Local most-probable routes and classical-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 associated with specific electron trajectories, which correspond to the local maximal amplitudes in photoelectron momentum distributions. By making classic-quantum correspondence, we obtain a simple criterion for these routes which is associated with the electron position at the tunnel exit. With comparing the identified routes with the classical limit and the single-color limit 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 Coulomb effect is also explored. Our work facilitates relevant studies on attosecond-resolved probing of electron motion with 2D laser fields.