Asymptotic expressions for guided TM and TE waves in a graphene parallel-plate waveguide

In this paper, the guidance conditions for graphene parallel-plate waveguides are examined. Asymptotic expressions are given for all TE and TM modes with different regions of validity for different frequencies. The behavior of propagation constants at optical frequencies is shown to be different from in the microwave regime due to a difference in conductivities. We show that asymptotic expressions for guided waves in a graphene parallel-plate waveguide using the Lambert W function give good approximations for finding the wavenumber along the propagation direction at optical frequencies for all TM/TE modes. The results from this paper can aid the design of graphene-based devices by providing simple formulas for the propagation constants.