Focusing radially polarized light by a concentrically corrugated silver film without a hole

We report a phenomenon of focusing a radially polarized beam from the visible range by a silver film with no hole on the optical axis and double-sided concentric corrugations. The axes of symmetry of grooves and the illuminating beam coincide. An Ag lens of 100 nm thickness, five grooves, of which the outermost has 5 microm diameter, at lambda=400 nm transmits 22% of electric energy and focuses light into a 0.2lambda2 spot area at a focal length close to 2lambda, while at lambda=500 nm the results are 11%, 0.16lambda2 and lambda, respectively. This Ag lens focuses without contribution of evanescent waves a far-field source into a far-field spot. The nanolens acts like a refractive optical system of high numerical aperture close to unity.