Abstract

The third-order nonlinear susceptibilities responsible for degenerate backward four-wave mixing in single-photon resonance are calculated for atomic lines with arbitrary values of total angular momentum J. All possible combinations for the polarization of three interacting beams have been considered.

© 1982 Optical Society of America

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References

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  1. R. L. Abrams and R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978).
    [Crossref] [PubMed]
  2. J. Nilsen and A. Yariv, “Nearly degenerate four-wave mixing applied to optical filters,” Appl. Opt. 18, 143–145 (1979).
    [Crossref] [PubMed]
  3. S. M. Wandzura, “Effects of atomic motion on wavefront conjugation by resonantly enhanced degenerate four-wave mixing,” Opt. Lett. 4, 208–210 (1979).
    [Crossref] [PubMed]
  4. T. Fu and M. Sargent, “Effect of signal detuning on phase conjugation,” Opt. Lett. 4, 366–368 (1979).
    [Crossref] [PubMed]
  5. L. M. Humphrey, J. P. Gordon, and P. F. Liao, “Angular dependence of line shape and strength of degenerate four-wave mixing in a Doppler-broadened system with optical pumping,” Opt. Lett. 5, 56–58 (1980).
    [Crossref] [PubMed]
  6. S. Saikan, “Angular momentum dependence of laser-induced birefringence and dichroism in atomic resonance lines,” J. Opt. Soc. Am. 68, 1184–1187 (1978).
    [Crossref]
  7. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974), pp. 388–399.
  8. J. Nilsen and A. Yariv, “Nondegenerate four-wave mixing in a Doppler-broadened resonant medium,” J. Opt. Soc. Am. 71, 180–183 (1981).
    [Crossref]
  9. S. Saikan, “Directional anisotropy of the backward four-wave mixing in gases,” J. Phys. Soc. Jpn. 50, 230–234 (1981).
    [Crossref]
  10. C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
    [Crossref]
  11. A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
    [Crossref]
  12. D. G. Steel, R. C. Lind, J. F. Lam, and C. R. Giuliano, “Polarization-rotation and thermal motion studies via resonant degenerate four-wave mixing,” Appl. Phys. Lett. 35, 367–379 (1979).
    [Crossref]

1981 (2)

S. Saikan, “Directional anisotropy of the backward four-wave mixing in gases,” J. Phys. Soc. Jpn. 50, 230–234 (1981).
[Crossref]

J. Nilsen and A. Yariv, “Nondegenerate four-wave mixing in a Doppler-broadened resonant medium,” J. Opt. Soc. Am. 71, 180–183 (1981).
[Crossref]

1980 (1)

1979 (4)

1978 (3)

1976 (1)

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

Abrams, R. L.

Fu, T.

Giuliano, C. R.

D. G. Steel, R. C. Lind, J. F. Lam, and C. R. Giuliano, “Polarization-rotation and thermal motion studies via resonant degenerate four-wave mixing,” Appl. Phys. Lett. 35, 367–379 (1979).
[Crossref]

Gordon, J. P.

Hänsch, T. W.

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

Humphrey, L. M.

Lam, J. F.

D. G. Steel, R. C. Lind, J. F. Lam, and C. R. Giuliano, “Polarization-rotation and thermal motion studies via resonant degenerate four-wave mixing,” Appl. Phys. Lett. 35, 367–379 (1979).
[Crossref]

Lamb, W. E.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974), pp. 388–399.

Liao, P. F.

Lind, R. C.

D. G. Steel, R. C. Lind, J. F. Lam, and C. R. Giuliano, “Polarization-rotation and thermal motion studies via resonant degenerate four-wave mixing,” Appl. Phys. Lett. 35, 367–379 (1979).
[Crossref]

R. L. Abrams and R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978).
[Crossref] [PubMed]

Nilsen, J.

Saikan, S.

S. Saikan, “Directional anisotropy of the backward four-wave mixing in gases,” J. Phys. Soc. Jpn. 50, 230–234 (1981).
[Crossref]

S. Saikan, “Angular momentum dependence of laser-induced birefringence and dichroism in atomic resonance lines,” J. Opt. Soc. Am. 68, 1184–1187 (1978).
[Crossref]

Sargent, M.

T. Fu and M. Sargent, “Effect of signal detuning on phase conjugation,” Opt. Lett. 4, 366–368 (1979).
[Crossref] [PubMed]

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974), pp. 388–399.

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974), pp. 388–399.

Steel, D. G.

D. G. Steel, R. C. Lind, J. F. Lam, and C. R. Giuliano, “Polarization-rotation and thermal motion studies via resonant degenerate four-wave mixing,” Appl. Phys. Lett. 35, 367–379 (1979).
[Crossref]

Wandzura, S. M.

Wieman, C.

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

Yariv, A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. G. Steel, R. C. Lind, J. F. Lam, and C. R. Giuliano, “Polarization-rotation and thermal motion studies via resonant degenerate four-wave mixing,” Appl. Phys. Lett. 35, 367–379 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[Crossref]

J. Opt. Soc. Am. (2)

J. Phys. Soc. Jpn. (1)

S. Saikan, “Directional anisotropy of the backward four-wave mixing in gases,” J. Phys. Soc. Jpn. 50, 230–234 (1981).
[Crossref]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

Other (1)

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974), pp. 388–399.

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Figures (1)

Fig. 1
Fig. 1

Optical arrangement for degenerate backward four-wave mixing. A nearly collinear geometry (θ ≃ 0) is considered in the present analysis.

Tables (1)

Tables Icon

Table 1 J Dependence of χ(3) Responsible for BFWM in a Two-Level Systema

Equations (5)

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P i ( 3 ) = j 6 0 [ χ 1122 ( 3 ) ( - ω , ω , ω , - ω ) A i B j C j * + χ 1212 ( 3 ) ( - ω , ω , ω , - ω ) A j B i C j * + χ 1221 ( 3 ) ( - ω , ω , ω , - ω ) A j B j C i * ] ,
P + ( 3 ) = 6 0 [ χ + + + + ( 3 ) ( - ω , ω , ω , - ω ) A + B + C + * + χ + - + - ( 3 ) ( - ω , ω , ω , - ω ) A - B + C - * + χ + + - - ( 3 ) ( - ω , ω , ω , - ω ) A + B - C - * ] ,
χ + + + + ( 3 ) = χ 1122 ( 3 ) + χ 1212 ( 3 ) ,             χ + - + - ( 3 ) = χ 1221 ( 3 ) + χ 1212 ( 3 ) , χ + + - - ( 3 ) = χ 1221 ( 3 ) + χ 1122 ( 3 ) .
χ + + + + ( 3 ) = B h ( η ) M 2 ( P M - 1 , M ) 4 , χ + - + - ( 3 ) = B h ( η ) M ( P M - 1 , M ) 2 1 γ a b [ γ a ( P M - 1 , M - 2 ) 2 + γ b ( P M + 1 , M ) 2 ] , χ + + - - ( 3 ) = B h ( η ) M ( P M - 1 , M ) 2 1 γ a b [ γ b ( P M - 1 , M - 2 ) 2 + γ a ( P M + 1 , M ) 2 ] ,
B = - N P 4 π γ a b 3 3 K u 0 γ γ a γ b ,             h ( η ) = i 1 + i η ,             η = ω 0 - ω γ ,