1. State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, China 2. Department of Physics, Shanghai Normal University, Shanghai 200234, China 3. Suzhou Jingpin Advanced Materials Co. Ltd., Jiangsu FOHO Science Park, Fenhu Town, Suzhou 215211, China 4. School of Physics, Peking University, Beijing 100871, China
By applying a nonperturbative quantum electrodynamic theory, we study ponderomotive resonances when an electron beam is scattered by a standing photon wave. Our study shows that the ponderomotive parameter up, the ponderomotive energy per laser-photon energy, for each of the two traveling laser modes possesses a minimum value ℏω/(mec2). Ponderomotive resonances occur only when the ratio of the laser photon energy to the electron rest-mass energy is a fraction, where the denominator is twice the square of a positive integer and the numerator is the total ponderomotive number, which is also a positive integer.
P. L. Kapitza and P. A. M. Dirac, The reflection of electrons from standing light waves, Proc. Camb. Philos. Soc. 29(02), 297 (1933)
https://doi.org/10.1017/S0305004100011105
2
L. S. Bartell, R. R. Roskos, and H. Bradford Thompson, Reflection of electrons by standing light waves: Experimental study, Phys. Rev. 166(5), 1494 (1968)
https://doi.org/10.1103/PhysRev.166.1494
3
H. Schwarz, H. A. Tourtellotte, and W. W. Gaertner, Direct observation of nonlinear scattering of electrons by laser beam, Phys. Lett. 19(3), 202 (1965)
https://doi.org/10.1016/0031-9163(65)90066-1
4
Y. Takeda and I. Matsui, Electron reflection by standing wave of giant pulse laser, J. Phys. Soc. Jpn. 25(4), 1202 (1968)
https://doi.org/10.1143/JPSJ.25.1202
R. Z. Olshan, A. Gover, S. Ruschin, and H. Kleinman, Observation of electron trapping and phase-area displacement in the interaction between an electron beam and two counter-propagating laser beams, Phys. Rev. Lett. 58(5), 483 (1987)
https://doi.org/10.1103/PhysRevLett.58.483
12
L. Rosenberg, Effect of virtual Compton scattering on electron propagation in a laser field, Phys. Rev. A 49(2), 1122 (1994)
https://doi.org/10.1103/PhysRevA.49.1122
D. S. Guo and G. W. F. Drake, Multiphoton ionization in circularly polarized standing waves, Phys. Rev. A 45(9), 6622 (1992)
https://doi.org/10.1103/PhysRevA.45.6622
15
D. S. Guo, T. Åberg, and B. Crasemann, Scattering theory of multiphoton ionization in strong fields, Phys. Rev. A 40(9), 4997 (1989)
https://doi.org/10.1103/PhysRevA.40.4997
16
L. V. Keldysh, Diagram technique for nonequilibrium processes, Sov. Phys. JETP 20(4), 1307 (1965)
D. S. Guo, J. T. Zhang, Z. R. Sun, J. T. Wang, J. Gao, Z.-W. Sun, and R. R. Freeman, Even-odd harmonics generated from above-threshold ionization, Front. Phys. 9(1), 69 (2014)
https://doi.org/10.1007/s11467-013-0378-9
20
D. S. Guo, C. Yu, J. Zhang, J. Gao, Z. W. Sun, and Z. Sun, On the cutoff law of laser induced high harmonic spectra, Front. Phys. 10(2), 215 (2015)
https://doi.org/10.1007/s11467-014-0447-8
21
C. Yu, J. T. Zhang, Z.-W. Sun, Z. R. Sun, and D.-S. Guo, A nonperturbative quantum electgrodynamic approach to the laser induced high harmonic generation, Front. Phys. 10, 103202 (2015)
https://doi.org/10.1007/s11467-014-0429-x
22
J. Gao, D. S. Guo, and Y. S. Wu, Resonant abovethreshold ionization at quantized laser intensities, Phys. Rev. A 61(4), 043406 (2000)
https://doi.org/10.1103/PhysRevA.61.043406
X. Hu, H. Wang, and D. S. Guo, Phased Bessel functions, Can. J. Phys. 86, 863 (2008)
27
D. S. Guo and G. W. F. Drake, Stationary solutions for an electron in an intense laser field (II): Multimode case, J. Phys. A 25(20), 5377 (1992)
https://doi.org/10.1088/0305-4470/25/20/018
28
D. L. Freimund and H. Batelaan, Bragg scattering of free electrons using the Kapitza−Dirac effect, Phys. Rev. Lett. 89(28), 283602 (2002)
https://doi.org/10.1103/PhysRevLett.89.283602
29
X. F. Li, J. T. Zhang, Z. Z. Xu, P.M. Fu, D. S. Guo, and R. R. Freeman, Theory of the Kapitza−Dirac diffraction effect, Phys. Rev. Lett. 92(23), 233603 (2004)
https://doi.org/10.1103/PhysRevLett.92.233603