Stability of CW Solutions of the FDML Laser
https://doi.org/10.18255/1818-1015-2014-3-35-54
Abstract
The problem of existense and stability of continuous wave (CW) solutions R exp(iΛt) of a Fourier Domain Mode Locking laser model is studied. This model consists of two differential equations with delay. The delay is sufficiently large. It is nessesary for the existense of CW solutions of this model that parameters determining the ”main part” of solution must lie on a certain curve (Γ(κ, g0)). Sufficient conditions of stability of CW solutions for all sufficiently large values of delay are found. The location of stability regions on Γ(κ, g0) is studied. In the case of zero linewidth enhancement factor α for all values of parameters of the linear attenuation factor per cavity round trip κ and the linear unsaturated gain parameter g0 the number of stability regions and their boundaries on Γ(κ, g0) are found analytically. The comparison of location of stability regions on Γ(κ, g0) in tha case of zero α and nonzero α is made.
About the Author
A. A. Kashchenko
P.G. Demidov Yaroslavl State University
Russian Federation
аспирант, Sovetskaya str., 14, Yaroslavl, 150000, Russia
Russian Federation
аспирант, Sovetskaya str., 14, Yaroslavl, 150000, Russia
References
1. Slepneva S., Kelleher B., O’Shaughnessy B., Hegarty S.P., Vladimirov A.G., and Huyet G. Dynamics of Fourier domain mode-locked lasers // Opt. Express. 2013. V. 21. P. 19240–19251.
2. Huber R., Wojtkowski M., and Fujimoto J.G. Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography // Opt. Express. 2006. V. 14. P. 3225–3237.
3. Vladimirov A.G. and Turaev D. Model for passive mode-locking in semiconductor lasers // Phys. Rev A. 2005. V. 72. P. 033808.
4. Vladimirov A., Turaev D., and Kozyreff G. Delay differential equations for mode-locked semiconductor lasers // Opt. Lett. 2004. V. 29. P. 1221–1223.
5. Vladimirov A. and Turaev D. A new model for a mode-locked semiconductor laser // Radiophysics and Quantum Electronics. 2004. V. 47. P. 769–776.
6. Kashchenko A. Stability of CW Solutions of Fourier Domain Mode Locked Laser //International Student Conference “Science and Progress”. 2013. P. 29.
7. Кащенко А.А. Устойчивость простейших периодических решений в уравнении Стюарта–Ландау с большим запаздыванием // Моделирование и анализ информационных систем. 2012. Т. 19, № 3. С. 136–141 (English transl.: Kashchenko A.A. Stability of the Simplest Periodic Solutions in the Stuart-Landau Equation with Large Delay // Automatic Control and Computer Sciences. 2013. V. 47, No. 7. P. 566–570.)
8. Васильева А.Б., Бутузов В.Ф. Асимптотические разложения решений сингулярно возмущенных уравнений. М.: Наука, 1973. [Vasil’eva A.B., Butuzov V.F. Asimptoticheskie razlozheniya resheniy singulyarno vozmushchennykh uravneniy. M.: Nauka, 1973 (In Russian)].
Review
For citations:
Kashchenko A.A. Stability of CW Solutions of the FDML Laser. Modeling and Analysis of Information Systems. 2014;21(3):35-54. (In Russ.) https://doi.org/10.18255/1818-1015-2014-3-35-54
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