Fresnel reflection and transmission coefficients for temporally dispersive attenuative media

Generalized Fresnel reflection and transmission coefficients are derived for both time-harmonic TE(s)- and TM(p)-polarized plane wave fields incident upon a planar interface separating two attenuative linear media, each described by a frequency-dependent complex-valued dielectric permittivity ∊j(ω) = ∊^″j(ω) + i∊^″j(ω), magnetic permeability µj(ω) = µ^″j(ω) + iµ^″j(ω), and electric conductivity σj(ω) = σ^′j(ω) + iσ^″j(ω), j = 1,2 while maintaining the real-valued form of Snell's law. The resultant effects of material loss on both the reflected and transmitted fields are presented, including the condition for the appearance of a polarizing angle.