Abstract

An external cw laser signal in injected into a microcavity laser, and the dynamics of the resulting coupled oscillator system are studied. By variation of the injection detuning and intensity, interesting nonlinear behavior and injection locking are experimentally observed. A theoretical model of this system based on coupled rate equations and including many-body gain effects is presented and yields good agreement with experiment.

© 1993 Optical Society of America

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References

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  1. M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), p. 52.
  2. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 29.
  3. R. Lang, IEEE J. Quantum Electron. QE-18, 976 (1982).
    [CrossRef]
  4. S. Kobayashi, in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 367–410.
  5. F. Mogensen, H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-21, 784 (1985).
    [CrossRef]
  6. R. Hui, A. D’Ottavi, A. Mecozzi, P. Spano, IEEE J. Quantum Electron. 27, 1688 (1991).
    [CrossRef]
  7. J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
    [CrossRef]
  8. I. Petitbon, P. Gallion, G. Debarge, C. Chabran, IEEE J. Quantum Electron. 24, 148 (1988).
    [CrossRef]
  9. R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
    [CrossRef]
  10. M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 884 (1972).
    [CrossRef]
  11. H. Haug, S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).

1992 (1)

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

1991 (2)

R. Hui, A. D’Ottavi, A. Mecozzi, P. Spano, IEEE J. Quantum Electron. 27, 1688 (1991).
[CrossRef]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
[CrossRef]

1988 (1)

I. Petitbon, P. Gallion, G. Debarge, C. Chabran, IEEE J. Quantum Electron. 24, 148 (1988).
[CrossRef]

1985 (1)

F. Mogensen, H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-21, 784 (1985).
[CrossRef]

1982 (1)

R. Lang, IEEE J. Quantum Electron. QE-18, 976 (1982).
[CrossRef]

1972 (1)

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 884 (1972).
[CrossRef]

Boggavarapu, D.

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

Chabran, C.

I. Petitbon, P. Gallion, G. Debarge, C. Chabran, IEEE J. Quantum Electron. 24, 148 (1988).
[CrossRef]

D’Ottavi, A.

R. Hui, A. D’Ottavi, A. Mecozzi, P. Spano, IEEE J. Quantum Electron. 27, 1688 (1991).
[CrossRef]

Debarge, G.

I. Petitbon, P. Gallion, G. Debarge, C. Chabran, IEEE J. Quantum Electron. 24, 148 (1988).
[CrossRef]

Florez, L. T.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
[CrossRef]

Gallion, P.

I. Petitbon, P. Gallion, G. Debarge, C. Chabran, IEEE J. Quantum Electron. 24, 148 (1988).
[CrossRef]

Gibbs, H. M.

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

Harbison, J. P.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
[CrossRef]

Haug, H.

H. Haug, S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).

Hu, Y. Z.

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

Hui, R.

R. Hui, A. D’Ottavi, A. Mecozzi, P. Spano, IEEE J. Quantum Electron. 27, 1688 (1991).
[CrossRef]

Jacobsen, G.

F. Mogensen, H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-21, 784 (1985).
[CrossRef]

Jewell, J. L.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
[CrossRef]

Jin, R.

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

Khitrova, G.

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

Kobayashi, S.

S. Kobayashi, in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 367–410.

Koch, S. W.

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

H. Haug, S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).

Lamb, W. E.

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 884 (1972).
[CrossRef]

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), p. 52.

Lang, R.

R. Lang, IEEE J. Quantum Electron. QE-18, 976 (1982).
[CrossRef]

Lee, Y. H.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
[CrossRef]

Mecozzi, A.

R. Hui, A. D’Ottavi, A. Mecozzi, P. Spano, IEEE J. Quantum Electron. 27, 1688 (1991).
[CrossRef]

Mogensen, F.

F. Mogensen, H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-21, 784 (1985).
[CrossRef]

Olesen, H.

F. Mogensen, H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-21, 784 (1985).
[CrossRef]

Petitbon, I.

I. Petitbon, P. Gallion, G. Debarge, C. Chabran, IEEE J. Quantum Electron. 24, 148 (1988).
[CrossRef]

Peyghambarian, N.

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

Sargent, M.

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), p. 52.

Scherer, A.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
[CrossRef]

Scully, M. O.

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), p. 52.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 29.

Spano, P.

R. Hui, A. D’Ottavi, A. Mecozzi, P. Spano, IEEE J. Quantum Electron. 27, 1688 (1991).
[CrossRef]

Spencer, M. B.

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 884 (1972).
[CrossRef]

Appl. Phys. Lett. (1)

R. Jin, D. Boggavarapu, G. Khitrova, H. M. Gibbs, Y. Z. Hu, S. W. Koch, N. Peyghambarian, Appl. Phys. Lett. 61, 1883 (1992).
[CrossRef]

IEEE J. Quantum Electron. (5)

R. Lang, IEEE J. Quantum Electron. QE-18, 976 (1982).
[CrossRef]

F. Mogensen, H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-21, 784 (1985).
[CrossRef]

R. Hui, A. D’Ottavi, A. Mecozzi, P. Spano, IEEE J. Quantum Electron. 27, 1688 (1991).
[CrossRef]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, IEEE J. Quantum Electron. 27, 1332 (1991).
[CrossRef]

I. Petitbon, P. Gallion, G. Debarge, C. Chabran, IEEE J. Quantum Electron. 24, 148 (1988).
[CrossRef]

Phys. Rev. A (1)

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 884 (1972).
[CrossRef]

Other (4)

H. Haug, S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1990).

S. Kobayashi, in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 367–410.

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), p. 52.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 29.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for investigating injection dynamics. M’s, mirrors; BS’s, beam splitters; L, lens; AOM’s, acousto-optic modulators; PMT’s, photomultiplier tubes; IF, interference filter; ND, neutral-density filter.

Fig. 2
Fig. 2

Sequence of frequency spectra as the injection intensity is increased for positive detunings: (a) Δ = 5.1 GHz, (b) Δ = 7.5 GHz.

Fig. 3
Fig. 3

Frequency spectra plots for (a) negative detuning (Δ = −3.0 GHz) as the injection level is increased and (b) positive detuning (Δ = 4.2 GHz). The thin solid curves are experimentally observed spectra, and the darker vertical lines are theoretically computed spectra with the injection located at the center of the figure in each case. The inset shows the theoretically computed phase portrait of the complex electric field.

Fig. 4
Fig. 4

Reciprocal of the injection power level needed to frequency lock the VCSEL as a function of detuning. The solid curve shows the functional form of the locking range equation asymmetry assuming α = 2.0

Equations (3)

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d E d t = Δ N d g d N E + c 2 L n E i t r cos ϕ ,
d ϕ d t = Δ + α d g d N Δ N c 2 L n E i E 0 t r sin ϕ ,
d Δ N d t = k n g ( N th ) E 0 2 γ Δ N k n g ( N ) E 2 ,

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