Complete polarization and phase control for focus-shaping in high-NA microscopy

We show that, in order to attain complete polarization control across a beam, two spatially resolved variable retardations need to be introduced to the light beam. The orientation of the fast axes of the retarders must be linearly independent on the Poincaré sphere if a fixed starting polarization state is used, and one of the retardations requires a range of 2π. We also present an experimental system capable of implementing this concept using two passes on spatial light modulators (SLMs). A third SLM pass can be added to control the absolute phase of the beam. Control of the spatial polarization and phase distribution of a beam has applications in high-NA microscopy, where these properties can be used to shape the focal field in three dimensions. We present some examples of such fields, both theoretically calculated using McCutchen's method and experimentally observed.