A nonperturbative quantum electrodynamic approach to the theory of laser induced high harmonic generation

Abstract

Using nonperturbative quantum electrodynamics, we develop a scattering theory for high harmonic generation (HHG). A transition rate formula for HHG is obtained. Applying this formula, we calculate the spectra of high harmonics generated from different noble gases shined by strong laser light. We study the cutoff property of the spectra. The data show that the cutoff orders of high harmonics are greater than that predicted by the “3.17” cutoff law. As a numerical experiment, the data obtained from our repeated calculations support the newly derived theoretical expression of the cutoff law. The cutoff energy of high harmonics described by the new cutoff law, in terms of the ponderomotive energy U_p and the ionization potential energy I_p, is 3.34U_p+ 1.83I_p. The higher cutoff orders predicted by this theory are due to the absorption of the extra photons, which participate only the photon-mode up-conversion and do nothing in the photoionization process.

Graphical abstract

Keywords

high harmonic generation (HHG) / cutoff law / strong laser physics / nonperturbative quantum electrodynamics / transition rate formula

References

[1] A. Mcpherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases, J. Opt. Soc. Am. B 4(4), 595 (1987)

[2] J. T. Zhang and D.-S. Guo, Spectral minimum and giant enhancement in photoelectron spectra from xenon atoms driven by intense midinfrared laser fields, Phys. Rev. Lett. 110(6), 063002 (2013)

[3] P. B. Corkum, Plasma perspective on strong field multiphoton ionization, Phys. Rev. Lett. 71(13), 1994 (1993)

[4] M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Theory of high-harmonic generation by lowfrequency laser fields, Phys. Rev. A 49(3), 2117 (1994)

[5] J. Gao, F. Shen, and J. G. Eden, Quantum electrodynamic treatment of harmonic generation in intense optical fields, Phys. Rev. Lett. 81(9), 1833 (1998)

[6] J. Gao, F. Shen, and J. G. Eden, Interpretation of highorder harmonic generation in terms of transitions between quantum Volkov states, Phys. Rev. A 61(4), 043812 (2000)

[7] L. H. Gao, X. F. Li, P. M. Fu, R. R. Freeman, and D.-S. Guo, Nonperturbative quantum electrodynamics theory of high-order harmonic generation, Phys. Rev. A 61(6), 063407 (2000)

[8] T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska , B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, Bright coherent ultrahigh harmonics in the keV X-ray regime from midinfrared femtosecond lasers, Science 336(6086), 1287 (2012)

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

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

[11] 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)

[12] D. M. Volkov, On a class of solutions of the Dirac equation, Z. Phys 94, 250 (1935)

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

[14] D.-S. Guo and G. W. Drake, Stationary solutions for an electron in an intense laser field (I): Single-mode case, J. Phys. A: Math. Gen. 25(11), 3383 (1992)

[15] X. Hu, H. X. Wang, and D.-S. Guo, Phased bessel functions, Can. J. Phys. 86(7), 863 (2008)

[16] J. Peatross and D. D. Meyerhofer, Intensity-dependent atomic-phase effects in high-order harmonic generation, Phys. Rev. A 52(5), 3976 (1995)

[17] W. R. Johnson, Atomic Structure Theory, 2007: Springer

[18] D.-S. Guo, C. Yu, J. T. Zhang, J. Gao, Z.-W. Sun, and Z. R. Sun, On the cutoff law of laser high harmonic spectra, Front. Phys. 10, 103201 (2015)

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg