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International Journal of Optics
Volume 2012 (2012), Article ID 831604, 18 pages
http://dx.doi.org/10.1155/2012/831604
Research Article

The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems

1Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, USA
2Department of Mathematics and Physics, Azusa Pacific University, P.O. Box 7000, Azusa, CA 91702-7000, USA

Received 6 May 2011; Accepted 24 June 2011

Academic Editor: Sonia Boscolo

Copyright © 2012 Eli Shlizerman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The onset of multipulsing, a ubiquitous phenomenon in laser cavities, imposes a fundamental limit on the maximum energy delivered per pulse. Managing the nonlinear penalties in the cavity becomes crucial for increasing the energy and suppressing the multipulsing instability. A proper orthogonal decomposition (POD) allows for the reduction of governing equations of a mode-locked laser onto a low-dimensional space. The resulting reduced system is able to capture correctly the experimentally observed pulse transitions. Analysis of these models is used to explain the sequence of bifurcations that are responsible for the multipulsing instability in the master mode-locking and the waveguide array mode-locking models. As a result, the POD reduction allows for a simple and efficient way to characterize and optimize the cavity parameters for achieving maximal energy output.