Abstract

An inversionless gain of anti-Stokes radiation above the oscillation threshold in an optically dense far-from-degenerate double-Λ Doppler-broadened medium accompanied by Stokes gain is predicted. The outcomes are illustrated with numerical simulations applied to sodium dimer vapor. Optical switching from absorption to gain via transparency controlled by a small variation of the medium and of the driving radiation parameters, which are at a level of less than one photon per molecule, is shown.

© 2000 Optical Society of America

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  1. G. E. Notkin, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 52, 1673 (1967); T. Ya. Popova, A. K. Popov, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 57, 444 (1969); T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovsky, Zh. Eksp. Teor. Fiz. 57, 850 (1969); S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (Elsevier, Amsterdam, 1991).
  2. T. Ya. Popova and A. K. Popov, J. Appl. Spectrosc. 12, 734 (1970), http://xxx.lanl.gov/abs/quant-ph/0005047 ; Sov. Phys. J. 13, 1435 (1970); A. K. Popov, Introduction in Nonlinear Spectroscopy (Nauka, Novosibirsk, Russia, 1983; in Russian).
    [CrossRef]
  3. I. M. Beterov, “Investigation of nonlinear resonant interaction of optical fields in a three-level gas laser,” Cand. Sci. Dissertation (Institute of Semiconductor Physics SD USSR AS, Siberian Academy of Sciences, Novosibirsk, Russia, 1970).
  4. M. O. Scully, Phys. Rep. 219, 191 (1992); O. Kocharovskaya, Phys. Rep. 219, 175 (1992); P. Mandel, Contemp. Phys. 34, 235 (1993); A. K. Popov and S. G. Rautian, Proc. SPIE 2798, 49 (1996); A. K. Popov, Bull. Russ. Acad. Sci. (Physics) 60, 927 (1996).
    [CrossRef]
  5. A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24625 (1999); S. E. Harris and L. V. Hau, Phys. Rev. Lett. 824611 (1999); S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1999).
    [CrossRef]
  6. M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, Phys. Rev. Lett. 82, 1847 (1999).
    [CrossRef]
  7. M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998); A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
    [CrossRef]
  8. U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
    [CrossRef]
  9. A. K. Popov and S. A. Myslivets, Quantum Electron. 27, 1004 (1997); A. K. Popov, Proc. SPIE 3485, 252 (1998).
    [CrossRef]
  10. A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
    [CrossRef]
  11. P. Dong, W. Man, and J. Y. Gao, Phys. Lett. A 265, 43 (2000).
    [CrossRef]

2000 (1)

P. Dong, W. Man, and J. Y. Gao, Phys. Lett. A 265, 43 (2000).
[CrossRef]

1999 (4)

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24625 (1999); S. E. Harris and L. V. Hau, Phys. Rev. Lett. 824611 (1999); S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1999).
[CrossRef]

M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, Phys. Rev. Lett. 82, 1847 (1999).
[CrossRef]

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
[CrossRef]

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
[CrossRef]

1998 (1)

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998); A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

1997 (1)

A. K. Popov and S. A. Myslivets, Quantum Electron. 27, 1004 (1997); A. K. Popov, Proc. SPIE 3485, 252 (1998).
[CrossRef]

1992 (1)

M. O. Scully, Phys. Rep. 219, 191 (1992); O. Kocharovskaya, Phys. Rep. 219, 175 (1992); P. Mandel, Contemp. Phys. 34, 235 (1993); A. K. Popov and S. G. Rautian, Proc. SPIE 2798, 49 (1996); A. K. Popov, Bull. Russ. Acad. Sci. (Physics) 60, 927 (1996).
[CrossRef]

1970 (1)

T. Ya. Popova and A. K. Popov, J. Appl. Spectrosc. 12, 734 (1970), http://xxx.lanl.gov/abs/quant-ph/0005047 ; Sov. Phys. J. 13, 1435 (1970); A. K. Popov, Introduction in Nonlinear Spectroscopy (Nauka, Novosibirsk, Russia, 1983; in Russian).
[CrossRef]

1967 (1)

G. E. Notkin, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 52, 1673 (1967); T. Ya. Popova, A. K. Popov, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 57, 444 (1969); T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovsky, Zh. Eksp. Teor. Fiz. 57, 850 (1969); S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (Elsevier, Amsterdam, 1991).

Beterov, I. M.

I. M. Beterov, “Investigation of nonlinear resonant interaction of optical fields in a three-level gas laser,” Cand. Sci. Dissertation (Institute of Semiconductor Physics SD USSR AS, Siberian Academy of Sciences, Novosibirsk, Russia, 1970).

Chichkov, B. N.

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
[CrossRef]

Dong, P.

P. Dong, W. Man, and J. Y. Gao, Phys. Lett. A 265, 43 (2000).
[CrossRef]

Feoktistov, A. A.

G. E. Notkin, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 52, 1673 (1967); T. Ya. Popova, A. K. Popov, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 57, 444 (1969); T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovsky, Zh. Eksp. Teor. Fiz. 57, 850 (1969); S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (Elsevier, Amsterdam, 1991).

Fleischhauer, M.

M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, Phys. Rev. Lett. 82, 1847 (1999).
[CrossRef]

Gao, J. Y.

P. Dong, W. Man, and J. Y. Gao, Phys. Lett. A 265, 43 (2000).
[CrossRef]

Harris, S. E.

Hemmer, P. R.

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998); A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

Hinze, U.

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
[CrossRef]

Loeffler, M.

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998); A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

Lukin, M. D.

M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, Phys. Rev. Lett. 82, 1847 (1999).
[CrossRef]

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998); A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

Man, W.

P. Dong, W. Man, and J. Y. Gao, Phys. Lett. A 265, 43 (2000).
[CrossRef]

Manuszak, D.

Matsko, A. V.

M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, Phys. Rev. Lett. 82, 1847 (1999).
[CrossRef]

Merriam, A. J.

Meyer, L.

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
[CrossRef]

Myslivets, S. A.

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
[CrossRef]

A. K. Popov and S. A. Myslivets, Quantum Electron. 27, 1004 (1997); A. K. Popov, Proc. SPIE 3485, 252 (1998).
[CrossRef]

Notkin, G. E.

G. E. Notkin, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 52, 1673 (1967); T. Ya. Popova, A. K. Popov, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 57, 444 (1969); T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovsky, Zh. Eksp. Teor. Fiz. 57, 850 (1969); S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (Elsevier, Amsterdam, 1991).

Popov, A. K.

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
[CrossRef]

A. K. Popov and S. A. Myslivets, Quantum Electron. 27, 1004 (1997); A. K. Popov, Proc. SPIE 3485, 252 (1998).
[CrossRef]

T. Ya. Popova and A. K. Popov, J. Appl. Spectrosc. 12, 734 (1970), http://xxx.lanl.gov/abs/quant-ph/0005047 ; Sov. Phys. J. 13, 1435 (1970); A. K. Popov, Introduction in Nonlinear Spectroscopy (Nauka, Novosibirsk, Russia, 1983; in Russian).
[CrossRef]

Popova, T. Ya.

T. Ya. Popova and A. K. Popov, J. Appl. Spectrosc. 12, 734 (1970), http://xxx.lanl.gov/abs/quant-ph/0005047 ; Sov. Phys. J. 13, 1435 (1970); A. K. Popov, Introduction in Nonlinear Spectroscopy (Nauka, Novosibirsk, Russia, 1983; in Russian).
[CrossRef]

Rautian, S. G.

G. E. Notkin, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 52, 1673 (1967); T. Ya. Popova, A. K. Popov, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 57, 444 (1969); T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovsky, Zh. Eksp. Teor. Fiz. 57, 850 (1969); S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (Elsevier, Amsterdam, 1991).

Scully, M. O.

M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, Phys. Rev. Lett. 82, 1847 (1999).
[CrossRef]

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998); A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

M. O. Scully, Phys. Rep. 219, 191 (1992); O. Kocharovskaya, Phys. Rep. 219, 175 (1992); P. Mandel, Contemp. Phys. 34, 235 (1993); A. K. Popov and S. G. Rautian, Proc. SPIE 2798, 49 (1996); A. K. Popov, Bull. Russ. Acad. Sci. (Physics) 60, 927 (1996).
[CrossRef]

Sharpe, S. J.

Tartakovsky, G.

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
[CrossRef]

Tiemann, E.

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
[CrossRef]

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
[CrossRef]

Wellegehausen, B.

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
[CrossRef]

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
[CrossRef]

Xia, H.

Yin, G. Y.

J. Appl. Spectrosc. (1)

T. Ya. Popova and A. K. Popov, J. Appl. Spectrosc. 12, 734 (1970), http://xxx.lanl.gov/abs/quant-ph/0005047 ; Sov. Phys. J. 13, 1435 (1970); A. K. Popov, Introduction in Nonlinear Spectroscopy (Nauka, Novosibirsk, Russia, 1983; in Russian).
[CrossRef]

JETP Lett. (1)

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen, and G. Tartakovsky, JETP Lett. 69, 912 (1999).
[CrossRef]

Opt. Commun. (1)

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, Opt. Commun. 166, 127 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

P. Dong, W. Man, and J. Y. Gao, Phys. Lett. A 265, 43 (2000).
[CrossRef]

Phys. Rep. (1)

M. O. Scully, Phys. Rep. 219, 191 (1992); O. Kocharovskaya, Phys. Rep. 219, 175 (1992); P. Mandel, Contemp. Phys. 34, 235 (1993); A. K. Popov and S. G. Rautian, Proc. SPIE 2798, 49 (1996); A. K. Popov, Bull. Russ. Acad. Sci. (Physics) 60, 927 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, Phys. Rev. Lett. 82, 1847 (1999).
[CrossRef]

M. D. Lukin, P. R. Hemmer, M. Loeffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998); A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

Quantum Electron. (1)

A. K. Popov and S. A. Myslivets, Quantum Electron. 27, 1004 (1997); A. K. Popov, Proc. SPIE 3485, 252 (1998).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

G. E. Notkin, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 52, 1673 (1967); T. Ya. Popova, A. K. Popov, S. G. Rautian, and A. A. Feoktistov, Zh. Eksp. Teor. Fiz. 57, 444 (1969); T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovsky, Zh. Eksp. Teor. Fiz. 57, 850 (1969); S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (Elsevier, Amsterdam, 1991).

Other (1)

I. M. Beterov, “Investigation of nonlinear resonant interaction of optical fields in a three-level gas laser,” Cand. Sci. Dissertation (Institute of Semiconductor Physics SD USSR AS, Siberian Academy of Sciences, Novosibirsk, Russia, 1970).

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Figures (3)

Fig. 1
Fig. 1

(a) Energy levels and (b) AWI, where Ω4=ω4-ωml, L4=α40-1, α40=α4 Gi=0,Ω4=0, G10=100, G30=40 MHz, Ω1=ω1-ωgl=0, and Ω3=ω3-ωmn=100 MHz.

Fig. 2
Fig. 2

(a) Macroscopic Stokes gain, (b) absorption, and (c)–(f) cross-coupling indices; Ω2ω2-ωgn=Ω1+Ω3-Ω4. Solid curves, same parameters as in Fig. 1(b); dashed curves, G1=43 MHz, G3=39 MHz (corresponding to L/L4=20, where the gain reaches its maximum value).

Fig. 3
Fig. 3

(a), (b) Coupled fields versus optical length (I2 is reduced by 104), (c) CQC optical switching. For (a) and (b) and for the inset in (c), Ω4=160 MHz, and for the inset in (b), Ω1=Ω2=Ω3=Ω4=0, where the remaining parameters are the same as in Fig. 1(b). (c) I4/I40=5×10-4 at Ω4=75 MHz and I4/I40=10-2 at Ω4=69 MHz; inset in (c), I4/I40=10-4 at G10=80 MHz and I4/I40=10-2 at G10=89 MHz.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

dE4,2z/dz=iσ4,2E4,2+iσ˜4,2E1E3E2,4*,
dE1,3z/dz=iσ1,3E1,3+iσ˜1,3E4E2E1,3*.
E2*=exp-α22z-βz-iγ2*RE40 sinhRz+E20*coshRz+βRsinhRz, E4=exp-α42z+βziγ4RE20* sinhRz+E40coshRz-βRsinhRz.

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