Generation of vector beams and their focal properties

We describe a convenient way to generate arbitrary vector beams by using a spatial light modulator, based on interferometric superposition of two orthogonally polarized beams. In our constructed optical setup, the SLM is used to produce a computer-generated holographic grating that diffracts a linearly polarized incident light into the +1st and -1st diffraction orders with desired wavefronts. After the two diffraction beams pass through two quarter wave-plates, the left- and right-handed circularly polarizations are yielded, respectively. Then a Rochi grating is utilized to recombine the two beams into single one such that any desired polarization configuration is achieved. We demonstrate the versatility of our method through optical experiment, in which a variety of polarization beams are realized. By making use of the incident wave with helical phase, our technique can produce both cylindrically symmetric and asymmetric polarizations. To the best of our knowledge, the experimental realization of cylindrically asymmetric polarization is reported for first time. We also study the focal properties of vector beam through a high numerical aperture lens. Starting from Richards-Wolf vectorial diffraction theory we calculate the focal field distribution and obtain some interesting focal volume structures, such as flat-topped focus, doughnut focus with special dark volume structure.