Waveguide Raman scattering for recovery of arbitrary thin-film concentration distributions

Quantitative Raman scattering measurements excited by the various eigenmodes of an optical waveguide were used to obtain depth profiles of poly(styrene-d(8)) (DPS) dispersed in poly(styrene) (PS) thin films without making any assumptions about the functional form of the spatial distribution of the deuterated material. The signal equations, which are ill-conditioned, were inverted to obtain the DPS distribution using a LaGrangian multiplier technique. Model calculations indicate that any arbitrary distribution can be profiled as long as the material can be prepared as an overlayer on an inert waveguiding substrate.