  In modern high-gain free-electron lasers, ultra-fast photon pulses designed
for studying chemical, atomic and biological systems are generated from a
serial of behaviors of high-brightness electron beam at the time-scale ranging
from several hundred femtoseconds to sub-femtosecond. Currently, radiofrequency
transverse deflectors are widely used to provide reliable, single-shot electron
beam phase space diagnostics, with a temporal resolution of femtosecond. Here,
we show that the time resolution limitations caused by the intrinsic beam size
in transverse deflectors, can be compensated with specific
transverse-to-longitudinal coupling elements. For the purpose, an undulator
with transverse gradient field is introduced before the transverse deflector.
With this technique, a resolution of less than 1fs root mean square has been
theoretically demonstrated for measuring the longitudinal profile and/or the
micro-bunching of the electron bunch.
