Tomographic Extraction of the Internuclear Separation Based on Two-Center Interference with Aligned Diatomic Molecules

We experimentally investigate the two-dimensional photoelectron momentum spectra of aligned diatomic molecules in an intense laser field. Our results reveal a novel prominent valley structure in the molecular alignment dependence of the high-energy photoelectron spectra along the laser polarization. Resorting to the molecular strong-field approximation and a simple semiclassical analysis, we show that this valley structure stems from the destructive two-center interference of the laser-driven rescattered electrons in diatomic molecules. Based on this two-center interference with aligned diatomic molecules, we demonstrate for the first time a tomographic method to extract the molecular internuclear separation, providing a more straightforward approach of molecular imaging, in comparison with, e.g., laser-induced electron diffraction and fixed-angle broadband laser-driven electron scattering.

Figure 1

The measured two-dimensional photoelectron momentum spectra of aligned diatomic molecules. $p_z$ and $p_x$ are the momenta of the electron along and perpendicular to the laser polarization, respectively. (a) For ${\mathrm{N}}_2$ with the alignment angle ${\theta }_L=30°$, (b) for ${\mathrm{N}}_2$ with ${\theta }_L=90°$, and (c) for ${\mathrm{O}}_2$ with ${\theta }_L=90°$. The peak intensities of the laser pulses are $1.2\times 10^{14}$ for ${\mathrm{N}}_2$ and $1.0\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ for ${\mathrm{O}}_2$, respectively. The momentum spectra have not been symmetrized, and data points in the white area are removed because of the influence of the spectrometer magnetic field [26, 33]. All of the spectra are normalized by 1 at their maxima.

Figure 2

Density plot of the measured (a) and simulated (b) photoelectron spectra of the back-rescattered electrons in the energy region of 25–70 eV with respect to the molecular alignment angle from 0° to 90°. The two dashed curves in panel (b) are based on the relation of $\cos [(p-k)R_0\cos {\theta }_L/2]=0$ for the long (red) and short (white) orbits, respectively. For more details, see text.

Figure 3

(a) Density plot of the measured photoelectron spectra along the laser polarization direction with respect to the alignment angle from 0° to 90° with 35 fs, 400 nm laser pulses with peak intensity of $2.0\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$. (b) Extracted electron yields in the energy region of $22.5\mathrm{eV}<E<24.5\mathrm{eV}$ with respect to the alignment angle. The error bars represent the standard deviation resulting from experimental uncertainties. The smooth evolution of the yields with the alignment angle is fitted to the interference term $\cos (pR\cos {\theta }_L/2{)}^2$. The solid red line is the yield calculated using the best-fit internuclear separation. The dashed black and blue lines are the calculated yields using the internuclear separations of 1.863 and 2.263 a.u., respectively. (c) The retrieved internuclear separations for various photoelectron energies. The error bars denote the error in the fitting with the least square method. The blue line denotes the well adopted internuclear separation of ${\mathrm{N}}_2$, $R_0=2.068\mathrm{a}.\mathrm{u}.$.