Solitons in a one-dimensional rhombic waveguide array

TL;DR

This paper analytically and numerically investigates transverse and longitudinal solitons in a one-dimensional rhombic waveguide array, revealing their formation as wave packet envelopes and confirming predictions through numerical simulations.

Contribution

It introduces analytical solutions for both transverse and longitudinal solitons in a rhombic lattice using multi-scale methods and validates them with numerical calculations.

Findings

Longitudinal solitons are derived as wave packet envelopes outside, on, and under the forbidden gap.

Discrete solitons are obtained from wave packets at the center of the Brillouin zone.

Numerical results agree well with analytical predictions.

Abstract

Two types of soliton solutions are analytically considered in a rhombic onedimensional lattice: transverse (discrete) solitons and longitudinal solitons. Based on the multi-scale method, longitudinal solitons are obtained as envelopes of wave packets outside the forbidden gap, on the gap and under the gap. A discrete soliton was obtained based on a wave packet from the center of the Brillouin zone. The numerical calculations are in good agreement with the analytical predictions.