Efficient Analysis of Wave Propagation in Metasurface Arrays Based on Eigenvalue Perturbation

We explore two types of eigenvalue perturbations to analyze the dispersion features of periodic arrays of metasurfaces (MSs) for arbitrary propagation angles. The perturbations describe the dependence of the dispersion upon physical quantities with closed-form expressions, which result in a deeper understanding and physical insights into the dependence of the effective parameters of the stack on the MS properties. Our analytical theory is applied to three representative examples of periodic structures containing linear MSs. Due to the underlying symmetries in the considered examples, the perturbation results are further simplified, shedding light into interesting opportunities offered by MS arrays for the manipulation of electromagnetic wave propagation.