Abstract
We observe that the asymmetric transmission (AT) through photonic systems with a resonant chiral response is strongly related to the far-field properties of eigenmodes of the system. This understanding can be used to predict the AT for any resonant system from its complex eigenmodes. We find that the resonant chiral phenomenon of AT is related to, and is bounded by, the nonresonant scattering properties of the system. Using the principle of reciprocity, we determine a fundamental limit to the maximum AT possible for a single mode in any chiral resonator. We propose and follow a design route for a highly chiral dielectric photonic crystal structure that reaches this fundamental limit for AT.