### Abstract

We analyze Lang and Kobayashi equations for a semiconductor laser subject to optical feedback. Using asymptotic methods, we derived in [1] a third order delay-differential equation for the phase of the laser field: ψ‴+ξψ″+ψ′-Δ + Λcos (ψ(s- θ)-ψ(s)) = 0 (*), where ξ, Δ, Λ and θ are scaled parameters proportionals to the laser damping coefficient, the angular frequency of the solitary laser (mod 2π), the feedback rate and the delay of the feedback, respectively. Time s is measured in units of the laser relaxation oscillations period. We have shown that Eq. (*) admits multiple branches of time-periodic states in agreement with the numerical bifurcation diagram of the original laser equations. Our analysis assumed that the delay θ is an O(1) quantity but in many experiments θ is numerically larger. We have modified the analysis in [1] and have found that large delays may lead to a secondary bifurcation to quasiperiodic intensity oscillations. This bifurcation has been suspected in earlier studied but has never been investigated analytically. We show that these quasiperiodic oscillations are characterized by two distinct frequencies: ω-1$/≈1 and ω-2$/ proportional to 1/θ. We analyze the bifurcation both analytically and numerically.

Original language | English |
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Title of host publication | Technical Digest - European Quantum Electronics Conference |

Pages | 166 |

Number of pages | 1 |

Publication status | Published - 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 European Quantum Electronics Conference, EQEC'96 - Hamburg, Ger Duration: Sep 8 1996 → Sep 13 1996 |

### Other

Other | Proceedings of the 1996 European Quantum Electronics Conference, EQEC'96 |
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City | Hamburg, Ger |

Period | 9/8/96 → 9/13/96 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Technical Digest - European Quantum Electronics Conference*(pp. 166)

**Quasiperiodic intensity oscillations in a laser subject to optical feedback.** / Gavrielides, A.; Kovanis, V.; Lythe, G.; Erneux, T.

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

*Technical Digest - European Quantum Electronics Conference.*pp. 166, Proceedings of the 1996 European Quantum Electronics Conference, EQEC'96, Hamburg, Ger, 9/8/96.

}

TY - GEN

T1 - Quasiperiodic intensity oscillations in a laser subject to optical feedback

AU - Gavrielides, A.

AU - Kovanis, V.

AU - Lythe, G.

AU - Erneux, T.

PY - 1996

Y1 - 1996

N2 - We analyze Lang and Kobayashi equations for a semiconductor laser subject to optical feedback. Using asymptotic methods, we derived in [1] a third order delay-differential equation for the phase of the laser field: ψ‴+ξψ″+ψ′-Δ + Λcos (ψ(s- θ)-ψ(s)) = 0 (*), where ξ, Δ, Λ and θ are scaled parameters proportionals to the laser damping coefficient, the angular frequency of the solitary laser (mod 2π), the feedback rate and the delay of the feedback, respectively. Time s is measured in units of the laser relaxation oscillations period. We have shown that Eq. (*) admits multiple branches of time-periodic states in agreement with the numerical bifurcation diagram of the original laser equations. Our analysis assumed that the delay θ is an O(1) quantity but in many experiments θ is numerically larger. We have modified the analysis in [1] and have found that large delays may lead to a secondary bifurcation to quasiperiodic intensity oscillations. This bifurcation has been suspected in earlier studied but has never been investigated analytically. We show that these quasiperiodic oscillations are characterized by two distinct frequencies: ω-1$/≈1 and ω-2$/ proportional to 1/θ. We analyze the bifurcation both analytically and numerically.

AB - We analyze Lang and Kobayashi equations for a semiconductor laser subject to optical feedback. Using asymptotic methods, we derived in [1] a third order delay-differential equation for the phase of the laser field: ψ‴+ξψ″+ψ′-Δ + Λcos (ψ(s- θ)-ψ(s)) = 0 (*), where ξ, Δ, Λ and θ are scaled parameters proportionals to the laser damping coefficient, the angular frequency of the solitary laser (mod 2π), the feedback rate and the delay of the feedback, respectively. Time s is measured in units of the laser relaxation oscillations period. We have shown that Eq. (*) admits multiple branches of time-periodic states in agreement with the numerical bifurcation diagram of the original laser equations. Our analysis assumed that the delay θ is an O(1) quantity but in many experiments θ is numerically larger. We have modified the analysis in [1] and have found that large delays may lead to a secondary bifurcation to quasiperiodic intensity oscillations. This bifurcation has been suspected in earlier studied but has never been investigated analytically. We show that these quasiperiodic oscillations are characterized by two distinct frequencies: ω-1$/≈1 and ω-2$/ proportional to 1/θ. We analyze the bifurcation both analytically and numerically.

UR - http://www.scopus.com/inward/record.url?scp=0029767490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029767490&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029767490

SP - 166

BT - Technical Digest - European Quantum Electronics Conference

ER -