Abstract

A single-mode diode laser subject to reflections from an externally pumped phase-conjugate mirror is theoretically investigated by using a rate-equation approach. In the phase plane defined by the amount of feedback and the frequency detuning between diode laser and phase-conjugate mirror, we found an island of locked steady-state behavior, surrounded by another type of steady-state behavior, referred to as the frequency-difference solution, and a region of self-pulsating relaxation oscillations.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).
  2. J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
  3. G. P. Agrawal, J. T. Klaus, Opt. Lett. 16, 1325 (1991).
  4. R. A. Fisher, Optical Phase Conjugation (Academic, New York, 1983).
  5. A. B. Pippard, Response and Stability (Cambridge U. Press, Cambridge, 1985).
  6. J. S. Cohen, R. R. Drenten, B. H. Verbeek, IEEE J. Quantum Electron. 24, 1989 (1988).
  7. C. H. Henry, IEEE J. Quantum Electron. QE-19, 1391 (1983).
  8. G. A. Acket, D. Lenstra, B. H. Verbeek, IEEE J. Quantum Electron. QE-20, 1163 (1984).
  9. D. Lenstra, B. H. Verbeek, A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985);J. Sacher, W. Elsässer, E. O. Göbel, Phys. Rev. Lett. 63, 155 (1989);J. Mørk, J. Mark, B. Tromborg, Phys. Rev. Lett. 65, 1999 (1990).
  10. Recently confirmed by G. P. Agrawal, G. R. Gray, “Effect of phase-conjugate feedback on the noise characteristics of semiconductor lasers,” Phys. Rev. A (to be published).

1991 (1)

1988 (1)

J. S. Cohen, R. R. Drenten, B. H. Verbeek, IEEE J. Quantum Electron. 24, 1989 (1988).

1985 (1)

D. Lenstra, B. H. Verbeek, A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985);J. Sacher, W. Elsässer, E. O. Göbel, Phys. Rev. Lett. 63, 155 (1989);J. Mørk, J. Mark, B. Tromborg, Phys. Rev. Lett. 65, 1999 (1990).

1984 (1)

G. A. Acket, D. Lenstra, B. H. Verbeek, IEEE J. Quantum Electron. QE-20, 1163 (1984).

1983 (1)

C. H. Henry, IEEE J. Quantum Electron. QE-19, 1391 (1983).

1979 (1)

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).

Acket, G. A.

G. A. Acket, D. Lenstra, B. H. Verbeek, IEEE J. Quantum Electron. QE-20, 1163 (1984).

Agrawal, G. P.

G. P. Agrawal, J. T. Klaus, Opt. Lett. 16, 1325 (1991).

Recently confirmed by G. P. Agrawal, G. R. Gray, “Effect of phase-conjugate feedback on the noise characteristics of semiconductor lasers,” Phys. Rev. A (to be published).

G. P. Agrawal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).

Auyeung, J.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).

Cohen, J. S.

J. S. Cohen, R. R. Drenten, B. H. Verbeek, IEEE J. Quantum Electron. 24, 1989 (1988).

den Boef, A. J.

D. Lenstra, B. H. Verbeek, A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985);J. Sacher, W. Elsässer, E. O. Göbel, Phys. Rev. Lett. 63, 155 (1989);J. Mørk, J. Mark, B. Tromborg, Phys. Rev. Lett. 65, 1999 (1990).

Drenten, R. R.

J. S. Cohen, R. R. Drenten, B. H. Verbeek, IEEE J. Quantum Electron. 24, 1989 (1988).

Dutta, N. K.

G. P. Agrawal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).

Fekete, D.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).

Fisher, R. A.

R. A. Fisher, Optical Phase Conjugation (Academic, New York, 1983).

Gray, G. R.

Recently confirmed by G. P. Agrawal, G. R. Gray, “Effect of phase-conjugate feedback on the noise characteristics of semiconductor lasers,” Phys. Rev. A (to be published).

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. QE-19, 1391 (1983).

Klaus, J. T.

Lenstra, D.

D. Lenstra, B. H. Verbeek, A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985);J. Sacher, W. Elsässer, E. O. Göbel, Phys. Rev. Lett. 63, 155 (1989);J. Mørk, J. Mark, B. Tromborg, Phys. Rev. Lett. 65, 1999 (1990).

G. A. Acket, D. Lenstra, B. H. Verbeek, IEEE J. Quantum Electron. QE-20, 1163 (1984).

Pepper, D. M.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).

Pippard, A. B.

A. B. Pippard, Response and Stability (Cambridge U. Press, Cambridge, 1985).

Verbeek, B. H.

J. S. Cohen, R. R. Drenten, B. H. Verbeek, IEEE J. Quantum Electron. 24, 1989 (1988).

D. Lenstra, B. H. Verbeek, A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985);J. Sacher, W. Elsässer, E. O. Göbel, Phys. Rev. Lett. 63, 155 (1989);J. Mørk, J. Mark, B. Tromborg, Phys. Rev. Lett. 65, 1999 (1990).

G. A. Acket, D. Lenstra, B. H. Verbeek, IEEE J. Quantum Electron. QE-20, 1163 (1984).

Yariv, A.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).

IEEE J. Quantum Electron. (5)

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).

J. S. Cohen, R. R. Drenten, B. H. Verbeek, IEEE J. Quantum Electron. 24, 1989 (1988).

C. H. Henry, IEEE J. Quantum Electron. QE-19, 1391 (1983).

G. A. Acket, D. Lenstra, B. H. Verbeek, IEEE J. Quantum Electron. QE-20, 1163 (1984).

D. Lenstra, B. H. Verbeek, A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985);J. Sacher, W. Elsässer, E. O. Göbel, Phys. Rev. Lett. 63, 155 (1989);J. Mørk, J. Mark, B. Tromborg, Phys. Rev. Lett. 65, 1999 (1990).

Opt. Lett. (1)

Other (4)

R. A. Fisher, Optical Phase Conjugation (Academic, New York, 1983).

A. B. Pippard, Response and Stability (Cambridge U. Press, Cambridge, 1985).

Recently confirmed by G. P. Agrawal, G. R. Gray, “Effect of phase-conjugate feedback on the noise characteristics of semiconductor lasers,” Phys. Rev. A (to be published).

G. P. Agrawal, N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Diode laser with external phase-conjugate feedback. The pump waves have frequency ωp.

Fig. 2
Fig. 2

Numerical simulation showing the relative amplitude variations versus time for the nearly locked solution (still in regime I, but very close to regime II) with Δω/2π = 0.5 GHz and C = 0.49.

Fig. 3
Fig. 3

Phase space of the diode laser with phase-conjugate feedback. Solid curves indicate sharp boundaries between the regimes, whereas the dotted curves indicate the more gradual boundary between regimes I and III. The dashed–dotted lines indicate the edge condition of locking.

Equations (7)

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

d d t E ( t ) = 1 2 ξ ( 1 + i α ) N ( t ) E ( t ) + γ E * ( t τ ) × exp { i [ 2 Δ ω ( t τ 2 ) + ϕ PCM ] } ,
d d t N ( t ) = [ 1 T 1 + ξ P ( t ) ] N ( t ) Γ 0 [ P ( t ) P 0 ] ,
E ( t ) = P s exp [ i ( Ω t + φ 0 ) ] , N ( t ) = N s .
Ω = γ 1 + α 2 sin ( arctan α + θ ) ,
γ 1 + α 2 | Δ ω | .
E ( t ) = { P 0 + 1 exp [ i ( ω t + φ 1 ) ] + 2 exp [ i ( ω t + φ 2 ) ] } exp ( i φ 0 ) ,
D ( s ) = ( s + 2 λ R ) { s 2 + 2 s γ cos θ + γ 2 [ 1 exp ( 2 s τ ) ] } + γ ξ P 1 + α 2 ( Γ 0 2 γ cos θ ) × { s + γ [ 1 + exp ( s τ ) ] } cos ( θ + arctan α ) .

Metrics