In spatially structured strong laser fields, quantum electrodynamical vacuum behaves like a nonlinear Kerr medium with modulated third-order susceptibility where new coherent nonlinear effects arise due to modulation. We consider the enhancement of v
acuum polarization and magnetization via coherent spatial vacuum effects in the photon-photon interaction process during scattering of a probe laser beam on parallel focused laser beams. Both processes of elastic and inelastic four wave-mixing in structured QED vacuum accompanied with Bragg interference are investigated. The phase-matching conditions and coherent effects in the presence of Bragg grating are analyzed for photon-photon scattering.
We show that a strong laser pulse combined with a strong x-ray pulse can be employed in a detection scheme for characterizing high-energy $gamma$-ray pulses down to the zeptosecond timescale. The scheme employs streak imaging technique built upon the
high-energy process of electron-positron pair production in vacuum through the collision of a test pulse with intense laser pulses. The role of quantum radiation reaction in multiphoton Compton scattering process and limitations imposed by it on the detection scheme are examined.
