Pancharatnam–Berry optical lenses

In this paper, we analyze a few aspects of Pancharatnam–Berry (PB) phase optical lenses. First, we provide theoretical formulas on how the optical efficiency, focal length, and point spread function depend on wavelength and validate them with numerical calculations based on Fresnel diffraction theory. Second, we perform numerical studies on how optical efficiency is affected by discretization of the PB phase. We find that phase discretization significantly lowers the optical efficiency for low f-number PB lenses.