Photonic crystal properties of self-assembled Archimedean tilings

Abstract

Inspired by self-assembly of binary colloidal mixtures, we simulate the photonic properties of Archimedean tilings composed of triangular and square cross-section rods. Large isotropic photonic bandgaps up to 29.6% (TE) and 29.3% (TM) are found for the 32·4·3·4 Archimedean tiling due to its high rotational symmetry. For each particle geometry, the relative dielectric contrasts were varied independently over the range ε = 2 to 16, consistent with the assembly of binary materials. Mode field distributions indicate that the bandgaps originate from Lorenz-Mie scattering for high dielectric particles in an air matrix (i.e., direct structures). For the inverted structures, bandgaps arise due to the redistribution of the mode field into air pores or into complementary regions of the high dielectric material. Equifrequency contour analysis and finite difference time domain simulations are performed for direct structures with high ε square rods and low ε triangular rods and vice versa. Negative refraction occurs at nearly all angles of incidence for a relative frequency of 0.27, and sub-wavelength imaging is demonstrated for the photonic crystal flatlens with a half-wave distance of 0.45λ. Self-collimation is observed for incident angles in the range (−45°, 45°). Additionally, a waveguide with the 32·4·3·4 structure displays slow light-based signal enhancement.