Abstract

We studied the conical emission in samarium (Sm) vapor under the near-resonant condition. The incident dye laser was tuned to the transition line, 4f66s2 7F4f6(7F)6s6p(1P0) (λ=562.601 nm), of the Sm atom. Using a high-temperature oven, we could obtain the atomic density of 8×1014 atoms/cm3, large enough to observe the conical emission. We observed one to three rings around the original laser beam, and the number of the rings depended on the laser intensity, the laser wavelength, and the atomic density. These results are attributed to the self-phase modulation of the laser beam interacting with the near-resonant atomic medium. We give a simple expression that describes the dependence of the locations of the rings on the laser intensity. We compare the experimental results with this expression quantitatively and then estimate the nonlinear susceptibility of Sm vapor.

© 2001 Optical Society of America

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References

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  1. D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
    [CrossRef]
  2. D. J. Harter and R. W. Boyd, “Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light,” Phys. Rev. A 29, 739–748 (1984).
    [CrossRef]
  3. D. J. Harter and R. W. Boyd, “Conical emission due to four-wave mixing enhanced by the ac Stark effect in self-trapped filaments of light,” Opt. Lett. 7, 491–493 (1982).
    [CrossRef] [PubMed]
  4. R. C. Hart, L. You, A. Gallagher, and J. Cooper, “Failures of the four-wave mixing model for cone emission,” Opt. Commun. 111, 331–337 (1994).
    [CrossRef]
  5. D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
    [CrossRef]
  6. L. You, J. Mostowski, J. Cooper, and R. Shuker, “Cone emission from laser-pumped two-level atoms,” Phys. Rev. A 44, R6998–R7001 (1991).
    [CrossRef] [PubMed]
  7. Y. Ben-Aryeh, “Cooperative effects in cone emission from laser-pumped two-level atoms,” Phys. Rev. A 56, 854–858 (1997).
    [CrossRef]
  8. M. L. Ter-Mikaelian, G. A. Torossian, and G. G. Grigoryan, “Conical emission in the quasiresonant media as a result of self-phase-modulation,” Opt. Commun. 119, 56–60 (1995).
    [CrossRef]
  9. J. J. Wu, Shu-Hsia Chen, J. Y. Fan, and G. S. Ong, “Propagation of a Gaussian-profile laser beam in nematic liquid crystals and the structure of its nonlinear diffraction rings,” J. Opt. Soc. Am. B 7, 1147–1157 (1990).
    [CrossRef]
  10. S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Laser-induced diffraction rings from a nematic-liquid-crystal film,” Opt. Lett. 6, 411–413 (1981).
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  11. R. W. Boyd, Nonlinear Optics (Academic, San Diego, 1992), p. 204.

1997 (1)

Y. Ben-Aryeh, “Cooperative effects in cone emission from laser-pumped two-level atoms,” Phys. Rev. A 56, 854–858 (1997).
[CrossRef]

1995 (1)

M. L. Ter-Mikaelian, G. A. Torossian, and G. G. Grigoryan, “Conical emission in the quasiresonant media as a result of self-phase-modulation,” Opt. Commun. 119, 56–60 (1995).
[CrossRef]

1994 (2)

R. C. Hart, L. You, A. Gallagher, and J. Cooper, “Failures of the four-wave mixing model for cone emission,” Opt. Commun. 111, 331–337 (1994).
[CrossRef]

D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
[CrossRef]

1991 (1)

L. You, J. Mostowski, J. Cooper, and R. Shuker, “Cone emission from laser-pumped two-level atoms,” Phys. Rev. A 44, R6998–R7001 (1991).
[CrossRef] [PubMed]

1990 (1)

1984 (1)

D. J. Harter and R. W. Boyd, “Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light,” Phys. Rev. A 29, 739–748 (1984).
[CrossRef]

1982 (1)

1981 (1)

1970 (1)

D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
[CrossRef]

Arakelian, S. M.

Ben-Aryeh, Y.

Y. Ben-Aryeh, “Cooperative effects in cone emission from laser-pumped two-level atoms,” Phys. Rev. A 56, 854–858 (1997).
[CrossRef]

Boyd, R. W.

D. J. Harter and R. W. Boyd, “Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light,” Phys. Rev. A 29, 739–748 (1984).
[CrossRef]

D. J. Harter and R. W. Boyd, “Conical emission due to four-wave mixing enhanced by the ac Stark effect in self-trapped filaments of light,” Opt. Lett. 7, 491–493 (1982).
[CrossRef] [PubMed]

R. W. Boyd, Nonlinear Optics (Academic, San Diego, 1992), p. 204.

Chekhov, D. I.

D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
[CrossRef]

Chen, Shu-Hsia

Cooper, J.

R. C. Hart, L. You, A. Gallagher, and J. Cooper, “Failures of the four-wave mixing model for cone emission,” Opt. Commun. 111, 331–337 (1994).
[CrossRef]

L. You, J. Mostowski, J. Cooper, and R. Shuker, “Cone emission from laser-pumped two-level atoms,” Phys. Rev. A 44, R6998–R7001 (1991).
[CrossRef] [PubMed]

Durbin, S. D.

Fan, J. Y.

Gaidarenko, D. V.

D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
[CrossRef]

Gallagher, A.

R. C. Hart, L. You, A. Gallagher, and J. Cooper, “Failures of the four-wave mixing model for cone emission,” Opt. Commun. 111, 331–337 (1994).
[CrossRef]

Grigoryan, G. G.

M. L. Ter-Mikaelian, G. A. Torossian, and G. G. Grigoryan, “Conical emission in the quasiresonant media as a result of self-phase-modulation,” Opt. Commun. 119, 56–60 (1995).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
[CrossRef]

Hart, R. C.

R. C. Hart, L. You, A. Gallagher, and J. Cooper, “Failures of the four-wave mixing model for cone emission,” Opt. Commun. 111, 331–337 (1994).
[CrossRef]

Harter, D. J.

D. J. Harter and R. W. Boyd, “Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light,” Phys. Rev. A 29, 739–748 (1984).
[CrossRef]

D. J. Harter and R. W. Boyd, “Conical emission due to four-wave mixing enhanced by the ac Stark effect in self-trapped filaments of light,” Opt. Lett. 7, 491–493 (1982).
[CrossRef] [PubMed]

Leonov, A. G.

D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
[CrossRef]

Mostowski, J.

L. You, J. Mostowski, J. Cooper, and R. Shuker, “Cone emission from laser-pumped two-level atoms,” Phys. Rev. A 44, R6998–R7001 (1991).
[CrossRef] [PubMed]

Ong, G. S.

Panteleev, A. A.

D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
[CrossRef]

Satostin, A. N.

D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
[CrossRef]

Shen, Y. R.

Shuker, R.

L. You, J. Mostowski, J. Cooper, and R. Shuker, “Cone emission from laser-pumped two-level atoms,” Phys. Rev. A 44, R6998–R7001 (1991).
[CrossRef] [PubMed]

Ter-Mikaelian, M. L.

M. L. Ter-Mikaelian, G. A. Torossian, and G. G. Grigoryan, “Conical emission in the quasiresonant media as a result of self-phase-modulation,” Opt. Commun. 119, 56–60 (1995).
[CrossRef]

Torossian, G. A.

M. L. Ter-Mikaelian, G. A. Torossian, and G. G. Grigoryan, “Conical emission in the quasiresonant media as a result of self-phase-modulation,” Opt. Commun. 119, 56–60 (1995).
[CrossRef]

Wu, J. J.

You, L.

R. C. Hart, L. You, A. Gallagher, and J. Cooper, “Failures of the four-wave mixing model for cone emission,” Opt. Commun. 111, 331–337 (1994).
[CrossRef]

L. You, J. Mostowski, J. Cooper, and R. Shuker, “Cone emission from laser-pumped two-level atoms,” Phys. Rev. A 44, R6998–R7001 (1991).
[CrossRef] [PubMed]

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

Opt. Commun. (3)

R. C. Hart, L. You, A. Gallagher, and J. Cooper, “Failures of the four-wave mixing model for cone emission,” Opt. Commun. 111, 331–337 (1994).
[CrossRef]

D. I. Chekhov, D. V. Gaidarenko, A. G. Leonov, A. A. Panteleev, and A. N. Satostin, “Conical emission and spectral behavior of strong near resonant laser wave at low-frequency detuning,” Opt. Commun. 105, 209–213 (1994).
[CrossRef]

M. L. Ter-Mikaelian, G. A. Torossian, and G. G. Grigoryan, “Conical emission in the quasiresonant media as a result of self-phase-modulation,” Opt. Commun. 119, 56–60 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

D. J. Harter and R. W. Boyd, “Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light,” Phys. Rev. A 29, 739–748 (1984).
[CrossRef]

L. You, J. Mostowski, J. Cooper, and R. Shuker, “Cone emission from laser-pumped two-level atoms,” Phys. Rev. A 44, R6998–R7001 (1991).
[CrossRef] [PubMed]

Y. Ben-Aryeh, “Cooperative effects in cone emission from laser-pumped two-level atoms,” Phys. Rev. A 56, 854–858 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
[CrossRef]

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, San Diego, 1992), p. 204.

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Figures (6)

Fig. 1
Fig. 1

Simple explanation for the conical emission. dϕ/dρ|ρ1=dϕ/dρ|ρ-1 and ϕ(ρ-1)-ϕ(ρ1)=2π; thus these two components interfere constructively. The same explanation is applicable to the next ring by ρ-2 and ρ2. |dϕ/dρ| has the maximum at the point ρ0=W0/2.

Fig. 2
Fig. 2

Numerical results on the locations of the rings and valleys in Eq. (7) (dotted curves) and the result of the approximate expression [Eq. (10), solid line] whose slope is 2/e.

Fig. 3
Fig. 3

Experimental setup: M, mirror; BS, beam splitter; L, lens (f=70 cm).

Fig. 4
Fig. 4

Dependence of the locations of the rings on the laser detuning δ=ω-ω0: (a) δ=56.7 GHz (nearly off-resonance), (b) δ=24.6 GHz, (c) δ=19.9 GHz, (d) δ=0 GHz, (e) δ=-11.4 GHz, and (f) δ=-15.2 GHz. N=8.5×1014 atoms/cm3 (850 °C). Laser-pulse energy is 20 µJ. CE is observed under both the blue and the red-detuned conditions.

Fig. 5
Fig. 5

Dependence of the locations of the rings on the atomic density: δ=28.4 GHz, and the laser-pulse energy is 20 µJ. The linear regression tells us the cone angle N1.08.

Fig. 6
Fig. 6

Dependence of the location of the outermost ring on the laser-pulse power. δ=15.0 GHz. N=8.5×1014 atoms/cm3 (850 °C). The linear regression tells us the slope in this figure is 1.3 mrad/µJ.

Equations (12)

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Einc(ρ, t)=E0(ρ)exp[i(kz-ωt)],
E0(ρ)=A exp(-ρ2/W02),
n=n0+n2 I,
ϕ(ρ)=ϕ0 exp(-2ρ2/W02),
ϕ0=12n2kLε0μ01/2|A|2,
E(ρ)=E0(ρ)exp{i[n0 kL+ϕ(ρ)]}.
I(kρ)0E0(ρ)exp[iϕ(ρ)]ρJ0(kρρ)dρ2,
ϕ=ϕ0e-2ϕ0W0e ρ-W02+orderof ρ-W023.
ρ-1W02-W0eπ2ϕ0.
kρ,1=dϕdρρ-12ϕ0eW0,
ϕ0eπ,
αc,1=kρ,1k=2eW0kϕ0=2LeW0n2 I.

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