Revisiting the hierarchical construction of higher-order exceptional points

Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety potential applications, particular optics and photonics. However, experimental realization is notoriously difficult. Recently, Zhong et al. [Q. Zhong, J. Kou, \ifmmode \mbox{\c{S}}\else \c{S}\fi{}. K. \"Ozdemir, R. El-Ganainy, Phys. Rev. Lett. 125, 203602 (2020)] introduced robust construction where unidirectional coupling two subsystems having same order leads generically to single point twice order. Here, we investigate this scheme different manner by exploiting nilpotency traceless part involved Hamiltonians. We generalize derive simple formula for spectral response strength composite system hosting higher-order point. Its relation strengths discussed. Moreover, nongeneric perturbations. The results are illustrated with an example.