Improved fitting equation for frequency-resolved femtosecond hyper-Rayleigh scattering experiments

Abstract

One approach to the experimental determination of the molecular second-order nonlinear polarizability, or the first hyperpolarizability, of fluorescent species by hyper-Rayleigh scattering is based on high-frequency demodulation of the time-delayed fluorescence contribution to the immediate scattering signal [Rev. Sci. Instrum.69, 2233 (1998)]. For typical fluorescence lifetimes of less than a nanosecond a detection bandwidth of more than 1 GHz is necessary. This bandwidth has not yet been realized. Measurements at successively higher modulation frequencies are performed instead. A fitting of the apparent hyperpolarizability as a function of the modulation frequency then reveals the inherent hyperpolarizability without the fluorescence contribution. An improved fitting function has been derived, resulting in the elimination of a small systematic error and in the reduction of the larger statistical uncertainty in the deduced value. Possible implications of the improved accuracy and precision are discussed.