Photoelectron emission from metal surfaces by ultrashort laser pulses

Electron emission from metal surfaces produced by short laser pulses is studied within the framework of the distorted-wave formulation. The proposed approach, named surface-Volkov (SV) approximation, makes use of the band-structure based (BSB) model and the Volkov phase to describe the interaction of the emitted electron with the surface and the external electric field, respectively. The BSB model provides a realistic representation of the surface, based on a model potential that includes the main features of the surface band structure. The SV method is applied to evaluate the photoelectron emission from the valence band of Al(111). Angular and energy distributions are investigated for different parameters of the laser pulse, keeping in all cases the carrier frequency larger than the plasmon one.

Figure 1

Photoelectron emission probability from the valence band of Al(111), as a function of the electron energy, for three different ejection angles: ${\theta }_e=30°$, 45°, and 90°. The parameters of the laser field are: $F_0=0.1\mathrm{a.u.}$ and $\omega =1\mathrm{a.u.}$, and the duration of the pulse is: (a) $\tau =4\mathrm{a.u.}$ and (b) $\tau =40\mathrm{a.u.}$

Figure 2

Similar to Fig. 1 for a laser pulse with a duration $\tau =100\mathrm{a.u.}$

Figure 3

Electron emission probability, as a function of the electron energy, for the ejection angle ${\theta }_e=90°$. The parameters of the laser field are: $F_0=0.1\mathrm{a.u.}$, $\omega =1\mathrm{a.u.}$, and $\tau =40\mathrm{a.u.}$ Dashed line, similar to Fig. 1; solid line (full circles), results including EI asymptotic conditions, as explained in the text.

Figure 4

Electron emission probability, as a function of the electron energy, for the ejection angle ${\theta }_e=90°$, considering different carrier-envelope phases. The parameters of the laser field are: $F_0=0.1\mathrm{a.u.}$, $\omega =1\mathrm{a.u.}$, and $\tau =40\mathrm{a.u.}$ Solid line, $\phi =0$; dotted line, $\phi =\pi ∕2$; dashed-dotted line, $\phi =3\pi ∕4$; dashed line, $\phi =\pi$.

Figure 5

Energy distribution of emitted electrons, as a function of the electron energy, for a laser field with $F_0=0.1\mathrm{a.u.}$ and $\omega =1\mathrm{a.u.}$ The duration of the pulse is: (a) $\tau =4\mathrm{a.u.}$ and (b) $\tau =40\mathrm{a.u.}$

Figure 6

Similar to Fig. 5 for a laser pulse with a maximum strength $F_0=0.05\mathrm{a.u.}$, a pulse duration $\tau =40\mathrm{a.u.}$, and a carrier frequency (a) $\omega =1\mathrm{a.u.}$ and (b) $\omega =0.5\mathrm{a.u.}$