Experimental Verification of Negative Index of Refraction by Lateral Beam Displacement

This paper reports investigation of negative refraction by measurement of lateral displacement of the beam refracted at the slab made out of ‘backward-wave’ meta-material. The meta-material was based on parallel plate waveguide loaded with double ring resonators. The slab was illuminated by 8 GHz microwave beam at several different angles of incidence. The beam was generated by horn antenna and location of the maximum of refracted beam was measured by an open rectangular waveguide. It was found that maximum always lied on the same side of the normal, where the incoming beam impinged the slab. This result is consisted with the theory and it proves phenomenon of negative refraction. INTRODUCTION The material which supports propagation of backward waves (‘left-handed material’ or ‘backward-wave material’) was analyzed theoretically in sixties by Veselago [1] and realized experimentally for the first time by Smith at al. [2] in 2000. Probably the most intriguing electromagnetic phenomenon associated with ‘backward-wave’ meta-material is ‘reversion’ of Snell law, i.e. negative refraction. So far, there have been several experimental studies of negative refraction based on pioneering paper published by Shelby et al.[3]. Shelby observed ‘anomalous’ refraction on the prism made out of ‘backward-wave’ meta-material. Sanz et al. [4] pointed out that prism made out of ordinary (‘forward-wave’) material with high loss exhibits spatial power distribution of the refracted beam similar to that in the case of ‘backward-wave’ material. Due to the shape of the prism, the different points of the wave front of the beam refracted within material travel along different distances and they are differently attenuated when they experience second refraction. This may lead to the incorrect interpretation of the experimental results. The same authors [4] proposed method of verification of negative refraction by measurements of lateral displacement of the beam refracted on the slab. In this paper, the proposed method [4] is used for experimental verification of negative refraction. THEORETICAL ANALYSIS Let us analyze the arrangement suggested in [4] (figure 1). The plane wave impinges from air ( r=1, μr=1) onto a slab made out of arbitrary but passive homogenous material (Re{ r‹›0} and Re{μr‹›0}, Im{ r 0} and Im{μr 0}; the e j t time dependence is assumed). In this case, the real part of index of refraction is described by generalized form of Snell law [1,2,3]: r r Re sin sin n Re 2 1 (1) Here, n stands for index of refraction, 1 stands for the incident angle of incoming ray, 2 is the angle of refraction and r and μr stand for relative permittivity and relative permeability of the slab, respectively. In the case of ordinary material (Re{ r›0} and Re{μr›0}, the propagation is in the form of forward waves. The refracted ray within a slab is located at the side of the normal adjacent to the side where incoming ray impinges the slab, thus one must choose positive sign in (1). In the case of ‘backward-wave’ material, the refraction is ‘anomalous’. The ray within the slab is located at the same side of the normal where the incoming ray impinges the slab and one must choose negative sign in (1). From figure 1, one easily finds the location of the second refracted ray that leaves the slab: