Hierarchy of terms in a multipole expansion

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Hierarchy of terms in a multipole expansion

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In the classical multipole expansion the various terms (dipoles, quadrupoles etc.) are ranked according to powers of the wavenumber k. When k→0 the dominant terms are those of lowest powers, provided the moments are k-independent. However, this situation does not always hold, and the hierarchy may be upset when the current structure markedly changes with k. The point is illustrated by the example of the confined modes of a dielectric resonator.

Inspec keywords: dielectric resonators; electromagnetic field theory

Other keywords: multipole expansion; dielectric resonator; confined modes; terms hierarchy; electromagnetic field theory

Subjects: Waveguide and microwave transmission line components; Steady-state electromagnetic fields; electromagnetic induction; Other dielectric applications and devices; Electric and magnetic fields

References

    1. 1)
      • J. van Bladel . On the resonances of a dielectric resonator of very high permittivity. IEEE Trans. , 199 - 208
    2. 2)
      • J. van Bladel . The multipole expansion revisited. Arch. Elektron. Ubertragungstech. , 407 - 411
http://iet.metastore.ingenta.com/content/journals/10.1049/el_19880334
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