We examine the general properties of the ellipsometric quantities ρ = rp/rs and τ = tp/ts for a nonabsorbing uniform film. At fixed angle of incidence and for variable thickness, τ moves periodically along circles (as is known) and ρ along quartics in the complex plane. For the special case of a film between like media we derive envelopes (and corresponding bounds on τ and ρ) as functions of the dielectric constants of the layer and its bounding medium. In the case of unlike media on either side of the film, bounds are found for Re τ and Im τ; for ε2 > ε1ε2 (where ε1, ε, and ε2 are, respectively, the dielectric constants of the medium from which light is incident, of the film, and of the substrate), we find an approximate upper bound for the ellipsometric quantity ρ¯ (defined as Im ρ when Re ρ = 0).
© 1987 Optical Society of America
Michael C. Dorf and John Lekner, "Reflection and transmission ellipsometry of a uniform layer," J. Opt. Soc. Am. A 4, 2096-2100 (1987)