Conditions for ponderomotive resonances in the Kapitza–Dirac effect

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 \hslash \omega /(m_{\mathrm{e}}{c}^{\mathrm{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.

Keywords

Kapitza–Dirac effect / strong laser physics / nonperturbative quantum electrodynamics

References

[1] P. L. Kapitza and P. A. M. Dirac, The reflection of electrons from standing light waves, Proc. Camb. Philos. Soc. 29(02), 297 (1933)

[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)

[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)

[4] Y. Takeda and I. Matsui, Electron reflection by standing wave of giant pulse laser, J. Phys. Soc. Jpn. 25(4), 1202 (1968)

[5] P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, High-intensity Kapitza−Dirac effect, Phys. Rev. Lett. 61(10), 1182 (1988)

[6] D. L. Freimund, K. Aflatooni, and H. Batelaan, Observation of the Kapitza−Dirac effect, Nature 413, 142 (2001)

[7] M. V. Fedorov, The Kapitza−Dirac effect in a strong radiation field, Sov. Phys. JETP 25(5), 952 (1967)

[8] M. V. Fedorov, Stimulated scattering of electrons by photons and adiabatic switching on hypothesis, Opt. Commun. 12(2), 205 (1974)

[9] R. Gush and H. P. Gush, Electron scattering from a standing light wave, Phys. Rev. D 3(8), 1712 (1971)

[10] E. A. Coutsias and J. K. McIver, Nonrelativistic Kapitza−Dirac scattering, Phys. Rev. A 31(5), 3155 (1985)

[11] 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)

[12] L. Rosenberg, Effect of virtual Compton scattering on electron propagation in a laser field, Phys. Rev. A 49(2), 1122 (1994)

[13] M. A. Efremov and M. V. Fedorov, Wavepacket theory of the Kapitza−Dirac effect, J. Phys. B 33(20), 4535 (2000)

[14] D. S. Guo and G. W. F. Drake, Multiphoton ionization in circularly polarized standing waves, Phys. Rev. A 45(9), 6622 (1992)

[15] D. S. Guo, T. Åberg, and B. Crasemann, Scattering theory of multiphoton ionization in strong fields, Phys. Rev. A 40(9), 4997 (1989)

[16] L. V. Keldysh, Diagram technique for nonequilibrium processes, Sov. Phys. JETP 20(4), 1307 (1965)

[17] D. M. Wolkow, Über eine Klasse von Lösungen der Diracschen Gleichung, Z. Phys. 94(3−4), 250 (1935)

[18] D. S. Guo, Exact wave functions for atomic electron interacting with photon fields, Front. Phys. 8(1), 39 (2013)

[19] 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)

[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)

[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)

[22] J. Gao, D. S. Guo, and Y. S. Wu, Resonant abovethreshold ionization at quantized laser intensities, Phys. Rev. A 61(4), 043406 (2000)

[23] D. S. Guo, Theory of the Kapitza−Dirac effect in strong radiation fields, Phys. Rev. A 53(6), 4311 (1996)

[24] B. Lippmann and J. Schwinger, Variational principles for scattering processes (I), Phys. Rev. 79(3), 469 (1950)

[25] M. Gell-Mann and M. L. Goldberger, The formal theory of scattering, Phys. Rev. 91(2), 398 (1953)

[26] 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)

[28] D. L. Freimund and H. Batelaan, Bragg scattering of free electrons using the Kapitza−Dirac effect, Phys. Rev. Lett. 89(28), 283602 (2002)

[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)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg