A theory of an optical breather of self-induced transparency for small area surface plasmon-polariton waves is constructed. The wave equation for an optical nonlinear electric field consisting of surface transverse magnetic modes, traveling along a two-dimensional layer of atomic systems (or semiconductor quantum dots), with a graphene monolayer (or graphene-like two-dimensional material), are shown to reduce to the nonlinear Schrödinger equation with damping. It is also shown that damped small intensity surface plasmon-polariton breathers can propagate in such a system and its characteristic parameters depends on the connected media, graphene conductivity, transition layer and transverse structures of the surface plasmon polariton. Explicit analytical expressions for the parameters of an optical surface breather are given. The breather and the soliton in graphene are compared with each other and the differences between their properties are contrasted.

• Received 8 February 2017

DOI:https://doi.org/10.1103/PhysRevA.95.053801