Rescattering time-energy analysis of high-order above-threshold ionization in few-cycle laser fields

A Wigner distributionlike function based on the improved strong-field approximation theory is proposed to calculate the rescattering time-energy distribution (RTED) of high-energy photoelectrons of atomic above-threshold ionization process in few-cycle laser fields with different frequencies. The RTED shows bell-like stripes and the outermost stripe is compared with semiclassical results given by the simple-man model with consideration of different positions of tunnel exit and different initial longitudinal momenta. Analysis indicates the existence of the tunnel exit. However, though it shifts farther away from the core with decreasing frequency, the position of the tunnel exit is significantly less than the prediction by adiabatic theory even for the low-frequency case which is well in the tunneling regime. Our results also imply that the effect of the tunnel exit is more important than that of the initial longitudinal momentum at the tunnel exit for the backward-scattering electrons. Moreover, the inner stripe structures in the RTED are attributed to interference between electrons with the same final energy emitted at different ionization times.