DISPERSION-RELATION AT POINT-L IN THE PHOTONIC BAND-STRUCTURE OF THE FACE-CENTERED-CUBIC LATTICE WITH ACTIVE OR CONDUCTIVE DIELECTRIC MEDIA

In this paper we develop a computational method for photonic band structures with active and conductive media by transforming Maxwell's equations into high-order nonlinear polynomial eigensystems based on the plane-wave expansion method with complex k vectors. Furthermore, by assuming an infinitely fast response of the material, we reduce the high-order polynomial eigensystems to lower-order (ordinary or quadratic) eigenproblems. Numerical computations were performed at point L for the fcc lattice structure with active nonconducting and nonactive conducting dielectric media by solution of the ordinary or linearized eigensystems. For both cases physical solutions with complex k vectors for Maxwell's equations were found between the two propagating modes; however, solutions were in the unphysical region of the tunneling dispersion relation for the passive media.