Integrating cold plasma equations into the Fourier modal method to analyze second harmonic generation at metallic nanostructures

We introduce a computational scheme to analyze second harmonic generation in periodic metallic nanostructures, i.e. metamaterials, that are composed of multiple layers. To describe the nonlinear polarization by the metallic constituents, we rely on a hydrodynamic model for the conduction electrons. Our computational approach is based on the Fourier modal method into which we incorporate the hydrodynamic plasma model. We detail physical and numerical peculiarities of the algorithm and we access aspects of convergence in a comprehensive manner. Finally, we provide further insights into the characteristics of intrinsic nonlinearities of metamaterials.