Abstract:
The most interesting phenomena in photonic crystals stipulate the presence of omnidirectional band gap, i.e. overlapping of stop bands in all directions. A higher rotational symmetry and an isotropy of quasicrystals in comparison with ordinary crystals give a hope to achieve a gap opening at lower dielectric contrasts. But nonperiodic nature of quasicrystals makes the size of stop bands lower than in the case of an ordinary periodic crystal. Another possibility to get a higher lattice isotropy (symmetry) is to use the so called quasicrystal approximants and periodic structures with a large unit cell. Within such a unit cell quasicrystal approximants are nearly identical to the actual quasicrystal. Outside of that unit cell, they qualitatively resemble the quasicrystal, but in a periodic manner. This chapter is devoted to investigation of a photonic band structure of such lattices. The transition from periodic structure to nonperiodic one is studied for 2D case by considering quasicrystal approximants of growing period. It is done in order to weigh advantages and disadvantages of quasicrystals. It is shown, that higher isotropy in the 2D case allows one to reduce the refractive index threshold necessary for the gap opening For the 3D case we consider different approximants of icosahedral quasicrystals with 8 and 32 "atoms" per unit cell and Si-34 structure with 34 "atoms" per unit cell. All considered structures demonstrate a photonic gap opening and a high isotropy of the band structure. At the same time there are no structures with refractive index threshold for gap opening lower than the best cases of periodic lattices, in particular, with diamond symmetry. © 2010 Nova Science Publishers, Inc. All rights reserved.
