Parallel and perpendicular transitions in the dissociation of O$_{2}^{+}$ caused by an ultrashort intense laser pulse

Laser-induced dissociation of O$_{2}^{+}$ has been experimentally studied using ultrashort ($\sim $50 fs) intense ($\sim $10$^{14}$ W/cm$^ {2})$ laser pulses at 790 nm. The O$^{+}$ and O fragments are measured in coincidence with a 3-dimensional momentum imaging system, which provides both angular and kinetic energy release (KER) distributions for dissociation. By analyzing the angular distribution of a specific range in the KER spectrum, the dissociation pathway may be deduced. In particular, a single photon parallel transition ($\Delta \Lambda $=0) is expected to have a cos$^{2}$\textit{$\theta $} distribution, while a perpendicular one ($\Delta \Lambda $=1) leads to a sin$^{2}$\textit{$\theta $} distribution. Therefore, a dissociation pathway requiring the exchange of $n \quad \Delta \Lambda $=0 photons and $m \quad \Delta \Lambda $=1 photons is expected to have a cos$^{2n}$\textit {$\theta $}sin$^{2m}$\textit{$\theta $} distribution. Thus, knowing $n$ and $m$ along with the KER range allows a plausible identification of the dissociation pathway.