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2D materials

2D materials

Model tackles nonlinear optics in 2D materials

10 Dec 2018 Anna Demming
Model response: Equation sheds light on the nonlinear optics of 2D materials. Credit: Shutterstock Inozemtsev-Konstantin
Model response: Equation sheds light on the nonlinear optics of 2D materials. Credit: Shutterstock Inozemtsev-Konstantin

True to form, observations of nonlinear behaviour in graphene – such as parametric frequency conversion, third harmonic generation and self -phase modulation – has revealed extremely strong responses. Despite the attention these nonlinear optical responses have attracted for photonic devices, gaps remain in how scientists understand the processes governing them. By devising a description for the effective electric field and the sheet current density in a 2D material under specified incident light beams, a collaboration of researchers in China, Canada, Belgium and the US provide a model for extracting nonlinear optical responses for all 2D materials.

Reporting in the first issue of the Journal of Physics: Photonics, JinLuo Cheng at the  Chinese Academy of Sciences in Changchun and University of Chinese Academy of Sciences in Beijing, Chunlei Guo at the Chinese Academy of Sciences in Changchun and Rochester University in the US, and co-authors highlight the discrepancies between theory and experiment that have hindered efforts to fully exploit the optical properties of graphene. Taking the third order effective susceptibility as a case in point, in their report they describe calculated values based on phenomenological relaxation time approximations for scattering as “about two orders of magnitude smaller than most values extracted from earlier experiments for lightly doped graphene.” They add, “Several effects have been considered that might bring theory in better agreement with these experiments, including saturation of the optical nonlinearity, the influence of cascaded second order processes, and novel plasmonic effects, but none of them can sufficiently enhance the calculated conductivities.”

Modelling with a “structure factor”

The researchers describe their approach as modelling the current density in graphene as a ‘current sheet’ described by a Dirac δ-function, where the current density is zero for all coordinates except those defining the position of the graphene monolayer. They then derive a key equation for graphene nonlinear optics using a structure factor that describes environmental effects. With their equation they can determine the effective electric fields and current density inside 2D materials as a response to incident laser beams.  The model also includes the feedback radiation from the structure’s own sheet current density.

Applying their results to a graphene covered multi-layered structure they explore the second and third harmonic generated signals, as well as the output light generated through second order nonlinearity for parametric frequency conversion processes. They conclude their equations are suitable for modelling the entire family of 2D materials including bi-layer graphene, functionalized graphene, monolayer transition-metal dichalcogenides, black phosphorene, silicene, stanene, and that their results provide “a starting point for further nonlinear optical investigations of graphene or 2D materials in  layered structures.”

Full details are provided in the first issue of Journal of Physics: Photonics.

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