We derive a pulse propagation equation for a graphene-clad optical fiber, treating the optical response of the graphene and nonlinearity of the dielectric fiber core as perturbations in asymptotic expansion of Maxwell equations. We analyze the effective nonlinear and attenuation coefficients due to the graphene layer. Based on the recent experimental measurements of the nonlinear graphene conductivity, we predict considerable enhancement of the effective nonlinearity for subwavelength fiber core diameters.
Gorbach, A. V., Marini, A., & Skryabin, D. V. (2013). Graphene-clad tapered fiber: Effective nonlinearity and propagation losses. Optics Letters, 38(24), 5244-5247. https://doi.org/10.1364/OL.38.005244