Uniqueness of determination of second-order nonlinear optical expansion coefficients of thin films

Abstract

Second-harmonic generation from surfaces and thin films can be described by up to three nonlinear expansion coefficients, which are associated with the quadratic combinations of the $p$- and $s$-polarized components of the fundamental beam and specific to the measured signal. It has been shown that the relative complex values of the coefficients can be uniquely determined by using a quarter-wave-plate to continuously vary the state of polarization of the fundamental beam [J. J. Maki, M. Kauranen, T. Verbiest, and A. Persoons, Phys. Rev. B 55, 5021 (1997)]. The proof is based on a specific and experimentally convenient initial state of polarization before the wave plate and on the assumption of the most general experimental situation where all three coefficients are nonvanishing, which implies that the sample or the experimental setup is chiral. We show both experimentally and theoretically that, surprisingly, the traditional experimental configuration fails in yielding unique values in a more specific, but common, achiral case. We identify new initial states of polarization that allow the coefficients to be uniquely determined even in the achiral case.