Abstract
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 u p , the ponderomotive energy per laser-photon energy, for each of the two traveling laser modes possesses a minimum value ћω/(m e c 2). 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. L. Kapitza and P. A. M. Dirac, The reflection of electrons from standing light waves, Proc. Camb. Philos. Soc. 29(02), 297 (1933)
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)
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)
Y. Takeda and I. Matsui, Electron reflection by standing wave of giant pulse laser, J. Phys. Soc. Jpn. 25(4), 1202 (1968)
P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, High-intensity Kapitza–Dirac effect, Phys. Rev. Lett. 61(10), 1182 (1988)
D. L. Freimund, K. Aflatooni, and H. Batelaan, Observation of the Kapitza–Dirac effect, Nature 413, 142 (2001)
M. V. Fedorov, The Kapitza–Dirac effect in a strong radiation field, Sov. Phys. JETP 25(5), 952 (1967)
M. V. Fedorov, Stimulated scattering of electrons by photons and adiabatic switching on hypothesis, Opt. Commun. 12(2), 205 (1974)
R. Gush and H. P. Gush, Electron scattering from a standing light wave, Phys. Rev. D 3(8), 1712 (1971)
E. A. Coutsias and J. K. McIver, Nonrelativistic Kapitza–Dirac scattering, Phys. Rev. A 31(5), 3155 (1985)
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)
L. Rosenberg, Effect of virtual Compton scattering on electron propagation in a laser field, Phys. Rev. A 49(2), 1122 (1994)
M. A. Efremov and M. V. Fedorov, Wavepacket theory of the Kapitza–Dirac effect, J. Phys. B 33(20), 4535 (2000)
D. S. Guo and G. W. F. Drake, Multiphoton ionization in circularly polarized standing waves, Phys. Rev. A 45(9), 6622 (1992)
D. S. Guo, T. Aberg, and B. Crasemann, Scattering theory of multiphoton ionization in strong fields, Phys. Rev. A 40(9), 4997 (1989)
L. V. Keldysh, Diagram technique for nonequilibrium processes, Sov. Phys. JETP 20(4), 1307 (1965)
D. M. Wolkow, Über eine Klasse von Lösungen der Diracschen Gleichung, Z. Phys. 94(3–4), 250 (1935)
D. S. Guo, Exact wave functions for atomic electron interacting with photon fields, Front. Phys. 8(1), 39 (2013)
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)
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)
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)
J. Gao, D. S. Guo, and Y. S. Wu, Resonant abovethreshold ionization at quantized laser intensities, Phys. Rev. A 61(4), 043406 (2000)
D. S. Guo, Theory of the Kapitza–Dirac effect in strong radiation fields, Phys. Rev. A 53(6), 4311 (1996)
B. Lippmann and J. Schwinger, Variational principles for scattering processes (I), Phys. Rev. 79(3), 469 (1950)
M. Gell-Mann and M. L. Goldberger, The formal theory of scattering, Phys. Rev. 91(2), 398 (1953)
X. Hu, H. Wang, and D. S. Guo, Phased Bessel functions, Can. J. Phys. 86, 863 (2008)
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)
D. L. Freimund and H. Batelaan, Bragg scattering of free electrons using the Kapitza–Dirac effect, Phys. Rev. Lett. 89(28), 283602 (2002)
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)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Yu, C., Zhang, J., Sun, Z. et al. Conditions for ponderomotive resonances in the Kapitza–Dirac effect. Front. Phys. 10, 104208 (2015). https://doi.org/10.1007/s11467-015-0499-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11467-015-0499-4