Terahertz-to-Infrared Up-Conversion by Plasmonic-Enhanced Sum Frequency Generation in Graphene Gratings

Abstract

The tunable parametric up-conversion of terahertz (THz) to mid-infrared (MIR) frequencies via the third-order nonlinear process of nondegenerate four-wave mixing in graphene gratings is investigated by solving the nonlinear boundary diffraction problem using the developed numerical-analytical approach. First, we designed the linear THz, IR absorption spectra of graphene gratings to support resonances of surface plasmon polaritons (SPP) modes in the THz, MIR ranges by choosing the pump <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{1}$</tex> and signal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f$</tex> <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> frequencies equal to the resonant frequencies of the fundamental and higher-order SPP modes. The results of mathematical modeling of nonlinear spectra, i.e., the intensity of the parametric emission of transmitted and reflected waves at the sum frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{f}_{3}=2f_{1}+f_{2}$</tex> in the MIR range for various chemical potential <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu_{c}$</tex> in the graphene ribbon gratings are obtained. It is shown the enhancement of efficiency of up-conversion of THz to MIR frequencies by several orders when the graphene gratings are resonantly excited at SPP mode resonance frequencies by the signal and pump waves.