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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 9 — Sep. 1, 2008
  • pp: 2299–2308

Numerical sampling rules for paraxial regime pulse diffraction calculations

Damien P. Kelly, Bryan M. Hennelly, Alexander Grün, and Karl Unterrainer  »View Author Affiliations


JOSA A, Vol. 25, Issue 9, pp. 2299-2308 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002299


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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.

© 2008 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(320.5550) Ultrafast optics : Pulses
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: March 10, 2008
Revised Manuscript: June 6, 2008
Manuscript Accepted: June 17, 2008
Published: August 19, 2008

Citation
Damien P. Kelly, Bryan M. Hennelly, Alexander Grün, and Karl Unterrainer, "Numerical sampling rules for paraxial regime pulse diffraction calculations," J. Opt. Soc. Am. A 25, 2299-2308 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-9-2299


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