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Dynamics of multisection semiconductor lasers

    J. Sieber Affiliation
    ; M. Radžiūnas Affiliation
    ; K. R. Schneider Affiliation

Abstract


We investigate the longitudinal dynamics of multisection semiconductor lasers based on a model, where a hyperbolic system of partial differential equations is nonlinearly coupled with a system of ordinary differential equations. We present analytic results for that system: global existence and uniqueness of the initial‐boundary value problem, and existence of attracting invariant manifolds of low dimension. The flow on these manifolds is approximately described by the so‐called mode approximations which are systems of ordinary differential equations. Finally, we present a detailed numerical bifurcation analysis of the two‐mode approximation system and compare it with the simulated dynamics of the full PDE model.


Daugiasekcijinių puslaidininkinių lazerių dinamika


Santrauka



Mes nagrinejame išilgine daugiasekcijiniu puslaidininkiniu lazeriu dinamika, kuri yra nusakoma netiesiškai susietomis hiperboline diferencialiniu lygčiu dalinemis išvestinemis bei paprastuju diferencialiniu lygčiu sistemomis. Mes pateikiame sekančias šios sistemos savybes: globalaus pradinio‐kraštinio uždavinio sprendinio egzistavimas bei vienatis; mažos dimensijos pritraukiančiojo invariantinio hiperpaviršiaus egzistavimas. Modelio dinamika šiame hiper‐paviršiuje yra apytiksliai nusakoma paprastuju diferencialiniu lygčiu sistema. Pabaigoje mes pateikiame detalia skaitine šios paprastuju diferencialiniu lygčiu sistemos bifurkacine analize ir lyginame ja su skaitiškai nustatyta pilnos diferencialiniu lygčiu dalinemis išvestinemis sistemos dinamika.


First Published Online: 14 Oct 2010

Keyword : laser dynamics, invariant manifold theory, hyperbolic systems of partial differential equations, model reduction, bifurcation analysis

How to Cite
Sieber, J., Radžiūnas, M., & Schneider, K. R. (2004). Dynamics of multisection semiconductor lasers. Mathematical Modelling and Analysis, 9(1), 51-66. https://doi.org/10.3846/13926292.2004.9637241
Published in Issue
Mar 31, 2004
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