Ideal Waveform to Generate the Maximum Possible Electron Recollision Energy for Any Given Oscillation Period

Abstract

We present the perfect waveform which, during a strong field interaction, generates the maximum possible electron recollision energy for any given oscillation period, over 3 times as high as that for a pure sinusoidal wave. This ideal waveform has the form of a linear ramp with a dc offset. A genetic algorithm was employed to find an optimized practically achievable waveform composed of a longer wavelength field, to provide the offset, in addition to higher frequency components. This second waveform is found to be capable of generating electron recollision energies as high as those for the perfect waveform while retaining the high recollision amplitudes of a pure sinusoidal wave. Calculations of high harmonic generation demonstrate this enhancement, by increasing the cutoff energy by a factor of 2.5 while maintaining the harmonic yield, providing an enhanced tool for attosecond science.

Waveforms for optimal sub-keV high-order harmonics with synthesized two- or three-colour laser fields

“…Tables 1-11. We comment that optimization of harmonics only from shorttrajectory electrons was not considered in the previous study 19 .…”

“…This is accomplished by synthesizing 'only' two-or three-colour laser fields without increasing the total laser power. We remark that in an early study 19 a 'perfect wave' was derived that can be synthesized with five-colour fields. In comparison, our optimized waveform generates higher harmonic cutoff than the 'perfect wave' (Supplementary Fig.…”

Tailoring the waveforms to extend the high-order harmonic generation cutoff

“…Such a form has been shown to provide an absolute maximum of the kinetic energy of the electron at the moment of its return to the nucleus. This energy was approximately 3 times larger than the corresponding energy for the pure cosine wave with the same period and field intensity [11]. To avoid using a strong DC field in practice, it was suggested in [11], that it could be replaced by an AC field of a lesser Ω/2 frequency, while the linear ramp could be replaced by a combination of the harmonics with frequencies nΩ.…”

“…If the desired goal is to increase the harmonics cut-off order, there is a possibility to find the optimum field parameters using a purely classical approach based on the electron trajectory analysis [10,11]. In the paper by Radnor et al [10] such an analysis, supplemented by the quantum calculation relying on the genetic algorithm, was used to show, that the optimum waveform allowing to maximize the recollision energy is a linear ramp with the DC offset F (t) = αt + β for t ∈ (0, T ), T being the period of oscillations.…”

Macroscopic scaling of high-order harmonics generated by two-color optimized waveforms in a hollow waveguide

“…To overcome low up-conversion efficiency of HHG, it has been proposed to modify the subcycle laser waveform by optimally synthesizing multicolor laser pulses [31][32][33][34][35][36][37] (see review in Ref. [38]).…”