Controlling electric fields spatially by graded metamaterials: Implication on enhanced nonlinear optical responses

The local electric field of a graded metal-dielectric cylinder, with complex permittivity given by a spatially dependent Drude model, has been derived analytically in terms of hypergeometric functions. Our results show that the electric field inside the cylinder can be confined in desired positions. Thus one can achieve the control of electric fields by fabricating graded metamaterials with specific material parameters. The enhanced nonlinear optical responses are also examined. The results suggest that the gradation-controlled field distribution may be a consequence of a combination of surface plasmon resonance and microgeometry in graded metamaterials.