Extending Electro-Optic Detection of Short Particle Beams Beyond the Transverse Phonon Resonance

A technique to noninvasively measure the longitudinal profile of an ultrashort charged particle beam is developed. This technique is based on three-wave mixing of the particle beam's self-fields and an optical probe in a nonlinear material. The resulting mixed field is then diagnosed by a cross-correlating frequency resolved optical gate, which provides both frequency and phase information about the generated pulse from which, in principle, the temporal profile can be reconstructed. An equation for the generated fields as well as numerical results showing the effects of a chirped probe pulse are presented.