We show that a super-resolution process with 100% visibility is characterized by the formation of a point of phase singularity in free space outside the lens in the form of a saddle with topological charge equal to -1. The saddle point is connected to two vortices at the end boundary of the lens, and the two vortices are in turn connected to another saddle point inside the lens. The structure saddle-vortices-saddle is topologically stable. The formation of the saddle point in free space explains also the negative flux of energy present in a certain region of space outside the lens. The circulation strength of the power flow can be controlled by varying the position of the object plane with respect to the lens.
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