Surface plasmon-polaritons in graphene, embedded into medium with gain and losses

The paper deals with the theoretical consideration of surface plasmon-polaritons in the graphene monolayer, embedded into dielectric with spatially separated gain and losses. It is demonstrated, that presence of gain and losses in the system leads to the formation of additional mode of graphene surface plasmon-polaritons, which does not have its counterpart in the conservative system. When the gain and losses are mutually balanced, the position of exceptional point-transition point between unbroken and broken [Formula: see text]-symmetry-can be effectively tuned by graphene's doping. In the case of unbalanced gain and losses the spectrum of surface plasmon-polaritons contains spectral singularity, whose frequency is also adjustable through the electrostatic gating of graphene.European Commission through the project 'Graphene—Driven Revolutions in ICT and Beyond' (Ref. No. 785219), and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. Additionally, YVB acknowledges financing from FEDER and the portuguese Foundation for Science and Technology (FCT) through project PTDC/FIS-MAC/28887/201