  We present a semi-analytical framework for computing the coupling of
radiative and guided waves in slowly varying (nearly uniform or nearly
periodic) surfaces, which is especially relevant to the exploitation of
nonlocal effects in large-area metasurfaces. Our framework bridges a gap in the
theory of slowly varying surfaces: aside from brute-force numerical
simulations, current approximate methods can model either guided or radiative
waves, but cannot easily model their coupling. We solve this problem by
combining two methods: the locally periodic approximation, which approximates
radiative scattering by composing a set of periodic scattering problems, and
spatial coupled-wave theory, which allows the perturbative modeling of guided
waves using an eigenmode expansion. We derive our framework for both nearly
uniform and nearly periodic surfaces, and we validate each case against
brute-force finite-difference time-domain simulations, which show increasing
agreement as the surface varies more slowly.
