Robust wave splitters based on scattering singularities in complex non-Hermitian systems

We have discovered specific conditions for generic scattering systems to act as wave splitters that are robust to any change in relative amplitude or phase of an arbitrary injected waveform. Specifically for complex systems with tunable parameters, these conditions for robust splitting (RS) are abundant, and by using multiple tunable parameters, the relative amplitude and phase of the output signals can also be tuned. The splitting property of the systems works for all possible input phase differences and amplitude ratios and does not require a particular coherent input signal. We show experimentally that the fixed splitting ratios and output phases at RS conditions are robust to 100 dB of relative power and 2π phase changes of the input waves to a complex non-Hermitian two-port system. We also demonstrate that the splitting power ratio can be tuned by multiple orders of magnitude, and the RS conditions can be tuned to any desired frequency with suitable tunable perturbations embedded in the system. Although this phenomenon is realized in two-port systems and involves some degree of attenuation, tunable robust splitting can be achieved between any two ports of multiport systems. These results are general to all wave scattering phenomena (electromagnetic, acoustic, etc.) and hold in generic complex scattering systems.