Electron spectrum of nonlinear cold emission from a metal under the action of a laser shot

The nonlinear emission of electrons from a metal under the action of a femtosecond moderate-intensity laser pulse (laser shot) has been studied. A theoretical model of the process has been constructed based on the 1D nonstationary Schrödinger equation in the vacuum half-space with given boundary conditions for the electron wavefunction. This equation has been solved using the Laplace transformation. It has been assumed that the states of free electrons in a metal, which are described by the Sommerfeld theory of metals, are insignificantly influenced by the laser field. The energy spectrum of emitted electrons has been obtained, and its dependence on the parameters of the lased shot has been found. The calculated spectrum of nonlinear electron emission from a tungsten nanotip under the action of a 6.5-fs-long laser shot generating a field of 9.26 V/nm agrees with the experimental data.