One-dimensional photonic crystals: Equivalent systems to single layers with a classical oscillator like dielectric function

One-dimensional photonic crystals are analyzed by using symmetric periodic multilayers to determine an equivalent dielectric function associated to these systems. This equivalent dielectric function has the characteristic shape of those dielectric materials composed by Lorentz oscillators in some of their bands. It is found that the equivalent longitudinal and resonance frequencies delimit the band gaps of the crystal where the dielectric function is negative. In this way a one-dimensional photonic crystal can be considered as a single thin film, and the dispersion curves of surface modes can be determined by applying the boundary conditions to this equivalent medium. In the case of non-symmetric truncated one-dimensional photonic crystals, the concept of total admittance is applied to determine the surface modes under the more general conditions.