Near-zero-index nonlinear surface polaritons controlled by the surface conductivity of graphene

We study transverse magnetic polarized nonlinear surface polaritons (NLSP) propagating along the interface (a conductive layer of zero thickness) of a magnetic optically linear medium and a magnetic optically nonlinear medium with saturable permittivity. We obtained the exact solution of Maxwell's equations for the NLSP and on this base investigated the dependences of the NLSP propagation constant on the NLSP energy flux and on the value of the dielectric permittivity at the surface of the nonlinear medium for different values of sheet conductance. The important for quantum information processing near-zero-index condition can be achieved if the products of permeability and permittivity of each medium are both negative. For both Kerr-like and saturable nonlinearities, the NLSP propagation constant trace for zero-conductivity splits into two traces for non-zero conductivity. Near the condition, the NLSP propagation constant is highly sensitive to the NLSP intensity as well as to the sheet conductance value.