TUNNELING IN PHOTONIC BAND STRUCTURES

The plane-wave method is modified for tunneling evanescent solutions o f Maxwell's equations with complex k vectors (tunneling modes). In our formulation the imaginary part of the k vectors is not necessarily pa rallel to the real part of the k vectors. We present computed complex photonic band structures of the simple-cubic (SC) and face-centered-cu bic (fcc) lattice structures at the symmetric points, such as X, M, an d R for the sc and X, L, W, U, and K for the fee with various directio ns of imaginary k vectors. In addition, relations between imaginary k Vectors and tunneling modes are examined at points X, M, R, and K. Tun neling electromagnetic modes can mathematically exist in the photonic band gaps among propagating eigenmodes even in an infinite photonic cr ystal. With the concept of electromagnetic tunnelings in photonic crys tals, we explain classically various kinds of important phenomena such as inhibition of the spontaneous emission and localized defect modes. The method developed here for solutions with complex eigenfrequencies and k vectors can be readily extended to media with loss or gain by a doption of complex dielectric constants.