Proposal for obtaining laser beat-frequency radiation in the far-infra red by the Smith-Purcell effect

In 1953 S. J. Smith and E. M. Purcell (Phys. Rev. 92, p. 1069) obtained visible radiation by passing an electron beam over the surface of a metallic optical grating. Subsequently other, less detailed, reports by W. W. Salisbury confirmed this effect. In this paper theoretical predictions are given of the power output, line width and coherence of such a source of radiation both in the visible and far infra red regions of the spectrum. When a thermionically derived electron beam is used, the random effect of shot emission does not render the resultant radiation completely incoherent. The coherence time is equal to the time of flight of an electron across the grating and thus the radiation is quasi-coherent. If however the arrival of an electron at the grating is not a completely random event, as when the electron beam is "pre-bunched", then there is a greatly enhanced radiative output at the bunching frequency or at harmonics of this frequency. When a photoemissive cathode is illuminated by two coherent light sources (i.e. lasers) of different optical frequencies the photocurrent has an A.C. component at the difference frequency between the two light sources. This corresponds to a form of partial "emission bunching" of the photo electron beam. The use of a suitably designed grating in conjunction with such an electron beam (suitably accelerated) would result in the production of different frequency radiation. This contribution presents some numerical calculations on this topic and describes briefly some initial experiments.