In this paper, hyperbolic metamaterials slot waveguides based on graphene have been proposed to explore the optical characteristics. The hyperbolic metamaterials are composed of graphene-dielectric alternating multilayer. It has been verified in our proposed structure that the optical field is enhanced efficiently in the slot region, which results in the optical gradient force becoming larger as the distance of slot region becomes smaller. Both numerical simulation and theoretical analysis systematically reveal that the stronger gradient force can be achieved through smaller slot gap or lower chemical potential. Furthermore, the optical properties of two coupled waveguides have been studied under the relation of incident wavelength, chemical potential of graphene, composition of graphene-dielectric multilayer (eg., number of periods, filling factor of graphene) of the waveguides in this work. We find that a larger gradient force can be obtained by adjusting the height of waveguides, either decreasing the thickness of dielectric with constant number of periods or compressing the number of periods with fixed graphene filling factor. Our results will be helpful to the study of the optical field in the infrared region and also has great potentials in nanoscale manipulation and plasmonic devices.
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