Enhanced Hong-Ou-Mandel Manifolds and figures of merit for linear chains of identical micro-ring resonators

We present an exact analytic expression for the Hong-Ou-Mandel (HOM) curve for any number of identical Micro-Ring Resonators (MRRs) in a linear chain. We investigate the extreme stability of this HOM curve, showing that the HOM effect in linear arrays of MRRs is highly robust. We further use this expression to derive three figures of merit for the HOM curve of linear chains of MRRs: the minimum tau value ($\tau_{c}$), the curvature ($\bar{\xi}_N$), and the $5\%$ tolerance in tau ($\delta\tau_{N}$). We promote these metrics to characterize the pros and cons of various linear chains of MRRs and inform design and fabrication.