Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators.

Theoretical investigations of graphene-based electro-optic plasmonic modulators with a dielectric ridge were analyzed and the results were presented. The effects of different ridge materials and different spacer dielectric functions were analyzed, showing that a 3 dB modulation with a 65 nm-long waveguide is possible with dielectric-loaded surface plasmon polariton waveguides (DLSPPWs), resulting in an energy per bit only 0.08 fJ/bit. The figure of merit, defined as the ratio between the extinction ratio and the insertion loss, was found to be about 5.2 with a low refractive index ridge and increased to over 17.3 for a high refractive index Si ridge, compared to 3.5 calculated and measured with photonic graphene-based waveguides. Additionally, it was shown that further improvement in terms of the figure of merit is possible with long-range dielectric-loaded surface plasmon polariton waveguides (LR-DLSPPWs), where it was calculated to exceed 72. For such waveguides, a 3 dB modulation was achieved with 10 μm-long waveguides with an energy per bit of 15.8 fJ/bit. The wavelength dependence of the graphene conductivity and, consequently, the attenuation of the waveguide were analyzed for different chemical potentials. It was shown that gate voltage applied across the graphene layers shifts the attenuation curve to shorter wavelengths, with the 3 dB modulation bandwidth exceeding 15 THz for a 12 μm-long DLSPP waveguide.