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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 30, Iss. 19 — Jul. 1, 1991
  • pp: 2801–2806

Transmission ellipsometry on transparent unbacked or embedded thin films with application to soap films in air

R. M. A. Azzam  »View Author Affiliations


Applied Optics, Vol. 30, Issue 19, pp. 2801-2806 (1991)
http://dx.doi.org/10.1364/AO.30.002801


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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 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, fo(ϕ) = 21/2 sinϕ tanϕ, which is verified experimentally by TELL measurements on a stable planar soap film in air at λ = 633 nm. The singularity of fo at ϕ = 90° is resolved; Δt is shown to have a maximum 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/λ is subsequently obtained from Δt. Finally, the ellipsometric function in reflection ρr is related to that in transmission ρt.

© 1991 Optical Society of America

History
Original Manuscript: July 13, 1990
Published: July 1, 1991

Citation
R. M. A. Azzam, "Transmission ellipsometry on transparent unbacked or embedded thin films with application to soap films in air," Appl. Opt. 30, 2801-2806 (1991)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-30-19-2801

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