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We derive analytical approximations for the variation of the effective indices of the fundamental transverse electric (TE) and transverse magnetic (TM) modes with the chemical potential of graphene in three common types of silicon graphene waveguides. In all cases, a third-order polynomial provides an excellent degree of approximation (<; 10<sup>-4</sup>) over the 1540-1560 nm wavelength band. The approximations can be useful in the design of complex-integrated photonic circuits where graphene is employed to tune the refractive of the dielectric waveguides.

Electro-Refraction Modulation Predictions for Silicon Graphene Waveguides in the 1540–1560 nm Region