A method for accurately modeling laser light fields in a multi-stage amplification system

Abstract

The application discloses a method for accurately simulating a laser light field in a multi-stage amplification system, comprising the following steps: measuring the intensity distribution and phase distribution of an initial signal light beam, decomposing and reconstructing to obtain the light field of the reconstructed initial signal light beam; collimating three pump light beams from the end face to be incident on three corresponding laser gain media respectively, and calculating the temperature distribution of each laser gain medium; giving the reconstructed initial signal light beam power, and starting to propagate in the form of a light field, and sequentially passing through three laser gain media for three times of amplification; axially equally slicing the three laser gain media, and in each slice, the signal light beam as the input light field is jointly modulated by the thermal effect and the gain effect; then inputting the modulated light field into the next slice, and finally obtaining the light field propagation of the laser light beam inside each laser gain medium. By using the application, the accurate simulation of the full-optical-path laser light field in the multi-stage amplification system can be realized.

Description

Technical Field

[0001] This invention relates to the field of solid-state laser technology, and in particular to a method for accurately simulating the laser light field in a multi-stage amplification system. Background Technology

[0002] High-power all-solid-state rod laser amplifiers based on the master oscillator power amplifier (MOPA) structure typically employ multi-stage amplifiers to boost the power of a low-power seed laser. This system achieves high performance due to its high conversion efficiency and good beam quality. MOPA systems typically employ end-pumping structures to achieve good spatial mode matching between the pump beam and the signal beam. The initial signal beam, typically in the milliwatt range, is output from a single-mode fiber or a resonator with a rod-shaped gain medium. To obtain optimal beam quality and amplification efficiency, simulation calculations are required to optimize the optical path of the amplification system. Because MOPA-structured laser amplification systems require higher output power, three to five stages of amplifiers are typically needed to boost the laser power to the hundreds of watts level. This means that the optical path length from the seed signal output from the seed source to the output of the amplification system increases to several meters, and the laser beam must be reflected and transmitted through multiple optical elements. This complexity poses a significant challenge to existing theoretical models, highlighting the importance and urgency of accurately simulating the laser optical field in multi-stage amplification systems.

[0003] In simulating beam propagation in all-solid-state lasers, traditional methods employ the ABCD matrix, as seen in the literature "Research on All-Solid-State 914nm Lasers." However, this theory neglects the influence of gain effects on the signal beam and simplifies the gain medium to a combination of a thin lens and a parallel plate. Existing research has shown that due to gain effects, pumping the gain medium with signal beams of different power and radii at the incident end face results in significant differences in the propagation of the amplified laser output. Therefore, the accuracy of calculations based on the ABCD theory is unreliable.

[0004] Existing literature has also proposed an "angular spectrum beam propagation method based on fast Fourier transform," which calculates laser propagation while considering the thermal and gain effects of the gain medium. Several numerical models based on this method have been developed, including end-pumped Nd:YVO4 resonators, Nd:YVO4 single-stage amplifiers, and Yb:YAG single-stage amplifiers. However, these models struggle to accurately simulate the optical field of the entire optical path in multi-stage laser amplification systems, lacking practical guiding significance. Summary of the Invention

[0005] To address the shortcomings of existing laser simulation methods in multi-stage amplification systems, this invention provides a method for accurately simulating the laser field in a multi-stage amplification system. This method can achieve accurate simulation of the laser field across the entire optical path in a multi-stage amplification system, and solves the problem of obtaining intensity and phase distribution information of the laser field under space-constrained conditions.

[0006] A method for accurately simulating the laser light field in a multi-stage amplification system includes the following steps:

[0007] (1) Measure the intensity distribution of the initial signal beam and decompose it using the normalized circular mirror confocal cavity Laguerre-Gaussian method;

[0008] (2) Measure the phase distribution of the initial signal beam and decompose it using normalized Zernike polynomials;

[0009] (3) Based on the intensity and phase information obtained from the decomposition, the light intensity distribution and phase distribution of the initial signal beam are reconstructed and integrated to obtain the light field of the reconstructed initial signal beam;

[0010] (4) The first pump beam, the second pump beam, and the third pump beam are collimated and incident on the first laser gain medium, the second laser gain medium, and the third laser gain medium from the end face, respectively, and the temperature distribution of each laser gain medium is calculated.

[0011] (5) Assign power to the initial signal beam for reconstruction and start propagating in the form of a light field, and amplify it three times in sequence through three laser gain media; calculate the thermal effect and gain effect on the input signal beam based on the temperature distribution of each laser gain medium;

[0012] (6) The three laser gain media are axially equidistantly sliced. In each slice, the signal beam is used as the input optical field and is subjected to the combined modulation of thermal effect and gain effect. Then the modulated optical field is input to the next slice until the optical field propagation of the laser beam inside each laser gain medium is obtained. The optical field propagation of the laser beam inside the laser gain medium and between adjacent laser gain media is calculated based on the step-by-step Fourier method of angular spectrum theory.

[0013] The specific process of step (1) is as follows:

[0014] The intensity distribution of the initial signal beam is measured using a CCD camera, the beam radius is calculated using the second-order moment method, and the initial signal beam is denoised.

[0015] The initial signal beam is decomposed into LG using the normalized circular mirror confocal cavity Laguerre-Gaussian method. 00 Model, LG 01 Model, LG 02 Model, LG 03 Model, LG 04 Model, LG 05 The modulus is represented as follows: , , , , , The corresponding light intensities are respectively , , , , , .

[0016] The specific process of step (2) is as follows:

[0017] The phase distribution of the initial signal beam is measured using a wavefront sensor;

[0018] The phase distribution of the initial signal beam is decomposed into DC terms using normalized Zernike polynomials. x Directional tilt item y The expressions for the directional tilt term, defocus term, 0° astigmatism term, 45° astigmatism term, 0° coma term, 90° coma term, 0° triceps aberration term, 45° triceps aberration term, spherical aberration term, 0° second-order astigmatism term, 45° second-order astigmatism term, 0° four-order triceps aberration term, and 45° four-order triceps aberration term are as follows: ~ .

[0019] In step (3), the intensity information obtained from the decomposition is reconstructed using the following formula:

[0020] ;

[0021] in, The initial signal beam intensity distribution after reconstruction; For the measurement of light intensity distribution information; Light intensity , , , , , The coefficient matrix;

[0022] The phase information obtained from the decomposition is reconstructed using the following formula:

[0023] ;

[0024] in, The initial signal beam phase distribution after reconstruction; Let be the coefficient matrix of the Zernike polynomial; Let be the matrix representing the Zernike polynomial;

[0025] The formula for integrating the light field of the reconstructed initial signal beam is:

[0026] ;

[0027] in, To reconstruct the optical field of the initial signal beam, For imaginary numbers, for Exponential function.

[0028] In step (4), the temperature distribution of each laser gain medium is calculated using a three-dimensional steady-state differential equation, and the formula is:

[0029] ;

[0030] in, For the first any position within the laser gain medium Temperature at that location; Within the laser gain medium Thermal conductivity coefficient on the axis; Within the laser gain medium Thermal conductivity coefficient on the axis; Within the laser gain medium Thermal conductivity coefficient on the axis; For the first any position within the laser gain medium The heat source at the edge. For a crystal with edge cooling, its boundary conditions can be determined by the following equation:

[0031] ;

[0032] ;

[0033] in, The heat transfer coefficient between the laser gain medium and the fixture; Room temperature; Let be the side length of the cross-section of the laser gain medium. Since the thermal conductivity between the front and rear ends of the crystal and air is very small, it can be considered as an adiabatic state.

[0034] In step (5), the initial signal beam power is assigned to the reconstructed signal beam, as shown in the following formula:

[0035] ;

[0036] in, The propagation optical field of the initial signal beam. The initial signal power, To reconstruct the optical field of the initial signal beam.

[0037] In step (5), the thermal effect is manifested as thermally induced refractive index and thermal deformation, and the gain effect is manifested as the gain distribution of stimulated emission cross section, both of which are functions dependent on temperature distribution.

[0038] Preferably, in step (6), the thickness of each slice does not exceed 1 mm.

[0039] In step (6), the optical field propagation of the laser beam is calculated using the split-step Fourier method based on angular spectrum theory both inside the laser gain medium and between adjacent laser gain media. Specifically, the optical field propagation inside the laser gain medium is as follows:

[0040]

[0041] in, Indicates the position within the laser gain medium The light field at that location; For Fourier transform operators; This is the inverse Fourier transform operator; m For the first m One slice; Indicates the position within the laser gain medium The light field at that location; The thickness of the slice; The signal light wavenumber in free space; Position within the laser gain medium The change in refractive index at that location; Position within the laser gain medium Gain coefficient at the location; The refractive index of the crystal; The wavelength of the signal beam; In the Fourier domain The spatial angular frequency of the axis; In the Fourier domain The spatial angular frequency of the axis.

[0042] In step (6), after obtaining the optical field propagation of the laser beam inside the laser gain medium and between adjacent laser gain media, for the laser beam at each position, the spot diameter of the laser beam is calculated by the second-order moment method, the intensity distribution of the laser beam is calculated by the square of the real part of the optical field, and the phase distribution of the laser beam is obtained by the normalized Zernike polynomial method of the imaginary part of the optical field.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. This invention achieves complete reproduction of the initial signal beam in experimental measurements by decomposing and reconstructing the intensity and phase distribution of the initial signal beam.

[0045] 2. This invention comprehensively considers the combined modulation of the thermal effect and gain effect within the laser gain medium of end-face pumped laser, resulting in more accurate propagation of the optical field during the gain amplification process of the signal beam within the gain medium.

[0046] 3. The accurate simulation of the laser field in the multi-stage amplification system of the present invention solves the problem of obtaining the intensity distribution and phase distribution information of the laser field under space-constrained conditions.

[0047] 4. Based on parameter settings such as signal beam, pump beam, and laser gain medium that are consistent with experimental measurement conditions, this invention can accurately simulate the propagation and changes of amplified laser beams in free space by multi-stage end-face pumped laser gain media.

[0048] 5. Based on the reconstructed signal beam, this invention achieves accurate simulation of the laser light field in the entire optical path of a multi-stage amplification system. It can obtain the beam diameter at any position on the laser propagation optical axis within the system, which is beneficial for the design of high-power multi-stage amplification systems based on the master oscillation power amplifier structure. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart illustrating a method for accurately simulating a laser light field in a multi-stage amplification system, according to an embodiment of the present invention.

[0051] Figure 2 For the actual measurement and simulation calculation of the initial signal in the embodiments of the present invention Comparison of axial and two-dimensional intensity distribution.

[0052] Figure 3 This is a comparison diagram of the phase distribution of the initial signal measured in practice and calculated in simulation in an embodiment of the present invention.

[0053] Figure 4 This is a comparison diagram of the intensity and phase distribution of the actual measurement results and the simulation calculation results of the far field before and after the waist of the first magnified beam in an embodiment of the present invention.

[0054] Figure 5 This is a comparison diagram of the intensity and phase distribution of the actual measurement results and the simulation calculation results of the far field before and after the waist of the second magnified beam in an embodiment of the present invention.

[0055] Figure 6 This is a comparison diagram of the intensity and phase distribution of the actual measurement results and the simulation calculation results of the far field before and after the beam waist of the third magnified beam in this embodiment of the invention.

[0056] Figure 7 The beam diameter is the actual measurement and simulation calculation of the entire optical path of the multi-stage amplification system in this embodiment of the invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0059] In this embodiment of the invention, the device includes an initial signal beam, a first pump beam, a first laser gain medium, a second pump beam, a second laser gain medium, a third pump beam, and a third laser gain medium. The first pump beam is connected to the first laser gain medium, the second pump beam is connected to the second laser gain medium, and the third pump beam is connected to the third laser gain medium.

[0060] The initial signal contains data information such as intensity distribution, phase distribution, beam diameter, wavelength, and power.

[0061] The first pump beam, the second pump beam, and the third pump beam all have data information on power, beam diameter, intensity distribution, wavelength, and beam quality.

[0062] The first, second, and third laser gain media all have data on their dimensions, absorption coefficient, thermo-optic coefficient, refractive index, thermal conductivity, thermal conversion coefficient, boundary heat transfer coefficient, ambient temperature, and initial stimulated emission cross section.

[0063] like Figure 1As shown, the present invention mainly includes the following steps: measuring the intensity distribution of the initial signal beam, decomposing and reconstructing it to obtain the intensity distribution of the reconstructed initial signal beam. Measuring the phase distribution of the initial signal beam, decomposing and reconstructing it to obtain the phase distribution of the reconstructed initial signal beam. Combining the reconstructed intensity distribution and phase distribution to construct a complete reconstructed initial signal beam light field, which serves as the initial signal beam in a multi-stage laser amplification system. N represents the amplification stage. In this embodiment, the multi-stage amplification system has three stages, with an upper limit of 3 for N. The initial signal beam propagates within the system as the first signal beam, at which point N=1. Each laser gain medium is subject to both thermal and gain effects, specifically manifested as thermally induced refractive index, thermal deformation, and gain distribution. The Nth signal beam enters the Nth laser gain medium pumped by the Nth pump beam and propagates within it, obtaining the Nth amplified beam. The Nth amplified beam propagates in free space after the Nth laser gain medium. The Nth amplified beam serves as the signal beam for the next amplification stage, assigned the value N=N+1, and the above process is repeated. When N>3, all laser beams are output, completing the simulation calculation of the laser field of the entire optical path in the multi-stage amplification system.

[0064] A method for accurately simulating the laser light field in a multi-stage amplification system specifically includes the following steps:

[0065] (1) Measure the intensity distribution of the initial signal beam and decompose it using the normalized circular mirror confocal cavity Laguerre-Gaussian method.

[0066] The intensity distribution of the initial signal beam was measured using a CCD camera, and the beam radius was calculated using the second-order moment method. And noise reduction processing is performed on the initial signal beam.

[0067] The initial signal beam is decomposed into the normalized circular mirror confocal cavity Laguerre-Gaussian method. , , , , , The corresponding light intensities are respectively , , , , , The specific formula is as follows:

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] in, The radius of the participating pattern decomposition ， Specifically, it is expressed as follows: , The beam radius is the initial signal to be measured. The beam quality factor of the initial signal being measured; For the measurement of light intensity distribution information; The measured peak light intensity; Light intensity , , , , , The coefficient matrix is ​​specifically represented as: .

[0076] (2) Measure the phase distribution of the initial signal beam and decompose it using normalized Zernike polynomials.

[0077] Normalized Zernike polynomial decomposition is used to ~ , respectively corresponding to the DC term, x Directional tilt item y The terms include: directional tilt, defocus, 0° astigmatism, 45° astigmatism, 0° coma, 90° coma, 0° triceps aberration, 45° triceps aberration, spherical aberration, 0° second-order astigmatism, 45° second-order astigmatism, 0° four-order triceps aberration, and 45° four-order triceps aberration. The specific expressions are as follows:

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] in, The radius of the beam; This refers to the measured wavefront phase information. This is the azimuth angle.

[0095] The coefficient matrix of the Zernike polynomial is specifically represented as:

[0096] ;

[0097] Z The matrix representing the Zernike polynomial is specifically expressed as:

[0098] .

[0099] (3) Based on the intensity and phase information obtained from the decomposition, the light intensity distribution and phase distribution of the initial signal beam are reconstructed and integrated to obtain the light field of the reconstructed initial signal beam.

[0100] The intensity information obtained from the decomposition is reconstructed using the following formula:

[0101] ;

[0102] in, The initial signal beam intensity distribution after reconstruction;

[0103] The phase information obtained from the decomposition is reconstructed using the following formula:

[0104] ;

[0105] in, The initial signal beam phase distribution after reconstruction;

[0106] The formula for integrating the light field of the reconstructed initial signal beam is:

[0107] ;

[0108] in, To reconstruct the optical field of the initial signal beam, It is a unit imaginary number.

[0109] (4) The first pump beam, the second pump beam, and the third pump beam are collimated and incident on the first laser gain medium, the second laser gain medium, and the third laser gain medium from the end face, respectively, and the temperature distribution of each laser gain medium is calculated.

[0110] The temperature distribution of each laser gain medium is calculated using a three-dimensional steady-state differential equation, and the formula is as follows:

[0111] ;

[0112] in, For the first any position within the laser gain medium Temperature at that location; Within the laser gain medium Thermal conductivity coefficient on the axis; Within the laser gain medium Thermal conductivity coefficient on the axis; Within the laser gain medium Thermal conductivity coefficient on the axis; For the first any position within the laser gain medium The heat source at the edge. For a crystal with edge cooling, its boundary conditions can be determined by the following equation:

[0113] ;

[0114] ;

[0115] in, The heat transfer coefficient between the laser gain medium and the fixture; At room temperature Let be the side length of the cross-section of the laser gain medium. Since the thermal conductivity between the front and rear ends of the crystal and air is very small, it can be considered as an adiabatic state.

[0116] (5) Assign power to the initial signal beam for reconstruction and start propagating in the form of a light field. The beam is amplified three times in sequence through three laser gain media. Calculate the thermal effect and gain effect on the input signal beam based on the temperature distribution of each laser gain medium.

[0117] The initial signal beam power for reconstruction is assigned as follows:

[0118] ;

[0119] in, The propagation optical field of the initial signal beam. The initial signal power, To reconstruct the optical field of the initial signal beam.

[0120] The reconstructed initial signal beam is used as the first signal beam and enters the first laser gain medium for amplification. The first amplified laser beam is used as the second signal beam and enters the second laser gain medium for amplification. The second amplified laser beam is used as the third signal beam and enters the third laser gain medium for amplification.

[0121] The thermal effects manifest as thermo-induced refractive index and thermal deformation, both of which are functions dependent on temperature distribution. The formula for the thermo-induced refractive index as a function of temperature is:

[0122] ;

[0123] in, The thermally induced refractive index of the laser gain medium; The initial refractive index of the laser gain medium; The thermo-optic coefficient of the laser gain medium; Any position within the laser gain medium Temperature at that location; Room temperature.

[0124] The thermal deformation formula of the laser gain medium as a function of temperature is:

[0125] ;

[0126] in, Thermal deformation of the laser gain medium; The initial refractive index of the laser gain medium; Poisson's ratio; The coefficient of thermal expansion; Any position within the laser gain medium Temperature at that location; Room temperature.

[0127] The gain effect manifests as the gain distribution of the stimulated emission cross section, which is a function of temperature distribution, as shown in the following formula:

[0128] ;

[0129] Any position within the laser gain medium The small-signal gain coefficient at that location is specifically expressed as follows:

[0130] ;

[0131] Any position within the laser gain medium Thermally stimulated emission cross section at the location, This represents the population inversion density. It is a temperature-dependent function, specifically manifested as follows:

[0132]

[0133] in, Any position within the laser gain medium The thermally induced stimulated emission section at the location; This represents the initial stimulated emission cross section of the laser gain medium; Any position within the laser gain medium The temperature at that location.

[0134] Any position within the laser gain medium Signal light intensity at the location;

[0135] Any position within the laser gain medium The saturation light intensity at a given location is expressed as follows:

[0136] ;

[0137] h It is Planck's constant. For pump frequency, This refers to the lifetime of the upper energy level.

[0138] (6) The three laser gain media are axially equidistantly sliced. In each slice, the signal beam is used as the input optical field and is subjected to the combined modulation of thermal and gain effects. Then, the modulated optical field is input to the next slice and the modulation calculation is repeated in the next slice. Until the laser optical field propagates to the last slice of the gain medium, the optical field propagation of the laser beam inside each laser gain medium is obtained. The optical field propagation of the laser beam inside the laser gain medium and between adjacent laser gain media is calculated based on the step-by-step Fourier method of angular spectrum theory.

[0139] The optical field propagation of the laser beam is calculated using the split-step Fourier method based on angular spectrum theory both inside the laser gain medium and between adjacent laser gain media. Specifically, the optical field propagation inside the laser gain medium is as follows:

[0140]

[0141] in, Indicates the position within the laser gain medium The light field at that location; For Fourier transform operators; This is the inverse Fourier transform operator; m For the first m One slice; Indicates the position within the laser gain medium The light field at that location; The thickness of the slice; The signal light wavenumber in free space; Position within the laser gain medium The change in refractive index at that location; Position within the laser gain medium Gain coefficient at the location; The refractive index of the crystal; The wavelength of the signal beam; In the Fourier domain The spatial angular frequency of the axis; In the Fourier domain The spatial angular frequency of the axis.

[0142] After obtaining the optical field propagation of the laser beam inside the laser gain medium and between adjacent laser gain media, for each position of the laser beam, the spot diameter is calculated using the second-order moment method, the intensity distribution is calculated using the square of the real part of the optical field, and the phase distribution is obtained using the normalized Zernike polynomial method for the imaginary part of the optical field. The specific formulas are as follows:

[0143] Formula for calculating the spot diameter of a laser beam:

[0144] ;

[0145] in, Within the laser gain medium The beam diameter of the on-axis signal light.

[0146] Formula for calculating the intensity distribution of a laser beam:

[0147] ;

[0148] Formula for calculating the phase distribution of a laser beam:

[0149] ;

[0150] in, Radial quantity of the beam; This is the beam angle vector.

[0151] The laser beam propagates in the form of an optical field in the multi-stage amplification system, completely preserving the spatial beam information, thus accurately simulating the evolution of the laser beam in the multi-stage amplification system.

[0152] In this embodiment of the invention, the initial signal is provided by single-mode fiber + solid-state pre-amplification, with an output wavelength of 1064 nm, an average power of 1 W, a repetition frequency of 2 MHz, a pulse width of 10 ps, ​​an experimentally measured beam quality factor of 1.13, and a beam diameter of 1.60 mm.

[0153] The intensity distribution of the initial signal was obtained by measurement using a CCD camera. After decomposition and reconstruction, the reconstructed intensity distribution of the initial signal was obtained. The experimental measurement and simulation calculation of the initial signal intensity distribution are as follows: Figure 2 As shown. Figure 2 In (a), the initial signal beam is in (b) is a comparison diagram of the intensity distribution on the axis, which is a comparison diagram of the intensity distribution of the initial signal beam on a one-dimensional plane.

[0154] The phase distribution is obtained by measurement using a wavefront sensor, and after decomposition and reconstruction, the reconstructed phase distribution of the initial signal is obtained. The experimental measurement and simulation calculation of the initial signal phase distribution are as follows: Figure 3 As shown.

[0155] The combined intensity and phase distributions after reconstruction constitute the complete reconstructed initial signal light field.

[0156] The reconstructed initial signal beam quality factor was 1.12, and the beam diameter was 1.60 mm, both close to the experimental measurements. The output wavelengths of the first, second, and third pump beams were all 878 nm, the pump power was 175 W, the beam diameter was 1.60 mm, the intensity distribution was described by a seventh-order super-Gaussian function, and the beam quality was 70. The first, second, and third pump beams in the simulation calculations all used the above values. The first, second, and third laser gain media were all Nd:YVO4 crystals, with the first laser gain media having a Nd:YVO4 crystal doping concentration of 0.2 at.%, and dimensions of 3×3×20 mm. 3 The first laser gain medium is a cuboid; the second laser gain medium has a neodymium doping concentration of 0.2 at.%, and its dimensions are 3×3×25 mm. 3 The third laser gain medium is a cuboid with a 2 mm long undoped end cap bonded to its front face; the crystal is neodymium doped at a concentration of 0.15 at.%, and its dimensions are 3×3×25 mm. 3 The material is a cuboid with a 2 mm long undoped end cap bonded to its front face. The values ​​described above are used for the first, second, and third laser gain media in the simulation calculations.

[0157] The beam propagation distance between the front faces of the first and second laser gain media is 250 mm, and the beam propagation distance between the front faces of the second and third laser gain media is 580 mm.

[0158] The initial signal beam, collimated as the first signal beam, is incident on the first laser gain medium. The experimentally measured and simulated values ​​of the beam diameter at the leading edge of the first laser gain medium are both 1.60 mm. After the first stage of amplification, the first amplified laser is output. The experimentally measured beam quality factor of the first amplified laser is 1.48, and the simulated value is 1.47; the experimentally measured power is 13.6 W, and the simulated value is 13.8 W, with an error of approximately 1%. The experimentally measured and simulated values ​​of the beam diameter of the first amplified laser at the trailing edge of the first laser gain medium are both 1.12 mm. During its propagation in free space 250 mm behind the first laser gain medium, the first amplified laser first converges and then diverges, with a beam waist diameter of 0.21 mm and a distance of 120 mm from the trailing edge of the first laser gain medium. The experimentally measured and simulated values ​​of the beam diameter of the first amplified laser at the leading edge of the second laser gain medium are both 1.20 mm. The experimentally measured and simulated values ​​of the beam intensity distribution and phase distribution of the first amplified laser at the trailing edge and leading edge of the first and second gain media are as follows: Figure 4 As shown, the experimental measurements and simulated values ​​are very similar.

[0159] The first amplified laser beam, acting as the second signal beam, is incident on the second laser gain medium and outputs as the second amplified laser beam after a second stage of amplification. The experimentally measured beam quality factor of the second amplified laser is 1.33, while the simulated value is 1.32; the experimentally measured power is 70.6 W, and the simulated value is 71.5 W, with an error of approximately 1%. The experimentally measured and simulated values ​​of the beam diameter of the second amplified laser beam at the rear end face of the second laser gain medium are both 1.10 mm. During its propagation in free space 580 mm behind the second laser gain medium, the second amplified laser beam first converges and then diverges, with a beam waist diameter of 0.52 mm and a distance of 280 mm from the rear end face of the second laser gain medium. The experimentally measured and simulated values ​​of the beam diameter of the second amplified laser beam at the front end face of the third laser gain medium are both 1.20 mm. The experimentally measured and simulated values ​​of the beam intensity and phase distribution of the second amplified laser beam at the rear end face of the second gain medium and the front end face of the third gain medium are as follows: Figure 5 As shown, the experimental measurements and simulated values ​​are very similar.

[0160] The second amplified laser beam, acting as the third signal beam, is incident on the third laser gain medium and outputs as the third amplified laser beam after third-stage amplification. The experimentally measured beam quality factor of the third amplified laser is 1.38, and the simulated value is 1.37; the experimentally measured power is 124.2 W, and the simulated value is 125.1 W, with an error of approximately 1%. The experimentally measured and simulated values ​​of the beam diameter of the third amplified laser beam at the rear end face of the third laser gain medium are both 1.40 mm. During its free-space propagation 600 mm behind the third laser gain medium, the third amplified laser beam first converges and then diverges, with a beam waist diameter of 0.49 mm and a distance of 320 mm from the rear end face of the second laser gain medium. The experimentally measured and simulated values ​​of the beam diameter of the second amplified laser beam at 600 mm from the rear end face of the third gain medium are both 1.22 mm. The experimentally measured and simulated values ​​of the beam intensity and phase distribution of the third amplified laser beam at the rear end face of the third gain medium and at 600 mm from the rear end face of the third gain medium are as follows: Figure 6 As shown, the experimental measurements and simulated values ​​are very similar.

[0161] In a three-stage laser amplification system, the experimentally measured and simulated values ​​of the diameter of the 1064 nm laser beam throughout the optical path are as follows: Figure 7 As shown in the figure. The results indicate that the simulated value of the laser beam diameter is consistent with the experimental measurement value, and the error is almost negligible.

[0162] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for accurately simulating the laser light field in a multi-stage amplification system, characterized in that, include: (1) The intensity distribution of the initial signal beam was measured and decomposed using the normalized circular mirror confocal cavity Laguerre-Gaussian method, resulting in LG. 00 Model, LG 01 Model, LG 02 Model, LG 03 Model, LG 04 Model, LG 05 The modes, and the corresponding light intensities are respectively , , , , , ; (2) The phase distribution of the initial signal beam is measured and decomposed using a normalized Zernike polynomial, which decomposes the phase distribution of the initial signal beam into DC terms, x Directional tilt item y The expressions for the directional tilt term, defocus term, 0° astigmatism term, 45° astigmatism term, 0° coma term, 90° coma term, 0° triceps aberration term, 45° triceps aberration term, spherical aberration term, 0° second-order astigmatism term, 45° second-order astigmatism term, 0° four-order triceps aberration term, and 45° four-order triceps aberration term are as follows: ~ ; (3) Based on the intensity and phase information obtained from the decomposition, the intensity and phase distributions of the initial signal beam are reconstructed, and the reconstructed light field of the initial signal beam is obtained by integrating the information. The formula is as follows: ； in, To reconstruct the optical field of the initial signal beam, The initial signal beam intensity distribution after reconstruction. The initial signal beam phase distribution after reconstruction. For imaginary numbers, for Exponential function; (4) The first pump beam, the second pump beam, and the third pump beam are collimated and incident on the first laser gain medium, the second laser gain medium, and the third laser gain medium from the end face, respectively. The temperature distribution of each laser gain medium is calculated using three-dimensional steady-state differential equations. (5) Assign power to the initial signal beam for reconstruction , The initial signal power is given; it begins to propagate in the form of a light field, and is amplified three times in sequence through three laser gain media; the thermal effect and gain effect on the input signal beam are calculated based on the temperature distribution of each laser gain medium. (6) The three laser gain media are axially equidistantly sliced. In each slice, the signal beam is used as the input optical field and is subjected to the combined modulation of thermal effect and gain effect. Then the modulated optical field is input to the next slice until the optical field propagation of the laser beam inside each laser gain medium is obtained. The optical field propagation of the laser beam inside the laser gain medium and between adjacent laser gain media is calculated based on the step-by-step Fourier method of angular spectrum theory.

2. The method for accurately simulating the laser light field in a multi-stage amplification system according to claim 1, characterized in that, In step (5), the thermal effect is manifested as thermally induced refractive index and thermal deformation, and the gain effect is manifested as the gain distribution of stimulated emission cross section, both of which are functions dependent on temperature distribution.

3. The method for accurately simulating the laser light field in a multi-stage amplification system according to claim 1, characterized in that, In step (6), the thickness of each slice shall not exceed 1 mm.

4. The method for accurately simulating the laser light field in a multi-stage amplification system according to claim 1, characterized in that, In step (6), after obtaining the optical field propagation of the laser beam inside the laser gain medium and between adjacent laser gain media, for the laser beam at each position, the spot diameter of the laser beam is calculated by the second-order moment method, the intensity distribution of the laser beam is calculated by the square of the real part of the optical field, and the phase distribution of the laser beam is obtained by the normalized Zernike polynomial method of the imaginary part of the optical field.

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