Theory of ultrashort nonlinear multiphoton photoelectric emission from metals

A phenomenological theory of the nonlinear multiphoton electron emission at the surface of a metal is proposed. We consider principally the situation of photocathodes illuminated by UV, visible, or near-infrared, picosecond, or femtosecond laser pulses. For ultrashort pulse duration, the temporal profiles of the electron gas and the lattice temperatures have to be considered separately, because of the local non-equilibrium between the electrons and the phonon gas. Both reflectivity and work function depend on the electron state density in the conduction band. To take into account the observed nonlinear enhancement of the photocurrent density consecutive to this nonequilibrium, we propose to replace the classical multiharmonic integer order N appearing in the generalized Fowler-Dubridge expression of the photoelectric current by a noninteger order k which depends on the absorbed laser intensity and can be related to N by a simple expression. This method makes the treatment of experimental data easier, i.e., the determination of the amplitude of the nonlinearity versus the incident and absorbed laser intensities, the state of polarization, and the angle of incidence of the laser beam. The method also gives a way to compare and analyze experimental data in the range of very high laser intensities until the laser damage threshold of metals, i.e., 100–300 GW/${\mathrm{cm}}^2$. It also makes possible an estimation of the N-photon photoemission cross sections. The application of this model to our experimental data from Au and W, reported earlier, is given as a justification of our model assumptions.