Configurational Entropy of Optical Bright Similariton in Tapered Graded-Index Waveguide

TL;DR

This paper calculates the Differential Configurational Entropy (DCE) for similariton waves in tapered graded-index optical waveguides, revealing how DCE minima relate to wave dispersion and guiding design.

Contribution

It introduces the calculation of DCE for similariton waves in tapered graded-index waveguides, linking entropy minima to wave dispersion characteristics.

Findings

DCE attains minimum saturation values within certain width ranges.

Lower width values reach saturation earlier and correspond to DCE minima.

Low DCE values indicate minimal momentum mode dispersion during propagation.

Abstract

Configurational entropy (CE) consists of a family of entropic measures of information used to describe the shape complexity of spatially-localized functions with respect to a set of parameters. We obtain the Differential Configurational Entropy (DCE) for similariton waves traveling in tapered graded-index optical waveguides modeled by a generalized nonlinear Schr\"odinger equation. It is found that for similariton's widths lying within a certain range, DCE attains minimum saturation values as the nonlinear wave evolves along the effective propagation variable $\zeta(t)$. In particular, saturation is achieved earlier for lower values of the width, which we show correspond to global minima of the DCE. Such low entropic values lead to minimum dispersion of momentum modes as the similariton waves propagate along tapered graded-index waveguides, and should be of importance in guiding their design.