Coherent modes of random electric and magnetic fields in a spherical volume

Whereas the coherent-mode representation of scalar fields has proven valuable from both theoretical and practical points of view, the coherent modes of vector-valued optical fields have received much less attention. We demonstrate that the coherent-mode structures of a stationary, random electric field and the corresponding magnetic field in a source-free, finite, spherical volume are, in general, not equivalent, i.e., the coherent modes of the magnetic field are not obtained from those of the electric field directly via Maxwell equations and suitable normalization. We also show that the converse holds when the volume is large compared to the wavelength. Similar results are further presented for arbitrary free fields, whose sources are at infinity, and for homogeneous free fields. A homogeneous and isotropic free field in a spherical volume is then considered, and the connection between its electric and magnetic coherent-mode decompositions is derived. An example of such a field is blackbody radiation.