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Numerical sampling rules for paraxial regime pulse diffraction calculations.

Damien P Kelly1, Bryan M Hennelly, Alexander Grün

  • 1Institut fur Photonik und Zentrum fur Mikro- und Nanostukturen, Technische Universitat Wien, Wien, Austria. damienpkelly@gmail.com

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Summary
This summary is machine-generated.

Accurate numerical calculations of ultrashort pulse fields require careful sampling of spectral components to avoid aliasing artifacts. This study proposes a guideline for appropriate sampling based on graphical considerations and diffraction wave analysis.

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Area of Science:

  • Optics and Photonics
  • Computational Physics
  • Wave Propagation

Background:

  • Ultrashort pulses are non-monochromatic, possessing a finite spectral distribution.
  • Accurate numerical simulations require considering diffraction patterns for multiple spectral components.
  • Previous methods lacked clear guidelines for spectral sampling in ultrashort pulse calculations.

Purpose of the Study:

  • To establish sampling rules for accurate numerical calculation of ultrashort pulse fields.
  • To investigate the impact of spectral undersampling on numerical results.
  • To propose a guideline for determining appropriate spectral sampling conditions.

Main Methods:

  • Analytical calculation of Fresnel diffraction for a 1-D slit.
  • Systematic variation of the number of spectral components.
  • Analysis of numerical artifacts (aliasing) in the spatial-temporal domain.
  • Comparison with boundary diffraction wave theory.

Main Results:

  • Undersampling the spectral profile leads to aliasing artifacts in numerical simulations.
  • A graphical guideline for appropriate spectral sampling is proposed.
  • A relationship between the sampling rule and aperture edge diffraction waves is identified.
  • Numerical results for 2-D apertures and a time-saving technique are presented.

Conclusions:

  • Appropriate spectral sampling is crucial for accurate numerical simulation of ultrashort pulse propagation.
  • The proposed guideline aids in selecting adequate sampling parameters, preventing numerical errors.
  • The findings offer practical insights for computational optics and wave propagation studies.