Transmitted spectra (a1)-(e1), transmitted phase shift responses and group indices (a2)-(e2) at diverse pump light intensities when the plasmonic waveguide between the two disk cavities is covered by a 0.5 nm thick graphene layer. The green dots stand for the group index of the transparent wavelength at 789 nm with values of 14.8, 7.9, 2.8, 7.9, and 14.8.