Low-Energy Photoelectrons in Strong-Field Ionization by Laser Pulses with Large Ellipticity

The 3D photoelectron momentum distributions created by the strong-field ionization of argon atoms and naphthalene molecules with intense, large ellipticity ($\sim 0.7$) femtosecond laser pulses are studied. The experiment reveals the presence of low-energy electrons for randomly oriented naphthalene, but not for argon. Our theory shows that the induced dipole part of the cationic potential facilitates the creation of the low-energy electrons. We establish the conditions in terms of laser pulse parameters and molecular properties for which this type of low-energy electrons can be observed and point to applications thereof.

Figure 1

Photoelectron momentum distributions produced when Ar atoms or naphthalene molecules are ionized by an intense elliptically polarized laser pulse. (a),(b) Experimental isosurface for the 3D PMD of Ar and naphthalene, respectively. (c),(d) Experimental and theoretical 2D PMD for Ar for $|p_x|<0.1$. The helicity and the orientation of the elliptically polarized laser field [in the $yz$ plane—see Eq. (1)] are sketched (in red) between panels (c) and (d).

Figure 2

Photoelectron momentum distributions from the ionization of naphthalene molecules. (a),(b) Experimental 2D PMD for $|p_x|<0.039$ and $|p_x|<0.015$, respectively. A small region around the center of the images has been removed. (c),(d) Theoretical 2D PMD when including the total potential for $|p_x|<0.039$ and $|p_x|<0.015$, respectively. (e),(f) Theoretical 2D PMD obtained when excluding the induced dipole potential for $|p_x|<0.039$ and $|p_x|<0.015$, respectively. The laser is elliptically polarized in the $yz$ plane [Eq. (1)]. The helicity and the orientation of the field ellipse are sketched (in red) between panels (a) and (b).

Figure 3

Photoelectron energy distributions from the ionization of naphthalene molecules. (a) Total energy distribution. (b),(c) Energy distributions for $|p_x|<0.039$ and $|p_x|<0.015$, respectively. In (a), (b), and (c) the red circles denote the experimental data, the black line shows theory with $V_{\mathrm{TOT}}$ [Eq. (2)], and the blue dots without $V_{\mathrm{ID}}$—all curves are normalized to their maximum values. The arrow denotes the energy acquired from the laser pulse by a classical free electron, ${\epsilon }^2{{\tilde{F}}_0}^2/2{\omega }^2$. The presence of low-energy electrons is evident in all cases. A peak at vanishing energy emerges when the transverse momentum $p_x$ is restricted to a narrow range perpendicular to the polarization plane.

Figure 4

Characteristic trajectory leading to low-energy electrons. (a) The full (black) curve with dots superimposed shows the results with the total force ${\mathbf{F}}_{\mathrm{TOT}}=-\nabla V_{\mathrm{TOT}}$, which is displayed along the trajectory at three instants of time. The (red) curve which follows the previously discussed curve most closely shows the trajectory including only the force from the laser field $-\mathbf{F}$, neglecting the Coulomb ${\mathbf{F}}_C=-\nabla V_C$ and the induced dipole ${\mathbf{F}}_{\mathrm{ID}}=-\nabla V_{\mathrm{ID}}$ forces. The last (blue) curve neglects ${\mathbf{F}}_{\mathrm{ID}}$. The molecule with its center of mass at the origin and exit point are shown on scale, and the initial momentum of all trajectories is $(p_x,p_y,p_z)=(0,0,-0.1)$. The dots and numbers correspond to those indicated in (b) showing $-\mathbf{F}$ only. (c) Trajectories as in (a) shown until the end of the laser pulse. (d) Components of the forces along the trajectory in $V_{\mathrm{TOT}}$ during the first optical cycle $T_p=2\pi /\omega$ after electron ejection. Full (dashed) curves denote the $y$ ($z$) components. The color scale is defined in panel (a).