Phase matching and harmonic generation in Bessel-Gauss beams

Journal of the Optical Society of America B: Optical Physics

Volumn 15, Issue 3, 1998, Pages 1096-1106

  Caron, C F R ^a   Potvliege, R M ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032357691     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.15.001096     Document Type: Article

References (19)

1. B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, "Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry," Phys. Rev. Lett. 71, 243-246 (1993).
2. S. P. Tewari, H. Huang, and R. W. Boyd, "Theory of self-phase-matching," Phys. Rev. A 51, 2707-2710 (1995); "Theory of third-harmonic generation using Bessel beams, and self-phase-matching," Phys. Rev. A 54, 2314-2325 (1996).
3. S. P. Tewari, H. Huang, and R. W. Boyd, "Theory of self-phase-matching," Phys. Rev. A 51, 2707-2710 (1995); "Theory of third-harmonic generation using Bessel beams, and self-phase-matching," Phys. Rev. A 54, 2314-2325 (1996).
4. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
5. V. E. Peet, "Resonantly enhanced multiphoton ionization of xenon in Bessel beams," Phys. Rev. A 53, 3679-3682 (1996).
6. F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).
7. J. K. Jabczynski, "A 'diffraction-free' resonator," Opt. Commun. 77, 292-294 (1990).
8. A. L'Huillier, L. A. Lompré, G. Mainfray, and C. Manus, "High-order harmonic generation in rare gases," in Atoms in Intense Laser Fields, M. Gavrila, ed., Advances in Atomic, Molecular and Optical Physics, Suppl. 1 (Academic, New York, 1992).
9. BG reduces to the exact Bessel form of Eq. (6) in the loose-focusing limit.
10. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. Schirripa Spagnolo, "Generalized Bessel-Gauss beams," J. Mod. Opt. 43, 1155-1166 (1996).
11. The cross section of the Gaussian beam of Fig. 1 would be larger, and for a fixed power its focal intensity would be smaller, if its confocal parameter were larger. One can optimize b and α so as to maximize the area of the focal plane irradiated above a given intensity for a given power. A numerical study showed that marginally larger areas can be achieved with an optimized Bessel-Gauss beam (α ≠ 0) than with an optimized Gaussian beam (α = 0); the difference between the two is a few percent at most.
12. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
13. A novel method of graphically investigating phase matching, based on this idea, has been devised recently by Balcou et al. for a purely Gaussian beam geometry: P. Balcou, P. Salières, A. L'Huillier, and M. Lewenstein, "Generalized phase-matching conditions for high harmonics: the role of field-gradient forces," Phys. Rev. A 55, 3204-3210 (1997).
14. This might be less important at high intensities, where the dipole moment usually saturates and ionization significantly reduces the number of atoms participating effectively in the harmonic generation process.
15. R. M. Potvliege and R. Shakeshaft, "Multiphoton processes in an intense laser field: harmonic generation and total ionization rates for atomic hydrogen," Phys. Rev. A 40, 3061-3079 (1989).
16. q cos qωt. 16. A detailed account of these calculations will be presented elsewhere.
17. el(ω) have the same sign.
18. The discussion above is consistent with the results of a recent experimental study of third-order harmonic generation in xenon comparing Gaussian and conical beams, published after completion of this manuscript [V. E. Peet and R. V. Tsubin, "Third-harmonic generation and multiphoton ionization in Bessel beams," Phys. Rev. A 56, 1613-1620 (1997)]. Peet and Tsubin examined the variation with frequency of the harmonic yield in the vicinity of a three-photon resonance and at much weaker intensities than considered in this work for a focused Gaussian beam, an annular beam (α ≈ 3°), and a Bessel beam (α = 17°). The harmonic yield obtained with the annular beam exceeded that obtained with a Gaussian beam of same power in a small spectral range close to the resonance. No third-harmonic emission was detected for the Bessel beam, presumably because of the very low intensity of the beam that could be achieved in the experiment and the reabsorption of the emitted harmonic photons within the medium (with the cone half-angle a being fairly large, harmonic generation could be efficient only very close to the resonance where absorption is important; see Eq. 44).
19. See, for example, P. Antoine, A. L'Huillier, M. Lewenstein, P. Salières, and B. Carré, "Theory of high-order harmonic generation by an elliptically polarized laser field," Phys. Rev. A 53, 1725-1745 (1996).