The Swiss Roll Metamaterial Revisited

In this work, we analytically model the Swiss roll metamaterial medium, showing that each unit cell can be thought of as a flux-coupled waveguide terminated in coupled inductors. The equivalent circuit model of the metamaterial accurately predicts its response, including its higher order resonances, even when made of a lossy, finite-thickness conductor. A closed-form solution for the response of this circuit model is then derived by solving a matrix equation of arbitrarily large dimensions. Along the way, we provide a general method for modeling the effective permeability of uniaxial, anisotropic metamaterials formed from axially invariant conducting inclusions.