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. KEYWORDS: optical chirality, asymmetric transmission, nanophotonics, photonic crystals, coupled-mode theory A strong chiral response is essential for realizing devices that can manipulate the polarization of light. Natural chiral materials rely on bulk properties including birefringence and result in thick and bulky devices for polarization control. Much stronger chirality can be realized by exploiting the interaction of light with artificial nanostructures.1−3 Such interactions are observed to be enhanced through local resonances such as those supported by plasmonic antennas, 4,5 periodically structured dielectric waveguides, 6 etc. Arrangements of subwavelength-sized optical scatterers, called metasurfaces, are known for their exotic light-steering properties and polarization-dependent response. 7,8 A better understanding of light− matter interaction at the nanoscale will help us to realize optical metasurfaces with designable vectorial near and far electromagnetic fields. Polarization-manipulating nanostructures are also important for realizing compact and/or on-chip polarization rotators, wave plates, and polarizing beam splitters. 9−13An extreme possible consequence of the chirality of a system is asymmetric transmission (AT), the difference in total transmittance when light with a certain polarization impinges from opposite sides of the system. 14 While it is possible to realize systems that radiate asymmetrically in opposite directions by breaking mirror symmetry in the propagation direction, 15 AT however requires a strongly chiral response. Notably, when an emitter is placed in asymmetrically transmitting systems, this strong chirality also implies a significant difference between the polarizations of the emitted light in opposite sides of the system. Realization of AT in nanostructures thus relates directly to potential functionalities such as polarization control of spontaneous emission, 16 spindependent light emission, 17,18 and enantioselective sensing. 19There has been a considerable number of experimental attempts at realizing strong chirality in nanostructures. Several of these have been shown to offer AT for circularly polarized light using both metallic 20−23 and dielectric 24,25 structures. However, to realize AT for linearly polarized light is significantly more challenging, as it strictly requir...