Planar gradient hyperbolic secant lens for subwavelength focusing and superresolution imaging

Integral relations to describe the propagation of a TE-wave from an external point source through the two-dimensional medium (plane interface) and the plane-parallel plate are proposed. We discuss three types of waves that contribute to the resulting light field, namely, the propagating waves and the firstand second-type surface waves. The comparison of near-field refractive lenses (SIL, NAIL) and a planar hyperbolic secant lens shows their numerical apertures to have close values, with the difference being as small as 5% for the Si-based optical elements. The FDTD-method simulation shows that by combining the gradient-index hyperbolic secant lens with a subwavelength diffraction grating or replacing it with its binary analog, the focal spot size can be made, respectively, 10% and 20% smaller than the diffraction-limited resolution in the 2D medium. We design a Si-based, planar binary microlens to generate a near-surface focal spot of full-width half-maximum size FWHM=0.102λ, where λ is the incident wavelength, which is practically devoid of side-lobes. It is shown that about 10 percent of the total incident beam energy goes to the far-field zone.