Expansion of an Incident Field by Means of Vectorial Spherical Harmonics - Analysis in Terms of Active and Reactive Powers

In this article, the coefficients of the spherical expansion of an incident plane wave on an empty sphere are analyzed in terms of active and reactive powers. These coefficients derive from the expansion of the field by means of the vectorial spherical harmonics (VSH), which is the formulation commonly used in the antenna domain. This expansion leads to an infinite number of non-negligible active power normalized coefficients. On one hand, the associated active power increases with respect to the degree of the coefficient. On the other hand, the reactive power is weak when the degree is small and strong when the band-limit is reached. Therefore the use of VSH normalization may cause issues when spherical harmonics are involved on the processing of antenna radiation patterns.