A comprehensive study on beam dynamics inside symmetrically chirped waveguide array mimicking the graded index media

TL;DR

This paper investigates beam dynamics in symmetrically chirped nonlinear waveguide arrays, demonstrating their behavior similar to graded index media and revealing conditions for stable beam propagation and soliton formation.

Contribution

It introduces a practical structure for chirped waveguide arrays and employs a semi-analytical approach to analyze their beam dynamics, bridging discrete and continuous models.

Findings

Chirped waveguide arrays mimic graded index media behavior.

Gaussian beams exhibit oscillatory trajectories similar to parabolic index media.

Nonlinear regimes support the formation of discrete solitons.

Abstract

In this article, we explore the beam dynamics within symmetrically chirped nonlinear waveguide arrays, focusing on linear and quadratic chirping schemes. We propose a practical structure for these arrays that enhances control over light propagation. By employing a continuous approximation of the discrete nonlinear Schr\"odinger equation (DNLSE), we utilize a semi-analytical variational method to analyze beam behavior under waveguide chirping. Our findings indicate that the symmetrically chirped waveguide arrays behave similarly to graded index systems, with varying coupling coefficients analogous to the refractive index in continuous media. We derive a steady-state solution and validate it against numerical simulations, alongside conducting a linear stability analysis to assess the robustness of these solutions. The results reveal that input Gaussian beams in such waveguide arrays follow an oscillatory trajectory akin to that in parabolic index media. Notably, under nonlinear conditions, these beams evolve as discrete solitons. Our rigorous investigation of the propagation characteristics in both linear and nonlinear regimes highlights the intricate dynamics of optical beams within the engineered chirped waveguide arrays, supported by comparisons to comprehensive numerical simulations.