Exponential modulation of fowler–Nordheim emission by an external quasistatic optical field

We analyze the modulation of Fowler–Nordheim field emission by an external optical field operating in the quasistatic regime. When the characteristic electron tunneling time is much shorter than the optical period, the emission current is governed by the instantaneous electric field at the emitter surface rather than by photon absorption processes. Because of the exponential dependence of Fowler–Nordheim tunneling on the electric field amplitude, even a relatively weak optical perturbation can produce a pronounced modulation of the emission current. This effect is strongly enhanced at nanoscale emitters due to geometric field enhancement. Theoretical estimates indicate that realistic parameters can yield modulation depths of several orders of magnitude. The proposed mechanism does not rely on plasmonic resonances or conventional photoemission processes and may provide a simple route toward optical control of ultrafast electron sources and nanoscale vacuum electronic devices.