Relativistic ionization rescattering with tailored laser pulses

The interaction of relativistically strong tailored laser pulses with an atomic system is considered. Due to special tailoring of the laser pulse, the suppression of the relativistic drift of the ionized electron and a dramatic enhancement of the rescattering probability is shown to be achievable. The high harmonic generation rate in the relativistic regime is calculated and shown to be increased by several orders of magnitude compared to the case of conventional laser pulses. The energies of the revisiting electron at the atomic core can approach the MeV domain, thus rendering hard x-ray harmonics and nuclear reactions with single atoms feasible.

Figure 1

By using optimized tailored pulses in the form of an APT instead of conventional sinusoidal pulses it is possible to reduce significantly the drift of the ionized electrons due to the Lorentz force of the laser field (the ionized electron trajectory with zero initial momentum in the sinusoidal pulse is shown as a dashed line, in the tailored pulse as a solid line). Therefore the rescattering probability can be increased by several orders of magnitude in the relativistic regime of laser-atom interactions. $x$ and $z$ are the laser polarization and propagation directions, respectively.

Figure 2

The tailored laser pulse in the form of an APT, with each pulse duration in the train being $\omega \tau =0.12\pi$: (a) Phase dependence of the electric field $\left[E\left(\eta \right)\right]$ of the tailored pulse (solid line) compared with a sinusoidal field (dashed line) with equal average intensities and central angular frequency $\omega =0.1\mathrm{a.u.}$ and (b) frequency spectrum $\left[S\left(k\right)\right]$ of the tailored pulse. The frequency components are phase locked.

Figure 3

Trajectory and kinetic energy of an HHG electron in the tailored wave (solid line) and in a sinusoidal wave (dashed line) with an averaged laser intensity of $5\times {10}^{19}\mathrm{W}∕{\mathrm{cm}}^2$. ($x$ and $z$ are the polarization and propagation direction of the laser field, respectively.) In the sinus wave, the rescattering electron is ionized with initial $z$-component of momentum $p_{z0}=-97\mathrm{a.u.}$, while in the tailored wave with $p_{z0}=-6\mathrm{a.u.}$

Figure 4

Harmonic emission rate in laser propagation direction via ${\log }_{10}(d{w}_n∕d\Omega )$ in Eq. (5), as a function of the harmonic energy with a laser intensity of (a) $5\times {10}^{18}\mathrm{W}∕{\mathrm{cm}}^2$ and (b) $5\times {10}^{19}\mathrm{W}∕{\mathrm{cm}}^2$. The main angular frequency is $\omega =0.1\mathrm{a.u.}$ The ionization potential is (a) $I_p=28\mathrm{a.u.}$ and (b) $I_p=62\mathrm{a.u.}$, respectively: (grey) within the dipole approximation and a sinusoidal field (dashed) with respect to the Klein-Gordon equation and a sinusoidal field, and (black) with respect to the Klein-Gordon equation and a tailored pulse.