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.

Chemical engineering of quasicrystal approximants in lanthanide-based coordination solids

“…1c ), the kagomé lattice, appears frequently 21 . Notably, ATs in materials have been hailed as a key component for exploring novel photonics applications 22 – 24 and to host peculiar magnetic phenomena, such as frustration 25 – 28 , which call for novel synthetic strategies to their authentication. Whereas for intermetallics 29 numerous quasicrystalline approximants have been isolated, ATs have remained almost elusive in metal-organic materials.…”

Two-dimensional tessellation by molecular tiles constructed from halogen–halogen and halogen–metal networks

“…Archimedean tiling (AT), an archetypical tessellate form, is based on the tessellation of regular polygons and can be classified into three regular tiling types and eight semi-regular tiling types 8 ; the former relies on basic tiling of one specific polygon (squares, triangles, or hexagons), while the latter consists of tessellations of more than one type of regular polygons. Compared with regular ATs, semi-regular ATs possess intriguing photonic 9 – 13 and diffusion 14 properties. Owing to their higher rotational symmetry than the traditional Bravais lattices, semi-regular ATs have been reported to exhibit isotropic photonic bandgaps, and the isotropy is enhanced with the increasing complexity of the structures 9 – 11 .…”

Complex k-uniform tilings by a simple bitopic precursor self-assembled on Ag(001) surface

“…The recent progress in the experimental realization of complex surface tessellations on an atomic and molecular level [7][8][9][10][11][12][13][14] is driven by the intriguing physical [15][16][17][18][19][20][21][22] and chemical 23 properties of these systems. In this respect, the supramolecular chemistry offers tools for engineering of distinct self-assembled surface geometries that present an expression of semiregular [24][25][26][27][28][29][30] , fractal [31][32][33][34][35] , quasicrystalline [36][37][38][39] , and random [3][4][5][6] tilings.…”