Degree of polarization in tightly focused optical fields.

We analyze the degree of polarization of random, statistically stationary electromagnetic fields in the focal region of a high-numerical-aperture imaging system. The Richards-Wolf theory for focusing is employed to compute the full 3 x 3 electric coherence matrix, from which the degree of polarization is obtained by using a recent definition for general three-dimensional electromagnetic waves. Significant changes in the state of partial polarization, compared with that of the incident illumination, are observed. For example, a wave consisting of two orthogonal and uncorrelated incident-electric-field components produces rings of full polarization in the focal plane. These effects are explained by considering the distribution of the spectral densities of the three electric field components as well as the correlations between them.