Numerical analysis of tight focusing and scattering of Singular Beams

Singular beams have recently been employed for metrological applications requiring nanoscale sensitivity. The achievable sensitivity depends on the numerical aperture of the involved optical system. While high numerical aperture provides more information about the investigated object, it introduces a number of difficulties when a rigorous analysis of the optical system is required. In this work we discuss three principle parts of numerical analysis of such systems: focusing, scattering and far-field propagation. For the focusing part a tight focusing of wavefronts with piecewise quasi constant phase is presented. For the scattering part the advantages and disadvantages of various methods (like FEM, FDTD, etc...) are discussed. For the far field propagation part issues related to the specifics of investigated problem are outlined.