In this paper we report phase modulation obtained by inducing a capacitive charge on graphene layers embedded in the core of a waveguide. There is a biasing regime in which graphene absorption is negligible but large index variations can be achieved
with a voltage-length product as small as $V_pi,L_pi simeq 0.04 $,V,cm . Examples of phase induced changes are computed for straight waveguides and for microring resonators showing the possibility to implement several optoelectronic functionalities as modulators, tunable filters, and switches.
