Optical analogues of Bloch-Zener oscillations in binary waveguide arrays: wavenumber evolution perspective

TL;DR

This paper investigates optical analogues of Bloch-Zener oscillations in binary waveguide arrays using a wavenumber-based approach, deriving simple laws for beam evolution and analyzing the effects of nonlinearity.

Contribution

It introduces a wavenumber-based analytical framework for Bloch-Zener oscillations in waveguide arrays and explores the impact of nonlinearity on these phenomena.

Findings

Derived simple laws for wavenumber evolution in BWAs.

Calculated propagation distances for Dirac point operation and turning points.

Found that Kerr nonlinearity negatively affects Bloch-Zener oscillations.

Abstract

We study optical analogues of Bloch oscillations and Zener tunneling in binary waveguide arrays (BWAs) with the help of the wavenumber-based approach. We analytically find two very simple laws describing the evolution of the central wavenumbers of beams in BWAs. From these simple laws, we can easily obtain the propagation distances in the analytical form where the beams operate at the Dirac points, and therefore, the Zener tunneling takes place due to the interband transition. We can also easily calculate the distances where beams reach the turning points in their motion. These distances just depend on the strength of the linear potential and the initial wavenumber of input beams. We also show that the nonlinearity of the Kerr type has a detrimental influence on the Bloch-Zener oscillations.