Soliton Properties in Coupled Nonlinear System with Dispersive Reflectivity: Finite Element Analysis

An optical soliton is a wavepacket that may pass through optical fibers or other nonlinear media without considerable spreading or deformation i.e. dispersion. They are generated by the interaction of nonlinearity and dispersion and thereafter confined in the medium. As a result, they have shown tremendously outstanding interest in fields like communication, medical imaging, and many others over the last few decades. The nonlinear Schrodinger equation (NLSE) describes the properties of a soliton properly. In this work, we analyze various soliton characteristics using a Finite element method rather than the conventional methods. In particular, the coupled NLSE describing a system having one core being semi-linear and the other one being linear is solved to find out the soliton solution ( both real and imaginary parts). Adding some perturbation like dispersive reflectivity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(m)$</tex> , the solution shows a correlation with the existing solution. The photonic bandgap, stability, and propagation of the soliton under different <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> conditions are studied extensively. How higher dispersive reflectivity can distort the soliton wave as well as give birth to sidelobes are identified. In particular, a bandgap of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1≤ω≤ 1</tex> is seen when dispersive reflectivity i s varied from a range of 0 to 1. We also have observed a maximum bandgap at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k=± 10</tex> . This study is important as it shows such an approach to analyzing soliton that doesn't require high-level programming language or multiple software which is based on heavy mathematical data, still providing adequate information about stability, bandgap, shapes, and sidelobes of soliton.