Phase-Matched Coupling and Frequency Conversion of Terahertz Waves in a Nonlinear Graphene Waveguide

Abstract

In this paper, we propose a novel technique for the phase-matched coupling and frequency conversion of terahertz (THz) waves. The principle of operation is based on nonlinear THz wave interaction in a graphene parallel plate waveguide filled with lithium niobate. The THz waves induce nonlinear polarization that modulates the effective permittivity of the waveguide by modifying the graphene conductivity. To model the evolution of the THz waves, small modulation amplitudes are presumed and a perturbation analysis is performed. First, two THz inputs (the pump and the signal) with distinct frequencies, that is, ${\boldsymbol{f}_1}$ and ${\boldsymbol{f}_2}$ , are considered. The two waves are coupled in a phase-matched fashion and show significant signal gain. Second, a third THz input with low intensity is considered at frequency ${\boldsymbol{f}_3}$ . Frequency conversion from ${\boldsymbol{f}_3}$ to a new frequency, that is, ${\boldsymbol{f}_4}$ , is attainable, assisted by the permittivity modulation induced by the co-propagating waves ${\boldsymbol{f}_1}$ and ${\boldsymbol{f}_2}$ . The generated frequency has a $\boldsymbol{\Omega } = {\boldsymbol{f}_1} - {\boldsymbol{f}_2}$ frequency detuning from the ${\boldsymbol{f}_3}$ frequency, that is, ${\boldsymbol{f}_4} = {\boldsymbol{f}_3} - ({{\boldsymbol{f}_1} - {\boldsymbol{f}_2}})$ . Thus, tunable frequency conversion can be achieved by controlling ${\boldsymbol{f}_1}$ , ${\boldsymbol{f}_2}$ , or ${\boldsymbol{f}_3}$ . Our numerical estimations show viable gain and conversion efficiency over the entire THz range considered, from $\text{0.1}$ to $\text{2}$ THz. The proposed technique is compact, tunable, and (in principle) spans the entire THz range.