Limits of Strong Field Rescattering in the Relativistic Regime

Recollision for a laser driven atomic system is investigated in the relativistic regime via a strong field quantum description and Monte Carlo semiclassical approach. We find the relativistic recollision energy cutoff is independent of the ponderomotive potential $U_p$, in contrast to the well-known $3.2U_p$ scaling. The relativistic recollision energy cutoff is determined by the ionization potential of the atomic system and achievable with non-negligible recollision flux before entering a “rescattering free” interaction. The ultimate energy cutoff is limited by the available intensities of short wavelength lasers and cannot exceed a few thousand Hartree, setting a boundary for recollision based attosecond physics.

Figure 1

(a) Trajectory (solid red line) for a photoelectron born (${\eta }_B$) and returning to the parent ion (${\eta }_R$) in an oscillating electric field (dashed blue line) for the peak $3.2U_p$ recollision. Corresponding ionization probability current $\mathbf{j}(\mathbf{r},{\eta }_B)$ for ${\mathrm{Ar}}^{4+}$ ionization at $4.6\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, 2400 nm (b); and ${\mathrm{Ar}}^{9+}$, $1.6\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$, 200 nm (c). In (b) and (c) the initial localized $\mathbf{j}(0,{\eta }_B)$ magnitude is divided by ten.

Figure 2

Normalized differential rescattering flux (a) via RCCSFA (line) and SCMC (symbol) for the laser wavelength $\lambda =800\mathrm{nm}$. Line color scales with ${\mathrm{\Gamma }}_R$: ${\mathrm{Ar}}^{5+}$ at $5.8\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=0.06$, square); ${\mathrm{Ar}}^{7+}$ $2.7\times {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=0.7$, circle); ${\mathrm{Ar}}^{8+}$ $5.6\times {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=3.8$, triangle); ${\mathrm{Ar}}^{8+}$ $1.3\times {10}^{17}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=13$, diamond); ${\mathrm{Ar}}^{8+}$ at $6\times {10}^{17}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=140$, square); ${\mathrm{Ar}}^{9+}$ at $1\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=320$, circle); ${\mathrm{Ar}}^{11+}$ at $2.8\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=1700$, triangle); ${\mathrm{Ar}}^{13+}$ at $6.3\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=6100$, diamond); ${\mathrm{Ar}}^{14+}$ at $1.3\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ (${\mathrm{\Gamma }}_R=20000$, square). In (a) the change from traditional rescattering (blue) to the relativistic cutoff region (orange) is highlighted in the background and a shadow line gives the typical highest possible $d{\overline{F}}_R/dϵ$ at optical frequencies. For clarity, long and short contributions to $d{\overline{F}}_R/dϵ$ are summed in the nonrelativistic limit ${\mathrm{\Gamma }}_R<1$. For RCCSFA with argon HCI [56], $d{\overline{F}}_R/dϵ$ at cutoff as a function of $U_p$ is shown in (b) and the relationship between $U_p$ and the recollision cutoff energy is given (c) for laser wavelengths 80 nm (blue), 800 nm (red), and 8000 nm (black) with shading to aid the eye.

Figure 3

ATI as a function of laser intensity and wavelength for photoelectron energies near $10U_p$. Blue lines indicate $U_p=10$, 100, 1000 a.u. The dashed line corresponds to ${\mathrm{\Gamma }}_R=1$. The color scale for ATI spans from ${10}^{-30}$ to ${10}^{-6}$ a.u.