Higher order exceptional points in infinite lattices

One of the hallmarks of non-Hermitian photonics is the existence of unique degeneracies, the so-called higher order exceptional points (HEPs). So far, HEPs have been examined mostly in finite coupled systems. In this paper, we present a systematic way to construct infinite optical waveguide lattices that exhibit exceptional points of higher order. The spectral properties and the sensitivity of these lattices around such points are investigated by employing the method of pseudospectra.