Kinetic Bandgap Analysis of Plasma Photonic Crystals

The dispersion relation of plasma and plasma-dielectric photonic multilayer structures is approached in terms of a one-dimensional Particle-in-Cell simulation. For several plasma-dielectric configurations, the system response is obtained using a pulsed excitation and a subsequent two-dimensional frequency analysis. It is first shown that the dispersion relation of a single, homogeneous plasma slab is well described by the cold-plasma model even at low pressures of 1 Pa. The study is extended to the simulation of plasma photonic crystals with a variety of configurations, based on the work of Hojo and Mase [J. Plasma Fusion Res. 80, 89 (2004)]. Considering a one-dimensional plasma photonic crystal made from alternating layers of dielectric and homogeneous plasma slabs, it is shown that the assumption of a cold-plasma description is well justified also in this case. Moreover, in this work the results are reformatted and analyzed in a band diagram representation, in particular based on the lattice constant $a$. Based on these considerations a scaling invariant representation is presented, utilizing a generalized set of parameters. The study is completed with an exemplary comparison of three plasma-dielectric photonic crystal configurations and their corresponding band diagrams.