Abstract
In this study, the transversal magnetic (TM) and electric (TE) modes of graphene plasmon in a homogeneous environment and three-layered systems were theoretically investigated. The dispersion relations of the graphene plasmon modes were derived in the framework of classical electrodynamics with plane wave modes and Neumann-Dirichlet boundary conditions. The graphene plasmon modes in the three-layer system reproduced exactly the same dispersion relations as freestanding graphene (Phys. Rev. Lett. 99, 016803 (2007)), as all layers had the same refractive index. The impulse matching condition between the graphene plasmon and guided photons and the propagation decay length of graphene plasmon were investigated by numerically solving the dispersion relations for different values of the Fermi-energy and the refractive index of the upper layer. The TE-mode graphene plasmon has potential for applications of graphene as a polarization-selective modulator due to its convenient impulse matching with guided photons in the region of telecom wavelengths, despite its low propagation decay rates.
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