Transformation of the vortex beam in the optical vortex scanning microscope

•The microscopic system with the embedded optical vortex is studied.•The analytical formula for the complex amplitude of the focused spot with off axis vortex is given.•Internal scanning for high-order vortex beam is analyzed.•Higher-order vortex is topologically unstable and splits into vortices with unit charge.

We investigate the microscopic system in which the Gaussian beam with embedded optical vortex is used. The optical vortex is introduced by vortex lens. The vortex lens shift induces a precise nanometer shift of the embedded vortices inside the focused spot. The analytical formula for the complex amplitude of the focused spot with off-axis vortex was calculated, to our knowledge, for the first time. This solution is an important step in the development of the optical vortex scanning microscope. Experimental results are also presented that demonstrate the behavior of such a beam in an experimental setup.