Observation of relativistic mass shift effects during high-intensity laser-electron interactions

The transition to multiphoton electron scattering in a high-intensity laser focus occurs when the oscillatory energy of a free electron in the laser field approaches the electron rest energy. Under these conditions the electron recoil due to the laser-field momentum can no longer be ignored, and free electrons acquire momentum in the direction of the wave vector of the laser. This momentum was predicted from both quantum-mechanical1 – 5 and classical considerations6,7 in the 1960’s and in a series of later calculations.8 – 13 A particularly simple formulation of the forward momentum in terms of conservation of energy and momentum from the field was shown by Reiss9 and by Corkum et al.14 The longitudinal momentum pz, which accompanies the energy absorption from multiple scattering in the focused laser field, is related to the perpendicular momentum by9,14