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Complex Valued Spectral Hermite Approximations for the Actively Mode-Locked Laser

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Abstract

We construct a numerical approximation of the governing equations of an actively mode-locked laser. The governing equation is complex valued and a novel scaling is employed that is designed to simplify the associated line integral in the complex plane. The resulting approximation is based on a set of shifted Hermite polynomials on an infinite line. Numerical comparisons are given with a finite difference scheme on a mapped domain as well as a finite element method on a truncated domain.

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Authors and Affiliations

  1. Department of Mathematics, Union College, Schenectady, NY, USA

    Kelly Black

  2. Franklin W. Olin College of Engineering, Needham, MA, USA

    John B. Geddes

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  1. Kelly Black
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  2. John B. Geddes
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Correspondence to Kelly Black.

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Black, K., Geddes, J.B. Complex Valued Spectral Hermite Approximations for the Actively Mode-Locked Laser. J Sci Comput 32, 427–448 (2007). https://doi.org/10.1007/s10915-007-9138-8

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  • DOI: https://doi.org/10.1007/s10915-007-9138-8

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