We show that the rigorous Fourier modal method yields the thin element approximation when the feature sizes and the period tend to infinity. The transversal eigenmodes of the structure can be divided into sets whose effective refractive index corresponds to the refractive indices of the grating. Each set can be treated as the thin element approximation with constant amplitude and piecewise continuous phase transmission. We also demonstrate that the primary reason for the rapid failure of the thin element approximation with thick binary structures is attributable to destructive interference of the waveguide modes.
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