Modeling the focusing of a radially-polarized laser beam with an initially flat-top intensity profile

Radially-polarized light beams present very interesting and useful behavior for creating small intensity spots when tightly-focused, and manipulating nanostructures or charged particles. The modeling of the propagation of such vector beams, however, is almost always done using the lowest-order fundamental radially-polarized beam due to the complexity of vector diffraction theory. We show how a flat-top radially-polarized beam can be modeled analytically using a sum of higher-order beams, and describe a number of interesting qualities, and compare to numerically-solved integral descriptions.