For light reflection at a planar interface between two homogeneous isotropic media with complex relative dielectric function ε, we show that the constant-principal-angle contours are a family of semicircles, whereas the constantprincipal-azimuth contours are a family of (segments of) hyperbolas in the complex ε plane. We also find the exact envelope curve of both families and hence determine the domain of the ε plane of multiple (three) principal angles that is bougded by the envelope curve and the real axis. A unique and peculiar interface with ε = (5 - j√2)/27 is shown to have three coincident principal angles of 30° and an associated curve of relative phase shift (Δ) versus angle of incidence that exhibits a distinct shoulder at the principal angle.
Journal of the Optical Society of America (1917-1983)
R. M. A. Azzam, "Contours of constant principal angle and constant principal azimuth in the complex ε plane," J. Opt. Soc. Am. 71, 1523-1528 (1981)