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(1961). An Estimation of Smith-Purcell Effect as the Light Source in the Infra-red Region. Optica Acta: International Journal of Optics: Vol. 8, No. 1, pp. 25-31.

The radiation emitted when a beam of electrons passes over the surface of a perfectly conducting metal is discussed. The electrons constituting the beam all move with the same velocity in the same straight line but the charge density along the beam may vary in an arbitrary manner. The metallic surface considered is any surface which may be obtained by a small perturbation of a plane. Perturbation theory is used to derive explicit expressions for the electromagnetic field generated. The mathematical techniques employed involve the use of the angular-spectrum-of-plane-waves representation of the electromagnetic field. The results obtained go far beyond those of previous (two-dimensional) theories. The special case of a sinusoidally varying surface is treated in detail and a numerical calculation yields the physically important quantity---the number of optical photons emitted per charge per unit path length---for a particular arrangement.

A rigorous solution is derived for the problem of radiation of the Smith–Purcell type (Smith and Purcell 1953) extracted from a radio-frequency bunched electric-current sheath, above a plane exhibiting a periodically varying surface reactance. The plane is regarded as a model of an optical reflection grating. The solution indicates that the presence of the grating will give rise to electromagnetic resonance effects which are closely related to the so-called Wood anomalies (Wood 1935; Twersky 1956; Hessel 1960; Hessel and Oliner 1962; Stewart and Gallaway 1962), encountered in optical-grating spectroscopy. Utilization of these resonances may be advantageous in the generation of millimeter waves.

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.