Temporal laser pulse shape effects in nonlinear Thomson scattering
  The influence of the laser pulse temporal shape on the Nonlinear Thomson Scattering on-axis photon spectrum is analyzed in detail. Using the classical description, analytical expressions for the temporal and spectral structure of the scattered radiation are obtained for the case of symmetric laser pulse shapes. The possibility of reconstructing the incident laser pulse from the scattered spectrum averaged over interference fringes in the case of high peak intensity and symmetric laser pulse shape is discussed. 
Vasily Kharin, Daniel Seipt, Sergey Rykovanov
physics.plasm-ph