Focusing property of the phase modulated radially polarized beam

The wavefront phase of incident radially polarized beam is modulated into two portions, the center circle portion and outer annular portion. The radially polarized and longitudinally polarized fields in focal region were investigated theoretically. Increasing the radius of the center circle with Π phase shift, the radially polarized field shows ring shape, and one ring pattern evolves to two-ring, and then three-ring pattern. The longitudinally polarized field turns into one spot, which splits into two spots, and then combines back into one spot with increasing the radius of the center circle. Maximum intensity ratio of longitude polarized to radially polarized fields increases, decreases, and then increases with the increasing radius. The effect of phase of the center portion affects the radially polarized and longitude polarized fields considerably. And the maximum intensity ratio evolution principle with increasing phase of the center circle portion differs considerably for different radius of the inner portion.