Photonic quasicrystalline and aperiodic structures

Discovery of quasicrystals and other deterministic aperiodic structures initiated new fields of research in solid-state photonics. In this review, we first make an overview of recently fabricated aperiodic systems, one-, two- and three-dimensional. Then we briefly discuss clarifying and supplementing definitions of binary chains, irrational cuts through higher-dimensional lattices and tiling with regular polygons or polyhedrons. A particular attention is paid to theoretical aspects of light propagation in aperiodic photonic structures, including analysis of the geometric structure factor for different systems and application of the two-wave approximation. In the main part of the article we review different aspects of the optical spectroscopy of long-range-ordered aperiodic systems, both nonresonant and resonant, and show its state of the art in reflection, transmission, absorption, photoluminescence and nonlinear optics. Emphasis is placed on resemblance and distinction between the third form of solid matter, aperiodic long-range ordered photonic structures, and conventional crystals or disordered materials.