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Effective schema for the rigorous modeling of grating diffraction with focused beams.

Joerg Bischoff1, Werner Neundorf

  • 1OSIRES Optical Engineering, Ilmenau, Germany. jb@osires.biz

Applied Optics
|June 2, 2011
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This study presents a new numerical integration method for focused beams interacting with gratings. It improves accuracy by dividing the aperture to handle singularities, enhancing diffraction modeling.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Area of Science:

  • Optics and Photonics
  • Computational Electromagnetics
  • Numerical Methods

Background:

  • Modal diffraction methods typically assume plane wave illumination.
  • Practical applications often involve focused beams, necessitating numerical integration.
  • Standard numerical integration methods struggle with gratings due to singularities and resonances, leading to inaccuracies.

Purpose of the Study:

  • To develop an accurate and efficient numerical integration methodology for focused beams interacting with gratings.
  • To overcome the limitations of conventional Gaussian quadrature formulas when applied to grating problems.
  • To mitigate artifacts like kinks and inaccuracies caused by non-smooth integrands.

Main Methods:

  • Subdividing the grating aperture along lines of Rayleigh singularities.
  • Mapping these subapertures onto unit squares for integration.
  • Applying Gaussian cubature formulas independently to each subarea.

Main Results:

  • Achieved significantly improved accuracy in numerical integration for grating diffraction.
  • Successfully addressed the issue of non-smooth integrands caused by singularities and resonances.
  • Reduced or eliminated artifacts such as kinks in the simulation results.

Conclusions:

  • The proposed methodology offers an efficient and accurate approach for simulating focused beam diffraction by gratings.
  • This method enhances the reliability of modal diffraction calculations in practical optical systems.
  • It provides a robust solution for overcoming numerical challenges in computational electromagnetics.