Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals

Abstract

We measured and calculated transmission spectra of two-dimensional quasiperiodic photonic crystals (PCs) based on a 5-fold (Penrose) or 8-fold (octagonal) symmetric quasiperiodic pattern. The photonic crystal consisted of dielectric cylindrical rods in air placed normal to the basal plane on vertices of tiles composing the quasiperiodic pattern. An isotropic photonic band gap (PBG) appeared in the TM mode, where electric fields were parallel to the rods, even when the real part of a dielectric constant of the rod was as small as 2.4. An isotropic PBG-like dip was seen in tiny Penrose and octagonal PCs with only 6 and 9 rods, respectively. These results indicate that local multiple light scattering within the tiny PC plays an important role in the PBG formation. Besides the isotropic PBG, we found dips depending on the incident angle of the light. This is the first report of anisotropic structures clearly observed in transmission spectra of quasiperiodic PCs. Based on rod-number and rod-arrangement dependence, it is thought that the shapes and positions of the anisotropic dips are determined by global multiple light scattering covering the whole system. In contrast to the isotropic PBG due to local light scattering, we could not find any PBGs due to global light scattering even though we studied transmission spectra of a huge Penrose PC with 466 rods.

The solitons redistribution in Bose–Einstein condensate in quasiperiodic optical lattice

“…Such quasiperiodic optical lattices can be created in the 2D case, as a combination of N = 4, N = 5 (Penrose tiling-a pattern of tiles, which completely cover an infinite plane in an aperiodic manner) or N 7 quasi-1D sublattices with wave vectors k (n) . The band-gap spectrum of 2D photonic crystals of the PT type has been studied in [43][44][45]. Recently the interesting properties of such lattices (e.g., Penrose lattices), have been discovered for quasiperiodic pinning arrays [46].…”

Ultrasonic investigation of phononic Penrose crystals

“…They investigated the dependence of the transmittance on the extension of the crystal sample and found that the spectral gaps can be found in rather small subsections of a structure. Their conclusion was that local scattering is governing the formation of bandgaps rather than global scattering and that therefore long-range periodic order is not a prerequisite for the existence of a gap (see also Hase et al [8]). Wang et al [9] then discovered, that there are sharp peaks in transmittance spectra of defect-free photonic quasicrystals, which are associated with modes strictly localized at singularities in the structure.…”

High-Impedance Surfaces with Aperiodically-Ordered Textures

“…Such geometries, intrinsically tied with the concept of "quasicrystals" in solid-state physics [4], are gaining a growing attention in many branches of science and technology [5]. In electromagnetics engineering, recent studies on EBG quasicrystals [7]- [13] have confirmed the possibility of obtaining effects and properties similar as those exhibited by periodic EBG structures, with potential advantages (e.g., larger bandgaps, lower and/or multiple frequencies of operation, higher isotropy, richer and more wavelength-selective defect states, easier achievement of phase-matching conditions) via a judicious exploitation of the additional degrees of freedom typically available in aperiodic structures. Interesting applications have been proposed to lasers [14], negative refraction and superlensing [15], nonlinear optical frequency conversion [16], wavelength-division multiplexing [17], enhanced transmission through subwavelength hole arrays [18], directive emission [19], etc.…”