Peer-Reviewed Journal Details
Mandatory Fields
Kelly, DP;Hennelly, BM;Grun, A;Unterrainer, K
2008
September
Journal Of The Optical Society Of America A-Optics Image Science And Vision
Numerical sampling rules for paraxial regime pulse diffraction calculations
Published
2 ()
Optional Fields
SPACE-BANDWIDTH PRODUCT ULTRASHORT PULSES LASER-PULSE PROPAGATION BEAMS SUPERRESOLUTION LIGHT ILLUMINATION ADAPTATION FRESNEL
25
2299
2308
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. (C) 2008 Optical Society of America.
WASHINGTON
1084-7529
Grant Details