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.
© 2008 Optical Society of America
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