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The optical properties of infinite planar array of scattering particles,metasurfaces and metagratings, are attracting special attention lately fortheir rich phenomenology, including both plasmonic and high-refractive-indexdielectric meta-atoms with a variety of electric and magnetic resonantresponses. Herein we derive a coupled electric and magnetic dipole (CEMD)analytical formulation to describe the reflection and transmission of suchperiodic arrays, including specular and diffractive orders, valid in thespectral regimes where only dipolar multipoles are needed. Electric and/ormagnetic dipoles with all three orientations arising in turn from a single orvarious meta-atoms per unit cell are considered. The 2D lattice Green functionis rewritten in terms of a 1D (chain) version that fully converges and can beeasily calculated. Modes emerging as poles of such lattice Green function canbe extracted. This formulation can be applied to investigate a wealth ofplasmonic, all-dielectric, and hybrid metasurfaces/metagratings of interestthroughout the electromagnetic spectrum.

physical review. b./physical review. b

Coupled electric and magnetic dipole formulation for planar arrays of  dipolar particles: metasurfaces with various electric and/or magnetic  meta-atoms per unit cell