Non-linear Optical Properties of 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. 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. 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 vacuum. In addition, we are capable to extract from our calculations the nonlinear polarization, the induced electric field and the charge distribution in order to provide more information about the behavior of this type of metamaterials.

References
[1] Physical Review B 99, 125408 (2019)
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