Low-order above-threshold ionization in intense few-cycle laser pulses

The low-energy end of the spectrum of photoelectrons detached from hydrogenic ions exposed to an intense low-frequency few-cycle pulse is calculated within the strong-field approximation (SFA). The effect on the detached photoelectron of the Coulomb field of the nucleus is taken into account quasiclassically. The results are compared with those of an ab initio solution of the time-dependent Schrödinger equation, for the case of an ${\mathrm{He}}^{+}$ ion irradiated by a $400\text{−}\mathrm{nm}$ pulse of $1\times {10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$ peak intensity. Many of the features of the ab initio spectra can be understood within the SFA.

Figure 1

The total detachment probability for an ${\mathrm{He}}^{+}$ ion irradiated by a 4-cycle $800\text{−}\mathrm{nm}$ pulse of zero carrier-envelope phase, as calculated within the SFA with (long-dashed curve) or without (short-dashed curve) the factor $I\left(r\right)$, vs the peak intensity of the pulse. Also shown is the prediction of Eq. (8) (solid curve).

Figure 2

The density of probability $P(E,\widehat{\mathbf{p}})$, in atomic units, that an electron is ejected from an ${\mathrm{He}}^{+}$ ion irradiated by a 4-cycle laser pulse of $400\text{−}\mathrm{nm}$ wavelength and $1\times {10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$ intensity. Thin solid curves: ab initio spectra. Dotted curves: predictions of the tunneling corrected SFA. Thick solid curves: predictions of the continuum and tunneling corrected SFA. (a): $\theta =10°$, $\varphi =0$; (b): $\theta =10°$, $\varphi =\pi ∕2$; (c): $\theta =170°$, $\varphi =\pi ∕2$.

Figure 3

The same as Fig. 2b, but for a laser pulse encompassing only 2 optical cycles.