  In this paper, a novel gradient index (GRIN) structural lens based on the
concept of generalized Luneburg lens (GLL) is proposed. This lens allows for
the realization of double foci and localization of energy flow between the two
focal spots, thereby achieving ultralong focusing. The double-foci GRIN lens
consists of two concentric circular regions with varying thickness defined in a
thin plate structure. The two concentric circular regions are designed to
realize continuous change of refractive indices with different profiles.
Numerical simulations and experimental studies are performed to obtain the
maximum displacement amplitude, full length at half maximum (FLHM), and full
width at half maximum (FWHM) of the focal region of the lens. The results
demonstrate that ultralong subwavelength focusing can be achieved for a
broadband frequency range. In addition, our results show that the FLHM and FWHM
can be tailored through the design of the focal length of the GLL. This offers
a simple and flexible approach of engineering the GLL focusing characteristics
and energy distributions for many applications.
