Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects

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.

Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals

“…Among the most intriguing applications, it is worth mentioning those to negative refraction and subwavelength imaging ("superlensing") 3,4,5,6 . The most typical PC configurations are based on dielectric inclusions (or voids) arranged according to periodic lattices in a host medium, and can thus be studied using well-established tools and concepts such as Bloch theorem, unit cell, Brillouin zone, equifrequency surfaces, etc.…”

Compact photonic-crystal superabsorbers from strongly absorbing media

“…The complex Bloch wave vector q, implies an e iqx envelope for the electric fields spatial maps across the PC, determining a relative amplitude and phase between points with a separation that is an integer multiple of the lattice constant a. 35,39 Thus we anticipate, that the larger Im(q) is, the quicker the electric-field amplitude decay within the PC; hence, the merit of having the reflectionless condition as close to the band-edge as possible.…”

“…The Bloch-envelope captures the relative phase for PC points that are spaced integer multiples of the lattice constant, a. 35,39 In other words, it provides a prediction for the electric field amplitude decay as the EM wave propagates from unit cell to unit cell of a semi-infinite PC. It is impressive to observe, how well this prediction captures the electric field decay from the front to the back layer for the case of Fig.…”

Analysis of Self-Collimation Based Cavity Resonator Formed by Photonic Crystal

“…K = nω c is the propagation constant of the wave in the air medium (n = 1), and K effective = n effective ω c is the propagation constant of the wave in the prism medium, where ω is the angular frequency of electromagnetic wave, and n effective is effective refractive index of the PC medium. To evaluate the effective index of the composite PC, vector nature of the electromagnetic waves is considered through Maxwell-Garnet relation [14], which is expressed as…”