Analytical modeling of highly tunable giant lateral shift in total reflection of light beams from a graphene containing structure

We report a distributed circuit modeling based on analytical study of the tunable enhanced lateral displacement of electromagnetic waves in total reflection of light beams from a graphene containing structure. The graphene containing structure considered here supports transverse magnetic surface modes whose dispersion properties can be controlled by applying an appropriate electrical voltage to the graphene. Using this property of the structure, coupling of the incident wave to the surface modes of the structure is used to enhance the lateral displacement of the totally reflected wave, known as Goos-Hänchen shift, while it is also shown that this large lateral shift can be controlled through adjusting the dispersion properties of the surface modes by applying an electrical voltage. Using the proposed circuit model, phase of the reflected plane wave is calculated to obtain the Goos-Hänchen shift under stationary phase approximation. This approximation is then modified by considering finite spatial width of the incident beam. Our calculations show that by coupling the incident wave to the surface modes of the structure, a giant Goos-Hänchen shift as high as 270 times of the free space wavelength; λ0, can be achieved. Furthermore, this large shift can be varied from 270 λ0 to 55 λ0 by changing the applied voltage from 0.5 V to 3 V. The results presented here can be used in designing graphene plasmonic based integrated optical devices such as optical switches.