Exceptional Points of PT-Symmetric Reflectionless States in Complex Scattering Systems.

We investigate experimentally and analytically the coalescence of reflectionless (RL) states in symmetric complex wave-scattering systems. We observe RL exceptional points (EPs), first with a conventional Fabry-Perot system for which the scattering strength within the system is tuned symmetrically and then with single- and multichannel symmetric disordered systems. We confirm that an EP of the parity-time (PT)-symmetric RL operator is obtained for two isolated quasinormal modes when the spacing between central frequencies is equal to the decay rate into incoming and outgoing channels. Finally, we leverage the transfer functions associated with RL and RL-EP states to implement first- and second-order analog differentiation.