General closed-form condition for enhanced transmission in subwavelength metallic gratings in both TE and TM polarizations

We present an intuitive reasoning and derivation leading to an approximated, simple closed-form model for predicting and explaining the general emergence of enhanced transmission resonances through rectangular, optically thick metallic gratings in various configurations and polarizations. This model is based on an effective index approximation and it unifies in a simple way the underlying mechanism of enhanced transmission as emerging from standing wave resonances of the different diffraction orders of periodic structures. The model correctly predicts the conditions for the enhanced transmission resonances in various geometrical configurations, for both TE and TM polarizations, and in both the subwavelength and non-subwavelength spectral regimes, using the same underlying mechanism and one simple closed-form equation, and does not require explicitly invoking specific polarization dependent mechanisms. The known excitation of surface plasmons polaritons or slit cavity modes, emerge as limiting cases of a more general condition. This equation can be used to easily design and analyze the optical properties of a wide range of rectangular metallic transmission gratings.