The effect of complex and negative indices in the transmission of electromagnetic waves through superlattices

We apply the transfer matrix method to study optical transmission properties of multilayered structures with complex and negative indices. We show that the true refraction angle of electromagnetic waves in complex permittivity media does not change sign at low frequencies. Based on the invariance of the slab's scattering amplitudes, we show that it is indifferent whether the negative sign be conveyed by the wave vector k or the admittance η. We show also that in the scattering approach language, the change of sign of ε{lunate} and μ leads to a change in the transmission amplitude phase from θ_t to - θ_t. We present some results for metallic slabs and superlattices containing right- and left-handed materials.