Few-cycle laser-pulse-assisted electron-atom potential scattering

$S$-matrix theory of electron-atom scattering assisted by a few-cycle laser pulse is introduced. The result obtained in the first Born approximation corresponds to the direct or single scattering, while the result in the second Born approximation corresponds to the rescattering or double scattering contribution to the laser-assisted scattering process. The rescattered electrons may acquire high energies while moving in the laser pulse. The dependence of the energy spectrum on the value of the carrier-envelope phase and the duration of the laser pulse is investigated. The abrupt cutoffs of the plateau structures in the energy spectra of the process are explained by the classical analysis. It is shown that the height of both the single and double scattering plateaus can be increased by orders of magnitude by choosing the heavier atomic targets.

Figure 1

The DCS for potential scattering of electrons on He atoms in the presence of a linearly polarized few-cycle laser pulse, as a function of the final electron energy $E_{\mathrm{f}}$. Only the direct (single) scattering is included. The laser pulse has a wavelength of 3100 nm and a peak intensity of $4.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, while the CEP is $\varphi =0^{\circ }$. The initial electron energy is $E_{\mathrm{i}}=15$ eV and the scattering angle of the final-state electrons is ${\theta }_{\mathrm{f}}=0^{\circ }$. The number of optical cycles $n_{\mathrm{p}}$ is denoted in each panel.

Figure 2

Classical analysis of the direct scattering solutions for the parameters of Fig. 1. The final electron energy $E_{\mathrm{f}}$ is presented as a function of the scattering time $t$, expressed in laser-pulse durations $T_{\mathrm{p}}$. The number of optical cycles $n_{\mathrm{p}}$ is denoted in each panel.

Figure 3

The DCS for potential scattering of electrons on Ne atoms in the presence of a linearly polarized few-cycle laser pulse, as a function of the final electron energy $E_{\mathrm{f}}$. Both the direct scattering and rescattering are included. The laser wavelength and peak intensity are 3100 nm and $2.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, respectively, while the number of optical cycles is $n_{\mathrm{p}}=4$. The initial electron energy is $E_{\mathrm{i}}=6$ eV and the scattering angle of the final-state electrons is ${\theta }_{\mathrm{f}}=0^{\circ }$. The CEP $\varphi$ is denoted in each panel.

Figure 4

Classical results for the maximum value of the final electron energy in the electron-atom scattering process as a function of the CEP $\varphi$. The other laser field parameters, the initial electron energy, and the scattering angle are the same as in Fig. 3. The results for direct scattering (dashed black line, denoted by D) and rescattering (solid blue line, denoted by R) are presented.

Figure 5

The DCS for potential scattering of electrons on He atoms in the presence of a linearly polarized few-cycle laser pulse, as a function of the final electron energy $E_{\mathrm{f}}$. Both the direct scattering and rescattering are included. The laser pulse has a wavelength of 3300 nm and a peak intensity of $3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The CEP of the pulse is $\varphi =0^{\circ }$ and the number of optical cycles is $n_{\mathrm{p}}=4$. The initial electron energy is $E_{\mathrm{i}}=10$ eV, while the scattering angle ${\theta }_{\mathrm{f}}$ is denoted in each panel.

Figure 6

Classical results for the maximum value of the final electron energy in the electron-atom scattering process as a function of the scattering angle ${\theta }_{\mathrm{f}}$. The laser field parameters and the initial electron energy are the same as in Fig. 5. The results for direct scattering (dashed black line, denoted by D) and rescattering (solid blue line, denoted by R) are presented.

Figure 7

The DCS for potential scattering of electrons on Ar atoms in the presence of a linearly polarized few-cycle laser pulse, as a function of the final electron energy $E_{\mathrm{f}}$. Both the direct scattering and rescattering are included. The laser wavelength and peak intensity are 3000 nm and $1.8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, respectively, while the CEP is $\varphi =0^{\circ }$. The initial electron energy is $E_{\mathrm{i}}=5$ eV and the scattering angle of the final-state electrons is ${\theta }_{\mathrm{f}}=0^{\circ }$. The number of optical cycles $n_{\mathrm{p}}$ is denoted in each panel.

Figure 8

The DCS for potential scattering of electrons in the presence of a linearly polarized few-cycle laser pulse, as a function of the final electron energy $E_{\mathrm{f}}$. Both the direct scattering and rescattering are included. The laser pulse has a wavelength of 3000 nm and a peak intensity of $2.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The CEP of the pulse is $\varphi =0^{\circ }$ and the number of optical cycles is $n_{\mathrm{p}}=4$. The initial electron energy is $E_{\mathrm{i}}=8$ eV, while the scattering angle is ${\theta }_{\mathrm{f}}=0^{\circ }$. The results for scattering of electrons on Xe (upper black line, denoted by Xe) and He atoms (lower red line, denoted by He) are presented.