In this paper we report on an electro-refractive modulator based on single or double-layer graphene on top of silicon waveguides. The graphene layers are biased to the transparency condition in order to achieve phase modulation with negligible amplitude modulation. By means of a detailed study of both the electrical and optical properties of graphene and silicon, as well as through optimization of the geometrical parameters, we show that the proposed devices may theoretically outperform existing modulators both in terms of V(π)L and of insertion losses. The overall figures of merit of the proposed devices are as low as 8.5 and 2dB∙V for the single and double layer cases, respectively.
