Numerical Simulation of Pulse Propagation in an Optical Fiber with Two Refractive Indices
https://doi.org/10.56304/S2304487X22010072
Abstract
Pulse propagation in an optical fiber with two refractive indices is numerically simulated within the mathematical model based on the nonlinear Schrödinger equation with periodic boundary conditions. Traveling wave variables are used in order to find an analytical solution. A system of two nonlinear ordinary differential equations for the real and imaginary parts is obtained. The exact solution of this system in the form of solitary waves is found by applying the generalized simplest equation method. The numerical solution of the problem is constructed using the pseudo-spectral method implemented in Python. The program code has been tested by comparing the numerical solution with the analytical one with the restrictions on the mathematical model parameters. The influence of the model parameters on the behavior of the numerical solution is analyzed for various values of the refractive index of the medium. The tables showing the dependence of the error on the parameter α are presented. The analytical and numerical solutions are plotted and analyzed for n = 1, 3, and 5.
About the Authors
K. V. Kan
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
References
1. Kudryashov N. A. Bright and dark solitons in a nonlinear saturable medium // Physics Letters A. 2022. P. 127913.
2. Kudryashov N. A. Stationary solitons of the model with nonlinear chromatic dispersion and arbitrary refractive index // Optik. 2022. V. 259. P. 168888.
3. Kudryashov N. A. Stationary solitons of the generalized nonlinear Schrödinger equation with nonlinear dispersion and arbitrary refractive index // Applied Mathematics Letters. 2022. P. 107888.
4. Biswas A. Optical soliton cooling with polynomial law of nonlinear refractive index // Journal of Optics. 2020. V. 49. 4. P. 580–583.
5. Biswas A. et al. Resonant optical solitons with quadratic-cubic nonlinearity by semi-inverse variational principle // Optik. 2017. V. 145. P. 18–21.
6. Biswas A. et al. Optical solitons having weak non-local nonlinearity by two integration schemes // Optik. 2018. V. 164. P. 380–384.
7. Mirzazadeh M. et al. Optical solitons and conservation law of Kundu–Eckhaus equation // Optik. 2018. V. 154. P. 551–557.
8. Kumar D., Aly R. S., Atish Kumar Joardar. Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology // Chinese journal of physics. 2018. V. 56. № 1. P. 75–85.
9. Kudryashov N. A., Lavrova S. F. Dynamical properties of the generalized model for description of propagation pulses in optical fiber with arbitrary refractive index // Optik. 2021. V. 245. P. 167679.
10. Kan K. V., Kudryashov N. A. Analiticheskoe i chislennoe reshenie obobshchennogo nelinejnogo uravneniya Shredingera s proizvol’nym koefficientom otrazheniya [Analytical and numerical solution of the generalized nonlinear Schrödinger equation with an arbitrary reflection coefficient]. Vestnik NIYaU MIFI, 2021, vol. 10, no. 5, pp. 412–417 (in Russian). doi: 10.1134/S2304487X21050072. – EDN SEVEXI.
11. Weideman J. A C., Herbst B. M. Split-step methods for the solution of the nonlinear Schrödinger equation // SIAM Journal on Numerical Analysis, 1986. V. 23.3. P. 485–507.
Review
For citations:
Kan K.V., Kudryashov N.A. Numerical Simulation of Pulse Propagation in an Optical Fiber with Two Refractive Indices. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2022;11(1):37-43. (In Russ.) https://doi.org/10.56304/S2304487X22010072
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