Abstract: Based on the Hamiltonian of carriers in bilayer graphene, the characteristic of the guided modes in asymmetric quantum-well waveguides is investigated. There exist three different kinds of motions depending on the incident energy of the electrons and the external potentials, i. e., quasi-classical motion, quantum Klein tunneling, and mixing of the former two. Given the wave functions for the different regions and using the continuity conditions at the interfaces of the potential barriers, the dispersion relationship for the guided modes in asymmetric waveguides is derived analytically. Meanwhile, the structure feature of the guided modes under three different cases is discussed. The study is very significant for the practical applications of graphene-based waveguide devices.

Key words: optoelectronics, asymmetric guided mode, continuity condition, dispersion relationship, bilayer graphene