Fundamental bounds on decay rates in asymmetric single-mode optical resonators

We derive tight upper and lower bounds of the ratio between decay rates to two ports from a single resonance exhibiting Fano interference, based on a general temporal coupled-mode theory formalism. The photon transport between these two ports involves both direct and resonance-assisted contributions, and the bounds depend only on the direct process. The bounds imply that, in a lossless system, full reflection is always achievable at Fano resonance, even for structures lacking mirror symmetries, while full transmission can only be seen in a symmetric configuration where the two decay rates are equal. The analytic predictions are verified against full-field electromagnetic simulations.