Abstract

Graphene supports surface plasmon polaritons with extreme field confinement and electrical tunability, but these waves are typically short-lived due to ohmic loss in the sheet. We show that embedding graphene in an active dielectric can counteract this loss and derive closed-form design rules for lossless propagation within the local linear model. Specifically, from the full Maxwell model of a conductive sheet we obtain the gain values required to make the propagation constant real, q'' = 0, and separately discuss the r = 0 boundary obtained from the real part of the complex-index radicand. The formulas are expressed directly in terms of the complex conductivity of graphene and the surrounding media, making them easy to evaluate and implement. Full-wave finite-element simulations in COMSOL verify dispersion and attenuation/amplification trends with and without gain for single- and double-layer graphene plasmonic structures.

Abstract

Graphene supports surface plasmon polaritons with extreme field confinement and electrical tunability, but these waves are typically short-lived due to ohmic loss in the sheet. We show that embedding graphene in an active dielectric can counteract this loss and derive closed-form design rules for lossless propagation within the local linear model. Specifically, from the full Maxwell model of a conductive sheet we obtain the gain values required to make the propagation constant real, q'' = 0, and separately discuss the r = 0 boundary obtained from the real part of the complex-index radicand. The formulas are expressed directly in terms of the complex conductivity of graphene and the surrounding media, making them easy to evaluate and implement. Full-wave finite-element simulations in COMSOL verify dispersion and attenuation/amplification trends with and without gain for single- and double-layer graphene plasmonic structures.

Abstract

Graphene supports surface plasmon polaritons with extreme field confinement and electrical tunability, but these waves are typically short-lived due to ohmic loss in the sheet. We show that embedding graphene in an active dielectric can counteract this loss and derive closed-form design rules for lossless propagation within the local linear model. Specifically, from the full Maxwell model of a conductive sheet we obtain the gain values required to make the propagation constant real, q'' = 0, and separately discuss the r = 0 boundary obtained from the real part of the complex-index radicand. The formulas are expressed directly in terms of the complex conductivity of graphene and the surrounding media, making them easy to evaluate and implement. Full-wave finite-element simulations in COMSOL verify dispersion and attenuation/amplification trends with and without gain for single- and double-layer graphene plasmonic structures.

Abstract

Graphene supports surface plasmon polaritons with extreme field confinement and electrical tunability, but these waves are typically short-lived due to ohmic loss in the sheet. We show that embedding graphene in an active dielectric can counteract this loss and derive closed-form design rules for lossless propagation within the local linear model. Specifically, from the full Maxwell model of a conductive sheet we obtain the gain values required to make the propagation constant real, q'' = 0, and separately discuss the r = 0 boundary obtained from the real part of the complex-index radicand. The formulas are expressed directly in terms of the complex conductivity of graphene and the surrounding media, making them easy to evaluate and implement. Full-wave finite-element simulations in COMSOL verify dispersion and attenuation/amplification trends with and without gain for single- and double-layer graphene plasmonic structures.