Ultrafast laser-induced electron emission from multiphoton to optical tunneling

Abstract

Based on a time-dependent quantum model, a relation between the onset of the optical tunneling regime and the metal work function is determined. In the multiphoton regime, the number of photons required for absorption is reduced from $n=3$ (at pulse length $\ensuremath{\tau}>20$ fs) to $n=2$ (at $\ensuremath{\tau}<8$ fs) due to the energy uncertainty principle. The phase of the laser is important for optical tunneling, but is only manifest in the multiphoton regime when the number of laser cycles is close to or less than 1. The effect of the field gradient at the tip can be important when the radius of the tip is 40 nm or smaller. The extension of the model to include nonequilibrium electron distribution due to ultrafast laser excitation is discussed. Comparisons with other models and experimental findings are presented.