Zener tunneling in two-dimensional photonic lattices

TL;DR

This paper analyzes Zener tunneling phenomena in two-dimensional photonic lattices, deriving analytical models and calculating tunneling probabilities for interband light transfer at band crossings.

Contribution

It provides the first analytical models for Zener tunneling in 2D photonic lattices, extending understanding of interband tunneling in these structures.

Findings

Identification of Zener tunneling at band crossings

Analytical models for tunneling probabilities

Extension to higher-order tunneling involving four bands

Abstract

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as was studied recently in experiments for optically-induced photonic lattices [H. Trompeter et al., Phys. Rev. Lett. \textbf{96}, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in a generic case of the Bragg reflection when the Bloch index crosses the edge of the irreducible Brillouin zone. Similarly, the higher-order Zener tunneling involves four Bloch bands when the Bloch index passes through a high-symmetry point on the edge of the Brillouin zone. We derive simple analytical models that describe the tunneling effect, and calculate the corresponding tunneling probabilities.