Buried and ridge graphene-based silicon waveguides for broadband polarization-insensitive amplitude and phase modulators

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.