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

Efficient perturbative framework for coupling of radiative and guided modes in nearly periodic surfaces