Second Harmonic Generation in Nanostructured Metamaterials.*

We present a theoretical study of second harmonic generation (SHG) in structured metamaterials; particularly, an array of cross-shaped vacuum inclusions within a silver host. We calculate the nonlinear susceptibility tensor, for a large number of geometrical configurations for the inclusions. We demonstrate that both, the SHG intensity and the resonance peaks are highly sensitive to even subtle changes in the geometry that break the centrosymmetry of the array of inclusions. We presented the results for calculation of non linear susceptibility of second order for a metamaterial composed by silver host and cross-shaped inclusions of vaccum. The dielectric functions of both materials are known. The intensity in nonlinear susceptibility tensor depends on the variation in the symmetry of the metamaterial. We present the three non-zero components of that tensor, calculated by Haydock Recursive Method.