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Analytical solution of the inverse optical problem for very thin films

B. HRISTOV1, P. GUSHTEROVA1,* , P. SHARLANDJIEV1

Affiliation

  1. Central Laboratory for Optical Storage and Processing of Information, Bulgarian Academy of Sciences, “Acad. G. Bontchev” Str., Bl. 101, 1113 Sofia, Bulgaria

Abstract

The determination of the complex refractive index (ñ) and the physical thickness (d) of very thin films (d ≅ λ/50, λ is the wavelength in VIS and NIR) is still a challenging task in the field of the inverse optical problems. The physical reality of these films makes difficult the application of methods, commonly used for the determination of ñ and d of thicker films. For several years we have been working on the development and the implementation of a method, designed especially for determination of ñ and d of very thin films. The nanothickness of the films allows us to develop in series of ñd/λ the Abelès characteristic matrix elements. Thus, approximated expressions for the film transmittance (Tf), front side (Rf) and backside (R ′ f) reflectance are derived. For estimation of ñ and d we use the system (1+Rf)/Tf, (1-Rf)/Tf and (1-R ′ f)/Tf. Here we apply an exact analytical approach to solve the system, obtained by development of the Abelès characteristic matrix elements to the 4-th power. For the first time, the set of equations for (1+Rf)/Tf, (1-Rf)/Tf and (1-R ′ f)/Tf is solved analytically. Besides the increase of the accuracy of the solutions, no initial information about the unknown parameters is needed..

Keywords

Very thin films, Optical constants, Exact analytical approach.

Submitted at: Nov. 1, 2006
Accepted at: Jan. 15, 2007

Citation

B. HRISTOV, P. GUSHTEROVA, P. SHARLANDJIEV, Analytical solution of the inverse optical problem for very thin films, Journal of Optoelectronics and Advanced Materials Vol. 9, Iss. 1, pp. 217-220 (2007)