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Ideal spatial phase profile for focusing an obliquely incident plane wave on a planar focal plane at a distance F from a planar metalens. The ideal phase profile for any given angle of incidence can be expressed as the sum of a linear phase gradient (a) to redirect the wave to the surface normal and a hyperbolic phase profile (b) to focus the wave. In (a)-(c) phase profiles for different polar angles of incidence, α, are represented using different colors and α = 0 corresponds to normal incidence. One particular phase profile for angle of incidence equal to 30 deg is highlighted with a bolder line. (d), (e) Ideal phase profile, as a function of the angle of incidence, α, for two different choices for the location of the focal spot: (d) r0 = Ftan(α) and (e) r0 = Fα. The phase is normalized by the product of the wavenumber, k0 = ω/c, and the focal length of the metalens, F, so that both plots can also be interpreted as the normalized group delay () required for achromatic focusing. In all plots ‘r’ is the radial coordinate on the metalens.
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