Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods

A number of simple analytic theories have been proposed to define an effective plasma frequency in two-dimensional (2D) periodic systems containing metallic elements such as an array of metal rods in a simple square lattice. Such metallic structures are considered using a frequency-dependent plane-wave complex band structure approach. Detailed results are presented for the pass and stop bands for a range of rod diameters. In addition, the value of the effective plasma frequency is extracted and compared with the predictions of existing analytic models. For the structures considered the effective plasma frequency is in the THz regime.