This thesis presents a Transmission Line Modeling (TLM) method approach to investigate the interaction between electromagnetic waves and complex media. TLM is a time domain numerical technique based on a circuit representation of Maxwell's equations: short impulses, capable of correctly sampling the propagation of electromagnetic waves, propagate in a transmission line network according to a local scattering algorithm. This work presents, in great detail, new expansions of TLM; thanks to the versatility these advances confer to the method, media as exotic as metamaterials can be simulated by employing TLM. In particular, invisibility cloaking devices, which constitute a special class in the realm of metamaterials, are deeply explored in this dissertation.
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