Symmetries and Selection Rules of the Spectra of Photoelectrons and High-Order Harmonics Generated by Field-Driven Atoms and Molecules

Abstract

Using the strong-field approximation we systematically investigate the selection rules for high-order harmonic generation and the symmetry properties of the angle-resolved photoelectron spectra for various atomic and molecular targets exposed to one-component and two-component laser fields. These include bicircular fields and orthogonally polarized two-color fields. The selection rules are derived directly from the dynamical symmetries of the driving field. Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent molecular orbital. In addition, we briefly discuss some properties of the high-order harmonic spectra generated by a few-cycle laser field. The symmetry properties of the angle-resolved photoelectron momentum distribution are also determined by the dynamical symmetry of the driving field. We consider the first two terms in a Born series expansion of the T matrix, which describe the direct and the rescattered electrons. Dynamical symmetries involving time translation generate rotational symmetries obeyed by both terms. However, those that involve time reversal generate reflection symmetries that are only observed by the direct electrons. Finally, we explain how the symmetry properties, imposed by the dynamical symmetry of the driving field, are altered for molecular targets.

Elliptic dichroism in strong-field ionization of atoms subjected to tailored laser fields

“…The top left and right panels correspond, respectively, to the two limiting cases of the OTC field ( ε = 0) and the bicircular field ( ε = 1) and their momentum distributions agree with previous results. 32,54 From the remaining panels we see that the rotational and reflection symmetries, which are characteristic for the OTC and bicircular fields, are violated for our more general BEOTC field. Comparing the left and right panels confirms that the simultaneous reversal of the sign of p x and the sign of the ellipticity is a symmetry transformation.…”

Exploring symmetries in photoelectron holography with two-color linearly polarized fields

“…Orthogonally polarized fields are potentially powerful tools for disentangling different types of intra-cycle interference, but their influence has been mostly interpreted using the Coulomb-free, standard SFA [51,54]. The same holds for the understanding of dynamical symmetries of the field and the target: although there is a considerable body of work in this direction [55], the influence of the residual potential remains largely unexplored. It is not yet clear how it will affect targets with specific geometries and/or internal degrees of freedom, which, per se, cause phase changes and modulations in holographic structures [72,96,[147][148][149].…”

“…We will adopt the notation (r, s) for the two frequencies involved, whereby the first and second index relates to the first and second wave, respectively [55,133] and refer to it as a (r, s) field.…”

“…2(D), the half cycle symmetry of the field means that the saddle points repeat identically every half cycle. This means that there will be no resulting asymmetry in the final momentum distributions of tunneled electrons [55]. Having the other symmetries broken means that the sub half cycle saddles have no symmetry which can lead to changes to the contrast of holographic interference patterns.…”

“…This interest led to a multitude of applications, such as the in situ characterization of attosecond pulses [19][20][21], the measurement of tunneling times [22][23][24][25][26][27][28][29][30][31][32][33][34][35], probing chiral systems [36][37][38][39], angular features in HHG, vortex-type interference [40] and the phase-of-the phase spectroscopy using collinear [41][42][43] or circularly polarized [44,45] two-color fields. Apart from the usual linearly polarized bichromatic fields [17] and few-cycle pulses [16], elliptically polarized fields [46], orthogonally polarized two-color (OTC) [27,33,[47][48][49][50][51][52][53][54][55] and bicircular [35][36][37][38][39]…”