Mechanism of superresolution in a planar hyperbolic secant lens

Integral representation for a TE-wave from a point source in 2D medium, located outside of this medium, was obtained (border of a medium division - straight line). Similar representation for a light field inside and outside of flat-parallel film was obtained too. Three types of waves noticed, which give contributions in a light field: propagating waves, surface weaves of first and second types. Comparison of a numerical aperture of a refraction near field lenses (SIL, NAIL) and a planar hyperbolic secant lens conducted. It is shown, that this lens are close each other and distinguish in a 5%. It is shown by modeling in a FullWAVE program, that adding a subwave diffractive grating to a secant hyperbolic gradient lens, or replacing this lens on a binary analog helps to overcome a diffractive limit in the given medium with smaller width of the focus spot on a 10% and 20%.