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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 28, Iss. 4 — Apr. 1, 2011
  • pp: 949–954

Phase effects in resonant multiphoton emission

J. Z. Kamiński  »View Author Affiliations

JOSA B, Vol. 28, Issue 4, pp. 949-954 (2011)

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The dependence of resonant multiphoton emission of electrons on the relative and carrier-envelope phases of bichromatic laser fields is studied theoretically by numerically solving the time-dependent Schrödinger equation. The laser field is described by a space- and time-dependent electric field. In order to solve numerically the Schrödinger equation, we modify the transfer-matrix algorithm such that it becomes numerically stable for a very large number of matching points. This modification enables one to investigate space effects related to a finite size of a laser focus. Numerical analysis shows the importance of finite penetration depth of laser fields in solids and the ponderomotive energy related to the quiver motion of electrons in the laser focus. We demonstrate that the energy spectrum of emitted electrons and the total photocurrent depend on the relative and carrier-envelope phases, indicating that multiphoton dynamics of electrons emitted from a solid surface can be efficiently controlled by varying these phases.

© 2011 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(240.4350) Optics at surfaces : Nonlinear optics at surfaces
(240.6675) Optics at surfaces : Surface photoemission and photoelectron spectroscopy

ToC Category:
Optics at Surfaces

Original Manuscript: November 15, 2010
Manuscript Accepted: February 2, 2011
Published: March 31, 2011

J. Z. Kamiński, "Phase effects in resonant multiphoton emission," J. Opt. Soc. Am. B 28, 949-954 (2011)

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  1. N. Tzoar and J. I. Gersten, “Theory of electronic band structure in intense laser fields,” Phys. Rev. B 12, 1132–1139 (1975). [CrossRef]
  2. M. R. Belić, “Quasi-energy band-structure of solids,” Solid State Commun. 62, 817–820 (1987). [CrossRef]
  3. F. H. M. Faisal and R. Genieser, “Exact solution of the Kronig-Penney model of 1D-crystals in strong laser fields,” Phys. Lett. A 141, 297–300 (1989). [CrossRef]
  4. J. Z. Kamiński, “Laser-induced modification of the energy band structure,” Acta Phys. Pol. A 83, 495–504 (1993).
  5. D. R. Mašović, M. R. Belić, and J. I. Gersten, “Solid in the kicking laser field,” Phys. Lett. A 373, 3289–3295 (2009). [CrossRef]
  6. R. P. Lungu, “Floquet solutions for two-dimensional quasi-free electrons interacting with a monochromatic laser field,” Phys. Scr. 75, 206–215 (2007). [CrossRef]
  7. H. Khosravi, N. Daneshfar, and A. Bahari, “Effect of a magnetic field on high-harmonic generation by carbon nanotubes,” Opt. Lett. 34, 1723–1725 (2009). [CrossRef] [PubMed]
  8. H. Hsu and L. E. Reichl, “Floquet-Bloch states, quasienergy bands, and high-order harmonic generation for single-walled carbon nanotubes under intense laser fields,” Phys. Rev. B 74, 115406 (2006). [CrossRef]
  9. H. Hsu and L. E. Reichl, “Modeling graphene layers and single-walled carbon nanotubes with regularized delta-function potentials,” Phys. Rev. B 72, 155413 (2005). [CrossRef]
  10. M. Faraggi, I. Aldazabal, M. S. Gravielle, A. Arnau, and V. M. Silkin, “Study of the induced potential produced by ultrashort pulses on metal surfaces,” J. Opt. Soc. Am. B 26, 2331–2236 (2009). [CrossRef]
  11. G. Saathoff, L. Miaja-Avila, M. Aeschlimann, M. M. Murname, and H. C. Kapteyn, “Laser-assisted photoemission from surfaces,” Phys. Rev. A 77, 022903 (2008). [CrossRef]
  12. J. C. Baggesen and L. B. Madsen, “Theory for time-resolved measurements of laser-induced electron emission from metal surfaces,” Phys. Rev. A 78, 032903 (2008). [CrossRef]
  13. M. N. Faraggi, M. S. Gravielle, and D. M. Mitnik, “Interaction of ultrashort laser pulses with metal surfaces: impulsive jellium-Volkov approximation versus the solution of the time-dependent Schrodinger equation,” Phys. Rev. A 76, 012903 (2007). [CrossRef]
  14. P. Dombi, F. Krausz, and G. Farkas, “Ultrafast dynamics and carrier-envelope phase sensitivity of multiphoton photoemission from metal surfaces,” J. Mod. Opt. 53, 163–172 (2006). [CrossRef]
  15. F. H. M. Faisal, J. Z. Kamiński, and E. Saczuk, “Photoemission and high-order harmonic generation from solid surfaces in intense laser fields,” Phys. Rev. A 72, 023412 (2005). [CrossRef]
  16. F. H. M. Faisal, J. Z. Kamiński, and E. Saczuk, “Photoemission from solid surfaces in intense laser fields,” Laser Phys. 16, 284–288 (2006). [CrossRef]
  17. V. A. Astapenko, “Radiative processes in a bichromatic laser field with multiple frequencies,” Quantum Electron. 36, 1131–1147 (2006). [CrossRef]
  18. F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001). [CrossRef]
  19. U. Mizutani, Introduction to the Electron Theory of Metals (Cambridge University, 2001). [CrossRef]
  20. H. B. Michelson, “The work function of the elements and its periodicity,” J. Appl. Phys. 48, 4729–4733 (1977). [CrossRef]
  21. E. Saczuk and J. Z. Kamiński, “Resonant tunneling in the presence of intense laser fields,” Phys. Status Solidi B 240, 603–609 (2003). [CrossRef]
  22. S. G. Davison and M. Ste¸ślicka, Basic Theory of Surface States (Clarendon, 2001).
  23. M. Shapiro and P. Brumer, “Laser control of product quantum state populations in unimolecular reactions,” J. Chem. Phys. 84, 4103–4104 (1986). [CrossRef]
  24. M. Shapiro and P. Brumer, “Coherent control of atomic molecular, and electronic processes,” Adv. At. Mol. Opt. Phys. 42, 287–345 (2000). [CrossRef]
  25. M. Shapiro and P. Brumer, “Coherent control of molecular dynamics,” Rep. Prog. Phys. 66, 859–942 (2003). [CrossRef]
  26. E. Moon, H. Wang, S. Gilbertson, H. Mashiko, M. Chini, and Z. Chang, “Advances in carrier-envelope phase stabilization of grating-based chirped-pulse amplifiers,” Laser Photon. Rev. 4, 160–177 (2010). [CrossRef]
  27. T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004). [CrossRef] [PubMed]
  28. A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004). [CrossRef] [PubMed]
  29. S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006). [CrossRef] [PubMed]
  30. A. T. Georges and N. E. Karatzas, “Modeling of ultrafast interferometric three-photon photoemission from a metal surface irradiated with sub-10 fs laser pulses,” Phys. Rev. B 77, 085436 (2008). [CrossRef]
  31. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001). [CrossRef] [PubMed]
  32. G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91, 253004 (2003). [CrossRef]
  33. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39, R203–R262 (2006). [CrossRef]

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