Abstract

We investigate experimentally the polarization dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback operating in the long-cavity regime. By means of an analysis of the correlation properties in the time domain and in the frequency domain a connection between a drift phenomenon and frequency components that deviate from the harmonics of the external cavity round-trip frequency is revealed. The latter frequency components are shown to result from an interaction of external cavity dynamics and relaxation oscillations. An analogy to the carrier-envelope effect in mode-locked lasers is drawn. Similar drift phenomena are observed also for other laser systems with delay.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  26. J. Reichert, R. Holzwarth, T. Udem, and T. W. H¨ansch, �??Measuring the frequency of light with mode-locked lasers,�?? Opt. Commun. 172, 59�??68 (1999).
    [CrossRef]
  27. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S.Windeler, J. L. Hall, and S. T. Cundiff, �??Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,�?? Science 288, 635�??639 (2000).
    [CrossRef] [PubMed]
  28. T. Udem, R. Holzwarth, and T. W. H´ansch, �??Optical frequency metrology,�?? Nature 416, 233�??247 (2002).
    [CrossRef] [PubMed]
  29. G. H. M. v. Tartwijk, A. M. Levine, and D. Lenstra, �??Sisyphus effect in semiconductor lasers with optical feedback,�?? IEEE J. Selec. Top. Quantum Electron. 1, 466�??472 (1995).
    [CrossRef]
  30. J. S. Cohen, R. R. Drenten, and B. H. Verbeek, �??The Effect of Optical Feedback on the Relaxation Oscillation in Semiconductor Lasers,�?? IEEE J. Quantum Electron. 24(10), 1989�??1995 (1988).
    [CrossRef]
  31. N. A. Loiko and A. M. Samson, �??Possible regimes of generation of a semiconductor laser with a delayed optoelectric feedback,�?? Opt. Commun. 93, 66�??72 (1992).
    [CrossRef]
  32. G. Giacomelli and A. Politi, �??Multiple scale analysis of delayed dynamical systems,�?? Physica D 145, 26�??42 (1998).
    [CrossRef]
  33. M. Bestehorn, E. V. Grigorieva, H. Haken, and S. A. Kaschenko, �??Order parameters for class-B lasers with a long time delayed feedback,�?? Physica D 145, 110�??129 (2000).
    [CrossRef]
  34. E. V. Grigorieva, H. Haken, and S. A. Kaschenko, �??Theory of quasiperiodicity in model of lasers with delayed optoelectronic feedback,�?? Opt. Commun. 165, 279�??292 (1999).
    [CrossRef]

84Phys. Rev. Lett. (1)

G. Giacomelli, M. Giudici, S. Balle, and J. R. Tredicce, �??Experimental evidence of coherence resonance in an optical system,�?? Phys. Rev. Lett. 84, 3298�??3301 (2000).
[CrossRef] [PubMed]

AIP Conference Proceedings (1)

B. Krauskopf and D. Lenstra, eds., Fundamental issues of nonlinear laser dynamics, vol. 548 of AIP Conference Proceedings (American Institute of Physics, Melville, 2000).

Appl. Phys. B (1)

M. P. v. Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. v. Poel, �??Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,�?? Opt. Commun. 110, 137�??140 (1994).
[CrossRef]

Appl. Phys. B. (1)

T. Ackemann, M. Sondermann, A. V. Naumenko, and N. A. Loiko, �??Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,�?? Appl. Phys. B 77, 739�??746(2003).
[CrossRef]

Chaos, Solitons & Fractals (1)

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, �??Dynamical behavior of semiconductor lasers with frequency selective optical feedback,�?? Chaos, Solitons & Fractals 10, 811�??818 (1999).

IEEE J. Quantum Electron. (4)

J. Mørk, B. Tromborg, and J. Mark, �??Chaos in Semiconductor Lasers with Optical Feedback: Theory and Experiment,�?? IEEE J. Quantum Electron. 28(1), 93�??108 (1992).
[CrossRef]

M. Ahmed and M. Yamada, �??Influence of Instantaneous Mode Competition on the Dynamics of Semiconductor Lasers,�?? IEEE J. Quantum Electron. 38(6), 682�??693 (2002).
[CrossRef]

F. Robert, P. Besnard, M. L. Chares, and G. M. Stephan, �??Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,�?? IEEE J. Quantum Electron. 33, 2231�??2238 (1997).
[CrossRef]

J. S. Cohen, R. R. Drenten, and B. H. Verbeek, �??The Effect of Optical Feedback on the Relaxation Oscillation in Semiconductor Lasers,�?? IEEE J. Quantum Electron. 24(10), 1989�??1995 (1988).
[CrossRef]

IEEE J. Selec. Top. Quantum Electron. (2)

G. H. M. v. Tartwijk, A. M. Levine, and D. Lenstra, �??Sisyphus effect in semiconductor lasers with optical feedback,�?? IEEE J. Selec. Top. Quantum Electron. 1, 466�??472 (1995).
[CrossRef]

K. Petermann, �??External optical feedback phenomena in semiconductor lasers,�?? IEEE J. Selec. Top. Quantum Electron. 1, 480�??489 (1995).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. 7 (1)

G. H. M. v. Tartwijk and D. Lenstra, �??Semiconductor lasers with optical injection and feedback,�?? J. Opt. B: Quantum Semiclass. Opt. 7, 87�??143 (1995).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

T. Udem, R. Holzwarth, and T. W. H´ansch, �??Optical frequency metrology,�?? Nature 416, 233�??247 (2002).
[CrossRef] [PubMed]

Opt. Commun. (4)

J. Reichert, R. Holzwarth, T. Udem, and T. W. H¨ansch, �??Measuring the frequency of light with mode-locked lasers,�?? Opt. Commun. 172, 59�??68 (1999).
[CrossRef]

N. A. Loiko and A. M. Samson, �??Possible regimes of generation of a semiconductor laser with a delayed optoelectric feedback,�?? Opt. Commun. 93, 66�??72 (1992).
[CrossRef]

E. V. Grigorieva, H. Haken, and S. A. Kaschenko, �??Theory of quasiperiodicity in model of lasers with delayed optoelectronic feedback,�?? Opt. Commun. 165, 279�??292 (1999).
[CrossRef]

I. Leyva, E. Allaria, and R. Meucci, �??Transient polarization dynamics in a CO2 laser,�?? Opt. Commun. 217, 335�??342 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

G. Giacomelli, F. Marin, and M. Romanelli, �??Multi-time-scale dynamics of a laser with polarized optical feedback,�?? Phys. Rev. A 67, 053,809 (2003).
[CrossRef]

Phys. Rev. A (5)

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, �??Description and analysis of low frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,�?? Phys. Rev. A 68, 033,805 (2003).
[CrossRef]

M. Sondermann, H. Bohnet, and T. Ackemann, �??Low Frequency Fluctuations and Polarization Dynamics in Vertical-cavity Surface-emitting Lasers with Isotropic Feedback,�?? Phys. Rev. A 67, 021,802 (2003).
[CrossRef]

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, �??Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,�?? Phys. Rev. A 68, 033,822 (2003).
[CrossRef]

A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, �??Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,�?? Phys. Rev. A 64, 023,801 (2001).
[CrossRef]

A. Gavrielides, T. C. Newell, V. Kovanis, R. G. Harrison, N. Swanston, D. Yu, andW. Lu, �??Synchronous Sisyphus effect in diode lasers subject to optical feedback,�?? Phys. Rev. A 60, 1577�??1580 (1999).
[CrossRef]

Phys. Rev. A. (1)

F. T. Arecchi, G. Giacomelli, A. Lapucci, and R. Meucci, �??Two-dimensional representation of a delayed dynamical system,�?? Phys. Rev. A 45, 4225�??4228 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, �??Andronov bifurcation and excitability in semiconductor lasers with optical feedback,�?? Phys. Rev. E 55, 6414�??6118 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

T. Heil, I. Fischer, W. Els¨a�?er, and A. Gavrielides, �??Dynamics of Semiconductor Lasers Subject to Delayed Optical Feedback: The Short Cavity Regime,�?? Phys. Rev. Lett. 87(24), 243,901 (2001).

Physica D (2)

G. Giacomelli and A. Politi, �??Multiple scale analysis of delayed dynamical systems,�?? Physica D 145, 26�??42 (1998).
[CrossRef]

M. Bestehorn, E. V. Grigorieva, H. Haken, and S. A. Kaschenko, �??Order parameters for class-B lasers with a long time delayed feedback,�?? Physica D 145, 110�??129 (2000).
[CrossRef]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S.Windeler, J. L. Hall, and S. T. Cundiff, �??Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,�?? Science 288, 635�??639 (2000).
[CrossRef] [PubMed]

Semiconductor quantum optoelectronics: F (1)

M. San Miguel, �??Polarization properties of vertical cavity surface emitting lasers,�?? in Semiconductor quantum optoelectronics: From quantum physics to smart devices, A. Miller, M. Ebrahimzadeh, and D. M. Finlayson, eds., pp. 339�??366 (SUSSP and Institute of Physics Publishing, Bristol, 1999).

Other (2)

W. H. Press, B. Flannery, S. Teukolsky, and W. Vettering, Numerical recipes: the art of scientific computing (Cambridge University Press, Cambridge, 1992).

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Characterization of the dynamics of a VCSEL with isotropic optical feedback: (a) measured time traces, (b) auto correlation functions, (c) cross correlation function, (d) power spectra of the polarization modes, (e) cross spectral density (CSD). In panels displaying data for both polarization modes, the red and blue lines denote the data corresponding to the two orthogonal polarization modes. The injection current is set to the threshold of the solitary laser. The threshold reduction with feedback is 6%. The detection bandwidth is 1 GHz.

Fig. 2.
Fig. 2.

Cross correlation function for the same parameters as in Fig. 1(c) but after elimination of the correlated (green line) and anticorrelated (red line) frequency components from the cross spectral density (see text for further explanations). The red line is raised by 0.2 units for better visibility.

Fig. 3.
Fig. 3.

Power spectrum of the dominant polarization mode and cross spectral density (CSD) of the dynamics of the both polarization modes for another device with a threshold reduction of 18% for injection currents 4% below (a,b) and 32% above (c,d) the threshold of the solitary laser, respectively. Red (blue) colour denotes anticorrelated (correlated) components. The inset in panel (d) is a magnification of the spectral components for frequencies larger than 2 GHz. The detection bandwidth is 6 GHz. The corresponding time series are amplified by 20 dB and the DC-component is cut off. The features near 1.7 GHz and 3.4 GHz in panel (b) are artefacts that are captured by the setup.

Fig. 4.
Fig. 4.

Auto correlation function (a) and power spectrum (b) of the dominant polarization mode of another device with isotropic feedback. The inset in (b) displays the frequencies (in GHz) of the spectral components at the first harmonic of the external cavity frequency as a function of the injection current normalized to the threshold of the solitary laser. The threshold reduction is 8%. The current is set to 0.95 times the threshold of the laser without feedback. The detection bandwidth is 1 GHz.

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