Calculation of the negative refractive index of a LHM slab by the free-space mapping of the laterally shifted refracted beam

In this paper, we present a novel method to calculate the effective negative refractive index of a left-handed material (LHM)—a composite of split-ring resonators (SRRs) and thin wire structures. A LHM slab was first fabricated and then the measured transmission and reflection results were used to determine the LHM passband. To obtain the effective negative-refractive index, a microwave beam was obliquely launched to illuminate the slab for which a 2D spatial-field profile of the refracted beam outside the slab was obtained by scanning the lateral shifting of the field with respect to normal for a band of frequencies. A lateral shift of the refracted beam towards the same side of the incident beam for the LHM passband confirmed negative refraction in the LHM slab and the refractive index calculated for that frequency region was conclusively negative according to Snell's law. The presented method provides an alternate and efficient way to measure the effective refractive index of a LHM.