Abstract

We report on fabrication and characterization of single-longitudinal- and transverse-mode semiconductor ring lasers. A bifurcation from bidirectional stable operation to a regime with alternate oscillations of the counterpropagating modes was observed experimentally and is theoretically explained through a two-mode model. Analytical expressions for the onset and the frequency of the oscillations are derived, and LI curves numerically evaluated. Good quantitative agreement between theory and measurements made over a large number of tested devices is obtained.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. O. Weiss and R. Vilaseca, Dynamics of Lasers (Weinheim, New York, 1991), and references therein.
  2. Q. L. Williams and R. Roy, Opt. Lett. 37, 470 (1988).
  3. E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
    [CrossRef] [PubMed]
  4. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
    [CrossRef]
  5. T. Krauss, P. J. R. Laybourn, and J. S. Roberts, Electron. Lett. 26, 2095 (1990).
    [CrossRef]
  6. J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997).
    [CrossRef]
  7. M. Sorel, G. Giuliani, S. Donati, and P. J. R. Laybourn, Appl. Phys. Lett. 80, 3051 (2002).
    [CrossRef]
  8. R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
    [CrossRef]
  9. F. C. Cheng, Phys. Rev. A 45, 5220 (1992).
    [CrossRef] [PubMed]
  10. T. Numai, IEEE J. Quantum Electron. 36, 1161 (2000).
    [CrossRef]
  11. M. San Miguel, Phys. Rev. Lett. 75, 425 (1995).
    [CrossRef] [PubMed]
  12. M. Sargent, Phys. Rev. A 48, 717 (1993).
    [CrossRef] [PubMed]
  13. C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
    [CrossRef] [PubMed]

2002 (1)

M. Sorel, G. Giuliani, S. Donati, and P. J. R. Laybourn, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

2000 (1)

T. Numai, IEEE J. Quantum Electron. 36, 1161 (2000).
[CrossRef]

1997 (1)

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997).
[CrossRef]

1995 (1)

M. San Miguel, Phys. Rev. Lett. 75, 425 (1995).
[CrossRef] [PubMed]

1993 (1)

M. Sargent, Phys. Rev. A 48, 717 (1993).
[CrossRef] [PubMed]

1992 (3)

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
[CrossRef] [PubMed]

F. C. Cheng, Phys. Rev. A 45, 5220 (1992).
[CrossRef] [PubMed]

E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
[CrossRef] [PubMed]

1990 (2)

T. Krauss, P. J. R. Laybourn, and J. S. Roberts, Electron. Lett. 26, 2095 (1990).
[CrossRef]

R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
[CrossRef]

1988 (1)

1985 (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

Ballantyne, J. M.

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997).
[CrossRef]

Cheng, F. C.

F. C. Cheng, Phys. Rev. A 45, 5220 (1992).
[CrossRef] [PubMed]

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

D’Angelo, E. J.

E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
[CrossRef] [PubMed]

Donati, S.

M. Sorel, G. Giuliani, S. Donati, and P. J. R. Laybourn, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Eliel, E. R.

R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
[CrossRef]

Etrich, C.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
[CrossRef] [PubMed]

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

Gil, L.

E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
[CrossRef] [PubMed]

Giuliani, G.

M. Sorel, G. Giuliani, S. Donati, and P. J. R. Laybourn, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Izaguirre, E.

E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
[CrossRef] [PubMed]

Krauss, T.

T. Krauss, P. J. R. Laybourn, and J. S. Roberts, Electron. Lett. 26, 2095 (1990).
[CrossRef]

Lau, S. T.

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997).
[CrossRef]

Laybourn, P. J. R.

M. Sorel, G. Giuliani, S. Donati, and P. J. R. Laybourn, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

T. Krauss, P. J. R. Laybourn, and J. S. Roberts, Electron. Lett. 26, 2095 (1990).
[CrossRef]

Leary, M. H.

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997).
[CrossRef]

Liang, J. J.

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997).
[CrossRef]

Mandel, P.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
[CrossRef] [PubMed]

Mindlin, G. B.

E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
[CrossRef] [PubMed]

Neelen, R. Centeno

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
[CrossRef] [PubMed]

Neelon, R. Centeno

R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
[CrossRef]

Numai, T.

T. Numai, IEEE J. Quantum Electron. 36, 1161 (2000).
[CrossRef]

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

Roberts, J. S.

T. Krauss, P. J. R. Laybourn, and J. S. Roberts, Electron. Lett. 26, 2095 (1990).
[CrossRef]

Roy, R.

San Miguel, M.

M. San Miguel, Phys. Rev. Lett. 75, 425 (1995).
[CrossRef] [PubMed]

Sanders, V. E.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

Sargent, M.

M. Sargent, Phys. Rev. A 48, 717 (1993).
[CrossRef] [PubMed]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

Scully, M. O.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

Sorel, M.

M. Sorel, G. Giuliani, S. Donati, and P. J. R. Laybourn, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Spreeuw, R. J. C.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
[CrossRef] [PubMed]

Spreew, R. J. C.

R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
[CrossRef]

Tredicce, J. R.

E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
[CrossRef] [PubMed]

van Druten, N. J.

R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
[CrossRef]

Vilaseca, R.

C. O. Weiss and R. Vilaseca, Dynamics of Lasers (Weinheim, New York, 1991), and references therein.

Weiss, C. O.

C. O. Weiss and R. Vilaseca, Dynamics of Lasers (Weinheim, New York, 1991), and references therein.

Williams, Q. L.

Woerdman, J. P.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
[CrossRef] [PubMed]

R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
[CrossRef]

Appl. Phys. Lett. (2)

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997).
[CrossRef]

M. Sorel, G. Giuliani, S. Donati, and P. J. R. Laybourn, Appl. Phys. Lett. 80, 3051 (2002).
[CrossRef]

Electron. Lett. (1)

T. Krauss, P. J. R. Laybourn, and J. S. Roberts, Electron. Lett. 26, 2095 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Numai, IEEE J. Quantum Electron. 36, 1161 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

R. J. C. Spreew, R. Centeno Neelon, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, Phys. Rev. A 42, 4315 (1990).
[CrossRef]

F. C. Cheng, Phys. Rev. A 45, 5220 (1992).
[CrossRef] [PubMed]

M. Sargent, Phys. Rev. A 48, 717 (1993).
[CrossRef] [PubMed]

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 46, 525 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

M. San Miguel, Phys. Rev. Lett. 75, 425 (1995).
[CrossRef] [PubMed]

E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, L. Gil, and J. R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, Rev. Mod. Phys. 57, 61 (1985).
[CrossRef]

Other (1)

C. O. Weiss and R. Vilaseca, Dynamics of Lasers (Weinheim, New York, 1991), and references therein.

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

(a) Geometry of the SRL device and layout of the contacts. PD1, PD2, photodiodes. (b) Detail of the output waveguide.

Fig. 2
Fig. 2

(a) Experimental (dc) LI curves of a sample SRL device. (b) Theoretical time-averaged LI curve obtained with α=3.5, s=0.005, c=0.01, kc=0.0044, kd=0.000327, γ=0.002, and τp=10 ps. The Hopf bifurcation boundary is μH=1.4.

Fig. 3
Fig. 3

Time traces of the intensities of modes 1 and 2 in the AO regime. (a) Experimental single-shot acquisition measured from PD1 and PD2 on a 50Ω oscilloscope: vertical scale, 50 mV/division; horizontal scale, 10 ns/division; ring current, 275 mA. (b) Result obtained through numerical simulations (solid curves) and from application of Eq. (8) (dashed curves): vertical scale, arbitrary units; horizontal scale, 10 ns/division. The parameters are the same as for Fig. 2, and μ=1.58.

Equations (8)

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

E·1,2= 1+iαN1-sE1,22-cE2,12-1×E1,2-kd+ikcE2,1,
N·= γμ-N-N1-sE12-cE22E12-N1-sE22-cE12E22,
I0=N0-1+kdηN0,
N0=μ1+I0-ηI02,
R·=½1+iαN0I0c-sR+R*-2kd+ikcR,
R·*=½1-iαN0I0c-sR+R*-2kd-ikcR*.
4kd=N0I0c-s,
Ω=2kd2+kc2-N0I02kd+αkc1/2.

Metrics