Modal Homogenization of High-Contrast Mie Metasurfaces: From Symmetry Control to Fano, ATS, and Bianisotropic Responses

We develop an asymptotic homogenization theory for high-permittivity Mie-resonant metasurfacesilluminated in transverse-electric (TE) polarization. In the subwavelength resonant regime, themetasurface is replaced by an effective interface equipped with frequency-dependent transmissionconditions involving three surface susceptibilities (γee, γmm, γem) that fully govern reflection andtransmission. A central ingredient is a so-called Static–Dynamic Cell Eigenproblem (SD-Cell EP)posed on the unit cell, coupling a dynamic Helmholtz equation inside the inclusion to a static Laplaceequation outside. Its real eigenvalues and eigenmodes yield a modal decomposition of the effectiveparameters, each resonance contributing as a simple pole. This structure naturally leads to reduceddescriptions (single-mode Lorentz, weakly coupled two-mode Fano, and strongly coupled Autler–Townes-type models) that retain physical transparency while remaining quantitatively accurate. Forsymmetric (rectangular) inclusions, the theory recovers purely electric or magnetic resonances andtheir transition from Lorentzian to Fano and Autler–Townes behavior. For asymmetric (triangular)inclusions, symmetry breaking activates electromagnetic coupling and turns the metasurface into areciprocal bianisotropic reflector, enabling strongly asymmetric scattering and, in the presence ofweak loss, nearly perfect one-sided absorption.