Complex cylindrical vector beam excludes the orientation dependence of the intensity of scanning fluorescence images of single molecules

A polarization inhomogeneous vector beam, which is the complex superposition of radially and azimuthally polarized beams, has been studied computationally and theoretically in application to scanning fluorescence microscopy of single molecules. It has been shown that its application makes it possible to almost exclude the dependence of the intensity maximum of the scanning fluorescence image of a single molecule on its orientation. It has been demonstrated that the scanning of one horizontal plane of a solid matrix containing impurity luminescent molecules provides images of all molecules located in a $1$-$\mu$m-thick layer, replacing three-dimensional scanning. Recommendations on the technical implementation of the proposed beam have been given.