Customized Vectorial Optical Fields in Homogeneous and Inhomogeneous Media

The ability to design vectorial optical fields with desired properties in different media has a significant impact on many applications including microscopy, optical trapping, micromachining, and data commu-nications. Here, we set up a framework, based on Maxwell's equations, that can be used to generate a desired three-dimensional vectorial optical field inside inhomogeneous and/or anisotropic media, where the generated field is either the exact or the closest physically possible rendition of the desired field. This approach is experimentally verified by generating two optical fields exhibiting interesting properties such as controllable states of polarization in a simple medium and self-healing behavior after a dielectric wall.