title: Numerical sampling rules for paraxial regime pulse diffraction calculations.
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.
authors.affiliation: Institut fur Photonik und Zentrum fur Mikro- und Nanostukturen, Technische Universitat Wien, Wien, Austria. damienpkelly@gmail.com
authors.forename: Damien P
authors.initials: DP
authors.lastname: Kelly
authors.forename: Bryan M
authors.initials: BM
authors.lastname: Hennelly
authors.forename: Alexander
authors.initials: A
authors.lastname: Grün
authors.forename: Karl
authors.initials: K
authors.lastname: Unterrainer