LAUSR

A graphene square waveguide with the small normalized mode area and the long propagation length is proposed and investigated in this letter. The square waveguide consists of graphene nanoring embedded into dielectric and four graphene ribbons added on the square dielectric. Due to the coupled between the graphene nanoring and ribbons in square waveguide, the electric field can be strongly confined. The normalized mode area can achieve $10^{-5}$ and the propagation length can be about 10 $\mu \text{m}$ at 35 THz. The dependencies of the normalized mode area and propagation length on structural parameters also are studied by separately changing the parameters in our work. Furthermore, the normalized mode area and propagation length can be tuned by changing the chemical potential of graphene ribbons. The structure of graphene square waveguide can be manufactured by chemical vapor deposition method and this waveguide have a great prospect in optical chip and large-scale optic-electronic integration.