Resonances in the Smith–purcell Effect

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.