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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 12 — Dec. 1, 1983
  • pp: 1777–1784

Ellipsometric formulas for an inhomogeneous layer with arbitrary refractive-index profile

J. C. Charmet and P. G. de Gennes  »View Author Affiliations


JOSA, Vol. 73, Issue 12, pp. 1777-1784 (1983)
http://dx.doi.org/10.1364/JOSA.73.001777


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Abstract

The reflectances of inhomogeneous layers are usually calculated by numerical solution of Maxwell's equations. This requires a specific model for the layer structure. We are interested here in the inverse problem: finding the refractive-index profile n(z) from ellipsometric data (ψ and Δ). We have calculated the reflectances explicitly in a first Born approximation [i.e., to first order in n(z) – n0, where n0 is the index of the pure liquid]. The effect of the reflecting wall at z = 0 is incorporated exactly. Finally, we express ψ and Δ in terms of the Fourier transform of the profile Γ(2q), where q is the normal component of the incident wave vector. The equation Γ(2q) = Γ′+iΓ″ is complex; one can construct Γ′(2q) and Γ″(2q) in terms of the experimental ψ and Δ for all the accessible span of q vectors. For thick diffuse layers of thickness e » λ/4π, this should allow for a complete reconstruction of the profile. For thin layers, e « λ/4π, what are really measured are the moments Γ0 and Γ1 (of orders 0 and 1) of the index profile. To illustrate these methods, we discuss two specific examples of a slowly decreasing index profile: (1) wall effects in critical binary mixtures and (2) polymer adsorption from a good solvent.

© 1983 Optical Society of America

Citation
J. C. Charmet and P. G. de Gennes, "Ellipsometric formulas for an inhomogeneous layer with arbitrary refractive-index profile," J. Opt. Soc. Am. 73, 1777-1784 (1983)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-12-1777

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