volume | PIER Journals

Abstract

Spherical harmonics are classical analysis tools in many science and engineering domains. For analyzing the electromagnetic fields of antennas in the frequency domain, the mostly used formulation is the one proposed by Hansen. This article proposes an alternative solution, relying on spin spherical harmonics. On a sphere, the tangential components of the electric and magnetic fields are represented by means of harmonics of spin ±1. Then new closed-form relations are established between the spin spherical harmonics and the ones formulated by Hansen. A sampling theorem and fast transforms that are consistent with spin spherical harmonics are used. The radiations of spin spherical harmonics of order 1 are related to elementary dipoles and Huygens sources in circular polarization. Finally, numerical experiments are performed with a horn antenna and a GNSS antenna installed on an aircraft. They show that a very large radiating system with a band-limit of 2048 can be efficiently analyzed by means of fast spin spherical harmonic transforms, with a computation time of 2 minutes, approximately.

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Dr. Alice Quennelle

Prof. Alexandre Chabory

Dr. Romain Contreres