Complete and absolute photonic bandgaps in highly symmetric photonic quasicrystals embedded in low refractive index materials

Abstract

It is firmly established that periodic lattice structures can support photonic bandgaps (PBG). However, complete and absolute photonic bandgaps (CAPBG) have only been achieved in high dielectric constant mediums such as GaAs (m = 13.6). An artificial quasiperiodic photonic crystal based on the random square-triangle tiling system was designed and fabricated. The photonic quasicrystal possesses 12-fold symmetry and was analysed using a finite difference time domain (FDTD) approach. High orders of symmetry in photonic quasicrystals have been shown to provide isotropic bandgaps across all the directions of propagation of light. As an outcome of these properties, this new class of photonic quasicrystal has been shown, for the first time, to possess a secondary non-directional CAPBG for a relatively low index material, silicon nitride (m = 4.08). These materials are compatible with integrated optical technologies. This allows the fabrication of efficient integrated optical PBG devices such as WDM filters and multiplexers to become a real possibility.

Discovery of ordered and quasi-ordered photonic crystal structures in the scales of the beetle Eupholus magnificus

“…Since ordered periodicities are not involved, these structures do not carry the usual geometrical constraints associated with periodic crystallographic restrictions. Quasi-ordered photonic crystal geometries therefore create a more isotropic optical scattering structure due to their relatively spherical Brillouin zone boundaries [6].…”

“…Where quasi-ordered PCs have been synthetically fabricated [6,7] their design has been limited to systems with no more than 12-fold rotational symmetry. This has only marginally reduced the requirement for use of such ultra-high index materials to create the FCPBG properties.…”

“…However, the more isotropic nature of quasi-ordered PCs offers the potential advantage of a more spherical Brillouin zone than an ordered PC. The possibility for complete photonic band-gap generation, using materials that have a lower refractive index contrast, therefore becomes available, making fabrication and compatibility of complete photonic band-gap devices more accessible [6]. This will allow the design of specific optical properties with the knowledge that only a low refractive index contrast is necessary.…”

Insights from nature: Optical biomimetics

“…In two-dimensional photonic crystals, there have been attempts to enhance the band gap response by using quasi-crystals [21,22]. These have exploited a periodic tiling such as Penrose tiling [23] as well as an inverse Fourier transform approach, and up to 18-fold symmetric structures have been obtained [24].…”

Properties of microcavities in two-dimensional photonic quasicrystals with octagonal rotational symmetry

“…2D photonic quasicrystals are structures possessing an aperiodic modulation of the relative permittivity with long-range order based upon quasicrystalline tilings, and they can be constructed by decorating the quasiperiodic tiling with the usual dielectric rods or cylinders. Several experimental and theoretical studies have shown evidence of 2D PBGs, accompanied by dips in the transmission spectrum, in different photonic structures based on quasicrystalline geometries [6][7][8][9][10][11][12][13][14][15]. Further, these studies have found that the band gap formed from photonic quasicrystals is due to the shortrange quasicrystalline structure and not due to the periodicity enforced by the boundary conditions of calculations based on a supercell approach [8].…”