Asymptotic Floquet theory for first order ODEs with finite Fourier series perturbation and its applications to Floquet metamaterials

Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider linear system of differential equations with time-periodic coefficient matrix. Assuming that the matrix depends analytically on small parameter, derive full expansion its Based this, prove only constant order exponents multiplicity higher than one will be perturbed linearly. The required can achieved via folding through certain choices periodicity Secondly, apply such an analysis metamaterials. provide characterization exceptional points pair subwavelength resonators time-dependent material parameters. are obtained if frequency components perturbations fulfill ratio, which determined by geometry dimer resonators.