Temporal scattering of a graphene plasmon by a rapid carrier density decrease

Abstract

Recently, the temporal control of graphene carrier density has emerged as a viable means to create various frequency shifting, modulation, and sensing photonic devices. Here we describe a general theoretical approach to calculate the graphene plasmon transformation after rapid changes of the Fermi level and carrier density. The approach is based on solving the Maxwell equations supplemented by the microscopic current equation. We derive formulas for the amplitudes of the transmitted and reflected plasmons after a rapid carrier density drop. The relation of these amplitudes and the Fourier transformed finite-difference time-domain (FDTD) fields is also established by introducing the concept of differential spectral transformation of wavepackets. The results of the analytical and FDTD approaches refute the claims of plasmon amplification under rapid carrier changes that appeared in recent theoretical studies. The presented theoretical and computational approaches form a basis of time-varying electromagnetics of graphene plasmonics.