Optical gap formation and localization properties of optical modes in deterministic aperiodic photonic structures.

We theoretically investigate the spectral and localization properties of two-dimensional (2D) deterministic aperiodic (DA) arrays of photonic nanopillars characterized by singular continuous (Thue-Morse sequence) and absolutely continuous (Rudin-Shapiro sequence) Fourier spectra. A rigorous and efficient numerical technique based on the 2D Generalized Multiparticle Mie Theory is used to study the formation of optical gaps and the confinement properties of eigenmodes supported by DA photonic lattices. In particular, we demonstrate the coexistence of optical modes with various degrees of localization (localized, extended and critical) and show that in-plane and out-of-plane optical energy confinement of extended critical modes can be optimally balanced. These results make aperiodic photonic structures very attractive for the engineering of novel passive and active photonic devices, such as low-threshold microlasers, sensitive detectors and bio-chemical sensors.