Simulation of Maxwell-Dirac equations in graphene nanostructures

Xuecang Zhang

doi:10.1117/12.2060296

10 September 2014 Simulation of Maxwell-Dirac equations in graphene nanostructures

Xuecang Zhang

Proceedings Volume 9168, Carbon Nanotubes, Graphene, and Associated Devices VII; 91680H (2014) https://doi.org/10.1117/12.2060296
Event: SPIE NanoScience + Engineering, 2014, San Diego, California, United States

Abstract

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.

Citation Download Citation

Xuecang Zhang "Simulation of Maxwell-Dirac equations in graphene nanostructures", Proc. SPIE 9168, Carbon Nanotubes, Graphene, and Associated Devices VII, 91680H (10 September 2014); https://doi.org/10.1117/12.2060296

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