Waveguide arrays interaction to second neighbors: Exact solution

TL;DR

This paper presents an exact analytical solution for light propagation in waveguide arrays considering second neighbor interactions, revealing a transition from Bessel to generalized Bessel functions and enhancing understanding of complex wave dynamics.

Contribution

It introduces an exact analytical framework accounting for second neighbor interactions in waveguide arrays, a novel approach for more realistic modeling.

Findings

Exact solutions exhibit a structural pattern transition

Propagation described by generalized Bessel functions

Provides deeper insight into wave dynamics in arrays

Abstract

We provide an analytical framework for describing the propagation of light in waveguide arrays, considering both infinite and semi-infinite cases. The interaction up to second neighbors is taken into account, which makes for a more realistic setup. We show that these solutions follow a distinctive structural pattern. This pattern reflects a transition from conventional Bessel functions to the lesser-known one-parameter generalized Bessel functions, offering new insights into the propagation dynamics in these systems.