Relativistic effects in nonrelativistic ionization

Radiation pressure effects recently observed by Smeenk et al. [C. Smeenk, L. Arissian, B. Zhou, A. Mysyrowicz, D. M. Villeneuve, A. Staudte, and P. B. Corkum, Phys. Rev. Lett. 106, 193002 (2011)] in atomic ionization by circularly polarized light are readily explained by the relativistic strong-field approximation (RSFA). The physical picture that emerges is determined by linear and angular momentum properties of the photons required for ionization, and it is largely independent of the atom being ionized. Radiation pressure follows from linear momenta carried by photons, and the angular momenta of the photons require the photoelectron to be in a circular orbit around the remnant ion. Two special features of the Smeenk et al. experiments are highlighted by the analysis. One is that this is the first verification of true relativistic effects in ionization. The other is that the circular trajectory picture from the RSFA analysis directly contradicts the physical picture that emerges from the length gauge. This is an exceptionally striking example of gauge-dependent differences in physical interpretations. Nevertheless, the distribution of momentum found by the Smeenk et al. experiments is accurately predicted by the RSFA. Results herein provide a universal theory to which the analysis of Titi and Drake [A. S. Titi and G. W. F. Drake, Phys. Rev. A 85, 041404(R) (2012)] represents an approximation. The physical properties of ionization by circularly polarized light also cast doubt on some predictions of rescattering theory.

Figure 1

This figure illustrates the effect of radiation pressure on the path of a photoelectron ionized by circularly polarized light. The circular orbit is the result of the summed angular momenta of the photons required for ionization. The forward displacement of the plane of the orbit is the result of photon linear momenta. The figure is taken from Ref. [12].

Figure 2

The angular distribution of photoelectrons predicted by an RSFA calculation, done with neither focal averaging nor saturation effects included. The peak of the angular distribution occurs at the angle given by Eq. (2). To illustrate an extreme effect of radiation pressure in order to mimic Fig. 1, the intensity is selected to be unrealistically high. The atom would be fully ionized at a much lower intensity.

Figure 3

Components of momentum parallel to the propagation direction of a circularly polarized laser field depend primarily on the frequency and intensity of the laser field rather than on properties of the atom being ionized. Part (a) is the prediction of Eq. (5) or (6) for the two wavelengths employed by Smeenk.The lines shown closely replicate those found by the experiments. Figure 3(b) is taken from Ref. [1].

Figure 4

An explicit calculation of the distribution of momentum components parallel to the direction of propagation of a circularly polarized laser beam, done with the RSFA [3] for the case of neon ionized by a laser of 800 nm in wavelength and an intensity of $8\times {10}^{14}$ W/cm${}^2$ is shown in part (a) of the figure. The approximation due to T&D [2] produces the result shown in part (b) of the figure, which is taken from Ref. [2]. The two calculations give nearly identical results, showing a slight tilt towards the beam propagation direction.

Figure 5

A momentum distribution measured by the Freiburg group [14] clearly shows the circular motion of a photoelectron produced by a circularly polarized laser beam. The propagation direction of the beam lies along the vertically oriented axis in the figure. The significance of this figure is discussed in Ref. [6].