### Abstract

Nonlinear dynamics studies have used laser diodes in a variety of external cavity and injection conditions as model systems for the transition to chaos. Most of these studies have concentrated on the transition to chaos as the strength of some parameter is increased. Chaotic dynamics can be observed in a laser diode under strong external optical injection. We observe that the chaotic dynamics can be strictly bounded between two optical injection levels. Both from above and below, the transition to chaos follows a period doubling route. This behavior can be modelled using a rate equation approach coupling a single-mode oscillating optical field with the carrier density. Using the four-wave mixing technique, we have determined the key dynamic parameters of a nearly single-mode laser diode. With these parameters we can make quantitative comparisons between experimentally measured spectra and numerically generated spectra using the coupled equation model. Figure 1 compares the calculated bifurcation diagram with experimentally measured operating regimes for a nearly single mode laser diode under optical injection at the free-running frequency. The injected field amplitude, normalized to the free-running field, is the variable for the diagram and extrema in the variation of the normalized optical field from the steady-state free-running value are shown. The calculated spectrum shows both forward and reverse bifurcations bounding a region of chaotic behavior. At injection power levels of approximately 2% of the oscillating power, we observe that the injection induced a longitudinal mode hop. A strictly single-mode model does not include mode-coupling effects, and further calculations are underway to quantify the influence of the weak side modes of the laser diode. We observe that the relaxation oscillation frequency changes as the injected field level is increased in the strong injection regime. Figure 2 compares the experimentally measured oscillation frequencies with the frequencies derived by a linear stability analysis of the coupled equation model. Over the range where the relaxation frequency more than doubles, the average optical power circulating within the diode cavity and the average carrier density have changed by only a few percent. The good agreement between the observed experimental data and the coupled equation model shows that the fixed parameter on which it is based, the gain of the laser diode, the cavity and spontaneous carrier relaxation rates, and the linewidth enhancement factor, are not strongly influenced by the optical injection. However, the dynamic response of the diode is clearly modified.

Original language | English |
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Title of host publication | Proceedings of the International Quantum Electronics Conference (IQEC'94) |

Publisher | Publ by IEEE |

Pages | 221-222 |

Number of pages | 2 |

ISBN (Print) | 0780319737 |

Publication status | Published - 1994 |

Externally published | Yes |

Event | Proceedings of the 21st International Quantum Electronics Conference (IQEC'94) - Anaheim, CA, USA Duration: May 8 1994 → May 13 1994 |

### Other

Other | Proceedings of the 21st International Quantum Electronics Conference (IQEC'94) |
---|---|

City | Anaheim, CA, USA |

Period | 5/8/94 → 5/13/94 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the International Quantum Electronics Conference (IQEC'94)*(pp. 221-222). Publ by IEEE.

**Reverse bifurcation and dynamics modification in an optically injected laser diode.** / Simpson, T. B.; Liu, J. M.; Kovanis, V.; Gavrielides, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the International Quantum Electronics Conference (IQEC'94).*Publ by IEEE, pp. 221-222, Proceedings of the 21st International Quantum Electronics Conference (IQEC'94), Anaheim, CA, USA, 5/8/94.

}

TY - GEN

T1 - Reverse bifurcation and dynamics modification in an optically injected laser diode

AU - Simpson, T. B.

AU - Liu, J. M.

AU - Kovanis, V.

AU - Gavrielides, A.

PY - 1994

Y1 - 1994

N2 - Nonlinear dynamics studies have used laser diodes in a variety of external cavity and injection conditions as model systems for the transition to chaos. Most of these studies have concentrated on the transition to chaos as the strength of some parameter is increased. Chaotic dynamics can be observed in a laser diode under strong external optical injection. We observe that the chaotic dynamics can be strictly bounded between two optical injection levels. Both from above and below, the transition to chaos follows a period doubling route. This behavior can be modelled using a rate equation approach coupling a single-mode oscillating optical field with the carrier density. Using the four-wave mixing technique, we have determined the key dynamic parameters of a nearly single-mode laser diode. With these parameters we can make quantitative comparisons between experimentally measured spectra and numerically generated spectra using the coupled equation model. Figure 1 compares the calculated bifurcation diagram with experimentally measured operating regimes for a nearly single mode laser diode under optical injection at the free-running frequency. The injected field amplitude, normalized to the free-running field, is the variable for the diagram and extrema in the variation of the normalized optical field from the steady-state free-running value are shown. The calculated spectrum shows both forward and reverse bifurcations bounding a region of chaotic behavior. At injection power levels of approximately 2% of the oscillating power, we observe that the injection induced a longitudinal mode hop. A strictly single-mode model does not include mode-coupling effects, and further calculations are underway to quantify the influence of the weak side modes of the laser diode. We observe that the relaxation oscillation frequency changes as the injected field level is increased in the strong injection regime. Figure 2 compares the experimentally measured oscillation frequencies with the frequencies derived by a linear stability analysis of the coupled equation model. Over the range where the relaxation frequency more than doubles, the average optical power circulating within the diode cavity and the average carrier density have changed by only a few percent. The good agreement between the observed experimental data and the coupled equation model shows that the fixed parameter on which it is based, the gain of the laser diode, the cavity and spontaneous carrier relaxation rates, and the linewidth enhancement factor, are not strongly influenced by the optical injection. However, the dynamic response of the diode is clearly modified.

AB - Nonlinear dynamics studies have used laser diodes in a variety of external cavity and injection conditions as model systems for the transition to chaos. Most of these studies have concentrated on the transition to chaos as the strength of some parameter is increased. Chaotic dynamics can be observed in a laser diode under strong external optical injection. We observe that the chaotic dynamics can be strictly bounded between two optical injection levels. Both from above and below, the transition to chaos follows a period doubling route. This behavior can be modelled using a rate equation approach coupling a single-mode oscillating optical field with the carrier density. Using the four-wave mixing technique, we have determined the key dynamic parameters of a nearly single-mode laser diode. With these parameters we can make quantitative comparisons between experimentally measured spectra and numerically generated spectra using the coupled equation model. Figure 1 compares the calculated bifurcation diagram with experimentally measured operating regimes for a nearly single mode laser diode under optical injection at the free-running frequency. The injected field amplitude, normalized to the free-running field, is the variable for the diagram and extrema in the variation of the normalized optical field from the steady-state free-running value are shown. The calculated spectrum shows both forward and reverse bifurcations bounding a region of chaotic behavior. At injection power levels of approximately 2% of the oscillating power, we observe that the injection induced a longitudinal mode hop. A strictly single-mode model does not include mode-coupling effects, and further calculations are underway to quantify the influence of the weak side modes of the laser diode. We observe that the relaxation oscillation frequency changes as the injected field level is increased in the strong injection regime. Figure 2 compares the experimentally measured oscillation frequencies with the frequencies derived by a linear stability analysis of the coupled equation model. Over the range where the relaxation frequency more than doubles, the average optical power circulating within the diode cavity and the average carrier density have changed by only a few percent. The good agreement between the observed experimental data and the coupled equation model shows that the fixed parameter on which it is based, the gain of the laser diode, the cavity and spontaneous carrier relaxation rates, and the linewidth enhancement factor, are not strongly influenced by the optical injection. However, the dynamic response of the diode is clearly modified.

UR - http://www.scopus.com/inward/record.url?scp=0028573117&partnerID=8YFLogxK

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M3 - Conference contribution

SN - 0780319737

SP - 221

EP - 222

BT - Proceedings of the International Quantum Electronics Conference (IQEC'94)

PB - Publ by IEEE

ER -