We report quadratic electrooptic derived third-order optical polarizab
ilities, gamma, on two thiazole azo dyes that we have previously demon
strated to possess large optical hyperpolarizabilities, beta. We demon
strate that the data are consistent with our previously introduced res
tricted three-level model for gamma. Specifically we show that the sus
ceptibility can be accounted for by two perturbative terms and that we
are also possibly observing the predicted enhancement in gamma for mo
lecules with large beta when the peak narrows. We also suggest that th
is mechanism offers an approach to systematic improvements for the rat
io Re[gamma]/Im[alpha].