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Two-dimensional metamaterial photonic crystals (2DMPCs) composed of dispersive metamaterials in a positive-refractive-index medium were investigated by incorporating finite-difference time-domain calculations into the auxiliary differential equation method. A distinct band gap was formed and the effects of positional and size disorder when the dispersive metamaterials are aligned in air were elucidated. In addition, using the self-consistent finite-difference frequency-domain method, an eigenmode analysis of 2DMPCs with positional disorder was performed. Finally, a numerical method for the inverse design of binary random metamaterial multilayers was proposed.

Numerical methods for design of metamaterial photonic crystals and random metamaterials