Open AccessImpulse response of nonlinear Schrödinger equation and its implications for pre-dispersed fiber-optic communication systems
Author(s) -
Shiva Kumar,
Jing Shao,
Xiaojun Liang
Publication year - 2014
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.22.032282
Subject(s) - physics , nonlinear schrödinger equation , impulse (physics) , nonlinear system , chirp , optical fiber , dispersion (optics) , soliton , optics , envelope (radar) , mathematical analysis , nonlinear optics , impulse response , classical mechanics , mathematics , quantum mechanics , telecommunications , laser , radar , computer science
In the presence of pre-dispersion, an exact solution of nonlinear Schrödinger equation (NLSE) is derived for impulse input. The phase factor of the exact solution is obtained in a closed form using the exponential integral. The nonlinear interaction among periodically placed impulses launched at the input is investigated, and the condition under which these pulses do not exchange energy is examined. It is found that if the complex weights of the impulses at the input have a secant-hyperbolic envelope and a proper chirp factor, they will propagate over long distances without exchanging energy. To describe their interaction, a discrete version of NLSE is derived. The derived equation is a form of discrete self-trapping (DST) equation, which is found to admit fundamental and higher order soliton solutions in the presence of high pre-dispersion. Nonlinear eigenmodes derived here may be useful for description of signal propagation and nonlinear interaction in highly pre-dispersion fiber-optic systems.