Abstract

Stimulated anti-Stokes Raman scattering experiments were performed with a Bessel pump beam in hydrogen gas in the pressure range from p=6×105 to 5×106 Pa. The interrelation between two conical Stokes modes and several anti-Stokes far-field rings could be explained if we take into account planar transverse wave-vector matching only. Planar and nonplanar transverse and longitudinal wave-vector matching are discussed in detail. The experiments are compared with numerical solutions of the coupled equations for Stokes and anti-Stokes fields.

© 2003 Optical Society of America

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References

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  1. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  2. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [Crossref] [PubMed]
  3. I. Golub, “Superluminal-source-induced emission,” Opt. Lett. 20, 1847–1849 (1995).
    [Crossref] [PubMed]
  4. S. Klewitz, P. Leiderer, S. Sogomonian, and S. Herminghaus, “Tunable stimulated Raman scattering by pumping with Bessel beams,” Opt. Lett. 21, 248–250 (1996).
    [Crossref] [PubMed]
  5. 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]
  6. L. Niggl and M. Maier, “Gain-guided modes in stimulated scattering processes with diffraction-free pump beams,” Opt. Commun. 154, 65–69 (1998).
    [Crossref]
  7. U. T. Schwarz, L. Niggl, and M. Maier, “Gain guiding in stimulated scattering processes with hollow Bessel pump beams,” Opt. Commun. 181, 413–423 (2000).
    [Crossref]
  8. S. Sogomonian, L. Niggl, and M. Maier, “Nonplanar phase-matching of stimulated anti-Stokes Raman scattering pumped by a Bessel beam,” Opt. Commun. 162, 261–266 (1999).
    [Crossref]
  9. R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
    [Crossref]
  10. V. Vaicaitis, A. Stabinis, A. Marcinkevicius, and V. Jarutis, “Second-order Stokes and anti-Stokes coupling in stimulated Raman scattering by Bessel beam,” Opt. Commun. 178, 461–467 (2000).
    [Crossref]
  11. S. Sogomonian, U. T. Schwarz, and M. Maier, “Phase-front transformation of a first-order Bessel beam in Raman-resonant four-wave mixing,” J. Opt. Soc. Am. B 18, 497–504 (2001).
    [Crossref]
  12. Landolt-Börnstein, Zahlenwerte und Funktionen: II. Band, 8. Teil, Optische Konstanten (Springer-Verlag, Berlin, 1962), Chap. 286, Table 5, pp. 6–885.
  13. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University, Cambridge, England, 1992).

2001 (1)

2000 (2)

U. T. Schwarz, L. Niggl, and M. Maier, “Gain guiding in stimulated scattering processes with hollow Bessel pump beams,” Opt. Commun. 181, 413–423 (2000).
[Crossref]

V. Vaicaitis, A. Stabinis, A. Marcinkevicius, and V. Jarutis, “Second-order Stokes and anti-Stokes coupling in stimulated Raman scattering by Bessel beam,” Opt. Commun. 178, 461–467 (2000).
[Crossref]

1999 (2)

S. Sogomonian, L. Niggl, and M. Maier, “Nonplanar phase-matching of stimulated anti-Stokes Raman scattering pumped by a Bessel beam,” Opt. Commun. 162, 261–266 (1999).
[Crossref]

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

1998 (1)

L. Niggl and M. Maier, “Gain-guided modes in stimulated scattering processes with diffraction-free pump beams,” Opt. Commun. 154, 65–69 (1998).
[Crossref]

1997 (1)

1996 (1)

1995 (1)

1989 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University, Cambridge, England, 1992).

Friberg, A. T.

Gadonas, R.

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

Golub, I.

Herminghaus, S.

Jarutis, V.

V. Vaicaitis, A. Stabinis, A. Marcinkevicius, and V. Jarutis, “Second-order Stokes and anti-Stokes coupling in stimulated Raman scattering by Bessel beam,” Opt. Commun. 178, 461–467 (2000).
[Crossref]

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

Klewitz, S.

Landolt-Börnstein,

Landolt-Börnstein, Zahlenwerte und Funktionen: II. Band, 8. Teil, Optische Konstanten (Springer-Verlag, Berlin, 1962), Chap. 286, Table 5, pp. 6–885.

Leiderer, P.

Maier, M.

S. Sogomonian, U. T. Schwarz, and M. Maier, “Phase-front transformation of a first-order Bessel beam in Raman-resonant four-wave mixing,” J. Opt. Soc. Am. B 18, 497–504 (2001).
[Crossref]

U. T. Schwarz, L. Niggl, and M. Maier, “Gain guiding in stimulated scattering processes with hollow Bessel pump beams,” Opt. Commun. 181, 413–423 (2000).
[Crossref]

S. Sogomonian, L. Niggl, and M. Maier, “Nonplanar phase-matching of stimulated anti-Stokes Raman scattering pumped by a Bessel beam,” Opt. Commun. 162, 261–266 (1999).
[Crossref]

L. Niggl and M. Maier, “Gain-guided modes in stimulated scattering processes with diffraction-free pump beams,” Opt. Commun. 154, 65–69 (1998).
[Crossref]

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]

Marcinkevicius, A.

V. Vaicaitis, A. Stabinis, A. Marcinkevicius, and V. Jarutis, “Second-order Stokes and anti-Stokes coupling in stimulated Raman scattering by Bessel beam,” Opt. Commun. 178, 461–467 (2000).
[Crossref]

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Niggl, L.

U. T. Schwarz, L. Niggl, and M. Maier, “Gain guiding in stimulated scattering processes with hollow Bessel pump beams,” Opt. Commun. 181, 413–423 (2000).
[Crossref]

S. Sogomonian, L. Niggl, and M. Maier, “Nonplanar phase-matching of stimulated anti-Stokes Raman scattering pumped by a Bessel beam,” Opt. Commun. 162, 261–266 (1999).
[Crossref]

L. Niggl and M. Maier, “Gain-guided modes in stimulated scattering processes with diffraction-free pump beams,” Opt. Commun. 154, 65–69 (1998).
[Crossref]

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]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University, Cambridge, England, 1992).

Schwarz, U. T.

S. Sogomonian, U. T. Schwarz, and M. Maier, “Phase-front transformation of a first-order Bessel beam in Raman-resonant four-wave mixing,” J. Opt. Soc. Am. B 18, 497–504 (2001).
[Crossref]

U. T. Schwarz, L. Niggl, and M. Maier, “Gain guiding in stimulated scattering processes with hollow Bessel pump beams,” Opt. Commun. 181, 413–423 (2000).
[Crossref]

Smilgevicius, V.

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

Sogomonian, S.

Stabinis, A.

V. Vaicaitis, A. Stabinis, A. Marcinkevicius, and V. Jarutis, “Second-order Stokes and anti-Stokes coupling in stimulated Raman scattering by Bessel beam,” Opt. Commun. 178, 461–467 (2000).
[Crossref]

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University, Cambridge, England, 1992).

Turunen, J.

Vaicaitis, V.

V. Vaicaitis, A. Stabinis, A. Marcinkevicius, and V. Jarutis, “Second-order Stokes and anti-Stokes coupling in stimulated Raman scattering by Bessel beam,” Opt. Commun. 178, 461–467 (2000).
[Crossref]

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

Vasara, A.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University, Cambridge, England, 1992).

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (5)

L. Niggl and M. Maier, “Gain-guided modes in stimulated scattering processes with diffraction-free pump beams,” Opt. Commun. 154, 65–69 (1998).
[Crossref]

U. T. Schwarz, L. Niggl, and M. Maier, “Gain guiding in stimulated scattering processes with hollow Bessel pump beams,” Opt. Commun. 181, 413–423 (2000).
[Crossref]

S. Sogomonian, L. Niggl, and M. Maier, “Nonplanar phase-matching of stimulated anti-Stokes Raman scattering pumped by a Bessel beam,” Opt. Commun. 162, 261–266 (1999).
[Crossref]

R. Gadonas, V. Jarutis, A. Marcinkevicius, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Transverse phase-matching in stimulated Raman scattering by a Bessel beam,” Opt. Commun. 169, 189–197 (1999).
[Crossref]

V. Vaicaitis, A. Stabinis, A. Marcinkevicius, and V. Jarutis, “Second-order Stokes and anti-Stokes coupling in stimulated Raman scattering by Bessel beam,” Opt. Commun. 178, 461–467 (2000).
[Crossref]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Other (2)

Landolt-Börnstein, Zahlenwerte und Funktionen: II. Band, 8. Teil, Optische Konstanten (Springer-Verlag, Berlin, 1962), Chap. 286, Table 5, pp. 6–885.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University, Cambridge, England, 1992).

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Figures (7)

Fig. 1
Fig. 1

(a) Nonplanar phase-matching geometry for conical beams. The configuration is to scale in the xy plane for p=10 bars, ϑ=2.7 mrad, and ψS=1. This nonplanar phase-matching configuration with ϕ=86° and φ=30° (see text) corresponds to exact phase matching and is marked with an asterisk in Fig. 2. (b) Transverse wave-vector matching geometry for the same configuration as in (a).

Fig. 2
Fig. 2

Central plot spans the ψS-ψA plane of the normalized Stokes and anti-Stokes angles. Thick straight lines mark planar transverse wave-vector matching; the corresponding planar scattering configurations are sketched in the small boxes. The position of these lines is independent of pump beam angle ϑP and hydrogen pressure. Within the shaded area nonplanar exact transverse wave-vector matching is possible. Thin curves correspond to exact longitudinal wave-vector matching [Eq. (4)], depending on ϑP (here ϑP=2.7 mrad) and pressure. Dashed vertical lines mark the normalized Stokes angles ψS=0.3 and 1.0. Intersections with thick lines of planar transverse wave-vector matching are marked by greek letters for association with peaks in the anti-Stokes spectra of Figs. 5 and 7.

Fig. 3
Fig. 3

Experimental setup: the intensity of the frequency-doubled (λP=532-nm) Nd:YAG laser is adjusted by a λ/2 wave plate and polarizer P, telescope T1 for beam expansion and collimation, Bessel beam generation by off-axis diffractive grating G, second telescope T2 to vary Bessel beam cone angle ϑP and to separate the desired order of the off-axis grating with pinhole B, mirrors M, dumps D, hydrogen gas cell H2, dichroic mirror S to separate the pump beam from Stokes and anti-Stokes beams. The far fields of the Stokes and anti-Stokes light are measured in the focal plane of lens L with cameras CCD1 and CCD2. Filters F1 and F2 transmit Stokes and anti-Stokes wavelengths λS=683 nm and λA=436 nm, respectively.

Fig. 4
Fig. 4

Measured (a) Stokes and (b) anti-Stokes far-field distribution. Hydrogen pressure was p=30 bars and the pump cone angle was ϑP=2.7 mrad.

Fig. 5
Fig. 5

Measured (a), (c) Stokes and (b), (d) anti-Stokes far-field spectra. The corresponding pairs (a), (b) and (c),(d) were measured simultaneously with one pump pulse, respectively. Hydrogen pressure was p=28 bars and the pump cone angle was ϑP=2.7 mrad.

Fig. 6
Fig. 6

(a), (c) Plot of the density-of-states-like quantity Nφϕ for two different values of normalized Stokes angle (a) ψS=1 and (c) ψS=0.3. (b), (d) Absolute values of the total phase mismatch |Δk|=|kP+kP-kS-kA| for the same values of (b) ψS=1 and (d) ψS=0.3, and a pressure p=28 bars.

Fig. 7
Fig. 7

Solid lines represent Stokes and anti-Stokes far fields as in Fig. 5 but for three different pressures: (a), (b) p=47 bars; (c), (d) p=30 bars; (e), (f ) p=10 bars. The dashed lines represent results from numerical integration of coupled Eqs. (9) and (10) of Stokes and anti-Stokes fields.

Equations (10)

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ΔK=2kP-kS-kA,
ΔK=-Cp,
kAϑA2+kSϑS2=2kPϑP2-2ΔK.
ψA2RA2+ψS2RS2=1.
Ri=ki1/22kP1-ΔKkPϑP21/2(i=S, A),
kA2ϑA2=kS2ϑS2-4kPkSϑPϑScosφ2cos ϕ+4kP2ϑP2cos2φ2.
ψA2=ψS2-4ψScosφ2cos ϕ+4 cos2φ2.
ψA=ψS+2.
z AS=i2kS 2AS+12 g˜S[|AP|2AS+AP2AA*exp(iΔKz)],
z AA=i2kA 2AA-12 g˜A[|AP|2AA+AP2AS*exp(iΔKz)].

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