## 2 Basic Experiment and Interpretation  
The first experiment on highly nondegenerate noncollinear CFWM was done by [PERSON] _et al._ at LOA (Laboratoire d'Optique Appliquee in Palaiseau, France) [11] and the experimental setup can be seen in Figure 2a. The laser source is a dye laser-amplifier system delivering an orange beam (frequency \(\omega_{0}\), \(\lambda_{0}\) = 618 nm, 80 fs) and a green beam (frequency \(\omega_{1}\), \(\lambda_{1}\) = 561 nm, 40 fs). Both beams are horizontally polarized and with near-Gaussian spatial profiles (approximately 5 mm diameter). The green beam was sent through a delay-line and both beams were coupled through a 50/50 beam splitter to impinge on a large section plane-convex lens (f = 30 cm) at an adjustable small angle. The lens focuses both beams in a thin slide of BK7 glass with 150 \(\upmu\)m thickness at an external angle \(\theta=2.9^{\circ}\). A thin glass slide was chosen to minimize self-phase modulation processes and it was also placed 1 cm before the focus of the lens to avoid laser-induced damage. At the plane of the slide both beams had 20 \(\upmu\)J energy, corresponding to intensities of 1.0 TW cm\({}^{-2}\) for the orange and 2.1 TW cm\({}^{-2}\) for the green beam. When both beams were temporally synchronized at the plane of the slide, a large set of multicolored beams (Figure 2b) was produced at both sides of the incident beams, consisting of two frequency-downshifted beams (we will call \(D_{n}\) the downconverted beam of order \(n\)) in the red and near infrared, as well as 11 frequency-upshifted beams (we will call \(U_{n}\) the upconverted beams of order \(n\)) extending into the blue and ultraviolet regions of the spectrum. The ultraviolet beams are seen as blue in the picture because the screen used was fluorescent, whereas the second downconverted beam could be observed with the help of a NIR viewer. The spectrum of the generated beams was registered by collecting the generated fan of beams with a large aperture aluminum-coated parabolic mirror M4 to minimize chromatic aberration and UV absorption and by sending the collimated beams to a spectrograph equipped with a CCD camera where the resulting spectrum is given in Figure 3. Two downconverted bands (\(D_{1}\) and \(D_{2}\)) can be seen to the left of the pump beams, while only 5 upconverted bands (\(U_{1}\) to \(U_{5}\)) are seen to the right, due to sensitivity limitations of the CCD in the blue and UV spectral ranges. All generated orders are broadband, with bandwidths of the order of those of the pump and signal beams (16 nm approximately) which are larger than the original laser bandwidths (5-6 mm) due to some self- and cross-phase modulation taking place within the slide. Energy measurements were done with a calibrated photodetector and the whole set of newly generated beams carried about 5%-10% of the total energy of the orange and green pulses. The spectrum of Figure 3 can be explained, to a very good approximation, by assuming a cascaded FWM process in the central frequency approximation. The two pump pulses drive the \(\chi^{(3)}\) medium  
Figure 2: (**a**) Experimental arrangement: BS, beam splitter; M1–M3, silver mirrors; M4, parabolic mirror; M5, M6, aluminum mirrors. Spacing between colors not at scale; (**b**) Picture of output beams as taken on a white card. Adapted from [11]. at the modulation frequency \(\omega_{m}=\omega_{1}-\omega_{0}\), giving rise to multiple pulses with frequencies \(\omega_{n}=\omega_{0}+n\omega_{m}\), where \(n\) is the integer beam order and \(n>1\)\((n<0)\) denotes frequency upconverted (downconverted) pulses. This can also be written as \(\omega_{n}=\omega_{n-1}+\omega_{m}\) or \(\omega_{n}=n\omega_{1}-(n-1)\omega_{0}\). Note that even though the total number of photons involved in a given process is \(2n\), this does not correspond to the order of the corresponding nonlinearities \((2n-1)\), but to that of an effective nonlinearity obtained via cascaded \(\chi^{(3)}\), _i.e._, third-order, processes.