Recent theoretical work has provided new insight into the physics of Electro-Optic detection of ultrashort relativistic electron beams.1 Typically, Electro-Optic detection has been restricted to bunches longer than ~ 100 fs. This limitation is due to the transverse optical (TO) phonon resonance that most Electro-Optic materials exhibit in the THz range. Once the electron bunch profile becomes short enough so that a significant portion of its frequency components reside above this resonance frequency, the temporal profile of the space charge field begins to distort as it propagates through the crystal. This distortion becomes more significant as the bunch becomes shorter and destroys the ability of current decoding techniques to resolve the original bunch profile. It is possible to circumvent this issue by realizing that for these higher frequency components it is no longer valid to rely on the formalism of Pockels effect. Instead, sum and difference frequency generation must be taken into account. Using nonlinear three-wave mixing to describe the process, a new technique that promises the order of magnitude increase in resolution necessary to measure the ultrashort bunches produced by laser wakefield accelerators has been developed. This technique provides both phase and amplitude information about the generated pulse from which, in principle, the temporal profile can be reconstructed
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