Quasiperiodic intensity oscillations in a laser subject to optical feedback

A. Gavrielides, V. Kovanis, G. Lythe, T. Erneux

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationTechnical Digest - European Quantum Electronics Conference
Pages166
Number of pages1
Publication statusPublished - 1996
Externally publishedYes
EventProceedings of the 1996 European Quantum Electronics Conference, EQEC'96 - Hamburg, Ger
Duration: Sep 8 1996Sep 13 1996

Other

OtherProceedings of the 1996 European Quantum Electronics Conference, EQEC'96
CityHamburg, Ger
Period9/8/969/13/96

Fingerprint

oscillations
lasers
asymptotic methods
differential equations
damping
semiconductor lasers
diagrams
coefficients

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Gavrielides, A., Kovanis, V., Lythe, G., & Erneux, T. (1996). Quasiperiodic intensity oscillations in a laser subject to optical feedback. In 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.

Technical Digest - European Quantum Electronics Conference. 1996. p. 166.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Gavrielides, A, Kovanis, V, Lythe, G & Erneux, T 1996, Quasiperiodic intensity oscillations in a laser subject to optical feedback. in Technical Digest - European Quantum Electronics Conference. pp. 166, Proceedings of the 1996 European Quantum Electronics Conference, EQEC'96, Hamburg, Ger, 9/8/96.
Gavrielides A, Kovanis V, Lythe G, Erneux T. Quasiperiodic intensity oscillations in a laser subject to optical feedback. In Technical Digest - European Quantum Electronics Conference. 1996. p. 166
Gavrielides, A. ; Kovanis, V. ; Lythe, G. ; Erneux, T. / Quasiperiodic intensity oscillations in a laser subject to optical feedback. Technical Digest - European Quantum Electronics Conference. 1996. pp. 166
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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.

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