Phase-Matched Coupling and Frequency Conversion of Terahertz Waves in a Nonlinear Graphene Waveguide (2017)

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, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , 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 f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> . Frequency conversion from f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> to a new frequency, that is, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , is attainable, assisted by the permittivity modulation induced by the co-propagating waves f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . The generated frequency has a Ω = f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> - f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> frequency detuning from the f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> frequency, that is, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> = f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> - (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> - f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ). Thus, tunable frequency conversion can be achieved by controlling f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , or f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> . Our numerical estimations show viable gain and conversion efficiency over the entire THz range considered, from 0.1 to 2 THz. The proposed technique is compact, tunable, and (in principle) spans the entire THz range.