Observation of Hybrid Degenerate Point in Projected Non-Hermitian Metasurfaces

Degeneracy appears ubiquitously in physical systems. Exceptional points, the non-Hermitian degeneracies, have unveiled numerous novel phenomena that have no counterparts in Hermitian degeneracies-diabolic points. Here, we observe a hybrid degenerate point (HP) in a projected non-Hermitian system, namely a subsystem obtained by projecting a metasurface characterized by a Hermitian scattering matrix. In the projected space, the metasurface is found naturally anchored at the merging point of two exceptional curves, each carrying opposite chirality. The HP exhibits a unique topology that encodes features of both Hermitian and non-Hermitian degeneracies, thereby exhibiting linear and square-root sensitivities simultaneously. We conceptually validate and experimentally confirm the projected HP using a passive and lossless acoustic metagrating, uncovering its unique singular behavior: the pronounced anisotropic sensitivity to perturbations. Our findings highlight the potential for exploring degenerate states via the projective Hilbert space and pave the way for extreme wave manipulation in open spaces.