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Scattering from Spheres: A New Look into an Old Problem.

Giuseppe Ruello1, Riccardo Lattanzi2

  • 1Department of Electrical Engineering and Information Technology, University of Napoli Federico II, 80125 Naples, Italy.

Electronics
|June 4, 2021
PubMed
Summary

We present a new electromagnetic scattering theory using inward/outward fields. This framework offers intuitive insights into scattering phenomena and provides closed-form solutions for fields and power, consistent with Mie theory.

Keywords:
Mie scatteringelectromagnetic scattering and propagationreflection coefficient

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Area of Science:

  • Electromagnetics
  • Optics
  • Theoretical Physics

Background:

  • Classical electromagnetic scattering is often described using incident and scattered fields.
  • The Lorenz-Mie formulation is a standard approach but can lack intuitive physical interpretation.
  • Understanding scattering from spheres is crucial in various optical and electromagnetic applications.

Purpose of the Study:

  • To introduce a novel theoretical framework for analyzing electromagnetic scattering from spheres.
  • To decompose the total field into inward and outward electromagnetic fields for intuitive analysis.
  • To provide closed-form solutions for fields, transmitted power, and scattered power.

Main Methods:

  • Decomposition of the total field into inward and outward spherical harmonic series.
  • Extension of non-uniform transmission line theory with impedance transfer.
  • Derivation of closed-form expressions for internal and external fields.
  • Evaluation of transmitted and scattered power using reflection coefficients.

Main Results:

  • The combination weights of spherical harmonics are interpreted as reflection and transmission coefficients.
  • A closed-form solution for fields inside and outside the sphere is derived.
  • Transmitted and scattered power are evaluated and linked to the reflection coefficient modulus.
  • The new method is shown to be consistent with Mie scattering theory.

Conclusions:

  • The proposed framework offers an intuitive physical interpretation of electromagnetic scattering, relating it to impedance matching and resonances.
  • The formulation is particularly useful for analyzing scattering involving inward traveling spherical waves from surrounding sources.
  • This approach provides a consistent and insightful alternative to classical scattering theories.