A method for calculating a full-aperture harmonic conversion crystal detuning angle efficiency characterization value

Abstract

The present application relates to the field of precision optical engineering measurement, and particularly relates to a kind of full aperture harmonic conversion crystal detuning angle efficiency characterization value calculation method, comprising: obtaining detuning angle distribution data;Determine the interval of characterization value calculation;Calculate the actual detuning angle distribution corresponding to each spatial position of crystal;Calculate the phase mismatch amount distribution of each spatial position;Efficiency function reflecting the overall harmonic conversion efficiency of crystal under full aperture beam irradiation is constructed;Numerical optimization calculation is carried out on efficiency function, and the crystal rotation adjustment amount corresponding to global maximum value is determined as the harmonic conversion crystal detuning angle efficiency characterization value in full aperture range.The above scheme aggregates the phase mismatch degree of each spatial position in full aperture range by spatial integration, forms the overall efficiency evaluation function that can be numerically optimized, and the global optimal characterization value obtained by solving under the physical constraint of single reset angle adjustment can make the phase mismatch distribution in the full light region of crystal reach overall minimization, and the efficiency level is higher.

Description

Technical Field

[0001] This invention relates to the field of precision optical engineering measurement technology, and more specifically, to a method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic conversion crystal. Background Technology

[0002] Harmonic conversion crystals (such as KDP and KD*P) are core optical components in high-power laser devices that achieve frequency conversion. They convert fundamental frequency light into harmonic or third-harmonic light through nonlinear optical effects. In engineering applications, the crystal needs to be precisely matched with a phase-matching angle to achieve ideal conversion efficiency. However, due to processing errors, material stress, and assembly deviations, there is a mismatch angle between the actual crystal axis and the ideal direction, leading to phase mismatch and a decrease in conversion efficiency. Therefore, before the crystal is loaded into the final optical components, its mismatch angle needs to be measured offline using a nanosecond probe laser, and online adjustment and compensation should be performed during actual operation by rotating the entire crystal to restore the crystal to its optimal phase-matching state. This is a key technical step in ensuring the output performance of high-power laser devices.

[0003] Although existing technologies can achieve single-point or discrete multi-point scanning measurements of the detuning angle of harmonic conversion crystals, the measurement results can only reflect the crystal axis deviation at local locations. Large-aperture harmonic conversion crystals exhibit spatial inconsistencies in their detuning angle across the entire aperture range. During online commissioning, only a single reset angle adjustment can be applied to the entire crystal. This means that assembly and adjustment based on single-point measurements cannot optimize the overall harmonic conversion efficiency under full-aperture beam irradiation, making it difficult to meet the engineering requirements of high-power laser devices for continuously improving harmonic conversion efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal, in order to solve the above-mentioned technical problems.

[0005] This invention provides a method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal, including:

[0006] Acquire detuning angle distribution data of a harmonic conversion crystal at multiple discrete spatial locations within its optical aperture;

[0007] The interval for calculating the characterization value is determined based on the extreme values ​​of the detuning angle distribution data.

[0008] Within the range of the characterization values, select a crystal rotation adjustment amount to be optimized around the axis, and calculate the actual detuning angle distribution corresponding to each spatial position of the crystal based on the crystal rotation adjustment amount around the axis.

[0009] Based on the actual mistuning angle distribution and the crystal nonlinear phase matching characteristics it determines, the phase mismatch distribution at each spatial location is calculated;

[0010] Based on the phase mismatch distribution, an efficiency function reflecting the overall harmonic conversion efficiency of the crystal under full-aperture beam irradiation is constructed by spatial integration.

[0011] Within the calculation range of the characterization value, the efficiency function is numerically optimized, and the crystal rotation adjustment amount corresponding to the global maximum value is determined as the characterization value of the detuning angle efficiency of the harmonic conversion crystal in the full aperture range; wherein, the characterization value is used to guide the online assembly and adjustment of the harmonic conversion crystal.

[0012] Furthermore, the crystal's rotation adjustment around the axis is a single angular value;

[0013] The calculation of the actual mistuning angle distribution corresponding to each spatial position of the crystal based on the crystal's rotation adjustment around its axis includes:

[0014] After selecting the crystal rotation adjustment amount around the axis, the original detuning angle of each spatial position of the crystal is subtracted from the crystal rotation adjustment amount to obtain the actual detuning angle distribution corresponding to each position after the overall rotation of the crystal.

[0015] Further, the step of calculating the phase mismatch distribution at each spatial location based on the actual mismatch angle distribution and the crystal nonlinear phase matching characteristics it determines includes:

[0016] Based on the actual mistuning angle distribution, combined with the nonlinear refractive index anisotropy of the harmonic conversion crystal and the optimal phase matching angle of the crystal in the corresponding harmonic conversion process, the degree of phase synchronization mismatch caused by deviation from the ideal phase matching condition at each spatial position is calculated, and the degree of phase synchronization mismatch is used as the phase mismatch amount to obtain the phase mismatch amount distribution data in the full aperture range.

[0017] Furthermore, the efficiency function, constructed using spatial integration based on the phase mismatch distribution, reflects the overall harmonic conversion efficiency of the crystal under full-aperture beam irradiation, includes:

[0018] Based on the phase mismatch at each spatial location in the phase mismatch distribution, the local harmonic conversion efficiency corresponding to that location is determined.

[0019] The overall harmonic conversion efficiency value of the crystal across the entire aperture range is obtained by spatial integration and statistical averaging of the local harmonic conversion efficiency at all spatial locations.

[0020] The overall harmonic conversion efficiency value is characterized as a functional relationship with respect to the crystal's rotation adjustment around the axis, and an efficiency function is obtained for numerical optimization.

[0021] Furthermore, the harmonic conversion efficiency includes the second harmonic conversion efficiency and the third harmonic conversion efficiency; wherein, the calculation of the third harmonic conversion efficiency is based on the intermediate field distribution of the fundamental frequency light after the second harmonic conversion and the phase mismatch during the third harmonic conversion process, and the cascade coupling efficiency is evaluated.

[0022] Furthermore, the detuned angle distribution data includes: discrete distribution data obtained by point-by-point measurement with a finite sampling density over the entire aperture range, or a continuous distribution surface function obtained by spatial interpolation of the discrete distribution data; wherein, the spatial integral is a weighted summation of the local efficiency of all sampling points under discrete data conditions, and is correspondingly transformed into a continuous integral operation over the entire aperture region under continuous function conditions.

[0023] Furthermore, the harmonic conversion crystal is a KDP-type crystal with angular phase matching characteristics, including potassium dihydrogen phosphate KDP crystal or potassium dideuterium phosphate KD*P crystal; the nonlinear phase matching characteristics are determined based on the birefringence effect of the KDP-type crystal and the relationship between the unusual light refractive index and the crystal space angle.

[0024] Furthermore, the calculation of the phase mismatch distribution incorporates the light transmission length parameter of the crystal, which is used to determine the effective action distance of the nonlinear interaction; based on the coupling relationship between the phase mismatch distribution and the light transmission length parameter, the phase mismatch degree corresponding to each spatial position is determined; the local harmonic conversion efficiency exhibits periodic modulation attenuation characteristics as the phase mismatch degree changes, and the modulation period is determined by the coherence length multiple corresponding to the product of the phase mismatch degree and the light transmission length.

[0025] Furthermore, obtaining the detuning angle distribution data includes:

[0026] Within the crystal's light-transmitting aperture, a pre-set orthogonal grid with equal or variable spacing is scanned, and the relative positions of the crystal and the probe laser beam are changed point by point.

[0027] At each measurement point, spatial coordinate information and the corresponding detuning angle measurement value are acquired synchronously.

[0028] Using the spatial coordinate information as an index and the measured detuning angle as a data element, a detuning angle distribution matrix that maps to the spatial position of the full caliber is constructed.

[0029] Furthermore, the method further includes: outputting the detuning angle efficiency characterization value in the form of an electronic signal to a crystal attitude online debugging system, wherein the online debugging system generates an angle compensation command based on the characterization value, and drives the crystal rotation mechanism to perform angular displacement motion around the phase matching axis according to the compensation command, so as to make the harmonic conversion efficiency approach the theoretical optimal value under full aperture light transmission conditions.

[0030] The above scheme achieves a methodological breakthrough from discrete local measurement to continuous overall characterization by constructing a global optimization model for harmonic conversion efficiency driven by full-aperture mistuning angle distribution data. This model uses the crystal's rotation adjustment around the axis as a unified compensation variable and aggregates the phase mismatch degree at each spatial position within the full aperture range through spatial integration to form a numerically optimized overall efficiency evaluation function. Under the physical constraint of a single reset angle adjustment, the globally optimal characterization value obtained by solving the solution can minimize the phase mismatch distribution in the full light transmission area of ​​the crystal, thereby improving the harmonic conversion efficiency under full-aperture beam irradiation to more than 99% of the theoretical limit, which is better than the efficiency level under the traditional single-point measurement and adjustment method.

[0031] On the other hand, an equivalent mapping mechanism between discrete sampling mode and continuous surface function was established, and the positive correlation between sampling density and the accuracy of characterization value calculation was clarified. This provides a quantitative criterion for the optimal selection of the number of measurement points in engineering practice. When the sampling density tends to infinity, the discrete detuned angle distribution data converges to the continuous spatial function, and the spatial integral is transformed into a continuous integral operation in the full-caliber region. At this time, the characterization value obtained is the theoretical optimal solution without discretization error, realizing the self-consistency and completeness of the calculation model under mathematical limit conditions.

[0032] On the other hand, by outputting the detuning angle efficiency characterization value to the crystal attitude online adjustment system in the form of electronic signals, generating angle compensation commands and driving the crystal rotation mechanism to perform angular displacement motion around the phase matching axis, a closed-loop assembly and adjustment strategy of offline calculation combined with online compensation is formed. This strategy avoids the traditional repeated trial and error assembly and adjustment mode, compresses the assembly and adjustment cycle from several hours to minutes, and at the same time ensures the repeatability and long-term stability of the assembly and adjustment results, improving the operation and maintenance efficiency and beam quality control level of high-power laser devices.

[0033] On the other hand, it can be compatible with the cascade efficiency evaluation of second and third harmonic conversion processes, and is applicable to various nonlinear optical crystals with angle phase matching characteristics such as KDP and KD*P. It has no strict limitations on process conditions such as crystal aperture, scanning step size, and probe laser parameters, and has portability and universality in many fields such as large-aperture high-power laser drivers, laser precision processing equipment, and mass production of nonlinear optical components.

[0034] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart illustrating the method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal provided in an embodiment of the present invention.

[0037] Figure 2 A flowchart illustrating the method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal in a certain application scenario provided by an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram of the probe laser scanning path in a certain application scenario provided by an embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram showing the distribution of measurement points of the harmonic conversion crystal in a certain application scenario provided by an embodiment of the present invention;

[0040] Figure 5 This is a schematic diagram of the detuning angle distribution of measurement points in a certain application scenario provided by an embodiment of the present invention;

[0041] Figure 6 This is a schematic diagram of the harmonic conversion efficiency curve across the entire aperture range in a certain application scenario provided by an embodiment of the present invention. Detailed Implementation

[0042] The embodiments of the technical solution of the present invention will be described in detail below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore only examples, and should not be used to limit the scope of protection of the present invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and the foregoing description of the drawings are intended to cover non-exclusive inclusion. In the description of the embodiments of the present invention, technical terms such as "first," "second," etc., are only used to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly indicating the number, specific order, or primary or secondary relationship of the indicated technical features. In the description of the embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified. The reference to "embodiment" herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the present invention. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0043] like Figure 1 As shown, this embodiment of the invention provides a method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal, including:

[0044] Step S110: Obtain the detuning angle distribution data of the harmonic conversion crystal at multiple discrete spatial locations within its aperture.

[0045] Optionally, the aforementioned harmonic conversion crystal is a KDP-type crystal with angular phase-matching characteristics. KDP-type crystals include potassium dihydrogen phosphate (KDP) crystals or potassium dideuterium phosphate (KD*P) crystals. The nonlinear phase-matching characteristics are determined based on the birefringence effect of KDP-type crystals and the relationship between the unusual optical refractive index and the crystal's spatial angle. The aforementioned harmonic conversion crystal refers to an anisotropic crystal material with a second-order nonlinear optical polarizability tensor. Through the phase-matching condition in nonlinear optical effects, it transfers the incident fundamental frequency laser energy to a frequency-doubled or sum-frequency beam, achieving laser frequency up-conversion. Typical materials include potassium dihydrogen phosphate (KDP) and potassium dideuterium phosphate (KD*P) crystals. These crystals possess high laser damage thresholds, wide spectral transmission ranges, and excellent nonlinear optical coefficients in the visible to near-infrared bands, and are therefore widely used in the terminal optical components of high-power laser drivers, laser fusion devices, and ultrashort pulse laser systems.

[0046] The aforementioned aperture refers to the effective optical aperture region in a harmonic conversion crystal that actually allows a high-power laser beam to pass through. Its geometric boundaries are typically determined by the mechanical dimensions of the crystal's light-transmitting surface, beam cutoff effects, and the spatial distribution of the nonlinear action region. In large-aperture high-power laser devices, the aperture can reach the order of hundreds of millimeters, constituting the terminal energy extraction window of the laser transmission link. The optical homogeneity, surface accuracy, and stress distribution of the crystal within the aperture directly affect the phase matching consistency of the entire beam cross-section, and are key engineering parameters restricting harmonic conversion efficiency and beam quality. The multiple discrete spatial positions within the aperture refer to a finite array of sampling points systematically defined within the light-transmitting region to characterize the full-aperture detuning angle distribution. These positions are distributed in the xy plane using geometric rules such as orthogonal grids or polar coordinates, covering the entire light-transmitting cross-section of the crystal. The number and spatial density of sampling points are determined based on the crystal aperture size, the spatial frequency of surface error, and the required computational accuracy, and are typically achieved using constant-step or variable-step scanning methods. Each discrete location corresponds to an independent spatial coordinate identifier. At this location, the crystal axis direction is measured using a nanosecond probe laser to obtain the local detuning angle, which is then used to construct a detuning angle distribution matrix.

[0047] Optionally, the aforementioned detuned angle distribution data includes: discrete distribution data obtained by measuring point by point with a finite sampling density over the entire aperture range, or a continuous distribution surface function obtained by spatial interpolation of the discrete distribution data; wherein, the spatial integral is a weighted summation of the local efficiency of all sampling points under discrete data conditions, and is correspondingly transformed into a continuous integral operation over the entire aperture region under continuous function conditions.

[0048] Optionally, step S110 above, which involves acquiring detuning angle distribution data, includes: scanning a path along a preset orthogonal grid with equal or variable spacing within the crystal's aperture, and changing the relative position of the crystal and the probe laser beam point by point; simultaneously acquiring spatial coordinate information and the corresponding detuning angle measurement value at each measurement point; using the spatial coordinate information as an index and the detuning angle measurement value as a data element to construct a detuning angle distribution matrix that maps to the spatial position of the entire aperture. For example, this implementation involves irradiating a point on the harmonic conversion crystal with a nanosecond probe laser, measuring the crystal axis direction and detuning angle value at that point, and driving the harmonic conversion crystal to move in a plane perpendicular to the beam propagation direction (generally, translation is performed in the x-direction according to a sampling step size; after the measurement of that row is completed, translation is performed in the y-direction by one step size, and then translation continues in the x-direction), measuring the detuning angle Δθ at different points. ij Obtain the detuning angle matrix across the entire caliber range:

[0049]

[0050] When the sampling frequency is infinitely large across the entire aperture range, the detuning angle at different locations is represented by a two-dimensional surface function Δθ(x,y).

[0051] Step S120: Determine the interval for calculating the characterization value based on the extreme values ​​of the detuning angle distribution data.

[0052] The extreme values ​​of the detuning angle distribution data, namely the minimum and maximum detuning angles across the entire aperture range, constitute the upper and lower boundaries of the possible deviations of all spatial positions of the crystal from the ideal phase-matching angle under the current spatial attitude. These boundaries are determined by objective physical factors such as crystal processing technology, material internal stress distribution, and initial assembly attitude, and possess an insurmountable physical reality. If the calculation interval of the characterization value exceeds this extreme value range, the assumed crystal rotation adjustment around the axis will exceed the crystal's actual detuning angle compensation capability, making the optimization result physically unrealizable. Conversely, if the interval is much larger than the extreme value span, computational resources will be consumed in the invalid search space, reducing the efficiency of numerical optimization. Therefore, the closed interval determined by the extreme values ​​can be used as the characterization value calculation domain, thereby ensuring that the subsequent optimization process unfolds within the physically feasible solution space, while achieving optimal allocation of computational resources and providing a compact search boundary with engineering constraints for solving the global maximum.

[0053] An example implementation of step S120 above is as follows: extract the minimum value Δθ from the detuning angle measurement results. min With the maximum value Δθ max Define the interval for calculating the detuning angle characterization value [Δθ]. min , Δθ max ].

[0054] Step S130: Select a crystal rotation adjustment amount to be optimized within the characterization value calculation interval, and calculate the actual detuning angle distribution corresponding to each spatial position of the crystal based on the crystal rotation adjustment amount.

[0055] The aforementioned crystal rotation adjustment amount to be optimized refers to a single angle value selected within the characterization value calculation range. This angle value is used to simulate the physical rotation angle performed by the harmonic conversion crystal around its phase matching axis during actual online commissioning. This adjustment amount, as the core optimization variable in this method, has engineering significance in providing unified reference translation compensation for the original detuning angle distribution of all discrete spatial positions across the crystal's full aperture range, thereby achieving equivalent angular displacement adjustment of the crystal's overall attitude at the numerical calculation level. The crystal rotation adjustment amount is not a preset fixed value, but a dynamically changing undetermined parameter within the search range defined by the detuning angle extreme value. Iterative adjustments are made through a numerical optimization algorithm to ensure that the full-aperture harmonic conversion efficiency function calculated based on this adjustment amount reaches its global maximum value, thereby determining the optimal compensation angle that enables the crystal to achieve the best phase matching state after actual assembly and commissioning.

[0056] Optionally, the aforementioned crystal rotation adjustment amount around the axis is a single angle value; step S130 calculates the actual detuning angle distribution corresponding to each spatial position of the crystal based on the crystal rotation adjustment amount around the axis, including: after selecting the crystal rotation adjustment amount around the axis, subtracting the crystal rotation adjustment amount around the axis from the original detuning angle of each spatial position of the crystal to obtain the actual detuning angle distribution corresponding to each position after the overall rotation of the crystal. For example, this implementation assumes that the detuning angle characterization value of the harmonic conversion crystal over the entire aperture range is Δθ. R (That is, the actual crystal is installed at this angle during the installation process, and the online crystal debugging will rotate the crystal around the axis by an angle Δθ) R Then the detuning angle at each point on the crystal becomes: When the sampling frequency of the detuning angle is infinite, we have: .

[0057] Step S140: Calculate the phase mismatch distribution at each spatial location based on the actual mismatch angle distribution and the nonlinear phase matching characteristics of the crystal determined by it.

[0058] The aforementioned nonlinear phase-matching characteristic of crystals refers to the ability of harmonic conversion crystals, based on their second-order nonlinear polarizability tensor and birefringence effect, to achieve wave vector matching between fundamental and harmonic light under specific polarization configurations and spatial angles. This characteristic determines the fundamental condition under which the harmonic light field generated by the nonlinear polarization field can be continuously and coherently superimposed during transmission. KDP-type crystals, due to their anisotropic lattice structure, exhibit different refractive index responses to ordinary and extraordinary polarized light. When the beam propagation direction is at a specific spatial angle relative to the crystal's optical axis, the ordinary and extraordinary refractive indices of the fundamental light are numerically equal; this angle is the optimal phase-matching angle. The nonlinear phase-matching characteristic of crystals has a certain angle dependence; the extraordinary refractive index varies nonlinearly with the spatial angle. Any angular deviation from the optimal phase-matching angle will disrupt the wave vector matching condition, leading to phase mismatch between the nonlinear polarization field and the harmonic light field, thus directly determining the physical mapping relationship between the mismatch angle and the phase mismatch amount. The aforementioned phase mismatch refers to the degree of wave vector mismatch at each spatial location in a harmonic conversion crystal due to the actual detuning angle deviating from the ideal phase-matching condition. It is typically characterized by Δk, with dimensions in radians per unit length of wavenumber, reflecting the relative difference between the cumulative phase of the nonlinear polarization field and the transmission phase of the harmonic optical field. This mismatch is determined by the actual detuning angle of the crystal at that spatial location, the intrinsic refractive indices of the ordinary and extraordinary rays, and the optimal phase-matching angle. Specifically, it manifests as the coupling variation of the refractive index difference with wavelength and angle. Since the detuning angle is spatially distributed across the entire aperture, the phase mismatch also forms a distribution function of Δk(x,y), the magnitude of which directly affects the harmonic conversion efficiency at local locations—a smaller phase mismatch results in a higher nonlinear coupling coefficient, and the energy conversion process is closer to the ideal coherent enhancement state; conversely, a larger mismatch leads to the return of harmonic energy to the fundamental frequency, resulting in a significant decrease in efficiency.

[0059] Optionally, step S140 may include: based on the actual detuning angle distribution, combined with the nonlinear refractive index anisotropy of the harmonic conversion crystal and the optimal phase matching angle of the crystal in the corresponding harmonic conversion process, calculating the degree of phase synchronization mismatch caused by deviation from the ideal phase matching condition at each spatial position, using the degree of phase synchronization mismatch as the phase mismatch amount, and obtaining the phase mismatch amount distribution data in the full aperture range.

[0060] Optionally, the light transmission length parameter of the crystal is introduced into the calculation of the phase mismatch distribution. The light transmission length parameter is used to determine the effective action distance of the nonlinear interaction. Based on the coupling relationship between the phase mismatch distribution and the light transmission length parameter, the phase mismatch degree corresponding to each spatial position is determined. The local harmonic conversion efficiency exhibits periodic modulation attenuation characteristics as the phase mismatch degree changes. The modulation period is determined by the coherence length multiple corresponding to the product of the phase mismatch degree and the light transmission length.

[0061] The above implementation method, for example: rotating about the axis by an angle Δθ R The phase mismatch Δk generated by each measured detuning angle on the subsequent harmonic conversion crystal ij The phase mismatch caused by the detuning angle in a second harmonic crystal (KDP) is calculated as follows:

[0062]

[0063] in, Spatial location Phase mismatch at the point; After the crystal is rotated around its axis for adjustment, its position... The residual detuning angle relative to the optimal phase matching angle; The basic definition of wave-vector mismatch, and These represent the wave vectors of the fundamental frequency light and the frequency harmonic light, respectively; and These are the angular frequencies of the fundamental frequency light and the harmonic frequency light, respectively; It is the speed of light in a vacuum; and These are the effective refractive indices of the fundamental frequency light and the harmonic light in the crystal at the corresponding frequencies; is the ordinary refractive index of the fundamental frequency light in the crystal, whose value does not change with the spatial angle, and is an intrinsic parameter of the material; and These represent the ordinary and extraordinary refractive indices of the frequency-doubled light in the crystal, respectively. The extraordinary refractive index is spatially angle-dependent and is the physical basis for achieving angle-phase matching. The optimal phase-matching angle for the bulk is the angle between the fundamental frequency wave vector direction and the crystal optical axis, without considering detuning, at which the ideal phase-matching condition is satisfied. ; and is the angular projection factor, used to calculate the equivalent value of the unusual light refractive index under the influence of the detuning angle.

[0064] The phase mismatch of the full-aperture harmonic conversion crystal is:

[0065]

[0066] Or Δk = Δk(x,y).

[0067] Step S150: Based on the phase mismatch distribution, an efficiency function reflecting the overall harmonic conversion efficiency of the crystal under full-aperture beam irradiation is constructed by spatial integration.

[0068] The aforementioned spatial integration method refers to a mathematical operation that weights and aggregates the local harmonic conversion efficiencies at all discrete spatial locations within the crystal's aperture based on their spatial coordinate distribution. This process achieves efficiency information fusion from point to surface. Under finite sampling density conditions, this operation manifests as an arithmetic weighted summation of the local efficiencies at all measurement points. The weights are determined by the proportion of the effective light-transmitting area occupied by each spatial location or its corresponding laser power density distribution. The final output is the average harmonic conversion efficiency value over the entire aperture. When the sampling density approaches infinity, the discrete summation operation converges to a double definite integral operation over the entire aperture region. At this point, the local efficiency, as the integrand, is continuously integrated over the integration domain defined by the crystal plane dimensions, thus rigorously characterizing the statistical characteristics of energy conversion on the entire light-transmitting surface. The core of this integration method lies in the spatially weighted averaging of the coupling effect between the phase mismatch degree and the crystal's light transmission length at each spatial location. This eliminates the representativeness error caused by spatial inconsistencies in single-point measurements, enabling the final efficiency function to truly reflect the comprehensive nonlinear conversion performance under the overall irradiation of a large-aperture beam. This provides a spatially complete evaluation benchmark for subsequent global extremum optimization. The aforementioned efficiency function is a single-valued function with the crystal's rotation adjustment around its axis as the independent variable and the full-aperture harmonic conversion efficiency as the dependent variable. This function is constructed by characterizing the spatial integration result of the phase mismatch distribution as a continuous mapping relationship with respect to the adjustment amount. The function construction process first uses the nonlinear coupled-wave equation, taking the product of the phase mismatch degree and the crystal's light transmission length at each spatial location as the coupling parameter, to calculate the local harmonic conversion efficiency corresponding to that location. This local efficiency exhibits periodic modulation attenuation characteristics as the phase mismatch degree changes. Then, through spatial integration, all local efficiencies are aggregated into a single value, which is the overall harmonic conversion efficiency across the full aperture range of the crystal under the current adjustment assumption. The output value of the efficiency function quantitatively describes the average effectiveness of energy conversion within the entire beam cross section after the crystal is rotated by a given adjustment amount. Its function shape exhibits a single-peak distribution characteristic in the adjustment range. The global maximum point corresponds to the crystal rotation angle around the axis that optimizes the overall phase mismatch distribution. This angle is the desired full-aperture mistunting angle efficiency characterization value, which can be directly used to guide the online assembly and adjustment operation of the crystal to approximate the theoretical maximum efficiency.

[0069] Optionally, step S150 may include: determining the local harmonic conversion efficiency corresponding to each spatial location based on the phase mismatch amount in the phase mismatch distribution; obtaining the overall harmonic conversion efficiency value over the entire aperture range of the crystal by spatial integration and statistical averaging of the local harmonic conversion efficiencies at all spatial locations; and characterizing the overall harmonic conversion efficiency value as a functional relationship with respect to the crystal's rotation adjustment amount around the axis to obtain an efficiency function for numerical optimization.

[0070] Optionally, the above harmonic conversion efficiency includes the second harmonic conversion efficiency and the third harmonic conversion efficiency; wherein, the calculation of the third harmonic conversion efficiency is based on the intermediate field distribution of the fundamental frequency light after the second harmonic conversion and the phase mismatch during the third harmonic conversion process, and the cascade coupling efficiency is evaluated.

[0071] For example, this implementation method involves constructing the harmonic conversion efficiency function of the harmonic conversion crystal under full-aperture laser irradiation using the phase mismatch Δk obtained through the above steps. Specifically, for single-point lasers, the conversion efficiency η of the second harmonic crystal... Sij With the third harmonic crystal conversion efficiency η Tij They are respectively:

[0072]

[0073] in, Spatial position during the second harmonic conversion process Local harmonic conversion efficiency at the location; This is the squared form of the Singer function; Spatial location Phase mismatch at the point; The transmission length of the second harmonic crystal in the direction of beam propagation; Based on spatial location Residual detuning angle at the location For nonlinear mapping functions of independent variables; After the crystal is rotated around its axis for adjustment, its spatial position... The residual detuning angle relative to the optimal phase matching angle; Spatial position during the third harmonic conversion process Local harmonic conversion efficiency at the location; The transmission length of the third harmonic crystal in the direction of beam propagation; Based on spatial location Residual detuning angle at the location is a nonlinear mapping function for the independent variable.

[0074] When the power density of a high-power laser is the same at all points along its aperture, the harmonic conversion efficiency (η) of a second-harmonic crystal and a third-harmonic crystal for the full aperture beam is... S With η T )for:

[0075]

[0076] in, The overall harmonic conversion efficiency of the second harmonic crystal across the entire aperture range; This represents the number of detuning angle sampling points of the harmonic conversion crystal in the x-direction; This represents the number of detuning angle sampling points of the harmonic conversion crystal in the y-direction; Spatial location The original detuning angle measurement value without crystal axis adjustment compensation; The selected amount of crystal rotation adjustment around the axis within the range of characterization value calculation; The overall harmonic conversion efficiency of the third harmonic crystal across the entire aperture range.

[0077] For the case where the sampling density of the detuning angle is infinite, we have:

[0078]

[0079] in, The light transmission dimension of the harmonic conversion crystal in the x-direction; The light transmission dimension of the harmonic conversion crystal in the y direction; It is the continuous spatial distribution function of the detuning angle within the light transmission aperture of the crystal.

[0080] Step S160: Perform numerical optimization calculation on the efficiency function within the characterization value calculation interval, and determine the crystal rotation adjustment amount around the axis corresponding to the global maximum value as the characterization value of the detuning angle efficiency of the harmonic conversion crystal under the full aperture range; wherein, the characterization value is used to guide the online assembly and adjustment of the harmonic conversion crystal.

[0081] For example, the real-time method of step S160 above is as follows: in the calculation interval [Δθ] min , Δθ max The detuning angle Δθ is used as the characterization value within the range. R Calculating the function described in step 6 yields the result within the interval [Δθ]. min , Δθ max Different detuning angles within the [inner] region, represented by Δθ R Find the harmonic conversion efficiency distribution curve under the corresponding full-aperture light transmission condition, and find the detuning angle characterization value Δθ corresponding to its maximum value. R By adjusting the crystal online to this angle, the optimal harmonic conversion efficiency under this sampling density can be obtained. The more measurement points selected for the crystal and the higher the sampling density, the higher the detuning angle Δθ calculated through the above steps will be. RThe more representative the angle at which the crystal needs to be adjusted to achieve optimal harmonic conversion efficiency during online debugging, the more measurement points should be taken during measurements across the entire aperture range to better approximate the crystal's detuning angle adjustment value across the entire aperture. Specifically, when the sampling density of the harmonic conversion crystal's detuning angle approaches infinity, the detuning angle at each point on the crystal becomes a continuous surface function Δθ(x,y) with respect to position. This is equivalent to measuring the crystal's detuning angle using full-aperture illumination. Therefore, the detuning angle value at this point represents the angle at which the crystal can be adjusted to achieve optimal harmonic conversion efficiency during online debugging without the influence of other environmental factors.

[0082] Optionally, the above-mentioned method for calculating the detuning angle efficiency characterization value of the full-aperture harmonic converter crystal can further include: outputting the detuning angle efficiency characterization value as an electronic signal to the crystal attitude online debugging system; the online debugging system generates an angle compensation command based on the characterization value, driving the crystal rotation mechanism to perform angular displacement motion around the phase matching axis according to the compensation command, so as to make the harmonic conversion efficiency approach the theoretical optimal value under full-aperture light transmission conditions. For example, after completing numerical optimization and obtaining the detuning angle efficiency characterization value, the main control calculation unit encodes the characterization value into a digital signal conforming to the input specification of the crystal attitude online debugging system. This signal, after level conversion and isolation driving, is transmitted to the command parsing module of the online debugging system via an industrial bus such as RS-422 or Ethernet. The angle compensation command generation algorithm built into the online debugging system uses the received characterization value as the target position parameter, combines it with the actual angle value fed back by the current crystal attitude sensor to perform deviation calculation, and generates a closed-loop control command frame containing the target angular displacement, motion velocity curve, and acceleration limit. This command frame, after verification, is sent to the servo driver of the crystal rotation mechanism. The crystal rotation mechanism typically consists of a high-precision stepper motor or a piezoelectric ceramic rotary table. Its rotation axis is precisely aligned with the crystal's phase-matching axis. After receiving control commands, the servo driver drives the motor to perform angular displacement according to preset kinematic parameters, rotating the crystal around the axis to the target angle corresponding to the specified value. During this process, an attitude sensor monitors the crystal angle in real time and feeds it back to the online debugging system. The system continuously corrects motion deviations through a PID control strategy until the crystal angle stabilizes at the target value and the position error is better than the micro-radian level. This achieves globally optimal compensation for the detuning angle at the physical level, allowing the harmonic conversion efficiency under full-aperture beam irradiation to approach the maximum achievable value determined by the theoretical model.

[0083] To facilitate understanding of the working principle of the above-described method for calculating the detuning angle efficiency of a full-aperture harmonic converter crystal, this invention provides a specific application example of this method in a certain application scenario. For example... Figure 2 As shown, in this application scenario, the calculation method for the detuning angle efficiency characterization value of the full-aperture harmonic converter crystal mainly includes:

[0084] Step 1: For a second harmonic KDP crystal with dimensions of 410mm × 410mm, adjust its aperture (400mm × 40mm) according to... Figure 3 The scanning path shown is used for scanning measurements, with a scanning step size of 40 mm. The distribution of the measurement points for the detuning angle of the harmonic conversion crystal is as follows. Figure 4 As shown, in this embodiment, there are 11×11 detuning angle measurement points spaced 40mm apart. Therefore, the detuning angle matrix is:

[0085]

[0086] Where i=j=11, their spatial distribution is as follows Figure 5 As shown.

[0087] Step 2: Take the minimum value Δθ from the deharmonicity angle measurement results. min =−1333μrad and the maximum value Δθ max =−1261μrad, and the calculation interval for the detuning angle characterization value is defined as [−1333, −1261];

[0088] Step 3: Assume the detuning angle of the harmonic conversion crystal over the entire aperture range is characterized by Δθ. R Then the detuning angle at each point on the crystal becomes:

[0089]

[0090] Step 4: Rotate the axis by the angle Δθ R The phase mismatch Δk generated by each measured detuning angle on the subsequent harmonic conversion crystal ij The phase mismatch caused by the detuning angle in a second harmonic crystal (KDP) is calculated as follows:

[0091]

[0092] The phase mismatch of the full-aperture harmonic conversion crystal is:

[0093]

[0094] Where i=j=11.

[0095] Step 5: Construct the harmonic conversion efficiency function of the harmonic conversion crystal under full-aperture laser irradiation based on the phase mismatch Δk obtained in Step 4. For single-point laser, the conversion efficiency η of the second harmonic crystal is... Sij for:

[0096]

[0097] When the power density of a high-power laser is the same at all points along its aperture, the harmonic conversion efficiency η of the second harmonic crystal for the full aperture beam is...S for:

[0098]

[0099] Step 6: Use the detuning angle characterization value Δθ within the calculation interval [−1333, −1261]. R By calculating the function, we can obtain the characteristic values ​​Δθ of different detuning angles within the interval [−1333, −1261]. R The corresponding harmonic conversion efficiency distribution curve under full aperture conditions is as follows: Figure 6 As shown. Find the detuning angle representation value Δθ corresponding to its maximum value. R =−1294.03μrad. When the crystal is tuned online to this angle, the optimal relative harmonic conversion efficiency of 99.18% is obtained under the sampling density conditions.

[0100] The above description is merely an embodiment of the present invention and is not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal, characterized in that, The method includes: Acquire detuning angle distribution data of a harmonic conversion crystal at multiple discrete spatial locations within its optical aperture; The interval for calculating the characterization value is determined based on the extreme values ​​of the detuning angle distribution data. Within the range of the characterization values, select a crystal rotation adjustment amount to be optimized around the axis, and calculate the actual detuning angle distribution corresponding to each spatial position of the crystal based on the crystal rotation adjustment amount around the axis. Based on the actual mistuning angle distribution and the crystal nonlinear phase matching characteristics it determines, the phase mismatch distribution at each spatial location is calculated; Based on the phase mismatch distribution, an efficiency function reflecting the overall harmonic conversion efficiency of the crystal under full-aperture beam irradiation is constructed by spatial integration. Within the calculation range of the characterization value, the efficiency function is numerically optimized, and the crystal rotation adjustment amount corresponding to the global maximum value is determined as the characterization value of the detuning angle efficiency of the harmonic conversion crystal in the full aperture range; wherein, the characterization value is used to guide the online assembly and adjustment of the harmonic conversion crystal.

2. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The crystal's rotation adjustment around the axis is a single angular value; The calculation of the actual mistuning angle distribution corresponding to each spatial position of the crystal based on the crystal's rotation adjustment around its axis includes: After selecting the crystal rotation adjustment amount around the axis, the original detuning angle of each spatial position of the crystal is subtracted from the crystal rotation adjustment amount to obtain the actual detuning angle distribution corresponding to each position after the overall rotation of the crystal.

3. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The step of calculating the phase mismatch distribution at each spatial location based on the actual mismatch angle distribution and the crystal nonlinear phase matching characteristics it determines includes: Based on the actual mistuning angle distribution, combined with the nonlinear refractive index anisotropy of the harmonic conversion crystal and the optimal phase matching angle of the crystal in the corresponding harmonic conversion process, the degree of phase synchronization mismatch caused by deviation from the ideal phase matching condition at each spatial position is calculated, and the degree of phase synchronization mismatch is used as the phase mismatch amount to obtain the phase mismatch amount distribution data in the full aperture range.

4. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The efficiency function, constructed based on the phase mismatch distribution and using spatial integration to reflect the overall harmonic conversion efficiency of the crystal under full-aperture beam irradiation, includes: Based on the phase mismatch at each spatial location in the phase mismatch distribution, the local harmonic conversion efficiency corresponding to that location is determined. The overall harmonic conversion efficiency value of the crystal across the entire aperture range is obtained by spatial integration and statistical averaging of the local harmonic conversion efficiency at all spatial locations. The overall harmonic conversion efficiency value is characterized as a functional relationship with respect to the crystal's rotation adjustment around the axis, and an efficiency function is obtained for numerical optimization.

5. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The harmonic conversion efficiency includes the second harmonic conversion efficiency and the third harmonic conversion efficiency; wherein, the calculation of the third harmonic conversion efficiency is based on the intermediate field distribution of the fundamental frequency light after the second harmonic conversion and the phase mismatch during the third harmonic conversion process, and the cascade coupling efficiency is evaluated.

6. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The detuned angle distribution data includes: discrete distribution data obtained by point-by-point measurement with a finite sampling density over the entire aperture range, or a continuous distribution surface function obtained by spatial interpolation of the discrete distribution data; wherein, the spatial integral is a weighted summation of the local efficiency of all sampling points under discrete data conditions, and is correspondingly transformed into a continuous integral operation over the entire aperture region under continuous function conditions.

7. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The harmonic conversion crystal is a KDP-type crystal with angular phase matching characteristics. The KDP-type crystal includes potassium dihydrogen phosphate KDP crystal or potassium dideuterium phosphate KD*P crystal. The nonlinear phase matching characteristics are determined based on the birefringence effect of the KDP-type crystal and the relationship between the unusual light refractive index and the crystal space angle.

8. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The calculation of the phase mismatch distribution incorporates the light transmission length parameter of the crystal, which is used to determine the effective action distance of the nonlinear interaction. Based on the coupling relationship between the phase mismatch distribution and the light transmission length parameter, the phase mismatch degree corresponding to each spatial position is determined. The local harmonic conversion efficiency exhibits periodic modulation attenuation characteristics as the phase mismatch degree changes, and the modulation period is determined by the coherence length multiple corresponding to the product of the phase mismatch degree and the light transmission length.

9. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to claim 1, characterized in that, The acquisition of the detuning angle distribution data includes: Within the crystal's light-transmitting aperture, a pre-set orthogonal grid with equal or variable spacing is scanned, and the relative positions of the crystal and the probe laser beam are changed point by point. At each measurement point, spatial coordinate information and the corresponding detuning angle measurement value are acquired synchronously. Using the spatial coordinate information as an index and the measured detuning angle as a data element, a detuning angle distribution matrix that maps to the spatial position of the full caliber is constructed.

10. The method for calculating the detuning angle efficiency characterization value of a full-aperture harmonic converter crystal according to any one of claims 1 to 9, characterized in that, The method further includes: The detuning angle efficiency characterization value is output to the crystal attitude online adjustment system in the form of an electronic signal. The online adjustment system generates an angle compensation command based on the characterization value and drives the crystal rotation mechanism to perform angular displacement motion around the phase matching axis according to the compensation command, so as to make the harmonic conversion efficiency approach the theoretical optimal value under full aperture light transmission conditions.

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