A New Lattice Boltzmann Scheme for Photonic Bandgap and Defect Mode Simulation in One-Dimensional Plasma Photonic Crystals

A novel lattice Boltzmann method (LBM) with a pseudo-equilibrium potential is proposed for electromagnetic wave propagation in one-dimensional (1D) plasma photonic crystals. The final form of the LBM incorporates the dispersive effect of plasma media with a pseudo-equilibrium potential in the equilibrium distribution functions. The consistency between the proposed lattice Boltzmann scheme and Maxwell's equations was rigorously proven based on the Chapman-Enskog expansion technique. Based on the proposed LBM scheme, we investigated the effects of the thickness and relative dielectric constant of a defect layer on the EM wave propagation and defect modes of 1D plasma photonic crystals. We have illustrated that several defect modes can be tuned to appear within the photonic bandgaps. Both the frequency and number of the defect modes could be tuned by changing the relative dielectric constant and thickness of the defect modes. These strategies would assist in the design of narrowband filters.