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Coupled Mode Equation and Optical Pulse Propagation in Presence of Apodization and Trapping Potential
Mousumi Ballav and A. Roy Chowdhury

Propagation of a solitary optical pulse in a fiber endowed with an apodized Bragg’s grating is analyzed in detail. In the first part we show how a generalized set of coupled Nonlinear Schrödinger like system with variable coefficient can be deduced for both forward and backward going wave. In the special situation, near criticality where the backward propagating wave can be neglected, a single NLS equation with variable coefficient materialize. A variational approach is then adopted to study the behaviour of a solitary pulse as a function of apodization and trapping potential generated due to inhomoginity. The ordinary differential equations governing the equation of width, chirp etc. indicate to the multistability of the situation. Further evaluation gives their behaviour as the pulse propagates. In the later part of the paper we numerically integrate genealized equation directly using ETDRK4 to study the evolution of the pulse. It is observed that the forward propagating pulse splits into multiple solitons, depending again on the type of apodization and trapping potential. Finally the reflectivity of the grating is computed and is seen to have a sensitive dependence on the parameter controlling apodization.

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