“…One of the ways to separate the contribution of the two nonlinearities and express of χ (3) eff,dir in terms of the product (d eff,I )(d eff,II ) is to use the azimuthal (Banks, Feit, and Perry [2002]) or input polarization (Kim and Yoon [2002]) dependence of χ (3) eff,dir and χ (3) eff,casc . The other way is to compare the TH signal obtained under the condition ∆k THG −→ 0 with the TH signal obtained under one of the conditions ∆k SHG −→ 0 or ∆k SFG −→ 0, where the signal is only proportional to the factor |χ (3) eff,casc | 2 (Akhmanov, Meisner, Parinov, Saltiel, and Tunkin [1977]; Chemla, Begley, and Byer [1974]), and calculate χ (3) eff,dir ; however this procedure gives two possible values due to an indeterminate sign.…”