Degree of polarization in 3D optical fields generated from a partially polarized plane wave.

We show that, for 3D random electromagnetic fields that are created by optical systems from a partially polarized plane wave, two different definitions of the 3D degree of polarization proposed in literature have a monotonic one-to-one correspondence, thus providing the same information about the field's polarization state. Examples of 3D fields obeying this result are the evanescent wave generated in total internal reflection, the tightly focused beam, and the far field scattered from an electric point dipole.