Geometric freedom for constructing curvilinear and variable size photonic bandgap structures

Summary form only given: In this study two new sub-classes of photonic bandgap materials, a) curvilinear-lattice photonic crystals, whose distinctive feature is that their individual scatterers are arranged in a curvilinear lattice and b) variable size photonic bandgap structures are introduced. We show that adhering to some restrictions in the acceptable lattice transformations; one can achieve omnidirectional photonic bandgaps for the whole area of such structures. We demonstrate, designing an efficient waveguide bend, that curvilinear-lattice photonic crystals can be employed for creation of original types of nano-photonic devices. For variable size photonic bandgap structures the effects of geometrical parameter variation on the properties of photonic crystals is studied. We show that long-range periodicity is not necessary for the formation of bandgaps, which leads to new flexible photonic crystal designs. Using the fact that in systems with large gaps the evanescent waves penetrate into the bulk only distances comparable to one lattice constant and also converting the bandgap maps into width and period set for a given frequency, we are able to use this new freedom for designing new (non periodic) scattering structures exhibiting a stop band