  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.
