Molecular orbital tomography using short laser pulses

Recently, a method to image molecular electronic orbitals using high-order harmonic generation was introduced by Itatani et al. [Nature 432, 876 (2004)]. We show that, while the tomographic reconstruction of general orbitals with arbitrary symmetry cannot be performed with long laser pulses, this becomes possible when extremely short pulses are used. This statement is shown both in a simplified wave-packet picture and more formally within the strong-field approximation. We present an analytical formula for the wave-packet composition of the recollision electron. An alternative reconstruction equation based on momentum matrix elements, rather than on dipole matrix elements, is proposed. We present simulations of the procedure for two-dimensional model systems based on numerical solutions of the time-dependent Schrödinger equation.

Figure 1

(Color online) Semiclassical distribution of return momenta on a linear scale (bars) and on a logarithmic scale (crosses) for the laser intensity $5\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ and wavelength $780\mathrm{nm}$. Electrons with an energy of 3.17 times the ponderomotive potential have $k\simeq \pm 2.57\mathrm{a.u.}$ In the inset the time-dependent electric field of the laser pulse is shown.

Figure 2

(Color online) Simulations of orbital tomography. From left to right: The ground state of 2D $\mathrm{H}_2{}^{+}$ with $R=2.0\mathrm{a.u.}$, its first excited state and the ground state of 2D ${\left(\mathrm{H}\text{−}\mathrm{He}\right)}^{2+}$ with $R=2.5\mathrm{a.u.}$ Top: The exact bound-state orbitals. Bottom: The real part of the reconstructed orbitals.