Spectral/Hermite Approximations and Transient Growth for the Actively Mode-Locked Laser
Professor Kelly Black
February 28, 2005
Tea and pastries will be served
An approximation technique for the governing equations for the mode-locked laser is examined. The technique centers on a transformation of the governing equations in which the resulting equations closely resemble the Hermite equation. The approximation of the system is constructed through a linear combination of Hermite polynomials resulting in a Hermite-spectral method. The stability of the method is discussed. Numerical comparisons with a finite difference scheme are also presented. Finally, we present comparisons of the bounds on the transient growth between the theoretical growth rates and numerical experiments.
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