Fowler - Nordheim emission modified by laser pulses in the adiabatic regime

We investigate enhanced field emission due to a continuous or pulsed oscillating field added to a constant electric field E at the emitter surface. When the frequency of oscillation, field strength, and property of the emitter material satisfy the Keldysh condition γ < 1/2 one can use the adiabatic approximation for treating the oscillating field, i.e. consider the tunneling through the instantaneous Fowler-Nordheim barrier created by both fields. Due to the great sensitivity of the emission to the field strength the average tunneling current can be much larger than the current produced by only the constant field. We carry out the computations for arbitrary strong constant electric fields, beyond the commonly used Fowler-Nordheim approximation which exhibit in particular an important property of the wave function inside the potential barrier where it is found to be monotonically decreasing without oscillations. PACS: 03.65.Ge; 79.70.+q; 85.45.Db; 85.45.Bz In a constant electric field the current due to electron tunneling from a metal is described by the commonly used Fowler-Nordheim (FN) equations [1]. They are modified to include arbitrary strong fields, see e.g. [2] and [3], though for practical needs the low field approximation made in [1] are usually sufficient. The triangular potential barrier used in these articles was corrected for image forces by Schottky [4]. They are important in constant electric fields, but an adequate method for treating them is not clear under laser radiation. Their physical origin is based on the rearrangement of the electron distribution inside the emitters; a time dependent process whose duration is not known well. To simplify the problem (and losing some precision) the Schottky term will not be included here. In experiments the constant electric fields are often supplemented by short laser pulses with electric component of amplitude F orthogonal to the metal surface. Here we carry out computations for a simple one-dimensional model of the emitting surface in order to explore a practically important [5], [6] situation when F can be treated adiabatically. This is possible under suitable conditions on the strengths of the constant field E and laser field F , frequency ω of the electromagnetic oscillations, and the emitter properties. A pulse of duration T is Also Department of Physics