Abstract

Conditions for gain and threshold of the inversionless laser are derived as a function of pump strength and relaxation rates. It is shown that lasing without inversion can be achieved most easily only in systems in which either conventional or Raman lasing is attainable. The threshold of the inversionless laser is shown to be orders of magnitude higher than that of the conventional laser. Practical implications, especially for intersubband lasers, are discussed.

© 1997 Optical Society of America

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  1. S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1066 (1989).
    [CrossRef] [PubMed]
  2. O. Kocharovskaya and P. Mandel, “Amplification without inversion: the double-lambda scheme,” Phys. Rev. A 42, 523–535 (1990).
    [CrossRef] [PubMed]
  3. M. O. Scully, “Resolving conundrums in lasing without inversion via solutions to simple models,” Quantum Opt. 6, 203–215 (1994), and references therein.
    [CrossRef]
  4. K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [CrossRef] [PubMed]
  5. J. Gao, C. Guo, X. Guom, and G. Jin, “Observation of light amplification without population inversion in sodium,” Opt. Commun. 93, 323–327 (1992).
    [CrossRef]
  6. A. Nottelmann, C. Peters, and W. Lange, “Inversionless amplification of picosecond pulses due to Zeeman coherence,” Phys. Rev. Lett. 70, 1783–1786 (1993).
    [CrossRef] [PubMed]
  7. A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
    [CrossRef] [PubMed]
  8. J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
    [CrossRef] [PubMed]
  9. A. Imamoglu and R. J. Ram, “Semiconductor lasers without population inversion,” Opt. Lett. 19, 1744–1746 (1994).
    [CrossRef] [PubMed]
  10. D. S. Lee and K. J. Malloy, “Analysis of reduced interband absorption mechanisms in semiconductor quantum wells,” IEEE J. Quantum Electron. 30, 85–92 (1994).
    [CrossRef]
  11. S. Basile and P. Lambropoulos, “Radiation amplification without population inversion in discrete three-level systems,” Opt. Commun. 78, 163–168 (1990).
    [CrossRef]
  12. O. Kocharovskaya and P. Mandel, “Frequency up-conversion in a three-level medium without inversion,” Opt. Commun. 84, 179–183 (1991).
    [CrossRef]
  13. O. Kocharovskaya, P. Mandel, and Y. V. Radeonychev, “Inversionless amplification in a three-level medium,” Phys. Rev. A 45, 1997–2005 (1991).
    [CrossRef]
  14. V. J. Sanchez-Morcillo, E. Roldan, and G. J. de Valcarcel, “Lasing without inversion via a self-pulsing instability,” Quantum Semiclas. Opt. 7, 889–899 (1995).

1995 (1)

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

1994 (4)

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

D. S. Lee and K. J. Malloy, “Analysis of reduced interband absorption mechanisms in semiconductor quantum wells,” IEEE J. Quantum Electron. 30, 85–92 (1994).
[CrossRef]

M. O. Scully, “Resolving conundrums in lasing without inversion via solutions to simple models,” Quantum Opt. 6, 203–215 (1994), and references therein.
[CrossRef]

A. Imamoglu and R. J. Ram, “Semiconductor lasers without population inversion,” Opt. Lett. 19, 1744–1746 (1994).
[CrossRef] [PubMed]

1993 (1)

A. Nottelmann, C. Peters, and W. Lange, “Inversionless amplification of picosecond pulses due to Zeeman coherence,” Phys. Rev. Lett. 70, 1783–1786 (1993).
[CrossRef] [PubMed]

1992 (1)

J. Gao, C. Guo, X. Guom, and G. Jin, “Observation of light amplification without population inversion in sodium,” Opt. Commun. 93, 323–327 (1992).
[CrossRef]

1991 (3)

O. Kocharovskaya and P. Mandel, “Frequency up-conversion in a three-level medium without inversion,” Opt. Commun. 84, 179–183 (1991).
[CrossRef]

O. Kocharovskaya, P. Mandel, and Y. V. Radeonychev, “Inversionless amplification in a three-level medium,” Phys. Rev. A 45, 1997–2005 (1991).
[CrossRef]

K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

1990 (2)

O. Kocharovskaya and P. Mandel, “Amplification without inversion: the double-lambda scheme,” Phys. Rev. A 42, 523–535 (1990).
[CrossRef] [PubMed]

S. Basile and P. Lambropoulos, “Radiation amplification without population inversion in discrete three-level systems,” Opt. Commun. 78, 163–168 (1990).
[CrossRef]

1989 (1)

S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1066 (1989).
[CrossRef] [PubMed]

Basile, S.

S. Basile and P. Lambropoulos, “Radiation amplification without population inversion in discrete three-level systems,” Opt. Commun. 78, 163–168 (1990).
[CrossRef]

Boller, K.-J.

K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Capasso, F.

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

Faist, J.

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

Gao, J.

J. Gao, C. Guo, X. Guom, and G. Jin, “Observation of light amplification without population inversion in sodium,” Opt. Commun. 93, 323–327 (1992).
[CrossRef]

Guo, C.

J. Gao, C. Guo, X. Guom, and G. Jin, “Observation of light amplification without population inversion in sodium,” Opt. Commun. 93, 323–327 (1992).
[CrossRef]

Guom, X.

J. Gao, C. Guo, X. Guom, and G. Jin, “Observation of light amplification without population inversion in sodium,” Opt. Commun. 93, 323–327 (1992).
[CrossRef]

Harris, S. E.

K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1066 (1989).
[CrossRef] [PubMed]

Hollberg, L.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

Imamoglu, A.

A. Imamoglu and R. J. Ram, “Semiconductor lasers without population inversion,” Opt. Lett. 19, 1744–1746 (1994).
[CrossRef] [PubMed]

K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Jin, G.

J. Gao, C. Guo, X. Guom, and G. Jin, “Observation of light amplification without population inversion in sodium,” Opt. Commun. 93, 323–327 (1992).
[CrossRef]

Kocharovskaya, O.

O. Kocharovskaya, P. Mandel, and Y. V. Radeonychev, “Inversionless amplification in a three-level medium,” Phys. Rev. A 45, 1997–2005 (1991).
[CrossRef]

O. Kocharovskaya and P. Mandel, “Frequency up-conversion in a three-level medium without inversion,” Opt. Commun. 84, 179–183 (1991).
[CrossRef]

O. Kocharovskaya and P. Mandel, “Amplification without inversion: the double-lambda scheme,” Phys. Rev. A 42, 523–535 (1990).
[CrossRef] [PubMed]

Lambropoulos, P.

S. Basile and P. Lambropoulos, “Radiation amplification without population inversion in discrete three-level systems,” Opt. Commun. 78, 163–168 (1990).
[CrossRef]

Lange, W.

A. Nottelmann, C. Peters, and W. Lange, “Inversionless amplification of picosecond pulses due to Zeeman coherence,” Phys. Rev. Lett. 70, 1783–1786 (1993).
[CrossRef] [PubMed]

Lee, D. S.

D. S. Lee and K. J. Malloy, “Analysis of reduced interband absorption mechanisms in semiconductor quantum wells,” IEEE J. Quantum Electron. 30, 85–92 (1994).
[CrossRef]

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Malloy, K. J.

D. S. Lee and K. J. Malloy, “Analysis of reduced interband absorption mechanisms in semiconductor quantum wells,” IEEE J. Quantum Electron. 30, 85–92 (1994).
[CrossRef]

Mandel, P.

O. Kocharovskaya and P. Mandel, “Frequency up-conversion in a three-level medium without inversion,” Opt. Commun. 84, 179–183 (1991).
[CrossRef]

O. Kocharovskaya, P. Mandel, and Y. V. Radeonychev, “Inversionless amplification in a three-level medium,” Phys. Rev. A 45, 1997–2005 (1991).
[CrossRef]

O. Kocharovskaya and P. Mandel, “Amplification without inversion: the double-lambda scheme,” Phys. Rev. A 42, 523–535 (1990).
[CrossRef] [PubMed]

Nikonov, D. E.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Nottelmann, A.

A. Nottelmann, C. Peters, and W. Lange, “Inversionless amplification of picosecond pulses due to Zeeman coherence,” Phys. Rev. Lett. 70, 1783–1786 (1993).
[CrossRef] [PubMed]

Peters, C.

A. Nottelmann, C. Peters, and W. Lange, “Inversionless amplification of picosecond pulses due to Zeeman coherence,” Phys. Rev. Lett. 70, 1783–1786 (1993).
[CrossRef] [PubMed]

Radeonychev, Y. V.

O. Kocharovskaya, P. Mandel, and Y. V. Radeonychev, “Inversionless amplification in a three-level medium,” Phys. Rev. A 45, 1997–2005 (1991).
[CrossRef]

Ram, R. J.

Robinson, H. G.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Scully, M. O.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

M. O. Scully, “Resolving conundrums in lasing without inversion via solutions to simple models,” Quantum Opt. 6, 203–215 (1994), and references therein.
[CrossRef]

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

Sivco, D. L.

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

Velichansky, V. L.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Zibrov, A. S.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

D. S. Lee and K. J. Malloy, “Analysis of reduced interband absorption mechanisms in semiconductor quantum wells,” IEEE J. Quantum Electron. 30, 85–92 (1994).
[CrossRef]

Opt. Commun. (3)

S. Basile and P. Lambropoulos, “Radiation amplification without population inversion in discrete three-level systems,” Opt. Commun. 78, 163–168 (1990).
[CrossRef]

O. Kocharovskaya and P. Mandel, “Frequency up-conversion in a three-level medium without inversion,” Opt. Commun. 84, 179–183 (1991).
[CrossRef]

J. Gao, C. Guo, X. Guom, and G. Jin, “Observation of light amplification without population inversion in sodium,” Opt. Commun. 93, 323–327 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

O. Kocharovskaya, P. Mandel, and Y. V. Radeonychev, “Inversionless amplification in a three-level medium,” Phys. Rev. A 45, 1997–2005 (1991).
[CrossRef]

O. Kocharovskaya and P. Mandel, “Amplification without inversion: the double-lambda scheme,” Phys. Rev. A 42, 523–535 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1066 (1989).
[CrossRef] [PubMed]

K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

A. Nottelmann, C. Peters, and W. Lange, “Inversionless amplification of picosecond pulses due to Zeeman coherence,” Phys. Rev. Lett. 70, 1783–1786 (1993).
[CrossRef] [PubMed]

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Quantum Opt. (1)

M. O. Scully, “Resolving conundrums in lasing without inversion via solutions to simple models,” Quantum Opt. 6, 203–215 (1994), and references therein.
[CrossRef]

Science (1)

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, C. Sirtori, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[CrossRef] [PubMed]

Other (1)

V. J. Sanchez-Morcillo, E. Roldan, and G. J. de Valcarcel, “Lasing without inversion via a self-pulsing instability,” Quantum Semiclas. Opt. 7, 889–899 (1995).

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Figures (2)

Fig. 1
Fig. 1

Optically coupled LWI schemes: (a) coherence induced between two upper levels; (b) coherence induced between two lower levels.

Fig. 2
Fig. 2

Absorption in the ladder scheme: (a) n3>n2, (b) n3<n2.

Equations (20)

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

n˙1=P1+knkWk1-n1kW1k,
n˙2=2Ωc2Tc23(n3-n2)+P2+knkWk2-n2k2W2k,
n˙3=-2Ωc2Tc23(n3-n2)+P3+knkWk3-n3kW3k,
n˙p=-2 Im(n1-n2)(ω13-ωs-ωc-i/Tc13)Ωs2-(n2-n3)Ωc2Ωc2ω32-ωc-i/Tc23(ω12-ωs-i/Tc12)(ω13-ωs-ωc-i/Tc13)-Ωc2,
n˙p=-Imn1-n2ω12-ωs-Tc-1-Ωc+n1-n2ω12-ωs-Tc-1+ΩcΩs2+Ren2-n3ω12-ωs-Tc-1-Ωc-n2-n3ω12-ωs-Tc-1+ΩcΩcTcΩs2,
n˙p=-2 n1-n2-(n3-n2)Ωc2Tc23Tc13(1/Tc12)+Ωc2Tc13Ωs2,
n˙p-2 n1-n2-(n2-n3)Ωc2Tc23Tc12(ωs-ω12)2Tc12Ωs2.
n˙p=-APτ3 fτ1-τ2/τ3+2Ωc2Tc23τ1-τ2-½Tc131-f τ2τ31+2Ωc2Tc23[(1-f)τ2+τ3],
Tc132τ3>τ1-τ2τ3-fτ2>1+τ3(1-f)/f+fτ2τ3-fτ2>1,
n˙p=-An1e-n2e-Ωc2Tc23(n3e-n2e)-2τ2+Tc131+2Ωc2Tc23(τ2+τ3).
n˙p=-A(n1e-n2e)-(n3e-n2e) τ2+½Tc13τ2+τ3,
(n1e-n3e)/(n3e-n2e)<(½Tc13-τ3)/(τ2+τ3)<0.
n˙p=-A(n1e-n2e)-(n1e-n3e) τ1+½Tc23τ1+τ3.
(n3e-n2e)/(n1e-n3e)<(½Tc23-τ3)/(τ1+τ3)<0.
n˙p2-(n1-n2)Tc-1(ωs-ω12)2+Tc-2Ωs2+(n3-n1)Tc(ωs-ω12)2+Tc-2Ωc2Ωs2+(n1-n2)Tc-1[(ωs-ω12)2+Tc-2]2Ωc2Ωs2.
n˙p=2AP Tc23[½Tc13τ3-τ2(τ1+κτ3)](Ωc2-Ωc,b2)1+2Ωc2Tc23(τ2+τ3),
Ωc,b2=τ12Tc23[(½Tc13-κτ2)τ3-τ1τ2],
τ2<½Tc13τ3/(τ1+κτ3)<½Tc13
n˙p160PTc13τ3 τ3τ1Ωs2.
n˙p=PTc13τ3Ωs2.

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