You have discussions about the Schwarz-Hora effect. I please may give attention to the following publications about this topic and shall be pleased to follow up comments or questions. Heinrich Hora and Peter H. Handel. Kapitza-Dirac effect with lasers and non-resonant interaction for quantum modulation of electron beams (Schwarz-Hora effect) Applied Physics Letters 102, 141119/1-4 (2013). H. Hora and P. H. Handel. Kapitza-Dirac effect and nonresonant nonlinear quantum interaction of laser and electron beams. in High Power, high energy and hig-intensity laser technology and research using extreme light:entering new frontiers with petawatt-class lasers J. Hein, G. Korn and L.O. Silva eds. Proceedings of SPIE Vol. 8780, paper 87801L /1-9.