Phase-mismatched degenerate four-wave mixing: complex third-order susceptibility tensor elements of C_60 at 768 nm

We describe and analyze an all-optical method to measure both the magnitude and the phase of each (complex) element of the χ(3) tensor that determines degenerate four-wave mixing in a thin isotropic film on a thick substrate. We use the method to characterize the χ(3) tensor of a 10-µm C60 film (on a CaF2 substrate) for 110-fs pulses at 768 nm. Using a fused-quartz plate as the nonlinear standard, we find the two independent Maker–Terhune elements of χ(3) to have magnitudes |c1221(-ω, ω, ω, -ω)|=(0.44±0.03)×10-12 esu and |c1122(-ω, ω, ω, -ω)|=(0.50±0.03)×10-12 esu and phase angles ϕ1221 and ϕ1122, whose magnitudes are 145°±17° and 139°±10°.