Minimization of light or dark focal spot size with controllable growth of side lobes in focusing systems with the high numerical aperture

Minimization of focal spot size (light or dark) is considered at various types of polarization due to additional apodization of a pupil of focusing system by optical element with a phase function which depends as polynomial on radius and vortical on angle. Coefficients in a radial polynomial were optimized in view of satisfaction of the certain conditions, in particular, preservation of power efficiency and maintenance of the certain level of side lobes. Searching of coefficients was carried out on by minimization of a functional with use of the Brent's method.