Recently a type of robust exceptional point was found that is insensitive to the coupling disorder in the bulk. Here we show that a disparity emerges when the number of coupled optical cavities in this one-dimensional array changes from even to odd. The robust exceptional point only exists in the former case, whereas in the latter the required coupling for the exceptional point depends inversely on the size of the cavity array and is subjected to coupling disorder in the bulk. We further show that the exceptional points in these two cases are second and third order, respectively. We elucidate the origin of the robust EP as a restricted bulk zero mode, which shares the same robustness against coupling disorder and has a finite amplitude adjacent to the boundary. This finding enables us to identify robust EPs in higher-dimensional systems reliably, which can exist in the presence of either sublattice symmetry or the non-Hermitian particle-hole symmetry evolved from it.

• Received 9 April 2020
• Accepted 27 May 2020

DOI:https://doi.org/10.1103/PhysRevA.101.063823