Topology and Manipulation of Scattering Singularities in Complex non-Hermitian Systems: Two-Channel Case

The control of wave scattering in complex non-Hermitian settings is an exciting subject—often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks, wavefront shaping protocols, active metasurface development, and more. At their core, these achievements rely on our ability to engineer the resonant spectrum of the underlying physical structures, which is conventionally accomplished by carefully imposing geometrical and/or dynamical symmetries. In contrast, by taking active control over the boundary conditions in complex scattering environments that lack artificially imposed geometric symmetries, we demonstrate via microwave experiments the ability to manipulate the spectrum of the scattering operator. This active control empowers the creation, destruction, and repositioning of exceptional point degeneracies (EPDs) in a two-dimensional parameter space. The presence of EPDs signifies a coalescence of the scattering eigenmodes, which dramatically affects transport. The scattering EPDs are partitioned in domains characterized by a binary charge, as well as an integer winding number, they are topologically stable in the two-dimensional parameter space, and they obey winding number-conservation laws upon interactions with each other, even in cases in which Lorentz reciprocity is violated; in this case, the topological domains are destroyed. The ramifications of this understanding are the proposition for a unique input-magnitude and phase-insensitive 50:50 in-phase/quadrature (I/Q) power splitter. Our study establishes an important step towards complete control of scattering processes in complex non-Hermitian settings.