## 4 Towards Single-Cycle Pulse Synthesis
Even though supercontinuum generation and laser action are coherent processes, the relative phase between the two pulses is not actively locked and can fluctuate due to normal thermal and mechanical perturbations and drifts in the system. The pulses are commensurate to within 0.2% (well within their \(\sim\)5 nm bandwidths), hence we can expect the resulting synthesized pulses to have the same CEP within the pulse train. The orange and green pulses are synchronized at the entrance plane of the fused silica slide FS1, and have energies of 32 and 38 \(\upmu\)J, respectively, near-transform-limited durations (measured using  
Figure 14: Experimental setup: (I) generation of CFWM pulses; (II) pulse recombination and synthesis; (III) pulse characterization by PG-XFROG (see text for details) [21]. SHG-FROG), beam radii of approximately 80 and \(100\,\upmu\)m, respectively, and similar intensities on the order of \(2\times 10^{12}\) W/cm\({}^{2}\) as they cross on the slide at an angle of \(\approx 3^{\circ}\). Under these conditions, a fan of 20 upconverted CFWM orders was generated up to 209 nm, as shown in Figure 15a. The total measured energy in the cascaded beams (excluding the pumps, _i.e._, orders 0 and 1) is \(>6\)\(\upmu\)J, so approximately 10% of the incident energy is transferred to the newly generated frequencies. To perform pulse synthesis all orders were collimated and recombined in a single 100 \(\upmu\)m white light spot using two \(\uplambda\)/8 Aluminum-coated off-axis parabolic mirrors P1 (f = 2.54 cm) and P2 (f = 5.08 cm) (Figure 14-II). A perforated screen was placed between these two mirrors to transmit only the central portions of the pumps and thus have a more balanced spectrum, but no additional amplitude filtering was performed. The total spectrum at the focal spot was measured with an intensity calibrated UV-NIR (200-1100 nm) spectrometer, but only 15 frequency upconverted orders could be detected due to the limited bandwidth of the mirrors, as shown in Figure 15b. All orders have been generated under simultaneous phase-matching conditions with a fast electronic nonlinearity, so they are phase-locked when exiting the first fused silica slide FS1. Additional propagation in air only adds negligible second-order dispersion and hence we expect a train of few-cycle pulses to be synthesized at the focus of P2. Temporal characterization was done with polarization gating XFROG (PG-XFROG) using an 80 fs pulse as the gate (Figure 14-III). This gating pulse was obtained from the main orange beam with a 50/50 beamsplitter (BS) and its polarization was rotated 45\({}^{\circ}\) with a half-wave plate. This pulse induces birefringence in another fused silica plate (FS2) placed at the focal plane of mirror P2, where the pulse synthesis using all CFWM orders is taking place. A second Glan-Thompson polarizer was used as analyzer (GTA) crossed with the original GTPs, which required collimating the beams with a third parabolic mirror P3 (f = 2.54 cm). Finally the total spectrum of the gated pulses was measured by focusing the output of the GTA with mirror P4 (f = 5.08 cm) onto an optical fiber with a large 400-\(\upmu\)m core coupled to a spectrometer (FCS). The PG-XFROG trace obtained by registering the spectrum of the gated pulses as a function of the delay of the gating pulse can be seen in Figure 16a, where up to 13 orders could be simultaneously gated, so they were synchronized, and also practically have no chirp. Since the gate pulse was long compared to the expected pulse train structure, information about  
Figure 15: **(a)** Direct (no filtering) image of the fan of multicolored CFWM pulses as seen projected on a phosphor-coated paper screen (the dark arrows denote the pump beams); **(b)** Corresponding two-octave spectrum measured at the focal plane of mirror P2. [21]. the temporal structure of the traces is lost and retrieval of the whole field with this trace is not reliable (see previous section where a simulated PG-XFROG trace using a 20 fs gate pulse showed the fine temporal structure).