## 4 Towards Single-Cycle Pulse Synthesis
### DUV Ultrashort Pulse Generation by Highly Nondegenerate FWM  
The observed fact that the generated orders are broadband deserves more attention, since the availability of sub-300 nm DUV ultrashort pulses with energies in the range of microjoules is important to study processes in photophysics, photochemistry and photobiology. Hence, although not a cascaded process, we also concentrated on studying the generation of the third harmonic of 800 nm via highly nondegenerate FWM [28]. Several techniques based on FWM in gaseous media have been employed by other groups, from third-order difference-frequency generation (DFG) of Ti:Sapphire laser pulses and their second-harmonic in hollow waveguides [3; 29] and in filaments [30; 31], to DFG of pre-chirped pulses in dual hollow-fiber systems [32]. Direct harmonic upconversion of few-cycle femtosecond pulses in gases [33; 34] has also been performed. This last method has enabled the generation of the shortest (sub-3-fs) DUV pulses to date [35]. The setup used for the generation of broadband pulses at 266 nm by mixing two ultrashort pulses at 800 nm and 400 nm respectively in an isotropic solid is shown in Figure 22, along with the part for the temporal measurement. A Titanium:Sapphire amplifier provides the fundamental signal (or idler) pulses at 800 nm (\(\omega\)) with 27 fs pulse duration, 1 mJ energy, horizontally polarized and at 1 kHz repetition rate. The pump pulses at 400 nm (2\(\omega\)) are generated in a type-I 200 \(\upmu\)m thick BBO crystal. To maximize the SHG, the chirp of the fundamental pulse was optimized and a refractive telescope reduced its beam size to 5 mm. A dichroic mirror separated the pump and signal beams and a half wave plate HWP was used to rotate the polarization plane of the signal beam by 90\({}^{\circ}\) so as to have the polarization parallel to the pump beam, which emerges perpendicularly polarized from the BBO crystal. Both pump and signal beams were focused with lenses to interact on a fused silica slide  
Figure 21: Temporal characteristics of the generated harmonics. Solid curve: intensity; dashed curve: phase [27]. FS at an internal angle of 15.75\({}^{\circ}\) as given by Equation (3) (external angle \(\uptheta=23.2^{\circ}\)) for the FWM process \(3\upomega=2\times(2\upomega)-\upomega\). The slide was placed 2 cm before the focus of the lenses to avoid damage. Synchronization is achieved with a delay line in the signal branch of the setup and in the plane of the slide the signal and pump beams had 314 \(\upmu\)J and 191 \(\upmu\)J with estimated intensities of 2.6 \(\times 10^{12}\) and 1.2 \(\times 10^{12}\) W/cm\({}^{2}\), respectively. Under these conditions we obtained 5-6 \(\upmu\)J DUV pulses emitted at around 266 nm at an external angle of 7\({}^{\circ}\). Figure 23 shows the spectra registered with a fiber coupled spectrometer for different delays, defining the 0 fs delay for the situation in which higher energy pulses were obtained (6 \(\upmu\)J). Different broadband spectra were obtained for delays ranging from \(-99\) fs to 99 fs and the dependence of the shape and central frequency can be explained by the cross-phase modulation between the pump and idler pulses. Integration of these spectra with reference to the energy measured for the one with 6 \(\upmu\)J (Figure 20, delay 0 fs) gives 1.5, 2.4, 3.85, 6.0, 4.75, 4.9 and 1.4 \(\upmu\)J for this series. The spectra are broad enough (Figures 23 and 24) to support ultrashort durations and the DUV (as well as the SHG pump pulses) were characterized by self-diffraction FROG (SD-FROG). The experimental details can be seen in Figure 22. Two holes with 1.6 mm diameter separated by 3.5 mm were drilled on a metallic mask and aligned so that both holes transmitted similar intensities from the central part of the DUV beam. A relative temporal delay was set between both pulses using d-shaped mirrors and a stepper motor stage (3.33 fs step).