Photonic waveguiding structures with loss and gain

Passive real-world waveguiding structures are inevitably lossy, and some of them, such as plasmonic waveguides, exhibit even very strong attenuation. Losses can be compensated by including active components with gain. In this paper we discuss properties of waveguiding structures with generally complex dielectric permittivity distributed across their cross-section. In particular, we focus on the existence of modes that exhibit balance between loss and gain and that can propagate unattenuated provided the suitable conditions are satisfied. Specifically, we examine power transmission in the structures with a balance of loss and gain supporting lossless propagation of two modes. We demonstrate that when both modes are excited simultaneously, the total transmitted power is not conserved as the modes propagate along the waveguide. We also show that even if one of the modes propagates with gain, the maximum attainable transmitted power is strongly influenced by back-reflections from the interface with the passive output waveguide. We also discuss the conditions for the existence of an un-attenuated propagation of a confined surface mode supported by the gain/loss nature of these photonic structures.