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.Comment: 18 pages, 8 figure
