The new term "Perfectly Periodic Photonic Quasi-Crystals" (P3QC) applies to 2-D and 3-D dielectric arrangements that
posses a high rotational order about a central pivot point (standard photonic quasi-crystal) and in the same pattern posses
a radial periodicity as viewed from the same central pivot point. These structures display no translational symmetry as
associated with standard photonic crystals. In a 2-D structure, P3QC periodicity is observed for the polar coordinates (r,
φ) and a unit cell of surface dS =rdrd θ serves as the building block of the pattern at each of the radial "Lattice Points".
A generating algorithm based on orthogonal functions is used to produce many different types of P3QC patterns for latter
analysis through FDTD simulations. The presence of bandgaps in the transmission spectrum for these structures is
observed when the dielectric fill factor, rotational order and dielectric contrast are carefully selected. Central localized
light states are commonly observed in these structures.