Abstract
The analogy between the electron wave nature in graphene electronics and the electromagnetic waves in dielectrics has suggested a series of optical-like phenomena, which is of great importance for graphene-based electronic devices. In this paper, we propose an asymmetric double-well potential on graphene as an electronic waveguide to confine the graphene electrons. The guided modes in this graphene waveguide are investigated using a modified transfer matrix method. It is found that there are two types of guided modes. The first kind is confined in one well, which is similar to the asymmetric quantum well graphene waveguide. The second kind can appear in two potential wells with double-degeneracy. Characteristics of all the possible guide modes are presented.