Local most-probable routes and classic-quantum correspondence in strong-field two-dimensional tunneling ionization

We study ionization of atoms in strong two-dimensional (2D) laser fields with various forms, numerically and analytically. We focus on the local most-probable tunneling routes (some specific electron trajectories) which are corresponding to the local maxima of photoelectron momentum distributions (PMDs). By making classic-quantum correspondence, we obtain a condition for these routes characterized by the electron position at the tunnel exit. With comparing the identified routes with the classical limit and the partial-decoupling approximation where it is assumed that tunneling is dominated by the main component of the 2D field, some semiclassical properties of 2D tunneling are addressed. The local maxima of PMD related to the local most-probable routes can be used as one of the preferred observables in ultrafast measurements.