Interlaced linear-nonlinear optical waveguide arrays

TL;DR

This paper investigates a coupled linear-nonlinear waveguide array system, revealing unique band-gap properties and stable solitary modes through analytical and numerical methods, with implications for designing advanced photonic structures.

Contribution

It introduces a novel interlaced linear-nonlinear lattice model for binary waveguide arrays, analyzing its band-gap structure and stability of localized modes.

Findings

Presence of an extra band-gap controlled by detuning.

Analytical and numerical confirmation of stable solitary modes.

Detailed stability analysis of periodic solutions.

Abstract

The system of coupled discrete equations describing a two-component superlattice with interlaced linear and nonlinear constituents is revisited as a basis for investigating binary waveguide arrays, such as ribbed AlGaAs structures, among others. Compared to the single nonlinear lattice, the interlaced system exhibits an extra band-gap controlled by the, suitably chosen by design, relative detuning. In more general physics settings, this system represents a discretization scheme for the single-equation-based continuous models in media with transversely modulated linear and nonlinear properties. Continuous wave solutions and the associated modulational instability are fully analytically investigated and numerically tested for focusing and defocusing nonlinearity. The propagation dynamics and the stability of periodic modes are also analytically investigated for the case of zero Bloch momentum. In the band-gaps a variety of stable discrete solitary modes, dipole or otherwise, in-phase or of staggered type are found and discussed.