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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 16, Iss. 9 — Sep. 1, 1999
  • pp: 1377–1384

Optimum conical angle of a Bessel–Gauss beam for low-order harmonic generation in gases

C. F. R. Caron and R. M. Potvliege  »View Author Affiliations


JOSA B, Vol. 16, Issue 9, pp. 1377-1384 (1999)
http://dx.doi.org/10.1364/JOSAB.16.001377


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Abstract

We determine the conical half-angle at which a weak, loosely focused Bessel–Gauss beam of fixed focal intensity and confocal parameter is most efficient at generating a given harmonic in a gaseous target of arbitrary density profile. Simple analytical results are compared with fully numerical calculations for hydrogen, xenon, and rubidium. The variation of the conversion efficiency with the conical half-angle is shown to depend on the properties of the medium only through the macroscopic dispersion.

© 1999 Optical Society of America

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(190.2620) Nonlinear optics : Harmonic generation and mixing

Citation
C. F. R. Caron and R. M. Potvliege, "Optimum conical angle of a Bessel–Gauss beam for low-order harmonic generation in gases," J. Opt. Soc. Am. B 16, 1377-1384 (1999)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-9-1377


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References

  1. T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993); “Nonlinear optics of Bessel beams,” 71, 209 (1993). [CrossRef] [PubMed]
  2. 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). [CrossRef] [PubMed]
  3. J. Peatross, J. L. Chaloupka, and D. D. Meyerhofer, “High-order harmonic generation with an annular laser beam,” Opt. Lett. 19, 942–944 (1994). [CrossRef] [PubMed]
  4. S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995); “Theory of third-harmonic generation using Bessel beams, and self-phase-matching,” Phys. Rev. A 54, 2314–2325 (1996). [CrossRef] [PubMed]
  5. S. Klewitz, P. Leiderer, S. Herminghaus, and S. Sogomonian, “Tunable stimulated Raman scattering by pumping with Bessel beams,” Opt. Lett. 21, 248–250 (1996). [CrossRef] [PubMed]
  6. V. E. Peet, “Resonantly enhanced multiphoton ionization of xenon in Bessel beams,” Phys. Rev. A 53, 3679–3682 (1996). [CrossRef] [PubMed]
  7. V. E. Peet and R. V. Tsubin, “Third-harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997). [CrossRef]
  8. K. Shinozaki, C. A. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997). [CrossRef]
  9. L. Niggl and M. Maier, “Efficient conical emission of stimulated Raman Stokes light generated by a Bessel pump beam,” Opt. Lett. 22, 910–912 (1997). [CrossRef] [PubMed]
  10. A. P. Piskarsas, V. Smilgevic̆ius, and A. P. Stabinis, “Optical parametric oscillator pumped by a Bessel beam,” Appl. Opt. 36, 7779–7782 (1997). [CrossRef]
  11. V. N. Belyĭ, N. S. Kazak, and N. A. Khilo, “Characteristics of parametric frequency conversion making use of Bessel beams,” Quantum Electron. 28, 522–525 (1998). [CrossRef]
  12. S. Klewitz, S. Sogomonian, M. Woerner, and S. Herminghaus, “Stimulated Raman scattering of femtosecond Bessel pulses,” Opt. Commun. 154, 186–190 (1998). [CrossRef]
  13. C. F. R. Caron and R. M. Potvliege, “Phase-matching and harmonic generation in Bessel–Gauss beams,” J. Opt. Soc. Am. B 15, 1096–1106 (1998). [CrossRef]
  14. C. F. R. Caron, “Harmonic generation in gases using Bessel–Gauss beams,” Ph.D. dissertation (University of Durham, Durham, UK 1998).
  15. F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987). [CrossRef]
  16. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. Schirripa Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
  17. D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996). [CrossRef] [PubMed]
  18. P. Pääkkönen and J. Turunen, “Resonators with Bessel–Gauss modes,” Opt. Commun. 156, 359–366 (1998). [CrossRef]
  19. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987); J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987); J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. OPLEDP 13, 79–80 (1988). [CrossRef] [PubMed]
  20. Z. Bouchal and M. Olivik, “Nondiffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995). [CrossRef]
  21. A. L’Huillier, X. F. Li, and L. A. Lompré, “Propagation effects in high-order harmonic generation in rare gases,” J. Opt. Soc. Am. B 7, 527–536 (1990). [CrossRef]
  22. 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, Supplement 1 (Academic, New York, 1992), pp. 139–206.
  23. C. F. R. Caron and R. M. Potvliege, Comput. Phys. Commun. (to be published).
  24. See, e.g., J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).
  25. For example, γ=1.4 for λ=1064 nm, q=3, |z|≤2 mm, b=50 mm, α=1.2 deg, and β=0.4 deg. That γ is close to unity means that the integral multiplying (1+2iz/b) in integral (18) is essentially real. For z≪b the imaginary part of this integral is proportional to z/b and to an integral of a combination of products of J0 and J1 functions, a power, and an exponential, while the real part is nearly constant in z and can be approximated by integral (17) taken at z=0. It is not surprising that the imaginary part is dominated by the real part, and hence that γ≈1, since the (rapid) oscillations of the J1 functions are out of phase with those of the J0 functions, while the J0 functions oscillate in phase in the real part when β≈α/q.
  26. This result is, of course, well known for rectangular density profiles. (See Ref. 24.)
  27. Another system fulfilling these conditions is krypton at λ≈ 348 nm and λ≈369 nm. Interesting differences between Gaussian and noncollinear beams have been described for resonant harmonic generation and multiphoton ionization in xenon at λ≈440 nm. (See Ref. 7.)
  28. We verified this by evaluating the contribution of pressure broadening to the absorption coefficient, for hydrogen and xenon at 355 nm, in the simple approaches of W. R. Ferrell, M. G. Payne, and W. R. Garrett, “Resonance broadening and shifting of spectral lines in xenon and krypton,” Phys. Rev. A 36, 81–89 (1987); and of G. Peach, “Collisional broadening of spectral lines,” in Atomic, Molecular, and Optical Physics Handbook, G. W. F. Drake, ed. (American Institute of Physics, Melville, New York, 1996), p. 669, Eq. (57.27). [CrossRef] [PubMed]
  29. W. F. Chan, G. Cooper, X. Guo, G. R. Burton, and C. E. Brion, “Absolute optical oscillator strengths for the electronic excitation of atoms at high resolution. III. The photoabsorption of argon, krypton and xenon,” Phys. Rev. A 46, 149–171 (1992). We took Ei=E0+11.67 eV in Eq. (29), 0.46 eV below the true 2P3/2 ionization threshold, to allow for the fact that the contribution of individual bound states cannot be isolated from the data given in this reference above that energy. [CrossRef] [PubMed]
  30. A. H. Kung, “Third-harmonic generation in a pulsed supersonic jet of xenon,” Opt. Lett. 8, 24–26 (1983). [CrossRef] [PubMed]
  31. T. M. Miller and B. Bederson, “Atomic and molecular polarizabilities—a review of recent advances,” Adv. At. Mol. Phys. 13, 1–55 (1977). [CrossRef]
  32. L. J. Zych and J. F. Young, “Limitation of 3547 to 1182 Å conversion efficiency in Xe,” IEEE J. Quantum Electron. 14, 147–149 (1978). [CrossRef]
  33. H. Puell, K. Spanner, W. Falkenstein, W. Kaiser, and C. R. Vidal, “Third-harmonic generation of mode-locked Nd:glass laser pulses in phase-matched Rb-Xe mixtures,” Phys. Rev. A 14, 2240–2257 (1976). [CrossRef]

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