Analytical study of resonance conditions in planar resonators

We propose a study of a generalized Airy-like formula of the transmittance through planar resonators. A complete and analytical analysis of total transmission conditions is given according to physical parameters. The homogeneous problem related to free oscillations of resonators, which leads to complex resonance frequencies and quality factors, is also resolved. After a quick validation on well-known parallel-plate dielectric layers behaving as Fabry-Perot resonators, our discussion is applied on subwavelength metallic lamellar gratings from an analytical modal theory assuming perfectly electric conductors.