Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals

Abstract

By using the sparse-matrix canonical-grid method, we performed large-scale multiple-scattering calculations to study band-edge states in large-sized two-dimensional photonic quasicrystals. We find that the band-edge states evolve in an abrupt and irregular way when the sample size is increased. New states with reduced symmetries can emerge at the band edge in large samples. Strong multifractal behaviors in the wave functions are also observed. Our findings unveil important differences between quasiperiodic and periodic systems at band edges.

Fast Light and Focusing in 2D Photonic Quasicrystals

“…In this work, we study electromagnetic wave propagation through planar photonic quasicrystals and focus on the band gap edge states. In distinction to previous works [11][12][13][14] that focused on the states with a low group velocity, we find propagating states with a very high phase velocity -fast light. We demonstrate how this phenomenon can be used for focusing with a plano-concave lens.…”

“…In particular, the Ref. [14] showed that the propagating states at the band gap edge evolve in abrupt way when the sample size is changed -a clear indication that these states are associated with transmission through localized states. This is very similar to resonant tunnelling through tunnel barriers in electronic transport in solids [21].…”

Lasing action in gallium nitride quasicrystal nanorod arrays

“…Recently, there are great interests in studying photonic quasicrystals, which may look random at first glance yet have well defined patterns. Their optical properties are fascinating and lie somewhere between those of periodic and random structures [11][12][13][14]. It therefore may provide a way to design a pseudo random laser with deterministic properties, which could be important for practical applications.…”

Sensitive label-free biosensing using critical modes in aperiodic photonic structures

“…The formation of photonic bandgaps and existence of critically-localized light states have already been demonstrated in one-dimensional (1D) and two-dimensional (2D) aperiodic structures based on the Fibonacci, Thue-Morse and Penrose structures [28][29][30][31][32][33]. In particular, band-edge states in Fibonacci and Penrose quasi-periodic structures have been shown to be critically localized multi-fractal wavefunctions with anomalous transport properties, and their use for the fabrication of low-threshold compact lasers has been suggested [34,35].…”