Numerical simulation method and system of a saturable absorber mode-locked fiber laser

Abstract

The application discloses a kind of numerical simulation method and system of saturable absorber mode-locked fiber laser, method includes the following steps: setting simulation parameter;Input a noise pulse as the initial pulse of simulation system;The numerical solution of nonlinear Schrödinger equation is calculated by improved step-by-step Fourier method, and the evolution result that pulse is transmitted in optical fiber is obtained;The shaping effect of saturable absorber to pulse is simulated using the transmissivity function of saturable absorber;Coupler solver redistributes the energy of pulse;Post-processing module saves the data when pulse stops running, and it is drawn into the curve graph and three-dimensional graph of pulse shape and pulse spectrum.The simulation method and system disclosed in the application can solve the problem of low calculation precision of dispersion term in fiber laser simulation, greatly improve the simulation accuracy, and can more accurately predict the output characteristics of mode-locked fiber laser.

Description

TECHNICAL FIELD

[0001] The present application relates to a numerical simulation method, in particular to a numerical simulation method and system of a saturable absorber mode-locked fiber laser. BACKGROUND

[0002] The saturable absorber mode-locked fiber laser is a common pulsed laser that can generate high-power ultrashort pulses in an optical fiber. In order to effectively design and optimize such devices, researchers need to conduct accurate numerical simulation and simulation.

[0003] The simulation method of the mode-locked fiber laser generally uses the nonlinear Schrodinger equation to describe the transmission of the optical signal in the optical fiber. The method for solving the nonlinear Schrodinger equation includes finite difference method, split-step Fourier method, etc. When the finite difference method is used to solve the numerical solution of the nonlinear Schrodinger equation, the calculation speed is relatively slow and the calculation time is large. The split-step Fourier algorithm only considers the dispersion coefficient corresponding to the center frequency of the initial pulse, and when the spectral range is large and the dispersion coefficient changes greatly with wavelength, there will be a large error. SUMMARY

[0004] To solve the above technical problems, the present application provides a numerical simulation method and system of a saturable absorber mode-locked fiber laser, which improves the split-step Fourier algorithm to more accurately predict the output characteristics of the mode-locked fiber laser.

[0005] To achieve the above purpose, the technical scheme of the present application is as follows:

[0006] A numerical simulation method of a saturable absorber mode-locked fiber laser, comprising the following steps:

[0007] Step 1, setting the calculation window size, split-step Fourier algorithm step size, sampling frequency and time sequence size through the calculation domain unit;

[0008] Step 2, setting the related parameters of the simulated optical fiber, saturable absorber and coupler in the physical model unit;

[0009] Step 3, inputting a noise pulse as the initial pulse of the simulation system through the input signal unit;

[0010] Step 4, the solving module receives the noise pulse input by the preprocessing module, the optical fiber solver describes the transmission of the optical signal in the optical fiber using the nonlinear Schrodinger equation, and uses the improved split-step Fourier method to solve the numerical solution of the nonlinear Schrodinger equation to obtain the evolution result of the pulse transmission in the optical fiber;

[0011] Step 5, the saturable absorber solver calculates the evolution result of the pulse transmission in the optical fiber, and uses the transmittance function of the saturable absorber to simulate the shaping effect of the saturable absorber on the pulse.

[0012] Step 6, the coupler solver receives the calculation results of the saturable absorber solver, simulates the energy redistribution process of the pulse, multiplies the pulse by a transmittance coefficient a, the value of a depends on the actual coupling ratio of the coupler used, and the obtained pulse is returned to step 4 as an input signal for iteration, and the program stops running when a set number of iterations is reached;

[0013] Step 7, the post-processing module saves the data when the pulse stops running, and draws it into a curve graph and a three-dimensional graph of the pulse shape and the pulse spectrum.

[0014] In the above scheme, the specific method of step 4 is as follows:

[0015] The transmission of an optical signal in an optical fiber is described by a nonlinear Schrödinger equation as follows:

[0016]

[0017] where A is the pulse envelope, z is the transmission distance, i is a pure imaginary number, β1 is the first-order dispersion, β2 is the second-order dispersion, T is the time moving with the group velocity of the pulse, g is the gain coefficient, α represents the loss, and γ represents the nonlinear coefficient;

[0018] When only the dispersion term is considered and the nonlinear term is not considered, the Fourier transform of equation (1) is transformed into the frequency domain as follows:

[0019]

[0020] where, is the Fourier transform of A, and ω is the frequency;

[0021] In the frequency domain, the entire pulse envelope is decomposed into a series of small single frequency components, and these frequency components satisfy the following equation set:

[0022]

[0023] where m is the number of discretized frequency components in the pulse envelope, is the component of ω m is the mth frequency component;

[0024] Solving the equation set (3) gives:

[0025]

[0026] where, is the is the

[0027] Taking inverse Fourier transform of formula (4) obtains:

[0028]

[0029] Wherein, A(z, T) is the pulse envelope at transmission distance z, A(0, T) is the initial pulse envelope, is inverse Fourier transform; F is Fourier transform;

[0030] Formula (5) is the solution of formula (1) only considering dispersion term;

[0031] Again, let the dispersion term be zero, Fourier transform of formula (1) and solve to obtain:

[0032]

[0033] Wherein, is the Fourier transform of A(z, T), is the Fourier transform of A(0, T);

[0034] Inverse transform of formula (6) obtains:

[0035]

[0036] Formula (7) is the solution of formula (1) only considering nonlinear term;

[0037] The A(z, T) obtained by considering dispersion term and considering nonlinear term are multiplied, that is, the approximate solution of the pulse at transmission distance z in the optical fiber, that is, the evolution result of the pulse at transmission distance z in the optical fiber is obtained.

[0038] In the above scheme, the specific method of step 5 is as follows:

[0039] The transmittance function of the saturable absorber is as follows:

[0040]

[0041] Wherein, I is the corresponding pulse instantaneous power, I sat is the saturation power of the saturable absorber, q is the saturation absorption of the saturable absorber, and q0 is the minimum absorption inherent to the saturable absorber;

[0042] The evolution result obtained in step 4 is multiplied by the transmittance function of the saturable absorber and then output.

[0043] A numerical simulation system of a saturable absorber mode-locked fiber laser comprises a preprocessing module, a solving module and a post-processing module, the preprocessing module is used for sequentially setting a calculation domain, a physical model and an input signal according to a type of a laser to be simulated; the solving module is used for receiving the input signal, and performing overall numerical calculation and local calculation on the input signal according to the set calculation domain and the physical model, and storing and outputting simulation data; and the post-processing module is used for performing curve drawing and three-dimensional drawing according to the output simulation data, and storing the simulation data as text.

[0044] In the above scheme, the preprocessing module comprises a calculation domain unit, a physical model unit and an input signal unit; the calculation domain unit is used for setting a calculation window size, a split-step Fourier algorithm step size, a sampling frequency and a time sequence size; the physical model unit is used for setting parameters of a fiber, a saturable absorber and a coupler, and establishing a saturable absorber mode-locked fiber laser model; and the input signal unit is used for selecting different types of signals as inputs of the laser.

[0045] In the above scheme, the solving module comprises a fiber solver, a saturable absorber solver and a coupler solver; the fiber solver is used for simulation analysis of pulse transmission on a gain fiber and a single-mode fiber by improving a split-step Fourier method; the saturable absorber solver is used for simulation analysis of pulse shaping and mode locking by the saturable absorber; and the coupler solver is used for simulation analysis of redistribution of pulse energy.

[0046] In the above scheme, the post-processing module comprises a text data unit, a curve drawing unit and a three-dimensional drawing unit; the text data unit is used for saving calculation data as a txt text format file; the curve drawing unit is used for generating a time domain shape and spectral characteristic curve of an output pulse; and the three-dimensional drawing unit is used for adding a time axis to results of different time nodes of the curve drawing unit, and generating a three-dimensional image.

[0047] Through the above technical scheme, the numerical simulation method and system of the saturable absorber mode-locked fiber laser provided by the application have the following beneficial effects:

[0048] The method of the application considers complexity of a fiber structure, improves a simulation method, combines advantages of a split-step Fourier method, transforms a signal into a frequency domain through Fourier transform, decomposes a signal envelope into a series of single frequency components in the frequency domain, calculates a dispersion term of a nonlinear Schrödinger equation through the split-step Fourier method, considers dispersion coefficients of all frequency components in the entire envelope in a calculation result, can solve a problem of low calculation precision of the dispersion term in fiber laser simulation, greatly improves simulation accuracy, and can more accurately predict output characteristics of a mode-locked fiber laser.

[0049] Meanwhile, the application provides a simulation system for modeling various components in the mode-locked fiber laser, and further develops a fiber solver, a saturable absorber solver and a coupler solver.

[0050] Through the simulation system and the simulation method, users can better understand the performance and characteristics of the mode-locked fiber laser, and optimize the design and performance. Therefore, the saturable absorber mode-locked fiber laser simulation system and the simulation method have important application value, and can be used in the design, optimization and production of fiber lasers. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description.

[0052] Figure 1 A numerical simulation system of a saturable absorber mode-locked fiber laser disclosed by the embodiments of the application is shown in the figure.

[0053] Figure 2 A numerical simulation method of a saturable absorber mode-locked fiber laser disclosed by the embodiments of the application is shown in the figure.

[0054] Figure 3 A schematic diagram of pulse frequency domain envelope decomposition in the application is shown in the figure. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application.

[0056] The application provides a numerical simulation system of a saturable absorber mode-locked fiber laser, as shown in the figure, including a preprocessing module, a solving module and a post-processing module. Figure 1 The preprocessing module is used for sequentially setting a calculation domain, a physical model and an input signal according to a type of laser to be simulated; the solving module is used for receiving the input signal, and performing overall numerical calculation and local calculation on the input signal according to the set calculation domain and the physical model, storing and outputting simulation data; and the post-processing module is used for performing curve drawing and three-dimensional drawing according to the output simulation data, and storing the simulation data as text.

[0057] Specifically, the preprocessing module includes a calculation domain unit, a physical model unit and an input signal unit; the calculation domain unit is used to set the calculation window size, the step Fourier algorithm step length, the sampling frequency and the time sequence size; the physical model unit is used to set the parameters of the fiber, the saturable absorber and the coupler, including the fiber length, the gain coefficient of the gain fiber, the recovery time of the saturable absorber, the transmittance coefficient of the coupler and the like, to establish the saturable absorber mode-locked fiber laser model; and the input signal unit is used to select different types of signals as the input of the laser.

[0058] The solving module includes a fiber solver, a saturable absorber solver and a coupler solver; the fiber solver is used for the simulation analysis of the transmission of the pulse on the gain fiber and the single-mode fiber by improving the step Fourier method; the saturable absorber solver is used for the simulation analysis of the pulse shaping and mode locking of the saturable absorber; and the coupler solver is used for the simulation analysis of the redistribution of the pulse energy.

[0059] The post-processing module includes a text data unit, a curve graph unit and a three-dimensional graph unit; the text data unit is used to save the calculation data as a txt text format file; the curve graph unit is used to generate the time domain shape and spectral characteristic curve of the output pulse; and the three-dimensional graph unit is used to add a time axis to the results of different time nodes of the curve graph unit to generate a three-dimensional image. The user can observe the three-dimensional image to understand the evolution process of the pulse, and can also use the text data to draw an image.

[0060] The application provides a numerical simulation method of a saturable absorber mode-locked fiber laser, as shown in the figure, including the following steps: Figure 2

[0061] Step 1: setting the calculation window size, the step Fourier algorithm step length, the sampling frequency and the time sequence size through the calculation domain unit;

[0062] Step 2: setting the parameters of the simulated fiber, saturable absorber and coupler in the physical model unit, including the fiber length, the gain coefficient of the gain fiber, the recovery time of the saturable absorber, the transmittance coefficient of the coupler and the like;

[0063] Step 3: inputting a noise pulse as the initial pulse of the simulation system through the input signal unit;

[0064] Step 4: receiving the noise pulse input by the preprocessing module, using the nonlinear Schrodinger equation to describe the transmission of the optical signal in the fiber, using the improved step Fourier method to solve the numerical solution of the nonlinear Schrodinger equation, and obtaining the evolution result of the pulse in the fiber through the fiber solver of the solving module;

[0065] The specific method is as follows:

[0066] ​The transmission of optical signals in optical fibers is described by the nonlinear Schrödinger equation as follows:

[0067]

[0068] where A is the pulse envelope, z is the transmission distance, i is a pure imaginary number, β1 is the first-order dispersion, β2 is the second-order dispersion, T is the time moving with the group velocity of the pulse, g is the gain coefficient, a represents the loss, and γ represents the nonlinear coefficient;

[0069] The split-step Fourier algorithm has the feature that the dispersion term and the nonlinear term are considered separately, i.e., the influence of the dispersion term is not considered when the nonlinear term is considered, and the influence of the nonlinear term is not considered when the dispersion term is considered. For mode-locked pulses, the first-order dispersion can be ignored, and when only the dispersion term is considered and the nonlinear term is not considered, the Fourier transform of equation (1) is transformed into the frequency domain as follows:

[0070]

[0071] where is the Fourier transform of A, and ω is the frequency;

[0072] The improved method is to replace the dispersion coefficient corresponding to the center wavelength as the dispersion coefficient of the entire pulse envelope in the frequency domain by decomposing the entire pulse envelope into a series of small single frequency components. As shown in Figure 3 the entire pulse envelope is decomposed into a series of small frequency components ω m These frequency components satisfy the equation set:

[0073]

[0074] where m is the number of frequency components discretized in the pulse envelope, is the component of ω m is the mth frequency component;

[0075] Solving the equation set (3) gives:

[0076]

[0077] where is the pulse transmitted to z, is the pulse at the transmission distance z = 0,

[0078] The inverse Fourier transform of equation (4) gives:

[0079]

[0080] Where A(z,T) is the pulse envelope at the transmission distance z, and A(0,T) is the initial pulse envelope. F is the inverse Fourier transform; F is the Fourier transform.

[0081] Equation (5) is the solution to equation (1) when only the dispersion term is considered;

[0082] Setting the dispersion term to zero, performing a Fourier transform on equation (1) and solving for it yields:

[0083]

[0084] in, The Fourier transform of A(z,T) Let A(0,T) be the Fourier transform of A.

[0085] Performing an inverse transformation on equation (6) yields:

[0086]

[0087] Equation (7) is the solution to equation (1) when only the nonlinear term is considered;

[0088] Multiplying A(z,T) obtained by considering the dispersion term and the nonlinear term, i.e. multiplying equation (5) and equation (7), we obtain the approximate solution of the pulse when it travels a distance z in the optical fiber, which is the evolution result of the pulse when it travels a distance z in the optical fiber.

[0089] Step 5: The saturable absorber solver calculates the evolution of the pulse propagation in the optical fiber and uses the transmittance function of the saturable absorber to simulate the shaping effect of the saturable absorber on the pulse.

[0090] The specific method is as follows:

[0091] The transmittance function of a saturable absorber is as follows:

[0092]

[0093] Where I is the instantaneous power of the corresponding pulse, I sat Let q be the saturation power of the saturable absorber, q be the saturation absorption of the saturable absorber, and q0 be the inherent minimum absorption of the saturable absorber.

[0094] The evolution result obtained in step 4 is multiplied by the transmittance function of the saturable absorber and then output.

[0095] Step 6: The coupler solver receives the calculation results from the saturable absorber solver, simulates the energy redistribution process of the pulse, multiplies the pulse by a transmittance coefficient 'a', the value of 'a' depends on the actual coupling ratio of the coupler used, and returns the resulting pulse as the input signal to step 4 for iteration. The user can set the number of iterations. When the set number of iterations is reached, the program stops running.

[0096] Step 7: The post-processing module saves the data from when the pulse stops running and plots it as a curve and a 3D graph of the pulse shape and pulse spectrum.

[0097] This invention enables the simulation of mode-locked fiber lasers with different optical fibers and different saturable absorbers through simple settings. Furthermore, due to the improvement of the split-step Fourier algorithm, the simulation accuracy is greatly improved, which brings great convenience to the design and optimization of saturable absorber mode-locked fiber lasers.

[0098] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A numerical simulation method for a saturable absorber mode-locked fiber laser, characterized in that, Includes the following steps: Step 1: Set the computation window size, step size of the split-step Fourier algorithm, sampling frequency, and time series size through the computation domain unit; Step 2: Set the relevant parameters of the simulated optical fiber, saturable absorber, and coupler in the physical model unit; Step 3: Input a noise pulse as the initial pulse for the simulation system through the input signal unit; Step 4: The solver receives the noise pulse input from the preprocessing module. The fiber solver uses the nonlinear Schrödinger equation to describe the transmission of the optical signal in the fiber. The improved split-step Fourier method is used to find the numerical solution of the nonlinear Schrödinger equation and obtain the evolution result of the pulse transmission in the fiber. Step 5: The saturable absorber solver calculates the evolution of the pulse propagation in the optical fiber and uses the transmittance function of the saturable absorber to simulate the shaping effect of the saturable absorber on the pulse. Step 6: The coupler solver receives the calculation results from the saturable absorber solver, simulates the energy redistribution process of the pulse, multiplies the pulse by a transmittance coefficient a, the value of a depends on the actual coupling ratio of the coupler used, and returns the resulting pulse as the input signal to step 4 for iteration. When the set number of iterations is reached, the program stops running. Step 7: The post-processing module saves the data when the pulse stops running and plots it as a curve and a 3D graph of the pulse shape and pulse spectrum. The specific method for step 4 is as follows: The propagation of optical signals in optical fiber can be described using the nonlinear Schrödinger equation as follows: （1） in, For pulse envelope, For transmission distance, It is a purely imaginary number. It is a first-order dispersion. It is a second-order dispersion. It is the time it takes for the pulse to move at a group velocity. This is the gain coefficient. Represents loss, Represents the nonlinear coefficient; When only the dispersion term is considered and the nonlinear term is ignored, the Fourier transform of equation (1) into its frequency domain form is as follows: （2） in, for Fourier transform, For frequency; In the frequency domain, the entire pulse envelope is decomposed into a series of small, single-frequency components, which satisfy the following set of equations: （3） in, This represents the number of discretized frequency components within the pulse envelope. for The amount, For the first One frequency component; Solving the system of equations (3), we get: （4） in, For pulse transmission to place , For transmission distance z=0 ; Taking the inverse Fourier transform of equation (4) yields: （5） in, For transmission distance The pulse envelope at that location, For the initial pulse envelope, This is the inverse Fourier transform; Fourier transform; Equation (5) is the solution to equation (1) when only the dispersion term is considered; Setting the dispersion term to zero, performing a Fourier transform on equation (1) and solving for it yields: （6） in, for Fourier transform, for Fourier transform; Inverse transformation of equation (6) yields: （7） Equation (7) is the solution to equation (1) when only the nonlinear term is considered; The results obtained by considering both dispersion and nonlinear terms. Multiplying them gives the distance the pulse travels in the optical fiber. An approximate solution for the time, i.e., the distance the pulse travels in the optical fiber. The evolutionary results over time.

2. The numerical simulation method for a saturable absorber mode-locked fiber laser according to claim 1, characterized in that, The specific method for step 5 is as follows: The transmittance function of a saturable absorber is as follows: （8） Where I is the instantaneous power of the corresponding pulse, I sat Let q be the saturation power of the saturable absorber, q be the saturation absorption of the saturable absorber, and q0 be the inherent minimum absorption of the saturable absorber. The evolution result obtained in step 4 is multiplied by the transmittance function of the saturable absorber and then output.

3. A numerical simulation system for a saturable absorber mode-locked fiber laser, employing the method described in claim 1, characterized in that... The system includes a preprocessing module, a solution module, and a post-processing module. The preprocessing module is used to sequentially set the computational domain, physical model, and input signal according to the type of laser to be simulated. The solution module is used to receive the input signal and perform overall numerical calculations and local calculations on the input signal according to the set computational domain and physical model, store and output simulation data. The post-processing module is used to draw curves and 3D graphs based on the output simulation data, and store the simulation data as text.

4. The numerical simulation system for a saturable absorber mode-locked fiber laser according to claim 3, characterized in that, The preprocessing module includes a computational domain unit, a physical model unit, and an input signal unit. The computational domain unit is used to set the computational window size, the step size of the split-step Fourier algorithm, the sampling frequency, and the size of the time series. The physical model unit is used to set the relevant parameters of the optical fiber, the saturable absorber, and the coupler, and to establish a saturable absorber mode-locked fiber laser model. The input signal unit is used to select different types of signals as the laser input.

5. The numerical simulation system for a saturable absorber mode-locked fiber laser according to claim 3, characterized in that, The solution module includes an optical fiber solver, a saturable absorber solver, and a coupler solver. The optical fiber solver, after improving the split-step Fourier method, is used for simulation analysis of pulse transmission in gain fiber and single-mode fiber. The saturable absorber solver is used for simulation analysis of pulse shaping and mode locking by the saturable absorber. The coupler solver is used for simulation analysis of pulse energy redistribution.

6. The numerical simulation system for a saturable absorber mode-locked fiber laser according to claim 3, characterized in that, The post-processing module includes a text data unit, a graph unit, and a 3D graph unit; the text data unit is used to save the calculated data as a txt text file; the graph unit is used to generate the time-domain shape and spectral characteristic curves of the output pulse; the 3D graph unit is used to add a time axis to the results of the graph unit at different time points to generate a 3D image.

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