Systematic study of the focal shift effect in planar plasmonic slit lenses

In this paper, we systematically studied the focal shift effect in planar plasmonic slit lenses. Through theoretical derivations and numerical simulations, we found that there is a focal length shift between the traditional design model and the finite-difference time-domain simulations. The shift is not only dependent on the Fresnel number (FN) of the lens, like traditional dielectric lenses, determined by the lens width and the designed focal length, but also on the surface plasmon polariton (SPPs) interaction on the lens surfaces, dependent on the slit numbers. We also found that the FN-induced focal shift is predominant when FN < 1. However, the SPP interaction-induced focal shift plays a major role when FN > 1. An approximated theoretical model is presented to estimate the focal shift of plasmonic slit lens with FN < 1.