Laser powered dielectric structures achieve high-gradient particle acceleration by taking advantage of modern laser technology capable of producing electric fields in excess of 10GV/m. These fields can drive the bulk dielectric beyond its linear response, and break the phase synchronicity between the accelerating field and the electrons. We show how control of the pulse dispersion can be used to compensate the effect of self-phase modulation and maximize the energy gain in the laser accelerator.In our experiment, a high brightness 8MeV e-beam is used to probe accelerating fields of 1.8GV/m in a grating-reset dielectric structure illuminated by a 45fs laser pulse with a fluence of 0.7J/cm$^2$.
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