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Nonradiating sources of Maxwell's equations

Peijun Li, Jue Wang

Abstract

This paper presents a thorough investigation into nonradiating sources of Maxwell's equations. Various characterizations are developed to clarify the properties of nonradiating sources, considering their varying degrees of regularity. Furthermore, the characterizations are examined on far-field patterns and near-field data of the electric field, along with the null spaces of integral operators. The study includes the explicit construction of several illustrative examples to demonstrate the presence of nonradiating sources in different null spaces.

Nonradiating sources of Maxwell's equations

Abstract

This paper presents a thorough investigation into nonradiating sources of Maxwell's equations. Various characterizations are developed to clarify the properties of nonradiating sources, considering their varying degrees of regularity. Furthermore, the characterizations are examined on far-field patterns and near-field data of the electric field, along with the null spaces of integral operators. The study includes the explicit construction of several illustrative examples to demonstrate the presence of nonradiating sources in different null spaces.
Paper Structure (12 sections, 12 theorems, 105 equations)

This paper contains 12 sections, 12 theorems, 105 equations.

Table of Contents

  1. Introduction
  2. Maxwell's equations
  3. Characterizations of nonradiating sources
  4. Characterizations with different regularity
  5. Far-field patterns
  6. Near-field data
  7. Null spaces
  8. Examples of nonradiating sources
  9. General nonradiating sources
  10. A nonradiating source in $\mathcal{N}_1(R)$
  11. A nonradiating source in $\mathcal{N}_2(R)$
  12. Conclusion

Key Result

Lemma 2.1

The solution $\boldsymbol E$ to EIN-gr1 satisfies the Silver--Müller radiation condition SMrc.

Theorems & Definitions (26)

  • Definition 2.1
  • Lemma 2.1
  • proof
  • Theorem 3.1
  • Proposition 3.2
  • Lemma 3.3
  • proof
  • Theorem 3.4
  • Theorem 3.5
  • proof
  • ...and 16 more