▎ 摘　　要

Graphene plays a substantial role in nano-scale optical engineering and miniature information signal processing systems gradually. In this letter, we propose a pipe-like substrate scheme to achieve the properly designed inhomogeneous, nonuniform conductivity distribution on a single sheet of graphene. The transverse-magnetic surface plasmon polariton wave supported by graphene will oscillate like water running in an inclined pipe and focus onto one point in a deep-subwavelength scale in the graphene sheet. Importantly, we find that this focusing behavior is robust and insensitive to the variance of background Fermi energy and incident frequency based on the analytic analysis. We verify our scheme by exploiting Hamiltonian optics and numerical calculation. This nano-scale optical manipulation will lead to the development of miniature optical system integration on a 1-atom-thick structure. Copyright (C) EPLA, 2016