We consider the design and modeling of metasurfaces that couple energy from guided waves to propagating wave fronts. To this purpose, we develop a comprehensive, multiscale dipolar interpretation for large arrays of complementary metamaterial elements embedded in a waveguide structure. Within this modeling technique, the detailed electromagnetic response of each metamaterial element is replaced by a polarizable dipole, described by means of an effective polarizability. In this paper, we present two methods to extract this effective polarizability. The first method invokes surface equivalence principles, averaging over the effective surface currents and charges induced in the element's surface in order to obtain the effective dipole moments, from which the effective polarizability can be inferred. The second method is based in the coupled-mode theory, from which a direct relationship between the effective polarizability and the amplitude coefficients of the scattered waves can be deduced. We demonstrate these methods on several variants of waveguide-fed metasurface elements (both one- and two-dimensional waveguides), finding excellent agreement between the two, as well as with the analytical expressions derived for circular and elliptical irises. With the effective polarizabilities of the metamaterial elements accurately determined, the radiated fields generated by a waveguide-fed metasurface can be found self-consistently by including the interactions between polarizable dipoles. The dipole description provides an effective perspective and computational framework for engineering metasurface structures such as holograms, lenses, and beam-forming arrays, among others.

• Received 10 July 2017
• Revised 16 October 2017

DOI:https://doi.org/10.1103/PhysRevB.96.235402