Time domain models of negative refractive index metamaterials

The physics and wave properties of materials with negative refractive index have been studied extensively in recent years. However, computationally efficient numerical models for such media are not readily available to designers who wish to create novel components that incorporate such materials. In addition to being numerically efficient and robust, they must incorporate the dispersive behavior of the refractive index and the wave impedance of metamaterials and allow for the imposition of realistic boundary geometries and properties. In this paper we present a 3D numerical model that is based on the distributed node TLM network in which reactive elements are embedded. The resulting periodic structure supports backward waves and constitutes an artificial medium with negative phase velocity and negative refractive index. When embedded in a time domain electromagnetic field simulator, this model provides a versatile simulation tool for metamaterial design. Since such a transmission line model is realizable it also provides a framework for the actual realization of 3D metamaterials. We derive the theoretical foundations for the model and show some validating simulation results that demonstrate its capabilities and potential.