A New Plane‐Wave Formulation for a Layered Medium: Applications to Metagratings

Abstract Electromagnetic wave interactions at planar interfaces are of fundamental importance, with Fresnel coefficients providing a precise description of reflection, transmission, and polarization changes. While standard Fresnel theory simplifies analysis by decomposing fields into Transverse Electric (TE) and Transverse Magnetic (TM) waves, this approach can become cumbersome for complicated sources located near interfaces or in multilayered media. This paper presents an alternative formulation that dispenses with TE/TM decomposition, instead working directly with the horizontal components of the plane‐wave spectrum. We derive 2 × 2 reflection and transmission matrices valid for arbitrarily layered media with planar interfaces, enabling the computation of reflected and transmitted plane‐wave spectra. We demonstrate the applicability of this approach by solving a Huygens' source problem relevant to the design of metagratings, structures comprised of scattering elements and planar interfaces.