Please use this identifier to cite or link to this item: https://oar.tib.eu/jspui/handle/123456789/2469
Files in This Item:
File SizeFormat 
68771513X.pdf949,84 kBAdobe PDFView/Open
Title: Longitudinal dynamics of semiconductor lasers
Authors: Philip, Jan
Issue Date: 2001
Published in: Report // Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V., Volume 20, ISSN 0946-8838
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We investigate the longitudinal dynamics of semiconductor lasers using a model which couples a hyperbolic linear system of partial differential equations nonlinearly with ordinary differential equations. We prove the global existence and uniqueness of solutions using the theory of strongly continuous semigroups. Subsequently, we analyse the long-time behavior of the solutions in two steps. First, we find attracting invariant manifolds of low dimension benefitting from the fact that the system is singularly perturbed, i. e., the optical and the electronic variables operate on differente time-scales. The flow on these manifolds can be approximated by the so-called mode approximations. The dimension of these mode approximations depends on the number of critical eigenvalues of the linear hyperbolic operator. Next, we perform a detailed numerical and analytic bifurcation analysis for the two most common constellations. Starting from known results for the single-mode approximation, we investigate the two-mode approximation in the special case of a rapidly rotating phase difference between the two optical components. In this case, the first-order averaged model unveils the mechanisms for various phenomena observed in simulations of the complete system. Moreover, it predicts the existence of a more complex spatio-temporal behavior. In the scope of the averaged model, this is a bursting regime.
Keywords: Semiconductor lasers; infinite-dimensional dynamical systems; invariant manifolds; bifurcation analysis
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.