Passband shapes that minimize the insertion loss and bandwidth of coupled-resonator bandpass filters

Numerous emerging applications of photonic integrated circuits are calling for extremely narrowband and/or low-insertion-loss bandpass filters. Both properties are fundamentally limited by resonator losses, i.e. the intrinsic quality factor of constituent resonant cavities. However, the choice of inter-cavity and bus couplings establishes tradeoffs between these two properties and the passband shape, which have been little explored. Using the widely-used second-order resonant system as example, we show that new classes of bandpass filter shapes provide the lowest insertion loss and the narrowest bandwidth for a given loss Q. They often yield an uncommon, asymmetric resonator coupling configuration, and the two classes we introduce straddle an ``exceptional point'' in the pole-zero configuration in the complex-frequency plane. A normalized design and conclusions based on a temporal coupled mode theory (CMT) model are presented, including a design tool to apply these results. These results may benefit loss-sensitive filtering applications such as quantum-correlated photon pair sources and RF-photonic integrated circuits.