Transformation Optics Approach for Goos-Hanchen Shift Enhancement at Metamaterial Interfaces

Since its first observation in 1947, the Goos-Hanchen effect an electromagnetic wave phenomenon where a totally reflected beam with finite cross section undergoes a lateral displacement from its position predicted by geometric optics has been extensively investigated for various types of optical media such as dielectrics, metals and photonic crystals. Given their huge potential for guiding and sensing applications, the search for giant and tunable Goos-Hanchen shifts is still an open question in the field of optics and photonics. Metamaterials allow for unprecedented control over electromagnetic properties and thus provide an interesting platform in this quest for Goos-Hanchen shift enhancement. Over the last few years, the Goos-Hanchen effect has been investigated for specific metamaterial interfaces including graphene-on-dielectric surfaces, negative index materials and epsilon near -zero materials. In this contribution, we generalize the approach for the investigation of the Goos-Hanchen effect based on the geometric formalism of transformation optics. Although this metamaterial design methodology is generally applied to manipulate the propagation of light through continuous media, we show how it can also be used to describe the reflections arising at the interface between a vacuum region and a transformed region with a metamaterial implementation. Furthermore, we establish an analytical model that relates the magnitude of the Goos-Hanchen shift to the underlying geometry of the transformed medium. This model shows how the dependence of the Goos-Hanchen shift on geometric parameters can be used to dramatically enhance the size of the shift by an appropriate choice of permittivity and permeability tensors. Numerical simulations of a beam with spatial Gaussian profile incident upon metamaterial interfaces verify the model and firmly establish a novel route towards Goos-Hanchen shift engineering using transformation optics