A method for regulating optical rogue waves in supercontinuum using asymmetric pulses

Abstract

The present invention discloses a method for regulating optical rogue waves in supercontinuum by using asymmetric pulses. This method adjusts parameters of the asymmetric pulses to replace adding weak triggers to symmetric pulses to effectively regulate optical rogue waves, and derives the objective function of optical rogue waves. Combining with the particle swarm optimization algorithm, the optimal pulse parameters for regulating optical rogue waves can be accurately and quickly found. The method of the present invention is simple to operate. One laser can realize pulse input, and can accurately find the optimal pulse parameters for regulating optical rogue waves, with high practicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of fiber laser, and specifically relates to a method for regulating optical rogue waves in supercontinuum by using asymmetric pulses. Background Art

[0002] When a long pulse is incident on the anomalous dispersion region of an optical fiber as a pump pulse, modulation instability realizes broadband noise amplification through phase-matched four-wave mixing, resulting in a series of fundamental solitons radiated during the generation of supercontinuum and dispersion waves that satisfy phase matching between solitons. Next, under the action of the Raman effect, multiple collisions between solitons or between solitons and dispersion waves redistribute the energy between solitons, ultimately leading to the generation of optical rogue waves. However, since the generation of optical rogue waves in an optical fiber system is unpredictable and instantaneous, they cannot be effectively utilized despite having a high peak intensity and a large redshift. Under the condition of noise-induced modulation instability, the generation of optical rogue waves is extremely unstable, and the extremely high intensity of optical rogue waves also poses a great hazard to signal transmission in the optical fiber system. At the same time, most of the energy of the output pulse is concentrated on the optical rogue waves, which greatly inhibits the generation of a smooth and broadband supercontinuum. Therefore, how to regulate optical rogue waves in supercontinuum has become an important topic. Summary of the Invention

[0003] The purpose of the present invention is to effectively regulate optical rogue waves in supercontinuum, and provide a method for regulating optical rogue waves in supercontinuum by using asymmetric pulses. This method uses asymmetric pulses to regulate optical rogue waves in supercontinuum, and combined with the particle swarm algorithm, the optimal pulse parameters for regulating optical rogue waves can be accurately and quickly found.

[0004] To achieve the above purpose, the technical solution provided by the present invention is: designing a method for regulating optical rogue waves in supercontinuum by using asymmetric pulses, characterized in that the method includes the following steps:

[0005] Step 1: According to the formula of the asymmetric pulse, select the variable parameters of the asymmetric pulse. According to the general value range of the variable parameters, uniformly select several data points within the value range of each variable parameter, and randomly and non-repeatedly combine the selected data of different variable parameters to obtain multiple parameter groups of asymmetric pulses with different variable parameters; obtain the spectral data of the above multiple asymmetric pulses with different variable parameters;

[0006] Step 2: Conduct statistical analysis on the values of the variable parameters in Step 1 and the corresponding spectral data of the asymmetric pulse, deduce the objective function of the optical rogue wave, and determine the effective value range of the variable parameters;

[0007] Step 3: Apply the particle swarm optimization algorithm to the analysis of optical rogue wave regulation. Set the objective function in Step 2 as the fitness function of the particle swarm optimization algorithm, and the effective value range of the variable parameters is the upper and lower limits of the population particles. Use the sum of the average peak power and four times the standard deviation of the output spectrum as the constraint condition of the particle swarm optimization algorithm. The value of the variable parameter corresponding to the best fitness value of the particle swarm optimization algorithm is the optimal variable parameter value. According to this optimal variable parameter value, a supercontinuum spectrum that meets the requirements can be obtained.

[0008] Compared with the existing technologies, the present invention has the following advantages: The method for regulating optical rogue waves in a supercontinuum spectrum using an asymmetric pulse according to the present invention replaces adding a weak trigger to a symmetric pulse by adjusting the parameters of the asymmetric pulse to effectively regulate the optical rogue waves, and derives the objective function of the optical rogue wave. Combining with the particle swarm optimization algorithm, the optimal pulse parameters for regulating the optical rogue wave can be accurately and quickly found. The method of the present invention is simple to operate, and a single laser can achieve pulse input, and can accurately find the optimal pulse parameters for regulating the optical rogue wave, with high practicality. Detailed implementation manners

[0009] The method for regulating optical rogue waves in a supercontinuum spectrum using an asymmetric pulse described in this embodiment includes the following steps:

[0010] Step 1: According to the formula of the asymmetric pulse, select the variable parameters of the asymmetric pulse. According to the general value range of the variable parameters, uniformly select several data points within the value range of each variable parameter, and randomly and non-repeatedly combine the selected data of different variable parameters to obtain multiple parameter groups of asymmetric pulses with different variable parameters. Obtain the spectral data of the above multiple asymmetric pulses with different variable parameters.

[0011] The specific process of obtaining the spectral data of the above multiple asymmetric pulses with different variable parameters can be to pump multiple asymmetric pulses with different variable parameters into a nonlinear optical fiber as pump light through a laser, and receive and output the spectral data through a spectral analyzer; it can also be calculated using the pump light transmission model in the optical fiber. The evolution of the optical pulse on the photonic crystal fiber can be described by the nonlinear Schrödinger equation, and the pulse transmission model along the optical fiber can be obtained by solving the nonlinear Schrödinger equation using the split-step Fourier method. The wavelength of the input asymmetric pulse is located in the anomalous dispersion region of the optical fiber.

[0012] As an embodiment, the variable parameter is at least one of the peak power of the asymmetric pulse, the truncation coefficient, the pulse duration, the chirp parameter, and the distribution factor.

[0013] Step 2: Conduct statistical analysis on the values of the variable parameters in Step 1 and the corresponding spectral data of the asymmetric pulses, deduce the objective function of the optical rogue wave, study the regulation effect of the variable parameters on the optical rogue wave, and determine the effective value range of the variable parameters; The specific process of Step 2 is as follows:

[0014] Step 2-1: Statistically analyze the spectral data of multiple asymmetric pulses with different parameters obtained in Step 1. Use the peak power as the abscissa and the number of occurrences of the peak power value as the ordinate to obtain the peak power statistical histogram of the output spectrum. Find the spectral peak with the most occurrences on the histogram as the node. Take the peak power on the right side of this node as the high-power part, and take the ratio of the value span of the high-power part (that is, the difference between the maximum peak power and the minimum peak power in this part, the same below) to the value span of all peak powers as the measurement standard for regulating the optical rogue wave effect, that is, the objective function; The higher the proportion of the high-power part, the more stable the generation of optical rogue waves during the transmission process. The lower the proportion, the less the generation of optical rogue waves during the transmission process;

[0015] Step 2-2: Statistically analyze the spectral data of multiple asymmetric pulses with different parameters obtained in Step 1. Select the values of the variable parameters corresponding to the frequency range exceeding 100 THz (ultra-broadband continuum generation condition) in the output spectrum, and conduct statistics on them respectively to determine the effective value range of each variable parameter.

[0016] Step 3: Apply the particle swarm optimization algorithm to the analysis of optical rogue wave regulation. Set the objective function in Step 2 as the fitness function of the particle swarm optimization algorithm, and use the sum of the average value and four times the standard deviation of the peak power of the output spectrum as the constraint condition of the particle swarm optimization algorithm. When the peak power of the output spectrum is lower than the constraint condition, it is considered that there is no generation of optical rogue waves during the generation of the ultra-broadband continuum by the asymmetric pulse pumping photonic crystal fiber; When there is a peak power higher than the constraint condition in the output spectrum, it is considered that there is generation of optical rogue waves during the generation of the ultra-broadband continuum by the asymmetric pulse pumping photonic crystal fiber. The value of the variable parameter corresponding to the best fitness value of the particle swarm optimization algorithm is the optimal variable parameter value. According to this optimal variable parameter value, the ultra-broadband continuum that meets the requirements can be obtained. The specific process of Step 3 is as follows:

[0017] Step 3-1: Randomly initialize the particle population, determine the maximum number of iterations and the population size, and specify the upper and lower limits of the population particles according to the effective value range of each variable parameter determined in Step 2;

[0018] Step 3-2: Obtain the spectral data of the asymmetric pulse corresponding to the initialized population particles, calculate the fitness function, and obtain the individual optimal position and the global optimal position for this iteration according to the fitness function; when it is necessary to regulate the generation of optical rogue waves in the supercontinuum, the maximum fitness function value is the best, and when it is necessary to regulate the non-generation of optical rogue waves in the supercontinuum, the minimum fitness function value is the best. Calculate the sum of the average value and four times the standard deviation of the spectral peak value of the asymmetric pulse corresponding to the population particles as the constraint condition of the particle swarm algorithm. When the output spectral power is lower than the constraint condition, it is considered that there is no generation of optical rogue waves in the process of generating supercontinuum by asymmetric pulse pumping of photonic crystal fiber; when there is power higher than the constraint condition in the output spectrum, it is considered that there is generation of optical rogue waves in the process of generating supercontinuum by asymmetric pulse pumping of photonic crystal fiber. When it is necessary to regulate the generation of optical rogue waves in the supercontinuum, if the output spectral power is lower than the constraint condition, a value not greater than 0.001 is assigned to the fitness function of the particle corresponding to the spectrum; when it is necessary to regulate the non-generation of optical rogue waves in the supercontinuum, if there is power higher than the constraint condition in the output spectrum, a value not less than 1000 is assigned to the fitness function of the particle corresponding to the spectrum;

[0019] Step 3-3: Update the velocity and position of each particle in the population, and its expression is:

[0020]

[0021] where, is the velocity of the i-th particle at the t-th iteration, is the velocity of the i-th particle at the (t + 1)-th iteration; the initial velocity value is randomly selected within the range of [V min , V max , V max , V min are the maximum and minimum values of the particle movement speed respectively; is the position of the i-th particle at the t-th iteration, is the position of the i-th particle at the (t + 1)-th iteration; w is the inertia weight, c1 is the individual learning factor, c2 is the group learning factor, and they are all constants; rand is a random number within the range of (0, 1), is the individual optimal position of the i-th particle at the t-th iteration; repmat(zbest, 1, sizpop) means copying the matrix zbest into 1×sizepop blocks, zbest is the global optimal position, and sizepop is the number of the initial population;

[0022] Step 3-4: Obtain the spectral data of the asymmetric pulses corresponding to the particles after the position is updated in Step 3-3, calculate the fitness function, and according to the operations in Step 3-2, obtain the individual optimal position and the global optimal position after this iteration; then perform the next iteration update of the velocity and position of the particles according to Step 3-3, and continuously repeat the operation process in Step 3-2 - Step 3-3 until the number of iterations reaches the set maximum value. The value of the variable parameter corresponding to the individual optimal position obtained after the last iteration is the optimal variable parameter value. According to this optimal variable parameter value, the supercontinuum spectrum that meets the requirements can be obtained.

[0023] To verify the effectiveness of the method, a pumping device for asymmetric pulses in photonic crystal fiber combined with the particle swarm algorithm was built. Multiple asymmetric pulses with different variable parameters were used as pump light by a laser and pumped into the nonlinear fiber, and the spectral data was received and output by a spectral analyzer.

[0024] The asymmetric pulse selects the Airy pulse, and its formula is:

[0025]

[0026] where t is time, i is the imaginary unit, represents the Airy function; variable parameters: P0 is the peak power, t0 is the pulse width, a is the truncation coefficient, C is the chirp parameter, χ0 is the distribution factor, and these five are the variable parameters.

[0027] The general value range of the peak power P0 is 500 - 1500, the general value range of the truncation coefficient a is 0.1 - 0.5, the general value range of the chirp parameter C is -3 - 3, the general value range of the pulse width t0 is 0.3 - 0.5, and the value range of the distribution factor χ0 is 0 - 1.

[0028] In this embodiment, t0 = 0.5 ps, a = 0.2, χ0 = 0 are selected, and the optimal values of the peak power P0 and the chirp parameter C are found using the method of the present invention. Uniform values are taken within the general value ranges of the peak power P0 and the chirp parameter C, and are randomly and non-repeatedly combined with t0, a, and χ0 to obtain 165 parameter groups of asymmetric pulses with different variable parameters; the spectral data of these 165 asymmetric pulses with different variable parameters is statistically analyzed to obtain the effective value range of each variable parameter.

[0029] Particle swarm algorithm parameter settings: The number of population particles is 15, the number of iterations is 10, the inertia weight w is 0.8; the individual learning factor c1 is 0.5, and the group learning factor c2 is 0.5. The nonlinear fiber is a single-mode photonic crystal fiber with a single zero-dispersion point. The parameters of the fiber at the pump wavelength are: nonlinear coefficient: γ = 0.015 W -1m -1 For each order of dispersion: β2 = -0.820 ps 2 / km, β3 = 6.87×10 -2 ps 3 / km, β4 = -9.29×10 -5 ps 4 / km, β5 = 2.45×10 -7 ps 5 / km, β6 = -9.79×10 -10 ps 6 / km, β7 = 3.95×10 -20 ps 7 / km, β8 = -1.12×10 -14 ps 8 / km, β9 = 1.90×10 -17 ps 9 / km, β 10 = -1.51×10 -19 ps 10 / km. The zero-dispersion point of this single-mode photonic crystal fiber is located at 1055 nm.

[0030] Taking the sum of the average value and four times the standard deviation of the peak power of the 100 output spectra pumped by an asymmetric pulse in a nonlinear fiber as the constraint condition, when the peak power of the output spectrum is lower than the constraint condition, it is considered that there is no optical rogue wave generated during the generation of supercontinuum spectrum by pumping the photonic crystal fiber with an asymmetric pulse; when there is a power higher than the constraint condition in the peak power of the output spectrum, it is considered that there is an optical rogue wave generated during the generation of supercontinuum spectrum by pumping the photonic crystal fiber with an asymmetric pulse. After calculation, when (P0, C) = (1397, -1.63), there is no optical rogue wave generated in the supercontinuum spectrum; when (P0, C) = (908, -0.1), the optical rogue wave is stably generated in the supercontinuum spectrum.

[0031] The method for regulating optical rogue waves in supercontinuum spectrum by using an asymmetric pulse in combination with a particle swarm optimization algorithm proposed in the above embodiments can effectively regulate optical rogue waves without adding a weak trigger, and can quickly and accurately obtain the optimal pulse parameters for effectively regulating optical rogue waves by an asymmetric pulse.

[0032] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solutions of the present invention, and these simple modifications all belong to the protection scope of the present invention.

[0033] Matters not described in the present invention are applicable to the prior art.

Claims

1. A method for regulating optical rogue waves in supercontinuum by using asymmetric pulses, characterized in that The method includes the following steps: Step 1: According to the formula of the asymmetric pulse, select the variable parameters of the asymmetric pulse. According to the general value range of the variable parameters, uniformly select several data points within the value range of each variable parameter, and randomly and non-repeatedly combine the data of different variable parameters selected to obtain multiple parameter groups of asymmetric pulses with different variable parameters; obtain the spectral data of the above-mentioned multiple asymmetric pulses with different variable parameters; the variable parameters are peak power, pulse width, truncation coefficient, chirp parameter, and distribution factor; Step 2: Conduct statistical analysis on the values of the variable parameters in Step 1 and the corresponding spectral data of the asymmetric pulse, deduce the objective function of the optical rogue wave, and determine the effective value range of the variable parameters; Step 3: Apply the particle swarm algorithm to the analysis of optical rogue wave regulation. Set the objective function in Step 2 as the fitness function of the particle swarm algorithm, and the effective value range of the variable parameters is the upper and lower limits of the population particles; and use the sum of the average value of the peak power of the output spectrum and four times the standard deviation as the constraint condition of the particle swarm algorithm; the value of the variable parameter corresponding to the best fitness value of the particle swarm algorithm is the optimal variable parameter value; according to this optimal variable parameter value, an ultra-broadband continuum that meets the requirements can be obtained.

2. A method for regulating optical rogue waves in supercontinuum by using asymmetric pulses according to claim 1, characterized in that The specific process of Step 2 is as follows: Step 2-1: Conduct statistics on the spectral data of the multiple asymmetric pulses with different parameters obtained in Step 1. Use the peak power as the abscissa and the number of occurrences of the peak power value as the ordinate to obtain the peak power statistical histogram of the output spectrum. Find the spectral peak with the most occurrences on the histogram as the node, take the peak power on the right side of this node as the high-power part, and take the proportion of the value span of the high-power part in the value span of all peak powers as the measurement standard for the effect of regulating the optical rogue wave, that is, the objective function; the higher the proportion of the high-power part, the more stable the generation of optical rogue waves during the transmission process, and the lower the proportion, the less the generation of optical rogue waves during the transmission process; Step 2-2: Conduct statistics on the spectral data of the multiple asymmetric pulses with different parameters obtained in Step 1. Select the variable parameter values corresponding to the frequency range exceeding 100 THz in the output spectrum, and conduct statistics on them respectively to determine the effective value range of each variable parameter.

3. A method for regulating optical rogue waves in supercontinuum using asymmetric pulses according to claim 1, characterized in that, The specific process of Step 3 is as follows: Step 3-1: Randomly initialize the particle population, determine the maximum number of iterations and the population size, and stipulate the upper and lower limits of the population particles according to the effective value range of each variable parameter determined in Step 2; Step 3-2: Obtain the spectral data of the asymmetric pulse corresponding to the initialized population particles, calculate the fitness function, and obtain the individual optimal position and the global optimal position of this iteration according to the fitness function; when it is necessary to regulate the stable generation of optical rogue waves in the supercontinuum, the maximum fitness function value is the best, and when it is necessary to regulate the non-generation of optical rogue waves in the supercontinuum, the minimum fitness function value is the best; calculate the sum of the average value of the spectral peak of the asymmetric pulse corresponding to the population particles and four times the standard deviation as the constraint condition of the particle swarm algorithm. When the output spectral power is lower than the constraint condition, it is considered that there is no generation of optical rogue waves in the process of generating supercontinuum by asymmetric pulse pumping of photonic crystal fiber; when the output spectrum has power higher than the constraint condition, it is considered that there is generation of optical rogue waves in the process of generating supercontinuum by asymmetric pulse pumping of photonic crystal fiber; when it is necessary to regulate the generation of optical rogue waves in the supercontinuum, if the output spectral power is lower than the constraint condition, a value not greater than 0.001 is assigned to the fitness function of the particle corresponding to the spectrum; when it is necessary to regulate the non-generation of optical rogue waves in the supercontinuum, if the output spectrum has power higher than the constraint condition, a value not less than 1000 is assigned to the fitness function of the particle corresponding to the spectrum. Step 3-3: Update the velocity and position of each particle in the population, and its expression is: Among them, is the velocity of the i-th particle at the t-th iteration, is the velocity of the i-th particle at the (t + 1)-th iteration; the initial velocity value is randomly selected within the range of [V min , V max , V max , V min are respectively the maximum and minimum values of the particle movement speed; is the position of the i-th particle at the t-th iteration, is the position of the i-th particle at the (t + 1)-th iteration; w is the inertia weight, c1 is the individual learning factor, c2 is the group learning factor, all of which are constants; rand is a random number within the range of (0, 1), is the individual optimal position of the i-th particle at the t-th iteration; repmat(zbest, 1, sizepop) means replicating the matrix zbest into 1×sizepop blocks, zbest is the global optimal position, and sizepop is the number of individuals in the initial population; Step 3-4: Obtain the spectral data of the asymmetric pulse corresponding to the particle after updating the position in Step 3-3, calculate the fitness function, and obtain the individual optimal position and the global optimal position after this iteration according to the operation in Step 3-2; then perform the next iteration update of the velocity and position of the particle according to Step 3-3, and continuously repeat the operation process in Step 3-2 - Step 3-3 until the iteration number reaches the set maximum value, and the value of the variable parameter corresponding to the best fitness value is the best variable parameter value; according to this best variable parameter value, the supercontinuum that meets the requirements can be obtained.

4. A method for controlling optical rogue waves in supercontinuum using asymmetric pulses according to claim 1, characterized in that The asymmetric pulse selects the Airy pulse, and its formula is: where t is time, and i is the imaginary unit, denotes the Airy function; P0 is the peak power, t0 is the pulse width, a is the truncation coefficient, C is the chirp parameter, and χ0 is the distribution factor. These five are variable parameters.

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