  We develop a fast, accurate, and robust technique to model the
electromagnetic response of a two-dimensional (2D) waveguide-fed metasurface
aperture. The geometry under consideration consists of a parallel-plate
waveguide with an array of subwavelength, complementary metamaterial elements
patterned into one of the conducting surfaces. To determine the radiated field,
we model each radiating element as a polarizable dipole, and account for mutual
interactions among elements via guided and radiated fields by applying a
coupled dipole framework. Using full-wave simulations of parallel-plate
waveguides with two types of metamaterial elements, we confirm the validity of
the proposed coupled dipole model and demonstrate the ability to predict
radiation patterns corresponding to arbitrarily arranged elements. We explore
the importance of including the mutual coupling among metamaterial elements to
arrive at accurate field predictions. The coupled dipole modeling framework
presented is scalable to extremely large apertures and can form the foundation
for a general, efficient, yet simple aperture analysis and synthesis tool.
