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Analytical determination of the complex refractive index of an opaque film deposited on a transparent substrate from the pseudo-Brewster angles of internal and external reflection

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Abstract

A new method is described for the explicit determination of the refractive index amd extinction coefficient of an opaque film deposited on a transparent substrate from purely angular, nonpolarimetric, measurements. In particular it is shown that the real and imaginary parts of the complex dielectric constant ε = εr –j εi of the film are obtained analytically, directly and noniteratively, from the pseudo-Brewster angles (PBAs) of internal and external reflection. This follows from a study of the properties of the contours of constant PBA in the complex ε plane. For this method to be accurate, one of the two PBAs should be <45°, i.e. the substrate should be sufficiently optically dense or the UV and VUV spectral range is of interest. Experimental errors of the PBAs may also render impossible the determination of εi when |εir|≪1. Simulated measurements on Ag and TiN films will be presented to demonstrate the method.

© 1988 Optical Society of America

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