Spectral Hermite Approximations for the Actively Mode-Locked Laser

Authors:
Kelly Black;John B. Geddes
Affiliations:
Visiting the Department of Mathematics and Statistics, Utah State University. kelly.black@unh.edu;Department of Mathematics and Statistics, University of New Hampshire. jbgeddes @cisunix.unh.edu
Venue:
Journal of Scientific Computing
Year:
2001

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Abstract

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 rate of decay of the resulting modes is examined for a simplified problem and difficulties in showing the stability of the method are also discussed. Numerical comparisons with a finite difference scheme are also presented.