  Surface plasmon polaritons (SPPs) are coherent electromagnetic surface waves
trapped on an insulator-conductor interface. The SPPs decay exponentially along
the propagation due to conductor losses, restricting the SPPs propagation
length to few microns. Gain materials can be used to counterbalance the
aforementioned losses. We provide an exact expression for the gain, in terms of
the optical properties of the interface, for which the losses are eliminated.
In addition, we show that systems characterized by lossless SPP propagation are
related to PT symmetric systems. Furthermore, we derive an analytical critical
value of the gain describing a phase transition between lossless and prohibited
SPPs propagation. The regime of the aforementioned propagation can be directed
by the optical properties of the system under scrutiny. Finally, we perform
COMSOL simulations verifying the theoretical findings.
