Controlling polarization of attosecond pulses with plasmonic-enhanced bichromatic counter-rotating circularly polarized fields

The use of bichromatic counter-rotating laser field is known to generate high-order harmonics with nonzero ellipticity. By combining such laser field with a plasmonic-enhanced spatially inhomogeneous field, we propose a way to influence the subcycle dynamics of the high-harmonic generation process. Using the numerical solution of the time-dependent Schrödinger equation combined with classical trajectory Monte Carlo simulations, we show that the change of the direction and the strength of the plasmonic field selectively enhances or suppresses certain recombining electron trajectories. This in turn modifies the ellipticity of the emitted attosecond pulses.

Figure 1

Conceptual illustration of the HHG driven by plasmonic-enhanced bichromatic counter-rotating circularly polarized fields. An incoming low intensity bicircular counter-rotating circularly polarized field (in blue) interacts with bowtie-shaped nano-objects and, as a result, a much intense spatially nonhomogeneous laser field is generated, able to produce polarization-resolved higher-order harmonics by the atoms located in the vicinity of the bow-tie elements.

Figure 2

High-order harmonic spectra (a)–(c) and time-frequency maps (d)–(f) calculated by solving 2D-TDSE. (g)–(i) represent the return energy versus time of the ionized electrons calculated from classical trajectory Monte Carlo simulations. The harmonics plotted in red (or blue) color in (a)–(c) are right- (or left-)circularly polarized. The Lissajous figure of the total bichromatic counter-rotating circularly polarized driving field is trefoil and shown in the inset. The field lobes are marked numerically as they are traversed in time, i.e., in time, the field follows the order 1-2-3 of the lobes. Also, the field lobes are color coded with respect to their ionization and recombination times. In other words, the return energy and time of the electron, which was ionized during, say, lobe 1 (green) is represented by green color in (g)–(i). Moreover, the first row [(a), (d), and (g)] is obtained for the spatially homogeneous field, i.e., ${\beta }_x={\beta }_y=0$. The second [(b), (e), and (h)] and third [(c), (f), and (i)] rows correspond to the cases when the plasmonic field is applied along $x$ axis (${\beta }_x=0.01$ a.u.; ${\beta }_y=0$) and along $y$ axis (${\beta }_x=0;{\beta }_y=0.01$ a.u.), respectively (see the text for more details).

Figure 3

Classical electron trajectories, which are returning back to the parent ion, ionized during three different lobes of the field. The plasmonic field is employed along $x$ direction with ${\beta }_x=0.01$ a.u. Some exemplary trajectories are highlighted by black arrows. The insets indicate the lobe during which the ionization takes place and the rotation direction of the laser electric field vector.

Figure 4

The total time-dependent electric field (in red) corresponding to an attosecond pulse train for different strength of plasmonic field along $x$ direction. The $x$ component (in blue), $y$ component (in orange), and Lissajous figure (in green) of the total field are also shown. $18\text{th}–24\text{th}$ harmonics window is used to synthesize an attosecond pulse train.