High-order multiphoton laser-assisted elastic electron scattering by Xe in a femtosecond near-infrared intense laser field: Plateau in energy spectra of scattered electrons

Multiphoton free-free transitions were observed in laser-assisted elastic electron scattering (LAES) by Xe atoms in a femtosecond near-infrared intense laser field. The distinct peak structures at the energy shifts of $n$-photons $(n=+1,+2,+3,+4,+5$, and $+6)$ were identified in the observed energy spectrum, and the energy and angular distributions of the LAES signals were in good agreement with those obtained by numerical simulations based on the Kroll-Watson theory. The LAES signal intensities at the scattering angles at 9.1° and 11.8° exhibited a clear plateau structure as a function of the harmonic order $n$, and the mechanism of these nonperturbative LAES processes was interpreted by a classical mechanical description.

Figure 1

(a) A raw image of scattered electrons with the laser field. The abscissa for the energy shift, $\mathrm{\Delta }E$, is drawn as the straight white arrow and the curved ordinate for the auxiliary scattering angle, θ′, is drawn as the curved white arrow. (b) A rescaled image of (a) for enhancing the visibility of weak signals. (c) A raw image of background signals.

Figure 2

Energy spectra of relative intensities of scattered electron signals. The relative intensity of each spectrum is normalized by the peak intensity of the elastic scattering signal. Error bars are estimated from the square roots of signal counts. (a) Red filled circles: electron signals with the laser field. Black open squares: background signals. (b) Red filled circles: the background-subtracted signals obtained by subtracting the background signals from the signals with the laser field. Green line: a LAES spectrum calculated by the Kroll and Watson formula [Eq. (1)]. (c) An expanded view of the square area enclosed by a broken line in (b).

Figure 3

Angular distributions of the LAES signals of (a) $n=+1$, (b) $n=+2$, (c) $n=+3$, (d) $n=+4$, (e) $n=+5$, and (f) $n=+6$ transitions. Red filled circles: recorded LAES signals. Green solid lines: calculated angular distributions by Kroll-Watson theory. The electrons in the range of $\theta <2^{\circ }$ are blocked by a Faraday cup placed in front of the energy analyzer and are not observed.

Figure 4

Logarithmic plots of the LAES signal intensities as a function of $n$ for the scattering angles of (a) $\theta =3.7^{\circ }$, (b) $\theta =6.4^{\circ }$, (c) $\theta =9.1^{\circ }$, and (d) $\theta =11.8^{\circ }$. Red filled circles: observed LAES signals. Green solid lines: LAES signals calculated by Kroll-Watson theory. Broken vertical lines represent the positions of the corresponding cutoff orders, $\left|\xi \right|$. In (a), the data point at $n=5$ is absent because the observed signal intensity after the background subtraction at $\theta =3.7^{\circ }$ in Fig. 3 yielded a negative value.