On the universality of the Discrete Nonlinear Schroedinger Equation

TL;DR

This paper demonstrates that the discrete nonlinear Schroedinger equation is a universal model capable of describing light propagation in a wide range of optical lattice systems, including complex tensorial and nonparaxial effects.

Contribution

The authors derive a general and simple form of the discrete nonlinear Schroedinger equation using symmetry analysis, establishing its broad applicability.

Findings

D-NLS equation applies to tensorial nonlinear systems

It remains valid with nonparaxial effects

It accurately models light in various optical lattices

Abstract

We address the universal applicability of the discrete nonlinear Schroedinger equation. By employing an original but general top-down/bottom-up procedure based on symmetry analysis to the case of optical lattices, we derive the most widely applicable and the simplest possible model, revealing that the discrete nonlinear Schroedinger equation is ``universally'' fit to describe light propagation even in discrete tensorial nonlinear systems and in the presence of nonparaxial and vectorial effects.