Attosecond helical pulses

Abstract

We find a solution of the wave equation in the paraxial approximation that describes the attosecond pulses with spatiotemporal helical structure in the phase and in the intensity recently generated by means of highly nonlinear optical processes driven by visible or infrared femtosecond vortex pulses. Having a simple analytical model for these helical pulses will greatly facilitate the study of their predicted applications, particularly their interaction with matter after their generation. It also follows from our analysis that the topological charge dispersion inherent to helical pulses allows to beat the minimum duration to which a pulsed vortex without charge dispersion is limited.

General laws of the propagation of ultrafast vortices in free space

“…Indeed the propagation dynamics of UFVs differs in substantial aspects from that of fundamental pulses without OAM because of a strong coupling between the temporal and OAM degrees of freedom in the UFV, as reported in [30][31][32][33][34] for Laguerre-Gauss-type UFVs and in [34][35][36] for nondiffracting X-type vortices. The effects of this coupling remain small, but are observable, at low topological charges and/or many-cycle durations, but become large and dominate the propagation dynamics when the single-cycle and high topological charge regimes are approached.…”

“…Given these huge experimental efforts, it is somewhat surprising the little amount of theoretical work on the propagation characteritics of UFVs [25][26][27][28][29][30][31][32][33][34][35][36], even in the a priori simplest situation of free-space propagation. A comprehensive theory of the propagation dynamics of UFVs, similar to that developed a few decades ago for fundamental, few-cycle pulses without OAM [37][38][39][40][41][42][43][44] when the single-cycle regime was reached [45], is still pending.…”

Time-varying optical vortices enabled by time-modulated metasurfaces

“…This torque is referred to as "self-torque" to be distinguished from the mechanical torque exerted on a scatterer by static OAM-carrying light beams in that it remains an inherent property of the light beam as it propagates in free-space after being generated in the absence of any external agent [31]. Such dynamic torqued light beam could potentially be used in numerous applications such as in optical tweezers [6,[32][33][34], attosecond pulses [35] and fundamental studies of Bose-Einstein condensates [36]. The underlying operating principle of such a timedependent OAM pulse can be attributed to the azimuthal frequency chirp imparted on the radiation emission at the microscopic scale due to the coherent properties of HHG.…”

Couplings between the temporal and orbital angular momentum degrees of freedom in ultrafast vortices with propagation-invariant temporal shape

“…There is increasing interest in synthesizing shorter and shorter vortices of the LG type, [24][25][26][27][28][29] which in the high intensity regime are used to generate highharmonics and attosecond vortices with large OAM [19][20][21][22][23]. From a theoretical point of view, it has been recently demonstrated [30][31][32] that pulsed LG beams with the so-called isodiffracting conditions [33] maintain a propagation-invariant pulse temporal shape as X-waves, even if they are subject to diffraction.…”

“…Notwithstanding these many investigations, funda-mental questions regarding ultrafast X and LG vortices remain unsolved. In recent years, a coupling between the temporal and OAM degrees of freedom in ultrashort (few-cycle and sub-cycle) pulses has been described theoretically in ultrafast X vortices [15,16] and LG vortices [30][31][32]. A consequence detailed in these works is that an arbitrarily short pulse cannot carry an arbitrarily high OAM, but there is a lower bound to its duration for given OAM.…”