Theoretical and computational analysis of second- and third-harmonic generation in periodically patterned graphene and transition-metal dichalcogenide monolayers

摘要

Remarkable optical and electrical properties of two-dimensional (2D)materials, such as graphene and transition-metal dichalcogenide (TMDC)monolayers, offer vast technological potential for novel and improvedoptoelectronic nanodevices, many of which relying on nonlinear optical effectsin these 2D materials. This article introduces a highly effective numericalmethod for efficient and accurate description of linear and nonlinear opticaleffects in nanostructured 2D materials embedded in periodic photonic structurescontaining regular three-dimensional (3D) optical materials, such asdiffraction gratings and periodic metamaterials. The proposed method buildsupon the rigorous coupled-wave analysis and incorporates the nonlinear opticalresponse of 2D materials by means of modified electromagnetic boundaryconditions. This allows one to reduce the mathematical framework of thenumerical method to an inhomogeneous scattering matrix formalism, which makesit more accurate and efficient than previously used approaches. An overview oflinear and nonlinear optical properties of graphene and TMDC monolayers isgiven and the various features of the corresponding optical spectra areexplored numerically and discussed. To illustrate the versatility of ournumerical method, we use it to investigate the linear and nonlinearmultiresonant optical response of 2D-3D heteromaterials for enhanced andtunable second- and third-harmonic generation. In particular, by employing astructured 2D material optically coupled to a patterned slab waveguide, westudy the interplay between geometric resonances associated to guiding modes ofperiodically patterned slab waveguides and plasmon or exciton resonances of 2Dmaterials.