Spectral caustic in two-color high-order harmonic generation: Role of Coulomb effects

Abstract

The high-order harmonic spectrum generated in two-color intense laser field under certain conditions has a pronounced maximum caused by the so called spectral caustic. Using a numerical solution of the 3D time-dependent Schrödinger equation we study the width of the maximum and the degree of the generation enhancement due to the caustic as a function of the fundamental intensity, wavelength, and atomic ionization potential. It is shown that the degree of this enhancement can be well quantitatively characterized by a single parameter: the ratio of the radius of the free electronic oscillation in the laser field to the atomic size. This behavior can be explained by the Coulomb attraction of the photoelectron to the parent ion, whereas the effect of this attraction on the width of the maximum is negligible. Choosing the field parameters providing a pronounced enhancement, we calculate the high harmonic macroscopic response taking into account the transient phase-matching. We show that the caustic feature can be used to provide a quasi-monochromatic XUV source with an almost linear frequency vs. time dependence. Such source can be used, in particular, for the time-resolved single-shot XUV imaging.

An enhancement method of waveform simulation in dual-color laser field imaging based on Internet of Things

“…4, 1054.8]. The harmonic shape after adjustment is basically consistent with the actual harmonicity, which is close to reality [15].…”

The imaginary part of the high-harmonic cutoff

“…In one dimension, this caustic can be precisely localized to a point, known as the 'fold' (more technically, the 'bifurcation set'), which marks the transition between the two regimes, and our harmonic-cutoff times are the precise embodiment of that understanding of the caustic. This view of the harmonic cutoff as a caustic has been used for some time [36][37][38], but recent years have seen a marked increase in interest in that perspective on the dynamics [39][40][41][42][43][44], as laser sources achieve better control over polychromatic combinations with high relative intensities (which is slated to continue to increase [80]). This has opened the door to the observation of higher-order catastrophes in strong-field observables, involving higherdimensional bifurcation sets; however, the theoretical understanding remains somewhat behind, and a quantitative understanding that reflects those structures has not yet followed.…”

“…In this sense, the complex harmonic-cutoff energy Ω hc is the bifurcation set for the catastrophe -suitably generalized to the complex variables involved -and it marks the location of the caustic. The formal study of caustics has seen increasing interest within attoscience [36][37][38][39][40][41][42][43][44], and our approach provides a useful tool for exploring and describing the higher-dimensional bifurcation sets at the heart of the higherorder catastrophes that become available as our control over short pulses of light becomes more finely tuned.…”

Suppression of individual peaks in two-colour high harmonic generation

“…Theoretical works have explored two-colour HHG numerically and analytically over a large range of parameters, and different parent atoms [16,17]. Additionally, others have reported on the effect of unconventional non-gaussian temporal pulse envelopes [18] and the role of atomic Coulomb potential on the spectral density brought about by two-colour HHG [19]. Such control has already found applications in high-harmonic spectroscopy to probe multi-electron effects in noble gases [20,21].…”