Analytical model of metasurfaces comprising meta-atoms with anisotropic polarizabilities and for arbitrary incident angles

The use of powerful numerical methods to study the optical properties of metasurfaces has led to an obvious need for the development of analytical models that provide meaningful physical analysis of the numerical results. In this paper, we present a general analytical approach to the study of electromagnetic resonances in metasurfaces consisting of meta-atoms with anisotropic dipole polarizabilities and irradiated with light under arbitrary angle of incidence. The presented approach allows us to clearly trace and explain features of coupling between electric and magnetic dipole moments in metasurfaces as well as identify the role of such coupling. For these purposes, the dependence of the dipole lattice sums on the angle of light incidence is also presented. Expressions for the specular transmission and reflection coefficients are presented with explicit inclusion of the incidence angles and the dipole moments of the particles in the array, which allows a clearer analysis of purely numerical results. The developed analytical method is tested to characterize the spectral resonances, including the generalized Brewster effect, of dielectric metasurfaces composed of rectangular silicon nanoprisms. In addition, we discuss the relationship and similarity between the results of coupled dipole and coupled dipole-quadrupole methods. Our analytical representation is an insightful and fast method for the characterization of collective resonances in metasurfaces for irradiation at an arbitrary angle of incidence. It could be especially useful for designing planar nanophotonic devices consisting of building blocks with noncanonical and complex shapes when considering their operation under special irradiation conditions.