Electric field tunable photonic Hall effect with liquid crystals

The Mie theory for electromagnetic scattering is extended to the case of coated metal sphere with liquid crystals. A new set of vector basis functions for the electric displacement vector inside the liquid crystal layer has been constructed. The expansion coefficients of transmitted and scattered fields are obtained analytically by applying the continuous boundary conditions. The dependence of the scattering property on the geometrical parameters has been investigated in detail. The appearance of photonic Hall effect for such a Mie scatterer is confirmed. It is interesting that such a photonic Hall effect not only depends on the ratio of the inner to outer radius of coated sphere, it is also tunable by the application of an external voltage.