Photonic band gaps of increasingly isotropic crystals at high dielectric contrasts

Abstract

Photonic band gaps (PBGs) are highly sensitive to lattice geometry and dielectric contrast. Here, we report theoretical and experimental confirmation of PBGs in photonic crystals (PhCs) with increasing levels of structural isotropy. These structures are: a standard 6-fold hexagonal lattice, a locally 12-fold Archimedean-like crystal, a true quasicrystal generated by non-random Stampfli inflation, and a biomimetic crystal based on Fibonacci phyllotaxis. Experimental transmission spectra were obtained at microwave frequencies using high-index alumina (ε = 9.61) rods. The results were compared to FDTD-calculated transmission spectra and PWE-calculated band diagrams. Wide and deep (> 60dB) primary TM gaps present in all high-index samples are related to reciprocal space vectors with the strongest Fourier coefficients. Their mid-gap frequencies are largely independent of the lattice geometry for comparable fill factors, whereas the gap ratios shrink monotonically as structural isotropy increases.

Photonic crystal and quasi-crystals providing simultaneous light coupling and beam splitting within a low refractive-index slab waveguide

“…Here, a square-triangle tiling random-Stampfli inflation rule is used to produce a lattice exhibiting long-range 12-fold symmetry 31 . The dodecahedral cell is inflated by the Stampfli inflation factor of and acts as the parent cell (black dash lines in Fig.…”

“…Unlike the periodic triangular lattice, a large number of cells (rods/holes) are required to construct the quasi-crystal structure in order to preserve the long term periodicity of the lattice. Here, a square-triangle tiling random-Stampfli inflation rule is used to produce a lattice exhibiting long-range 12-fold symmetry 31 . The dodecahedral cell is inflated by the Stampfli inflation factor of and acts as the parent cell (black dash lines in Fig.…”