For light reflection at a planar interface between two homogeneous isotropic media with complex relative dielectric function ∊, we show that the constant-principal-angle contours are a family of semicircles, whereas the constant-principal-azimuth contours are a family of (segments of) hyperbolas in the complex ∊ plane. We also find the exact envelope curve of both families and hence determine the domain of the ∊ plane of multiple (three) principal angles that is bougded by the envelope curve and the real axis. A unique and peculiar interface with 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.
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