Transmission spectrum of a photonic crystal with complex permittivity in THz range

A photonic crystal is formed by an alternating arrangement of two dielectric with different permittivity, which are assumed as constant and with real values. In a linear dielectric media, nonmagnetic, inhomogeneous with a real permittivity, the harmonic magnetic field satisfies an eigenvalues equation where the operator over the magnetic field is linear and hermitian. We can simulate a PC with absorption by inserting slices with complex permittivity dielectric. In this case the problem is redefined using a harmonic electric field, for which a generalized eigenvalues equation is obtained. Taking into account properties of the electric field is possible to demonstrate that the operator over the electric field is linear and hermitian. In this work the characteristics of this operator are determined, which allow us to treat numerically the problem of the electromagnetic radiation transmission by a one dimensional photonic crystal in THz range.