Loss-compensated nonlinear modes and symmetry breaking in amplifying metal-dielectric-metal plasmonic couplers

We theoretically investigate the propagation of surface plasmon polaritons in an amplifying plasmonic coupler (metal-amplifying dielectric-metal). We study the loss-compensated nonlinear stationary modes of the system by deriving coupled-mode equations for the optical amplitudes, predicting the existence of a mode with broken symmetry for gain values higher than a characteristic threshold. We analyze the stability of symmetric, antisymmetric, and nonsymmetric modes by solving the linearized system for small perturbations and by numerically integrating coupled-mode equations in propagation. We find that, while the antisymmetric mode stays always stable or marginally stable, the stability of symmetric and nonsymmetric modes is more involved.