# Theoretical Study: High Harmonic Generation by Light Transients
In this work, we address how temporal field synthesis of a few-cycle pulse at 2 \(\upmu\)m with weaker few-cycle pulses at the second and third harmonic of its carrier frequency leads to a non-sinusoidal temporal shape which fulfills the above-mentioned criteria. Field synthesis of few-cycle pulses allows for tailoring of the light's electric field at sub-cycle scale and consequently controlling electron trajectories and optimization of harmonic yields. In this study, our focus will be on generation of isolated attosecond pulses. Even though we limited ourselves to the dipole response of a single atom, the ionization rate caused by each waveform is also optimized, as it is of great importance when considering propagation and phase-matching in the gas. Non-sinusoidal waveforms, scalable in average-power and energy, can be generated from waveform synthesizers based on Yb:YAG laser technology [17; 18; 19]. Here, a high-energy, high-power Yb:YAG laser serves as the pump source [20]. A multi-octave, low-energy seed spectrum with a carrier-envelope phase stability is generated directly from the Yb:YAG amplifier [21] and divided to several spectral regions by using a broadband beam splitter [22]. Each spectral region is amplified to higher energies in multi-stage optical parametric amplifiers pumped by different harmonics of the Yb:YAG amplifier [23]. Eventually, the broadband amplified pulses are compressed into few-cycle pulses, and coherently recombined (see Figure 1). This laser structure serves as a promising tool for extending the HHG cutoff to keV photon energies, as here: (i) the addition of the longer wavelengths to the driving field enables the recollision of accelerated electrons with more energy; (ii) confining the multioctave field down to a single field cycle at multi-terawatt peak power level enables full control over ionization [24]; and (iii) tailoring the chirp of the waveform allows for better control of tunneling ionization, releasing the electrons and of their subsequent sub-cycle trajectories. Figure 2 compares the single dipole response of a 5 fs, Gaussian pulse at 800 nm achievable from the current Ti:Sa laser technology with the dipole response of the sub-cycle waveform generated from a similar laser structure discussed in [PERSON] et al. [18]. The spectra used for generation of such a waveform are shown in Figure 2a, with broadband spectra centered at 540 nm (visible (VIS), 880 nm (near-infrared (NIR), and 2.1 um (mid-infrared(MIR). The energy distribution between the three spectra for the shown synthesized waveform in Figure 2b is (VIS:NIR:MIR) 0.3:0.85:1, which is the dictated ratio for having the maximum optical-to-optical conversion efficiency from the described laser structure. The three spectra with zero spectral phase, are coherently combined at zero delay and the carrier-envelope phase (CEP) of the resulting waveform is scanned for generation of the highest cutoff energy. For this simulation, we used a nonadiabatic model based on the modified Lewenstein model [25; 26; 27]. At the similar peak intensity of 52.8 \(\times\) 10\({}^{14}\) W/cm\({}^{2}\) and when both waveforms have interacted with He, the HHG spectrum of the sub-cycle waveform reaches 1.7 keV, generating a 1.7 times higher cutoff than the Gaussian pulses at 800 nm (Figure 2c). As it is shown in the spectrogram of the light-transient in Figure 2c, the substantial ionization is limited to one optical half-cycle, obviating the need for spectral filtering or sophisticated gating techniques which are limiting the obtainable bandwidth. However, in this case, a fraction of about 70% of the atom is ionized. The presented calculation shows that although sub-cycle pulses are required and interesting for many pump-probe experiments, they are not the optimal approach for generating keV photons. Figure 1: Schematic architecture of a three-channel optical parametric chirped pulse amplifier (OPCPA) field synthesizer seeded and pumped by picosecond Yb:YAG lasers.