## 4 Towards Single-Cycle Pulse Synthesis
### DUV Ultrashort Pulse Generation by Highly Nondegenerate FWM
Both pulses were focused with an aluminum mirror (f = 200 mm) in a second fused silica slide were a self-diffraction beam was generated and later isolated to measure its spectrum in a fiber coupled spectrometer. Figure 25 shows the measured FROG traces and corresponding retrievals using standard Femtosoft FROG software, which gives 27.3 fs DUV pulses with a spectral width of 5.7 nm and a time-bandwidth-product of 0.67. The FROG measurement of the SHG pulses resulted in a duration of 48.6 fs. Figure 22: Experimental setup for ultrashort deep ultraviolet (DUV) pulse generation by highly nondegenerate four-wave mixing (FWM) and temporal characterization via SD-FROG. DM: Dichroic mirror, HWP: Half-wave plate; M1-M3: Aluminum mirrors; M4-M8: 45\({}^{\circ}\) dielectric mirrors. Inset: idler, pump and generated DUV beam, directly projected onto a white card [28]. The model described in Section 3 also predicts broadband generation of the third-harmonic of 800 nm at a central wavelength of 266 nm. Using the experimental parameters given in this section and for different internal angles \(\theta\) = 15.0\({}^{\circ}\), 15.7\({}^{\circ}\) (the angle of perfect phase-matching) and 16.4\({}^{\circ}\) different  
Figure 24: Broadest experimental spectrum obtained in our-set-up, capable of supporting sub-4-fs [28]. Figure 25: **(a)** Experimental and **(b)** retrieved SD-FROG traces of the DUV pulses (in log scale); **(c)** retrieved pulse in the time and **(d)** frequency domains [28]. broadband spectra were obtained for different delays between pump and signal pulses. In Figure 26 (\(\theta\) = 15.0\({}^{\circ}\)) we can see double band spectral structures which are enhanced in its blue portion for negative delays and in its redder portion for positive delays. The two situations are of course not symmetrical because of the different group velocities of the pulses, where the idler can catch up with the pump in situations of positive delay but will always come before the pump for negative delays. We also see that the different pulses have chirp and the more intense ones, generated at delays of \(-\)20 fs, 0 fs and 20 fs, have a clear positive chirp, mainly due to self- and cross-phase modulation. This positive chirp is in agreement with the experimental results of Figure 23, where the retrieved pulse shows also positive chirp. The calculated emission angle for the 266 nm pulse obtained for 0 fs relative delay between pump and idler was 7.3\({}^{\circ}\), with an output energy efficiency of 3.6% with respect to the pump pulse and a pulse width of 19.7 fs (9 fs TL duration), all in reasonable agreement with the experimental results. For other interaction angles (\(\theta\) = 15.7\({}^{\circ}\) (Figure 27) and \(\theta\) = 16.4\({}^{\circ}\) (Figure 28)) higher efficiencies are obtained (12.5% and 6.9% respectively) but with narrower bandwidths. The situation with \(\theta\) = 15.0\({}^{\circ}\) seems to better represent the experimental one. We see that the change in interaction angle from 15 to \(16.4^{\circ}\) also produces a significant shift/tuning of the central frequency of the generated DUV pulses. This is due to the large angular sensitivity of the geometric phase matching condition for the highly nondegenerate FWM process involving \(\omega\) and \(2\omega\) beams crossing at a very large angle. Figure 26: Simulated spectral intensity and phase of the generated DUV signal for \(\theta\) =15.0\({}^{\circ}\) and different delays between idler and pump pulses (The intensities in the first and the last plots have been multiplied by a factor of 5). Negative delay: idler arrives before pump, positive delay: idler arrives after pump [28]. Figure 28: Simulated spectral intensity and phase of the generated DUV signal for \(\theta=16.4^{\circ}\) and different delays between idler and pump pulses. (negative and positive delays as in Figure 23; note the scale factors for the first and last two intensity plots) [28].