Coherence properties of the electric field generated by an incoherent source of currents distributed on the surface of a sphere

Abstract

We derive analytical expressions of the cross-spectral density of the electric field arising from an incoherent source whose current density is located on the surface of a sphere. Our approach is based on the series expansion in terms of vector spherical harmonics of the electric field generated by the aforementioned current distribution. We analyze in detail the spectrum, the degree of coherence, and the degree of polarization of the electric field for all regions in space (from the near field to the far field). The relationship of the high-order harmonics to the coherence properties is discussed. The spectrum turns out to be isotropic and it is different from that of the source. We found that the degree of coherence and degree of polarization are strongly influenced by the size of the source. We show the appearance of special features: a zone with a high degree of coherence in the near field for a subwavelength source, the radial degree of coherence is nearly constant in an extended region where two radial points belong to the far field, and a particular radial distance for which the degree of polarization vanishes (3D unpolarized light).