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    Numerical sampling rules for paraxial regime pulse diffraction calculations


    Kelly, Damien P. and Hennelly, Bryan M. and Grun, Alexander and Unterrainer, Karl (2008) Numerical sampling rules for paraxial regime pulse diffraction calculations. Journal of the Optical Society of America A., 25. pp. 2299-2308. ISSN 1084-7529

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    Abstract

    Sampling rules for numerically calculating ultrashort pulse fields are discussed. Such pulses are not monochromatic but rather have a finite spectral distribution about some central (temporal) frequency. Accordingly, the diffraction pattern for many spectral components must be considered. From a numerical implementation viewpoint, one may ask how many of these spectral components are needed to accurately calculate the pulse field. Using an analytical expression for the Fresnel diffraction from a 1-D slit, we examine this question by varying the number of contributing spectral components. We show how undersampling the spectral profile produces erroneous numerical artifacts (aliasing) in the spatial–temporal domain. A guideline, based on graphical considerations, is proposed that determines appropriate sampling conditions. We show that there is a relationship between this sampling rule and a diffraction wave that emerges from the aperture edge; comparisons are drawn with boundary diffraction waves. Numerical results for 2-D square and circular apertures are presented and discussed, and a potentially time-saving calculation technique that relates pulse distributions in different z planes is described.

    Item Type: Article
    Additional Information: The definitive version of this article is available at http://dx.doi.org/10.1364/JOSAA.25.002299 © 2008 Optical Society of America
    Keywords: Numerical sampling; paraxial regime; pulse diffraction calculations;
    Academic Unit: Faculty of Science and Engineering > Computer Science
    Faculty of Science and Engineering > Electronic Engineering
    Item ID: 5784
    Depositing User: Dr. Bryan Hennelly
    Date Deposited: 09 Feb 2015 16:58
    Journal or Publication Title: Journal of the Optical Society of America A.
    Publisher: Optical Society of America
    Refereed: Yes
    URI:

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