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The time-domain Cartesian multipole expansion of electromagnetic fields.

Elias Le Boudec1, Chaouki Kasmi2, Nicolas Mora3

  • 1Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland. elias.leboudec@epfl.ch.

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Summary

This study introduces a novel time-domain Cartesian multipole expansion for solving Maxwell's equations. This method provides efficient semi-analytical solutions for complex, time-varying current distributions, aiding in transient electromagnetic studies.

Keywords:
Electromagnetic radiationMaxwell’s equationsMultipole expansionPartial differential equations

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Area of Science:

  • Electromagnetism and Computational Physics

Background:

  • Analytical solutions for Maxwell's equations are limited for practical transient phenomena.
  • Numerical methods are computationally expensive and memory-intensive.
  • Existing semi-analytical methods like multipole expansion can be complex for real-world applications.

Purpose of the Study:

  • To develop a novel semi-analytical method for time-domain solutions of Maxwell's equations.
  • To address the limitations of analytical and numerical approaches for complex current distributions.
  • To enable efficient analysis of transient electromagnetic phenomena.

Main Methods:

  • Development of the time-domain Cartesian multipole expansion.
  • Introduction of the concept of current "pixels" for arbitrary planar geometries.
  • Application to imaging intricate current distributions.

Main Results:

  • Derivation of semi-analytical solutions for arbitrary localized time-varying current distributions.
  • Successful application in imaging complex current distributions.
  • Validation against analytical and finite-difference time-domain (FDTD) methods.

Conclusions:

  • The time-domain Cartesian multipole expansion offers an efficient semi-analytical alternative to numerical simulations.
  • The method simplifies the study of transient electromagnetic fields for complex geometries.
  • This approach enhances the feasibility of analyzing broadband electromagnetic phenomena.