Analytical and numerical characterization of a one and two-dimensional plasma photonic crystal with smooth variations in density

Plasma photonic crystals (PPCs) have the potential to significantly expand the capabilities of current microwave and millimeter wave filtering and switching technologies by providing high speed (μs) control of energy band-gap/pass characteristics in the GHz through low THz range. Furthermore, plasma-based devices can be used in higher power applications than their solid-state counterparts without experiencing significant changes in function or incurring damage. Plasmas with periodic variations in density result naturally from instabilities or self organization, or can be created intentionally. In either case, due to their gaseous nature plasmas cannot support discontinuous density profiles and necessarily have finite density gradients. In this work a dispersion relation is derived for one- and two-dimensional cold plasma photonic crystals with an arbitrary density profile, and is validated against a discontinuous Galerkin (DG) finite element model (FEM) solution of the same problem. The dispersion relation is then used to quantify the effect of various density profiles (sinusoidal, elliptic sinusoidal, piecewise constant, and piecewise linear) on dispersion characteristics.