▎ 摘　　要

An asymmetric quantum well in graphene can act as a slab waveguide for electron waves in a manner analogous to the electromagnetic waves in dielectrics. Guided modes and the probability current density are analyzed in the graphene electron waveguide induced by asymmetric electrostatic potential. The modes in an asymmetric graphene waveguide include guided modes, "cover modes", "substrate modes" and "radiation modes". The conditions for a guided mode are quantified. It is found that the fundamental mode is absent when both the Klein tunneling and classical motion are present. The confinement of electrons for lower order mode is stronger than for higher order mode. We hope that these characteristics in asymmetric graphene waveguide can provide potential applications in graphene-based waveguide devices.