Strong-field approximation in a rotating frame: High-order harmonic emission from p states in bicircular fields

Abstract

High-order harmonic generation with bicircular fields -the combination of counter-rotating circularly polarized pulses at different frequencies -results in a series of short-wavelength XUV harmonics with alternating circular polarizations, and experiments show that there is an asymmetry in the emission between the two helicities: a slight one in helium, and a larger one in neon and argon, where the emission is carried out by p-shell electrons.Here we analyze this asymmetry by switching to a rotating frame in which the field is linearly polarized; this induces an effective magnetic field which lowers the ionization potential of the p + orbital that co-rotates with the lower-frequency driver, enhancing its harmonic emission and the overall helicity of the generated harmonics, while also introducing nontrivial effects from the transformation to a non-inertial frame in complex time. In addition, this analysis directly relates the small asymmetry produced by s-shell emission to the imaginary part of the recollision velocity in the standard strong-field-approximation formalism.Light is one of our main tools for the investigation of the internal structure of dynamics of matter, and in this role we employ all of its characteristics: its spatial and temporal aspects, its coherence as a wave phenomenon, and its polarization as a vector effect. As we probe deeper into the structures of materials and molecules, and as we look with increasing detail at their dynamics, it becomes necessary to use higher frequencies and shorter pulses, and here the process of high-order harmonic generation (HHG) stands out as a simple and effective way to produce bright, short, coherent pulses of high-frequency radiation [1].The process of HHG is essentially driven by the ionization of gases by a strong, long-wavelength laser pulse, which then drives the photoelectron back to its parent ion with a high energy, which it emits as a single photon. This permits a large flexibility in the emission process, and its sub-laser-cycle nature allows us to probe atomic and molecular systems at their own timescales. Unfortunately, however, its collision-driven nature has long left unavailable one of the crucial tools in the toolbox -the use of circular polarizations [2].A number of attempts have been made over the years to produce high-order harmonics with circular or elliptical polarization [3][4][5][6][7][8], which would enable detailed time-resolved studies of magnetic materials and chiral molecules, but they have generally suffered from complex configurations, low efficiencies, and limited harmonic ellipticities. These limitations were recently overcome by combining counter-rotating circularly polarized drivers [9,10], in a so-called 'bicircular' configuration; this produces fully circular harmonics at similar efficiency to linear-polarization schemes, and it can be implemented with minimal modifications to existing beamlines [11].The simplest configuration uses drivers with equal intensities at frequencies ω 1 = ω and ω 2 = 2ω, in which case the field...

Conservation of Torus-knot Angular Momentum in High-order Harmonic Generation

“…This produces a smaller broadening, shown in Fig. 4(c), with a different origin: the intensity ratio affects the quantum-path dynamics [40], which alters both the action and the vector aspects of the recollision [39]. Note that similarly, even in the unperturbed case, quantumpath dynamics and phase-matching effects should contribute to radial structures in the HHG emission [49,59].…”

“…One particularly relevant example is the three-foldsymmetric trefoil field present in the 'bicircular' HHG configurations [22][23][24][25][26][34][35][36][37][38][39][40][41] used to produce circularlypolarized harmonics. This field consists of two counterrotating circularly-polarized drivers at different frequencies, and exhibits the same configuration after a polarization rotation by an angle 2π/n, with n ≥ 3.…”

Strong-field control and enhancement of chiral response in bi-elliptical high-order harmonic generation: an analytical model

“…A promising example of a such field tailoring is the generation of two-color bi-circularly polarized radiation, which results from combining a circularly polarized driver with a counter-rotating second harmonic [51][52][53][54]. Intense bicircular fields can efficiently generate attosecond pulses with circular and elliptical polarization in the XUV domain [55][56][57][58][59][60][61][62][63][64][65][66][67] and spin-polarized electron currents that recollide with the core [68,69], as well as probe molecular dynamical symmetry breaking [70,71].…”

A dynamical symmetry triad in high-harmonic generation revealed by attosecond recollision control

“…As with equation (1), the emerging symmetries of equation (2) constrain the harmonics to be circularly polarized. Both numerical simulations and the repeating of the experiment in Ne gas, utilizing chiral p-orbitals [24,[50][51][52]54], indicate that the unsuppressed harmonics are circularly polarized (see supplementary).…”