Fano resonance formula for lossy two-port systems.

We provide a modified Fano resonance formula applicable to dissipative two-port resonance systems. Based on a generic coupled-resonator model, the formula embodies loss-related correction terms and fundamental resonance parameters that can be determined by an analytic method or experimentally as opposed to finding phenomenological parameters by fitting to numerical results. The theory applies physically meaningful resonance parameters including resonance frequency, total decay rates, and partial radiation probabilities. For example, it shows that the classic Fano shape parameter q is given directly in terms of the phase difference between the resonant and non-resonant transmission pathways. Our new resonance formula quantitatively expresses the resonance spectra pertaining to modal nanophotonic and surface-plasmonic thin-film structures as verified by comparing with exact numerical models.