Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface

Abstract

The complex Fresnel reflection coefficients r(p) and r(s) of p- and s-polarized light and their ratio ρ=r(p)/r(s) at the pseudo-Brewster angle (PBA) φ(pB) of a dielectric-conductor interface are evaluated for all possible values of the complex relative dielectric function ε=|ε|exp(-jθ)=ε(r)-jε(i), ε(i)>0 that share the same φ(pB). Complex-plane trajectories of r(p), r(s), and ρ at the PBA are presented at discrete values of φ(pB) from 5° to 85° in equal steps of 5° as θ is increased from 0° to 180°. It is shown that for φ(pB)>70° (high-reflectance metals in the IR) r(p) at the PBA is essentially pure negative imaginary and the reflection phase shift δ(p)=arg(r(p))≈-90°. In the domain of fractional optical constants (vacuum UV or light incidence from a high-refractive-index immersion medium) 0<φ(pB)<45° and r(p) is pure real negative (δ(p)=π) when θ=tan(-1)(√(cos(2φ(pB)))), and the corresponding locus of ε in the complex plane is obtained. In the limit of ε(i)=0, ε(r)<0 (interface between a dielectric and plasmonic medium) the total reflection phase shifts δ(p), δ(s), Δ=δ(p)-δ(s)=arg(ρ) are also determined as functions of φ(pB).