Sub-wavelength focusing in loaded transmission line negative refractive index metamaterials

We have previously demonstrated that a new class of planar Negative Refractive Index Metamaterials (NRIMs) can be constructed by periodically loading a host transmission line medium with inductors and capacitors in a dual (high-pass) configuration, and we have experimentally demonstrated focusing of a cylindrical wave inside such a NRIM, using a single-interface prototype. In this paper, we examine the conditions required to observe sub-wavelength focusing using a theory based on the plane-wave expansion of cylindrical waves, supplemented by permeability and permittivity functions characteristic to our NRIMs. This theory is validated by full-wave simulations and experimental data for a single-interface structure, and subsequently applied to the study of a two-interface (NRIM slab lens) structure. Finally, we present microwave circuit simulations showing clear, sub-wavelength focusing in a realizable NRIM lens.