Abstract

Measurement of the fringes produced by interference between direct and reflected light in the Lloyd mirror configuration can give information about the refractive-index profile of the reflecting surface, as has recently been shown. The experiment is performed near grazing incidence, and the analysis given so far has been based on the short-wave approximation, which is known to fail at grazing incidence, and no account has been taken of the difference between s and p polarizations. I give exact reflection phases for the solvable exponential refractive-index profile for both polarizations and develop general results for an arbitrary smooth profile that are valid near grazing incidence. I find that, for profiles that are slowly varying on the scale of the wavelength, the path-integral approximation to the phase is accurate except for the first few interference fringes, which come from glancing incidence reflections. The s and p phases are very nearly equal under the same conditions. Explicit formulas are given for dielectric function profiles that are linear or quadratic in the depth. The characteristic length of the quadratic profile may be found from the variation in the fringe spacing.

© 1996 Optical Society of America

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