Modification of a polarization sphere for the representation of partially polarized electromagnetic waves

A four-dimensional polarization sphere is proposed for the representation and analysis of partially polarized waves. It is shown that an actual partially polarized wave (PPW) can be correlated with a point on the left hemisphere, making possible the determination of the distance between the PPW and the receiving antenna as well as the distance between different PPWs. Attention is given to the problem of determining the parameters of a PPW formed by a sum of incoherent waves. In addition, consideration is given to the possibility of using the left as well as the right hemisphere to represent and analyze 2 x 2 Hermitian matrices of arbitrary definiteness.