Three-Dimensional Polarization Control in Microscopy

We propose an approach to optical microscopy that enables full control over the three-dimensional polarization vector at the focal spot of a high-numerical-aperture lens. The input field to the lens is linearly polarized and no polarization optics are needed. This technique utilizes the azimuthal spatial degree of freedom of the input field. We find that only a small set of low-order azimuthal spatial harmonics contributes to the focused field on axis, and a simple transformation exists between the linear vector space of these harmonics and the three-dimensional polarization-vector space. Controlling the relative complex weights of these azimuthal harmonics produces any desired three-dimensional state of polarization.