Photonic Band Structures of 1D and 2D Periodic Systems with Metallic Components in the Presence of Dissipation

Abstract

We present a new approach for calculating the dispersion curves of electromagnetic waves in periodic media which contain metallic components characterized by a complex, frequency-dependent dielectric function.The formalism is based on the use of a position-dependent dielectric function and the plane wave technique. Because of the complex form of the dielectric function the reduction of the band structure calculation to the solution of a single standard eigenvalue problem is not possible. Instead, a generalized eigenvalue problem has to be solved. At low filling fractions of the metallic components (f ≤ 1%) the generalized eigenvalue problem is reduced to the problem of solving sets of nonlinear simultaneous equations which correspond to the diagonal terms of the matrix equation in the plane wave representation, with the non-diagonal elements taken into account perturbatively. The resulting complex band structure yields besides the dispersion curves also the attenuation of each mode as it propagates through the system. The method has been applied to the calculation of the photonic band structures of electromagnetic waves propagating through both 1D and 2D periodic systems. The real part of the photonic band structure for small filling fractions is not significantly affected by the presence of the dissipation.Both parts of the complex photonic band structure exhibit different behaviour depending on the polarization of the electromagnetic waves.