ABSTRACT
Electromagnetic bandgap quasicrystals comprise the class of artificial composites with scattering centers located in the vertices of a quasiperiodic tiling of space. This chapter discusses optical properties and possible utilization of photonic quasicrystals (PQC) in photonic applications. Based on the existence of the bandgaps for finite PQCs, it analyzes their applications as simple and advanced photonic-integrated components. The feature of PQC to possess multiresonant but distinct diffraction pattern fertilizes a lot of potential nonlinear applications of quasicrystals. The canonical two-dimensional (2D) octagonal tiling can be obtained by projection from the 4D hypercubic lattice. The orientation of the 2D physical subspace is chosen as one of the two unique invariant subspaces with respect to the action of the symmetry group of the regular octagon. An alternative approach to study infinite PQCs employs a plane wave expansion using the reciprocal lattice vectors defined by the strongest peaks in the diffraction pattern of the corresponding PQC lattice.
