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

Abstract

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 improved optoelectronic nanodevices, many of which rely on nonlinear optical effects in these 2D materials. This paper introduces a highly effective numerical method for efficient and accurate description of linear and nonlinear optical effects in nanostructured 2D materials embedded in periodic photonic structures containing regular three-dimensional (3D) optical materials, such as diffraction gratings and periodic metamaterials. The proposed method builds upon the rigorous coupled-wave analysis and incorporates the nonlinear optical response of 2D materials by means of modified electromagnetic boundary conditions. This allows one to reduce the mathematical framework of the numerical method to an inhomogeneous scattering matrix formalism, which makes it more accurate and efficient than previously used approaches. An overview of linear and nonlinear optical properties of graphene and TMDC monolayers is given and the various features of the corresponding optical spectra are explored numerically and discussed. To illustrate the versatility of our numerical method, we use it to investigate the linear and nonlinear multiresonant optical response of 2D-3D heteromaterials for enhanced and tunable second-and third-harmonic generation. In particular, by employing a structured 2D material optically coupled to a patterned slab waveguide, we study the interplay between geometric resonances associated to guiding modes of periodically patterned slab waveguides and plasmon or exciton resonances of 2D materials.

A new scheme to enhance the third-harmonic generation in graphene

“…Graphene has been widely used in photonic devices [3,4], as its physical properties [5,6] can be easily and ultrafast tuned via electric gating and chemical doping. In addition to applications to passive devices, its nonlinear optical properties have also been effectively employed to active nanophotonic devices [7][8][9], primarily because the local optical field can be strongly enhanced upon the generation of surface plasmons of graphene structures.…”

Simultaneous Tunable Enhancement of SHG and THG in Graphene Optical Gratings

“…The widths of the graphene ribbons, 1 and 2 , and the thickness, , of the spacer are quantities we optimize to achieve a so-called double resonance [4], that is to have a plasmon mode at the fundamental frequency (FF) and also a plasmon mode at the SH or TH. To model the linear and nonlinear optical response of graphene gratings, we used a numerical method implementing a combination of the generalized-source algorithm and finite-different time-domain method [3].…”

“…Because of large optical field enhancements achievable in graphene via excitation of surface plasmons, this truly twodimensional (2D) physical system [1] provides a promising material platform for enhancing nonlinear optical interactions at the nanoscale [2][3][4]. In this paper, we demonstrate that by matching plasmon resonances in mutually interacting graphene gratings separated by a thin dielectric spacer, the second-harmonic (SH) and third-harmonic (TH) can be simultaneously enhanced by more than eight orders of magnitude as compared to that in a graphene sheet.…”

Enhanced optical nonlinearities in 2D-3D heteromaterials

“…In this paper, we will review some recent results [4,5] pertaining to nonlinear optical effects in nanostructured bulk optical media containing homogeneous or nanopatterned 2D materials.We will first introduce and briefly discuss some theoretical concepts and methods widely used in the study of optical properties of periodic structures and photonic devices, such as metamaterials, diffractive optical elements, and plasmonic structures. In particular, we will explain how the mathematical formulation of these methods can be extended to incorporate quadratic and cubic nonlinear optical effects in 2D materials, a key feature that makes these methods powerful tools for the exploration of nonlinear optical effects at the nanoscale.…”

“…In this paper, we will review some recent results [4,5] pertaining to nonlinear optical effects in nanostructured bulk optical media containing homogeneous or nanopatterned 2D materials.…”