Propagation and refraction of left-handed plasmons on a semiconducting substrate covered by graphene

We show that a plasmonic semiconductor substrate can support highly confined surface plasmons when it is covered by a graphene layer. This occurs when the imaginary part of graphene conductivity and real part of the effective permittivity of the surrounding medium become simultaneously negative. Full-wave electromagnetic simulations demonstrate the occurrence of negative refraction and two-dimensional lensing at the interface separating regions supporting conventional right-handed graphene plasmons and left-handed surface plasmon polaritons.