Circuit Model for Plasmons on Graphene with One-Dimensional Conductivity Profile

The scattering of graphene surface plasmons normally incident on a line discontinuity in graphene surface conductivity is investigated. The effect of the length of the transition region on the reflection and transmission coefficients is studied. It is shown that the reflection coefficient is reduced by widening the transition region. Based on the results obtained, a transmission line model is derived for the graphene sheet in which the discontinuity is represented by a simple circuit. This model is next used to design graphene-based bandpass and bandstop filters with arbitrary bandwidth in the terahertz regime.