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In this paper, for the first time, we derive the appropriate form of Maxwell-Dirac equations for simulation of the coupling transport of electromagnetic fields and carriers in graphene nanostructures, and propose a time splitting spectral method for the numerical solution of this multiphysics problem.In this time splitting spectral method, we split each time step into three substeps. In each substep, we split the linear and nonlinear parts of the complicated nonlinear coupling Maxwell-Dirac system, then iteratively solving each simple part by linearizing the nonlinear part. The time derivatives are discretized by finite difference method with second order accuracy schemes. The spatial differential operators are approximated by spectral differentiation matrices. The proposed numerical method is validated by numerical examples that simulate the propagation of electromagnetic wave in graphene nanowaveguides.

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