs them categorized by cavity stability: if the cavity is unstable, it returns core parameters such as stability identifier, effective g-parameter, infinite threshold power, and zero-value output power; if the cavity is stable, it outputs full parameters such as stability identifier, effective g-parameter, beam parameters (beam waist radius, gain center spot), pump-laser mode overlap factor, average absorption coefficient, threshold power, and output power, comprehensively presenting the optical-thermal coupling simulation results of the plano-concave cavity solid-state laser.

[0065] In this embodiment, a pump source model is constructed to calculate the pump intensity and photon flux; the crystal heat source distribution is solved based on the pump intensity, and the three-dimensional temperature field and thermal lens focal length are obtained using the step-by-step Fourier method; the equivalent g-parameters and radius of curvature of the resonant cavity are dynamically updated using the thermal lens focal length for stability analysis; the pump absorption and gain distribution are calculated by combining the pump intensity, photon flux, and crystal boundary reflection characteristics; the pump-laser mode overlap factor is calculated based on the beam parameters calculated according to the equivalent g-parameters, the pump intensity, and the laser intensity; the laser threshold power is calculated, and the output power is calculated by combining the threshold power and the input pump power; the steady-state laser field is iteratively solved based on the equivalent g-parameters, the thermal lens focal length, and the gain distribution, and the simulation results are finally output. This achieves dynamic coupling feedback between the thermal lens focal length and the resonant cavity parameters, significantly improving the simulation accuracy.

[0066] Furthermore, this embodiment of the invention also proposes a storage medium storing a steady-state simulation program for a solid-state laser. When the steady-state simulation program for the solid-state laser is executed by a processor, it implements the steps of the steady-state simulation method for the solid-state laser as described above.

[0067] Furthermore, this invention also proposes a computer program product storing a steady-state simulation program for a solid-state laser. When the steady-state simulation program for the solid-state laser is executed by a processor, it implements the steps of the steady-state simulation method for the solid-state laser as described above.

[0068] This application embodiment also provides a steady-state simulation device for a solid-state laser, including a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other through the communication bus. The memory is used to store the steady-state simulation program for the solid-state laser. When the processor executes the program stored in the memory, it implements the aforementioned steady-state simulation method for the solid-state laser.

[0069] The communication bus mentioned in the aforementioned steady-state simulation equipment for solid-state lasers can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc.

[0070] The communication interface is used for communication between the aforementioned solid-state laser steady-state simulation equipment and other devices.

[0071] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0072] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0073] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk (SSD)).

[0074] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0075] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0076] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0077] It should be understood that the above are merely illustrative examples and do not constitute any limitation on the technical solutions of the present invention. In specific applications, those skilled in the art can make settings as needed, and the present invention does not impose any restrictions on this.

[0078] It should be noted that the workflow described above is merely illustrative and does not limit the scope of protection of this invention. In practical applications, those skilled in the art can select some or all of the workflow to achieve the purpose of this embodiment according to actual needs, and no restrictions are imposed here.

[0079] In addition, for technical details not described in detail in this embodiment, please refer to the steady-state simulation method of solid-state lasers provided in any embodiment of the present invention, which will not be repeated here.

[0080] Furthermore, it should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0081] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0082] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory (ROM) / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0083] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

[0084] It is understood that the system provided in the embodiments of the present invention corresponds to the method provided in the embodiments of the present invention, and the explanation, examples and beneficial effects of the relevant content can be referred to the corresponding parts of the above method.

Claims

1. A steady-state simulation method for a solid-state laser, characterized in that, The steady-state simulation method for the solid-state laser includes: A pump source model is constructed, and the pump light intensity and pump photon flux are calculated using the pump source model. The distribution of heat sources inside the crystal is calculated based on the pump light intensity. The three-dimensional temperature field of the crystal is obtained by iterative calculation of the distribution of heat sources inside the crystal. The focal length of the thermal lens is obtained based on the solution of the three-dimensional temperature field of the crystal. Based on the focal length of the thermal lens, the effective g-parameter and radius of curvature of the resonant cavity are dynamically updated, and the stability analysis of the resonant cavity is performed based on the updated effective g-parameter and radius of curvature. Here, the g-parameter is the core parameter describing the stability of the resonant cavity's geometric structure. The beam parameters are calculated based on the effective g-parameters, including the laser beam waist radius and the center spot size of the gain medium; The pump absorption and gain distribution are calculated based on the pump intensity, pump photon flux, and crystal boundary reflection characteristics. The pump-laser mode overlap factor is calculated using the laser beam waist radius, the center spot size of the gain medium, the pump intensity, and the spatial distribution of the laser intensity. The laser threshold power including thermal lens feedback is calculated based on the gain distribution and the pump-laser mode overlap factor combined with the total cavity loss. The laser output power is calculated based on the laser threshold power and the input pump power. Based on the effective g-parameter, the focal length of the thermal lens, and the gain distribution, the steady-state laser field modulated by the thermal lens is solved by iterative round trip. The simulation results are output, including at least the resonant cavity stability analysis results, beam parameters, laser threshold power, laser output power, pump-laser mode overlap factor, and steady-state laser field distribution data.

2. The steady-state simulation method for solid-state lasers as described in claim 1, characterized in that, The crystal boundary reflection characteristics are used to determine whether total internal reflection occurs based on the incident angle of light incident on the side boundary and Snell's law. If total internal reflection does not occur, the average reflectivity of s-polarization and p-polarization is calculated using Fresnel's formula as the side Fresnel reflectivity. The side Fresnel reflectivity is used to correct the transmission and absorption distribution of pump light in the crystal.

3. The steady-state simulation method for solid-state lasers as described in claim 1, characterized in that, The effective g-parameter of the dynamically updated resonant cavity is calculated based on the focal length of the thermal lens to obtain optical power. Based on the position of the thermal lens within the cavity (center of the medium), update the effective g-parameters of the laser cavity: , ,in, For the original g parameters, These represent the distances from the left and right endoscopes to the thermal lens, respectively.

4. The steady-state simulation method for a solid-state laser as described in claim 1, characterized in that, The formula for determining the stability of a resonant cavity is g1g2. If 0 < g1g2 < 1, then the resonant cavity is considered to be in a stable state. L is the cavity length. The radius of curvature of the endoscope is denoted as .

5. The steady-state simulation method for a solid-state laser as described in claim 1, characterized in that, The laser beam waist radius calculation process is as follows: based on the effective g-parameter of the resonant cavity, the cavity length, and the laser wavelength, combined with the formula: in, Where L is the wavelength, L is the cavity length, and g1 and g2 are the effective g parameters; The size of the central spot in the gain medium is calculated based on the laser beam waist radius and Rayleigh distance, using the following formula: Where z is the distance from the gain center to the beam waist. This is the Rayleigh distance.

6. The steady-state simulation method for a solid-state laser as described in claim 1, characterized in that, The laser threshold power is the pump power scaled by the desired gain / average gain. The average gain is obtained by combining the total loss with the gain integral and the pump-laser mode overlap factor. The desired gain is... , For the length of the gain medium, Total loss.

7. The steady-state simulation method for a solid-state laser as described in claim 1, characterized in that, The calculation rule for the laser output power is as follows: when the input pump power is less than the threshold power, the output power is 0; when the input pump power is greater than or equal to the threshold power, the output power = slope efficiency × (input pump power - threshold power), where the slope efficiency combines quantum efficiency, mode extraction efficiency, output coupling coefficient and intrinsic loss correction, the quantum efficiency is solved based on the ratio of pump photon energy to laser photon energy and the quantum efficiency coefficient, and the mode extraction efficiency is solved based on the ratio of the steady-state field mode weight to the global gain.

8. A steady-state simulation device for a solid-state laser, characterized in that, The steady-state simulation device for the solid-state laser includes: a memory, a processor, and a steady-state simulation program for the solid-state laser stored in the memory and executable on the processor. The steady-state simulation program for the solid-state laser is configured to implement the steps of the steady-state simulation method for the solid-state laser as described in any one of claims 1 to 7.

9. A storage medium, characterized in that, The storage medium stores a steady-state simulation program for a solid-state laser, which, when executed by a processor, implements the steps of the steady-state simulation method for a solid-state laser as described in any one of claims 1 to 7.

10. A computer program product, characterized in that, The computer program product stores a steady-state simulation program for a solid-state laser, which, when executed by a processor, implements the steps of the steady-state simulation method for a solid-state laser as described in any one of claims 1 to 7.

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