### Abstract

The problem of the scattering of an electromagnetic plane wave with arbitrary polarization and angle of incidence from a perfectly conducting spherical shell with a circular aperture is solved with a generalized dual series approach. This canonical problem encompasses coupling to an open spherical cavity and scattering from a spherical reflector. In contrast to the closed sphere problem, the electromagnetic boundary conditions couple the TE and TM modes. A pseudodecoupling of the resultant dual series equations system into dual series problems for the TE and TM modal coefficients is accomplished by introducing terms that are proportional to the associated Legendre functions P_{0}^{-m}. The solutions of the TE and TM dual series problems require the further introduction of terms proportional to P_{n} ^{-m}, where 0≤n < m. These functions effectively complete the standard spherical harmonic basis set when an aperture is present and guarantee the satisfaction of Meixner's edge conditions. Having generated the modal coefficients, all desired electromagnetic quantities follow immediately. Numerical results for the currents induced on the open spherical shell and for the energy density of the field at its center are presented for the case of normal incidence.

Original language | English (US) |
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Pages (from-to) | 1293-1314 |

Number of pages | 22 |

Journal | Journal of Mathematical Physics |

Volume | 28 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1987 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*28*(6), 1293-1314. https://doi.org/10.1063/1.527533