  In this paper, four easy-to-fabricate graphene-based Si waveguide modulators
are presented to overcome the strong polarization dependency of graphene-based
modulators. The modulation features of two newly proposed structures, i.e. two
graphene-based buried silicon waveguides in addition to two standard ridge
silicon waveguides at the telecommunication wavelength of $\lambda=1.55 \mu m$
are studied. The results show that for certain widths of each waveguide (the
height is constant), the amplitude and phase modulations clearly become
polarization-insensitive. The amplitude modulation depths for both the TE and
TM modes are equal for these optimized waveguides with the precision of
$10^{-4} dB/{\mu m}$. Moreover, in some of the proposed modulators, the maximum
variations of the real parts of the effective mode indices (EMI) for both the
TE and TM modes coincide with each other with an excellent precision ($5\times
10^{-5}$). This precision value is much smaller than the standard criterion
value for confirming a polarization-insensitive phase modulation. Furthermore,
the performances of all the structures are studied for all optical
telecommunication wavelengths. Even without making any changes to the
structures designed at $1.55 \mu m$ at appropriate wavelength intervals, the
structures exhibit polarization-insensitive behaviors.
