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Computational study of second- and third-harmonic generation in periodically patterned 2D-3D heteromaterials

Remarkable optical and electrical properties of graphene and other two-dimensional (2D) materials provide significant potential for novel optoelectronic applications and devices, many of which depend on nonlinear optical effects in these 2D materials. In this paper we use a theoretical and computational formalism we have recently introduced to efficiently and accurately compute the linear and nonlinear optical response of nanostructured 2D materials embedded in periodic structures containing regular three-dimensional (3D) materials, such as diffraction gratings or periodic metamaterials. Thus, we use the proposed method to demonstrate enhanced nonlinear optical interactions in periodically patterned photonic nanostructures via resonant excitation of phase-matched nonlinear waveguide modes, enhanced nonlinearity of nanostructures containing graphene and other 2D nanomaterials, such as WS2, and multi-continua Fano resonances for increasing the nonlinear efficiency of hybrid 2D-3D photonic heteromaterials.