Mode matching in second order susceptibility metamaterials

We present an effective model for a subwavelength periodically patterned metallic layer, its cavities being filled with a nonlinear dielectric material, which accounts for both the linear and second order behavior. The effective non linear susceptibility for the homogenized layer is driven by the nonlinearity of the dielectric material and by the geometrical parameters, thus leading to much higher susceptibility than existing materials. This leads to a huge enhancement of non linear processes when used together with resonances. Furthermore, multiple resonances are taking place in the metallic cavities, and we investigate the mode matching situations for frequency conversion processes and show how it enhances further their efficiency.