A rapid modeling method for chirped pulse amplification systems and a computer-readable storage medium.

Abstract

This invention discloses a rapid modeling method for a chirped pulse amplification (CPA) system, comprising: acquiring multiple sets of sample data of CPA with different parameters and a set of reference data with fixed parameters; converting the sample data and reference data from the time domain to the frequency domain, and extracting the frequency domain amplitude and phase of the pulse, as well as the frequency domain amplitude and phase of the reference data; unwinding the phase of the sample data and the phase of the reference data, and extracting the phase with concentrated energy to obtain a small-range difference phase; normalizing the frequency domain amplitude and the difference phase of the sample data, and inputting the concatenated I(ω) into a neural network for training to obtain the predicted frequency domain amplitude and difference phase; adding the difference phase to the phase of the reference data to obtain the absolute phase, obtaining the frequency domain envelope through the frequency domain amplitude and the absolute phase, and then performing an inverse Fourier transform to obtain the entire output of the chirped pulse amplification.

Description

Technical Field

[0001] This invention relates to the field of laser technology, and more particularly to a rapid modeling method for a chirped pulse amplification system capable of rapid disassembly. Additionally, it relates to a computer-readable storage medium. Background Technology

[0002] Chirped pulse amplification (CPA) technology was awarded the Nobel Prize in Physics in 2018. It has driven the development of high-power lasers, ultrafast lasers, and nonlinear optics, and has wide applications in biomedicine, precision industrial manufacturing, national defense, and basic science. CPA can be divided into three processes: broadening, amplification, and compression. First, a short laser pulse to be amplified is broadened in the time domain by introducing dispersion. During the amplification process in the gain fiber, the broadened pulse is affected by nonlinear effects, leading to complex pulse phase changes. Finally, the compression process is sensitive to pulse phase errors; otherwise, the pulse will be distorted and cannot be compressed. Therefore, precise capture of phase changes is necessary to achieve accurate modeling of the CPA technique.

[0003] However, current methods for capturing phase changes in chirped pulse amplification simulations have various drawbacks, such as:

[0004] Method 1: This method employs a step-by-step and iterative approach, utilizing the Step-by-Step Fourier Transform (SSFM) algorithm and the fourth-order Runge-Kutta algorithm (RK4) to numerically solve the chirped pulse amplification process by solving the generalized nonlinear Schrödinger equation (GNLSE) and the rate equation (RE) respectively. This method captures the phase changes during the chirped pulse amplification process. However, this method is slow and has high complexity.

[0005] Method 2: This method employs a data-driven approach, using training data generated in Method 1 to train the neural network, which then performs predictions. However, due to the large range of phase values ​​after unwrapping the pulses, and the sensitivity of pulse compression to phase errors, the phase prediction accuracy of the neural network is insufficient. For example, for a pulse with a width of 120 fs, the phase range after unwrapping during chirped pulse amplification is 0–100,000 rad, while the phase error required for pulse compression is less than 0.01 rad, which is difficult to achieve in current neural network models.

[0006] Therefore, it is necessary to design a fast modeling method for chirped pulse amplification systems to solve the above problems. Summary of the Invention

[0007] The present invention aims to solve at least one of the technical problems existing in the prior art.

[0008] Therefore, this invention provides a rapid modeling method for chirped pulse amplification systems, which can achieve high-precision prediction of pulse phase changes during chirped pulse amplification.

[0009] A rapid modeling method for a chirped pulse amplification system according to a first aspect of the present invention includes:

[0010] S1. Obtain sample data E(t) of CPA with multiple sets of different parameters and a set of baseline data with fixed parameters.

[0011] S2, Combine the sample data E(t) and the baseline data Transform from the time domain to the frequency domain E(ω), respectively The converted frequency domain values ​​are then extracted to obtain the pulse's frequency domain amplitude A(ω) and frequency domain phase φ(ω), as well as the frequency domain amplitude of the reference data. and frequency domain phase

[0012] S3. Compare the phase φ(ω) of the sample data with the phase of the reference data. Perform unwinding operation and extract the phase with concentrated energy to obtain a small-range difference phase Δ(ω);

[0013] S4. Normalize the frequency domain amplitude A(ω) and difference phase Δ(ω) of the sample data respectively, and input the I(ω) obtained by concatenating the two into the neural network for training to obtain the predicted frequency domain amplitude A(ω) and difference phase Δ(ω).

[0014] S5. Compare the difference phase Δ(ω) with the reference data phase. The absolute phase φ(ω) is obtained by adding the two values, and the frequency domain envelope E(ω) is obtained by using the frequency domain amplitude A(ω) and the absolute phase φ(ω). Finally, an inverse Fourier transform (ifft) is performed to obtain the entire output of the chirped pulse amplification.

[0015] The beneficial effects of this invention are as follows: This rapid modeling method for chirped pulse amplification systems improves the phase prediction accuracy of the neural network by subtracting the frequency domain phase of the sample data from the reference frequency domain phase before neural network training. This is because accurate prediction of phase changes during chirped pulse amplification is necessary, and the phase changes of chirped pulses are complex and have a large range after unwinding. Therefore, compared to the commonly used SSFM+RK4 method 1, this method is faster and less complex in modeling chirped pulse amplification systems. Compared to the direct data-driven method 2, this method can more accurately capture phase changes in chirped pulse amplification simulations during modeling.

[0016] Preferably, the sample data E(t) and a set of reference data with fixed parameters are... The generalized nonlinear Schrödinger equation and rate equation are obtained by solving the distributed Fourier method and the fourth-order Runge-Kutta algorithm.

[0017] More preferably, the sample data E(t) and a set of reference data with fixed parameters... Both are M*N matrices, where M represents the number of steps in the step-Fourier transform and N represents the vector dimension of the matrix impulse.

[0018] Preferably, the sample data E(t) and the benchmark data Perform a Fourier transform (fft) to convert both from the time domain to the frequency domain E(ω). The formula for calculating E(ω) in the frequency domain is as follows: The calculation formula simply requires replacing the sample data E(t) with the baseline data. That's all;

[0019]

[0020] Where e is the base of the natural logarithm, j is the imaginary unit, ω is the angular frequency, and t is time.

[0021] More preferably, when extracting the frequency domain E(ω), the real part E of E(ω) is extracted separately. Re (ω) and the imaginary part E Im (ω), to obtain the frequency domain amplitude A(ω) and frequency domain phase φ(ω), where the formula for calculating the frequency domain amplitude A(ω) is as follows:

[0022]

[0023] Among them, E Re (ω) and E Im (ω) represents the real and imaginary parts of E(ω), respectively.

[0024] Preferably, the formula for calculating the phase difference Δ(ω) is as follows:

[0025]

[0026] Where φ(ω) is the reference data phase, This represents the phase in the frequency domain.

[0027] More preferably, the normalization process uses the following calculation formula:

[0028]

[0029] Here, max represents finding the maximum value in the array, and min represents finding the minimum value in the array.

[0030] Preferably, the formula for calculating the frequency domain envelope E(ω) using the frequency domain amplitude A(ω) and absolute phase φ(ω) is as follows:

[0031] E(ω)=A(ω)·cos(φ(ω))+A(ω)·sin(φ(ω))·1j

[0032] Where j is the imaginary unit.

[0033] More preferably, an inverse Fourier transform (ifft) is performed to obtain the following formula for calculating the total output E(t) of the chirped pulse amplification:

[0034]

[0035] A second aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the modeling method described in the first aspect of the present invention.

[0036] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0039] Figure 1 A schematic diagram of a rapid modeling method for the invented chirped pulse amplification system;

[0040] Figure 2 This is a frequency domain comparison diagram of the rapid modeling method for the chirped pulse amplification system of the present invention and Method 1;

[0041] Figure 3 This is a time-domain comparison diagram of the rapid modeling method for the chirped pulse amplification system of the present invention and Method 1;

[0042] Figure 4 This is a schematic diagram of the frequency domain amplitude and differential phase splicing in the fast modeling method of the chirped pulse amplification system of the present invention;

[0043] Figure 5 This is a flowchart of the rapid modeling method for the chirped pulse amplification system of the present invention. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0045] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, features defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0046] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0047] See Figure 1 This invention discloses a fast modeling method for a chirped pulse amplification system, comprising the following steps:

[0048] S1. Obtain sample data E(t) of CPA with multiple sets of different parameters and a set of baseline data with fixed parameters.

[0049] S2, combine the data E(t) from the sample dataset with the baseline data. Transform from the time domain to the frequency domain E(ω), respectively The two are then extracted separately to obtain the frequency domain amplitude A(ω) and frequency domain phase φ(ω) of the pulse, as well as the frequency domain amplitude of the reference data. and frequency domain phase

[0050] S3. Compare the phase φ(ω) of the sample data with the phase of the reference data. Perform unwinding operation and extract the phase with concentrated energy to obtain a small-range difference phase Δ(ω);

[0051] S4. Normalize the frequency domain amplitude A(ω) and difference phase Δ(ω) of the sample data respectively, and input the I(ω) obtained by concatenating the two into the neural network for training to obtain the predicted frequency domain amplitude A(ω) and difference phase Δ(ω).

[0052] S5. Compare the difference phase Δ(ω) with the reference data phase. The absolute phase φ(ω) is obtained by adding the two values, and the frequency domain envelope E(ω) is obtained by using the frequency domain amplitude A(ω) and the absolute phase φ(ω). Finally, an inverse Fourier transform (ifft) is performed to obtain the entire output of the chirped pulse amplification.

[0053] First, the generalized nonlinear Schrödinger equation and rate equation are solved using the distributed Fourier method and the fourth-order Runge-Kutta algorithm to obtain multiple sets of CPA sample data E(t) with different parameters and a set of baseline data with fixed parameters. Sample data E(t) and a set of reference data with fixed parameters Both are M*N matrices, where M represents the number of steps in the step-Fourier transform and N represents the vector dimension of the matrix impulse.

[0054] Then, the data E(t) from the sample dataset and the baseline data are combined. Performing a Fourier transform (fft) to convert them from the time domain to the frequency domain, we obtain E(ω). The formula for calculating E(ω) in the frequency domain is as follows:

[0055]

[0056] Where e is the base of the natural logarithm, j is the imaginary unit, ω is the angular frequency, and t is time.

[0057] It should be noted that, The calculation formula simply requires replacing the sample data E(t) with the baseline data. Therefore, the calculation formula will not be described in detail here.

[0058] Furthermore, when extracting E(ω) in the frequency domain, the real part E of E(ω) is extracted separately. Re (ω) and the imaginary part E Im (ω), to obtain the frequency domain amplitude A(ω) and frequency domain phase φ(ω), where the formula for calculating the frequency domain amplitude A(ω) is as follows:

[0059]

[0060] Among them, E Re(ω) and E Im (ω) represents the real and imaginary parts of E(ω), respectively.

[0061] Similarly, for the frequency domain amplitude of the reference data and frequency domain phase The same operation can be used to obtain it.

[0062] Then the phase φ(ω) of the sample data is compared with the phase of the reference data. An unwrap operation is performed, at which point the phase range is very large. However, in the pulse edge region, because the energy is weak, the phase is meaningless. This is achieved by combining φ(ω) and... After subtraction, the phase range of the energy concentration region is small, while the phase range of the weak and meaningless energy is large. Therefore, the phase is segmented to extract the phase of energy concentration, resulting in a small-range difference phase Δ(ω). The formula for calculating this difference phase Δ(ω) is as follows:

[0063]

[0064] Where φ(ω) is the reference data phase, This represents the phase in the frequency domain.

[0065] Then we normalize the frequency domain amplitude A(ω) and the difference phase Δ(ω) of the sample data respectively. By passing both... Figure 3 The matrix I(ω) is obtained by concatenating the elements in a certain way, resulting in an M*2N matrix. The normalization process described above is calculated using the following formula:

[0066]

[0067] Here, max represents finding the maximum value in the array, and min represents finding the minimum value in the array.

[0068] Subsequently, a sliding window of size L*N is used to obtain data. The first set of data is obtained by copying I(ω) L-1 times. Then, the window is slid one step at a time to obtain an M*L*N matrix. This matrix is ​​then input into a Long Short-Term Memory (LSTM) artificial neural network in a recurrent neural network for training to obtain the predicted frequency domain amplitude A(ω) and the difference phase Δ(ω), which are then reconstructed.

[0069] The difference phase Δ(ω) is compared with the reference data phase. The absolute phase φ(ω) is obtained by summing the values, thus capturing the phase change in the chirped pulse amplification simulation. Then, the frequency domain envelope E(ω) is obtained through the frequency domain amplitude A(ω) and the absolute phase φ(ω). The formula for calculating the frequency domain envelope E(ω) is as follows:

[0070] E(ω)=A(ω)·cos(φ(ω))+A(ω)·sin(φ(ω))·1j

[0071] Where j is the imaginary unit.

[0072] Perform an inverse Fourier transform (ifft) to obtain the entire output E(t) of the chirped pulse amplification. The formula for calculating E(t) is as follows:

[0073]

[0074] Where e is the base of the natural logarithm, j is the imaginary unit, ω is the angular frequency, and t is time.

[0075] Therefore, this modeling method improves the phase prediction accuracy of the neural network by subtracting the frequency domain phase of the sample data from the reference frequency domain phase before training the neural network. This is because accurate prediction of phase changes in the chirped pulse amplification process is necessary, and the phase changes of chirped pulses are complex and have a large range after unwinding. Therefore, compared to the commonly used SSFM+RK4 method 1, this method is faster and less complex in modeling chirped pulse amplification systems; and compared to the direct data-driven method 2, this method can more accurately capture phase changes in chirped pulse amplification simulations.

[0076] Additionally, see Figures 2 to 3 , Figures 2 to 3 The image shows a comparison between the simulation results of CPA using the method proposed in this patent and Method 1. Figure 2 Frequency domain pulse intensity and phase diagram; Figure 3 This is a time-domain pulse intensity and phase diagram. Through... Figure 2 and Figure 3 Analysis shows that this method can achieve high-precision modeling of chirped pulse amplification systems. The modeling results are consistent with those of SSFM+RK4 method 1, but with lower complexity. Therefore, in scenarios involving complex and sensitive phase changes, the method of subtracting the phase of the sample data from the phase of the reference data before feeding it into the neural network can achieve more accurate phase prediction.

[0077] A computer-readable storage medium according to a specific embodiment of the present invention stores a computer program thereon, and when the computer program is executed by a processor, it is used to implement the steps of the modeling method described in any of the above embodiments of the present invention.

[0078] The above description is based on the preferred embodiments of the present invention. Through the above description, those skilled in the art can make various changes and modifications without departing from the technical concept of the present invention. The technical scope of the present invention is not limited to the contents of the specification, but must be determined by the scope of the claims.

Claims

1. A method of fast modeling of a chirped pulse amplification system, characterized in that, Comprising the following steps: S1, acquiring sample data E(t) of a chirp pulse amplification system with different parameters and reference data with fixed parameters S2, the sample data E(t) and the reference data are respectively converted from the time domain to the frequency domain E(ω), and the converted frequency domains are respectively extracted to respectively obtain the frequency domain amplitude A(ω) and the frequency domain phase φ(ω) of the pulse, and the frequency domain amplitude and the frequency domain phase S3, the phase φ(ω) of the sample data is compared with the reference data phase The unwrapping operation is performed, and the phase with energy concentration is extracted to obtain a small range difference phase Δ(ω); S4, the sample data frequency domain amplitude A(ω) and difference phase Δ(ω) are normalized respectively, and the I(ω) obtained by splicing the two is input into the neural network for training to obtain the predicted frequency domain amplitude A(ω) and difference phase Δ(ω); S5, the difference phase Δ(ω) is added to the reference data phase to obtain the absolute phase φ(ω), and then the frequency domain envelope E(ω) is obtained through the frequency domain amplitude A(ω) and the absolute phase φ(ω), and then an inverse Fourier transform is performed to obtain the entire output of the chirped pulse amplification; Wherein: ω is the angular frequency, t is the time.

2. The method of claim 1, wherein, The sample data E(t) and a set of parameter-fixed reference data The generalized nonlinear Schrödinger equation and the rate equation are solved by the distribution Fourier method and the fourth-order Runge-Kutta algorithm.

3. The method of claim 2, wherein, The sample data E(t) and a set of parameter-fixed reference data Both are M*N matrices, where M represents the number of steps of the step Fourier, and N represents the vector dimension of the matrix pulse.

4. The method of claim 1, wherein, sample data E(t) and reference data Fourier-transformed (fft) to convert both from the time domain to the frequency domain E(ω), where the calculation formula for the frequency domain E(ω) is as follows, The calculation formula for the frequency domain E(ω) is as follows, which can be replaced with the reference data Wherein: e is the base of natural logarithm, j is the imaginary unit, ω is the angular frequency, t is the time.

5. The method for fast modeling of a chirped-pulse amplification system of claim 4, wherein, When extracting the frequency domain E(ω), the real part E Re (ω) and the imaginary part E Im (ω) of E(ω) are extracted respectively to obtain the frequency domain amplitude A(ω) and the frequency domain phase φ(ω), wherein the calculation formula of the frequency domain amplitude A(ω) is as follows: where E Re (ω) and E lm (ω) are the real and imaginary parts of E(ω), respectively.

6. The method of claim 1, wherein, The calculation formula of the difference phase Δ(ω) is as follows: where φ(ω) is the absolute phase, is the reference data phase.

7. The method of claim 1, wherein, The normalization processing adopts the following calculation formula: Wherein, max represents the maximum value in the array, and min represents the minimum value in the array.

8. The method for fast modeling of a chirped-pulse amplification system of claim 1, wherein, The calculation formula of the frequency domain envelope E(ω) obtained through the frequency domain amplitude A(ω) and the absolute phase φ(ω) is as follows: E(ω)=A(ω)·cos(φ(ω))+A(ω)·sin(φ(ω))·1j Wherein, j is the imaginary unit.

9. The method for fast modeling of a chirped-pulse amplification system of claim 8, wherein, The calculation formula of making an inverse Fourier transform (ifft) to obtain the whole output E(t) of the chirp pulse amplification is as follows:

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the modeling method in any one of claims 1 to 9.

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