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Differential theory of diffraction by finite cylindrical objects.

Nicolas Bonod1, Evgeny Popov, Michel Nevière

  • 1Institut Fresnel, Unité Mixte de Recherche Associée au Centre National de la Recherche Scientifique No 6133, Université de Provence, Faculté des Sciences et Techniques de St Jérôme, 13397 Marseille Cedex 20, France.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|March 18, 2005
PubMed
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We developed a new method to solve Maxwell equations using a Fourier-Bessel basis for analyzing electromagnetic fields around cylindrical objects. This approach accurately models near-field effects in metallic structures, aiding in optical device design.

Area of Science:

  • Electromagnetism
  • Computational Physics
  • Optics

Background:

  • Solving Maxwell equations is crucial for understanding electromagnetic phenomena.
  • Cylindrical coordinates and Fourier-Bessel bases offer advantages for specific geometries.
  • Accurate numerical methods are needed for analyzing complex structures.

Purpose of the Study:

  • To present a differential theory for solving Maxwell equations in cylindrical coordinates.
  • To apply a Fourier-Bessel basis projection for numerical analysis.
  • To investigate the convergence and applications of this method for dielectric and metallic cylinders.

Main Methods:

  • Developing a differential theory for Maxwell equations.
  • Projecting equations onto a Fourier-Bessel basis.

Related Experiment Videos

  • Implementing basis truncation with correct factorization rules.
  • Studying convergence for various cylinder types and lengths.

    • Main Results:

    • Demonstrated a convergent numerical method for Maxwell equations in cylindrical coordinates.
    • Validated the approach for dielectric and metallic cylinders of finite length.
    • Applied the method to map near-field electromagnetic patterns within a hole in a metallic film.

    Conclusions:

    • The Fourier-Bessel basis method provides an effective approach for solving Maxwell equations in cylindrical geometries.
    • This method is suitable for analyzing near-field phenomena in nanophotonic structures.
    • The study offers a valuable tool for designing and understanding optical devices involving metallic films.