Pure-phase apodizer for generating double ring-shaped focuses

We propose two design methods of concentric multi-belt pure phase apodizer and phase modulation functions for generating two ring-shaped focuses by focusing the linearly polarized doughnut-shaped beam with a high numerical aperture objective. The phase modulation functions for odd and even belt are verified effectively by numerical simulation. The distance of the two focuses and the position of each focus can be controlled or separately adjusted by the use of liquid crystal spatial phase modulation. It could be useful in optical trapping, particle stacking, alignment and transportation. © 2012 Chinese Optics Letter.