We recently demonstrated a phase compensated metalens that cannot only achieve super-resolution, but also possesses the Fourier transform capability. The metalens consists of a metamaterial slab and a plasmonic waveguide coupler (PWC). We have now ascertained the requirements for the metamaterial and the detailed design principles for the PWCs. Simulations of metalenses with a new type of PWC geometry have confirmed that the new metalenses also possess super-resolution and the Fourier transform function. The hyperbolic metalens shows an anomalous focus shifting behavior, which may be used to design exotic optical systems with new functionalities.