EM wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects

TL;DR

This paper systematically analyzes anomalous refractive effects in two-dimensional photonic crystals using wave vector diagrams, revealing conditions for negative refraction and revisiting phase velocity concepts.

Contribution

It introduces a comprehensive wave vector diagram approach to study refractive phenomena in 2D photonic crystals, identifying conditions for negative refraction and proposing experimental setups.

Findings

Identified four cases leading to negative refraction.

Revisited the definition and physical interpretation of phase velocity.

Extended analysis from high to low index contrast photonic crystals.

Abstract

We systematically study a collection of refractive phenomena that can possibly occur at the interface of a two-dimensional photonic crystal, with the use of the wave vector diagram formalism. Cases with a single propagating beam (in the positive or the negative direction) as well as cases with birefringence were observed. We examine carefully the conditions to obtain a single propagating beam inside the photonic crystal lattice. Our results indicate, that the presence of multiple reflected beams in the medium of incidence is neither a prerequisite nor does it imply multiple refracted beams. We characterize our results in respect to the origin of the propagating beam and the nature of propagation (left-handed or not). We identified four distinct cases that lead to a negatively refracted beam. Under these findings, the definition of phase velocity in a periodic medium is revisited and its physical interpretation discussed. To determine the ``rightness'' of propagation, we propose a wedge-type experiment. We discuss the intricate details for an appropriate wedge design for different types of cases in triangular and square structures. We extend our theoretical analysis, and examine our conclusions as one moves from the limit of photonic crystals with high index contrast between the constituent dielectrics to photonic crystals with low modulation of the refractive index. Finally, we examine the ``rightness'' of propagation in the one-dimensional multilayer medium, and obtain conditions that are different from those of two-dimensional systems.