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 multi-channel symmetric disordered systems. We identify that an EP of the parity-time (PT)-symmetric RL-operator is obtained when the spacing between central frequencies of two natural resonances of the system is equal to the decay rate into incoming and outgoing channels. Finally, we leverage the transfer functions associated with RL and RL-EPs states to implement first- and second-order analog differentiation.