Document Type

Article

Publication Date

7-1-1991

Abstract

The ratio ρt = Tp/Ts of the complex amplitude transmission coefficients for the p and s polarizations of a transparent unbacked or embedded thin film is examined as a function of the film thickness-to-wavelength ratio d/λ and the angle of incidence Φ for a given film refractive index N. The maximum value of the differential transmission phase shift (or retardance), Δt = argρt, is determined, for given N and Φ, by a simple geometrical construction that involves the iso-Φ circle locus of ρt in the complex plane. The upper bound on this maximum equals arctan{[N - (1/N)]/2} and is attained in the limit of grazing incidence. An analytical noniterative method is developed for determining N and d of the film from ρt measured by transmission ellipsometry (TELL) at Φ = 45°. An explicit expression for d Δt of an ultrathin film, d/λ « 1, is derived in product form that shows the dependence of Δt on N, Φ, and d/λ separately. The angular dependence is given by an obliquity factor, f0(Φ) = 2½ sinΦ tanΦ, which is verified experimentally by TELL measurements on a stable planar soap film in air at λ = 633 nm. The singularity of f0 at Φ = 90° is resolved; Δt is shown to have a aximum just short of grazing incidence and drops to 0 at Φ = 90°. Because N and d/λ are inseparable for an ultrathin film, N is determined by a Brewster angle measurement and d/λis subsequently obtained from Δt Finally, the ellipsometric function in reflection ρr is related to that in transmission Pt.

Journal Name

Applied Optics

Comments

This paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-30-19-2801. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

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