Tight focusing of a cylindrical vector beam by a hyperbolic secant gradient index lens

In this Letter, we investigate the tight focusing of a second-order cylindrical vector beam by a hyperbolic secant gradient index lens with a thickness of 10 µm, a radius of 9.43 µm, and a refractive index on the axis of 3.47 (silicon). It is shown that the lens forms the reverse energy flow near its shadow surface. Moreover, it was obtained that the spherical hole in the center of the shadow plane with a diameter of 0.3 µm allows us to localize the direct energy flow inside the lens material and with the reverse energy flow in an area of free space.