Higher-order exceptional points: A route for flat-top optical filters

We study theoretically the formation and properties of higher-order exceptional points (EPs) in optical parity-time symmetric systems (PTSSs) consisting of a finite number of coupled resonators. The analysis shows that only specific configurations of such PTSSs exhibit high-order EPs. We derive the conditions for the formation of higher-order EP in these PTSSs and discuss the properties of the eigenmodes. By taking advantage of the fundamental link between EPs and the formation of a white-light cavity, we utilize the conditions at which high-order EPs are formed for designing broadband, maximally flat, optical filters. By selecting the coupling coefficients between the resonators accordingly we show the bandwidth of such coupled cavity filters cannot only be enhanced substantially compared to other common design approaches, but also provide flat spectral response where these design approaches fail completely.