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Circular dichroism spectroscopy is an important tool for detecting chiral molecules. Chirality is a feature of many biologically active molecules and hence circular dichroism, which is the difference in absorption of leftand right-handed circularly polarized light beams, is a spectroscopic footprint of a given molecule configuration and potentially composition. At the same time, intrinsic molecular chirality is weak which complicates the application of CD spectroscopy. The CD signal can be substantially enhanced by using nanophotonic structures that provide strong electromagnetic field enhancement. It has been recently shown that optimal nanostructure for CD enhancement should be achiral and preserve helicity upon scattering. An example of such structure is a dielectric nanodisk that supports both electric and magnetic multipoles and enables optimal response by multipolar interference. This latter condition cannot be fulfilled in substrate supported nanostructures, which are however relatively simple to fabricate and hence are omnipresent in nanophotonics. In this work we study the optical chirality enhancement by substrate supported nanostructures. We provide a T-matrix method based framework to theoretically describe the optical response of chiral molecules coupled with substrate supported nanostructures. We utilize the Riemann-Silberstein transformation to obtain free space multipoles with well defined helicity. Then, we propagate the multipolar fields through the layer system to obtain their counterparts for substrate supported nanostructures. We study the helicity change resulting from off-substrate reflection and seek means to minimize it by multipolar interference and to maximize the chirality enhancement. Finally, we exemplify the obtained method and theoretical results by studying the archetypical example of a substrate supported dielectric nanodisk.
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