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We derive a new scaling law for the photon spectral density in nonlinear Thomson/Compton scattering, extending the findings of Heinzl, Seipt, and Kämpfer [Phys. Rev. A 81, 022125 (2010)PLRAAN1050-294710.1103/PhysRevA.81.022125]. This allows one to easily include the effects of general scattering geometries, e.g., side injection, and of a finite-size detector on the photon spectrum. The scaling law is employed to study substructures emerging in the nonlinear Thomson/Compton spectra due to temporally shaped laser pulses scattering off relativistic electrons. We determine optimum scattering geometries for an experimental verification of these substructures

Scaling law for the photon spectral density in the nonlinear Thomson-Compton scattering