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Spherical Vector Waves

Spherical Vector Waves

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There is a special interest in finding solutions of the Maxwell equations in source-free, homogeneous, isotropic materials in the spherical coordinate system (r, 8, φ). The reason this is at least twofold: (1) we aim at developing efficient tools to solve scattering problems with spherical symmetries, and (2) outside the circumscribed sphere of the scatterer, the are naturally expanded in vector waves with spherical symmetries-we have already Chapter 4 that the scattered field in the far zone is a spherical wave. For these reasons, study solutions to the source-free Maxwell equations.

Chapter Contents:

  • 7.1 Preparatory Discussions
  • 7.2 Definition of Spherical Vector Waves
  • 7.2.1 Expansions of the Fields
  • 7.3 Orthogonality and Reciprocity Relations
  • 7.3.1 Spherical Scalar Waves
  • 7.3.2 Power Transport
  • 7.4 Some Properties of the Spherical Vector Waves
  • 7.4.1 Linear Independence
  • 7.4.2 The Translation Matrices
  • 7.5 Expansion of the Green Dyadic
  • 7.5.1 The Green Function in Free Space
  • 7.5.2 The Green Dyadic for the Electric Field in Free Space
  • 7.5.3 Free-Space Green Dyadic
  • 7.6 Null-Field Equations
  • 7.7 Expansion of Sources
  • 7.7.1 Expansion of a Plane Wave
  • 7.7.2 Expansion of a Vertical Electric Dipole
  • 7.8 Far Field Amplitude and the Transition Matrix
  • 7.8.1 Scattering Dyadic
  • 7.8.2 Cross Sections
  • 7.8.3 Generalized Optical Theorem
  • 7.8.4 The Decrease of the Scattered Field
  • 7.9 Dipole Moments of a Scatterer
  • Problems for Chapter 7

Inspec keywords: Maxwell equations

Other keywords: spherical wave; spherical vector waves; Maxwell equations; scattering problems; spherical symmetries; isotropic materials; spherical coordinate system

Subjects: Electromagnetic wave propagation; Maxwell theory: general mathematical aspects

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