▎ 摘　　要

We investigate the influence that an embedded graphene layer has on guided modes of optical waveguides using exact numerical calculations and a convenient perturbation theory. The latter is found to be highly accurate allowing the graphene-induced changes of modal propagation constants to be determined as the product of a numerical factor characterizing the modal properties of the bare waveguide and the optical conductivity of graphene. In this manner, the influence of the waveguide geometry and the electro-optical properties of graphene on the modulation efficiency can be considered and optimized separately. This result is then used to illustrate the basic electro-absorptive and electro-refractive modulator design principles on a planar waveguide toy model with realistic parameters.