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The linear response of non-Hermitian resonant systems demonstrates various intriguing features such as the emergence of non-Lorentzian lineshapes. Recently, we have developed a systematic theory to understand the scattering lineshapes in such systems and, in doing so, established the connection with the input/output scattering channels. Here, we follow up on that work by presenting a different, more transparent derivation of the resolvent operator associated with a non-Hermitian system under general conditions and highlight the connection with the structure of the underlying eigenspace decomposition. Finally, we also present a simple solution to the problem of self-orthogonality associated with the left and right Jordan canonical vectors and show how the left basis can be constructed in a systematic fashion. Our work provides a unifying mathematical framework for studying non-Hermitian systems such as those implemented using dielectric cavities, metamaterials, and plasmonic resonators. 

Chiral exceptional points (CEPs) have been shown to emerge in traveling wave resonators via asymmetric back scattering from two or more nano-scatterers. Here, we provide a new perspective on the formation of CEPs based on the coupled oscillator model. Our approach provides an intuitive understanding for the modal coalescence that signals the emergence of CEPs and emphasizes the role played by dissipation throughout this process. In doing so, our model also unveils an otherwise unexplored connection between CEPs and other types of exceptional points associated with parity-time symmetric photonic arrangements. In addition, our model also explains qualitative results observed in recent experimental work involving CEPs. Importantly, the tight-binding nature of our approach allows us to extend the notion of CEP to discrete photonics setups that consist of coupled resonator and waveguide arrays, thus opening new avenues for exploring the exotic features of CEPs in conjunction with other interesting physical effects such as nonlinearities and topological protections.