Figure 1

Sequential two-photon ionization of H by a Gaussian-shaped pulse of 30 fs duration and resonant carrier frequency of $\omega =3/8\text{a.u.}=10.20$ eV, which fits to the energy of the H(1$s$)–H(2$p$) excitation. Shown are the populations of the ground state H(1$s$) and of the resonant state H(2$p$) as functions of the peak intensity after the laser pulse has expired. The vertical lines indicate the peak intensities at which the spectra depicted in Fig. 2 are computed.Reuse & Permissions

Figure 2

Sequential two-photon ionization of H by a Gaussian-shaped pulse of 30 fs duration and resonant carrier frequency of $\omega =E_R=3/8\mathrm{a}.\mathrm{u}.=10.20\mathit{eV}$, which fits to the energy of the H(1$s$)–H(2$p$) excitation. Shown are the photoelectron spectra computed via Eqs. (2) for different peak intensities indicated in the figure near each curve. The central electron energy ${\varepsilon }_0=2\omega -E_F=0.25\mathrm{a}.\mathrm{u}.=6.80\mathit{eV}$ at which the photoelectron spectrum has its maximum in the weak-field case is indicated by a vertical line.Reuse & Permissions

Figure 3

Sequential two-photon ionization of H by a Gaussian-shaped pulse of 30 fs duration, carrier frequency of $\omega =3/8\text{a.u.}=10.20$ eV, and peak intensity of $1.3\times {10}^{13}$ W/cm${}^2$. Shown are the photoelectron spectrum computed numerically (open circles; taken from Fig. 2) and the spectrum obtained in the stationary phase approximation via the explicit expression (7) (solid curve). The two individual contributions to the spectrum, describing in Eq. (7) the separate distributions of photoelectrons emitted at times when the pulse arrives and expires, are shown by broken curves.Reuse & Permissions

Figure 4

Intense laser pulse of resonant carrier frequency induces a time-dependent coupling $\Delta g\left(t\right)$ between the ground and intermediate states. The energies of the resulting two decoupled resonances follow adiabatically the pulse envelope $g\left(t\right)$ in two opposite directions (dashed curves). As a result, the photoelectron emitted by a second photon along the pulse envelope has at every moment $t$ predominantly a specific kinetic energy $\varepsilon$. These are the times at which the energies of the decoupled resonances move across the energy position $\delta =\varepsilon -{\varepsilon }_0$ of the continuum state. These passage times and the kinetic electron energy are simply connected via $\varepsilon =2\omega -E_F\mp \Delta g\left(t_s\right)$. The pulse envelope first grows and then falls, and for a Gaussian pulse there are exactly two times at which the emitted electron wave has the same energy $\varepsilon$. These two waves emitted with a time delay with respect to each other interfere, giving rise to the strongly modulated distribution of the photoelectrons shown on the energy axis. Resonance $|-\rangle$ is responsible for the low-energy part of the spectrum, and resonance $|+\rangle$ for the high-energy part.Reuse & Permissions

Figure 5

Resonant Auger electron spectrum of Ne computed for a Gaussian-shaped pulse of 5 fs duration, carrier frequency of 867.12 eV, and peak intensity of $2\times {10}^{18}$ W/cm${}^2$. Shown are the spectrum computed numerically via Eq. (8)) as described in Refs. [28, 36] (open circles) and the spectrum obtained in the stationary phase approximation via the explicit expression (13) (solid curve). The two individual contributions to the spectrum, from times when the pulse arrives and expires, are shown by broken curves.Reuse & Permissions