Abstract
A finite-difference method is used to solve the nonlinear Schrödinger equation. A not frequently used numerical method is developed by replacing the time end space derivate by central-difference replacements. Results from solving the nonlinear Schrödinger equation by using the numerical method called method of lines are used to simulate the propagation of Gaussian pulses in optical fibers. Gaussian input pulse was used for the analysis of dispersion effects. For the simulation was chosen the nonlinear Schrödinger equation modified for dispersion mode. Based on the changes of the chirp parameter have been achieved final shapes of transmitted Gaussian pulses. The main objective was to demonstrate the impact of the broadening factor of the pulse and also to clarify the correlation between the change in phase and frequency chirp. The main goal of this paper is to describe and simulate effects of dispersion by using short Gaussian and hyperbolic secant optical pulses. The effect of dispersion caused frequency shift which can be compensated by effect of self-phase modulation. Frequency chirp caused by the dispersion effects can be compensated by generating opposite frequency chirp with SPM effect. This compensation can lead to fundamental soliton pulse shape generation. Temporal solitons are attractive for optical communications because they are able to maintain their width even in presence of fiber dispersion. Only a fundamental soliton maintains its shape and remains chirp-free during propagation inside optical fibers.
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Acknowledgements
This work was partly supported by the Slovak Research and Development Agency under the project APVV-0025-12 and by the R&D operational programme Centre of Excellence of Power Electronics Systems and Materials for their Components No. OPVaV-2008/2.1/01-SORO, ITMS 2622012003 funded by European Community.
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This article is part of the topical collection on optical wave and waveguide theory and numerical modelling 2016.
Guest edited by Krzysztof Anders, Xuesong Meng, Gregory Morozov, Sendy Phang, and Mariusz Zdanowicz.
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Ladányi, L., Scholtz, Ľ. & Müllerová, J. Numerical simulations of dispersion effects in chirped Gaussian and soliton pulses. Opt Quant Electron 49, 105 (2017). https://doi.org/10.1007/s11082-017-0937-3
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DOI: https://doi.org/10.1007/s11082-017-0937-3