Capturing near-field circular dichroism enhancements from far-field measurements

Molecular circular dichroism (CD) spectroscopy faces significant limitations due to the inherent weakness of chiroptical light-matter interactions. In this view, resonant optical antennas constitute a promising solution to this problem, since they can be tuned to increase the CD enhancement factor, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="italic">f</a:mi><a:mi>CD</a:mi></a:msub></a:math>, a magnitude describing the electromagnetic near-field enhancement of scatterers associated with a given helicity. However, an exact analytical expression of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi mathvariant="italic">f</c:mi><c:mi>CD</c:mi></c:msub></c:math> remains elusive. Here, we derive an exact multipolar expansion of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi mathvariant="italic">f</e:mi><e:mi>CD</e:mi></e:msub></e:math>, which is valid to deduce the integrated near-field CD enhancements of chiral molecules in the presence of scatterers of any size and shape under general illumination conditions. Our exact analytical findings extend previous approximate expressions of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi mathvariant="italic">f</g:mi><g:mi>CD</g:mi></g:msub></g:math> that are restricted to the dipolar regime. In addition to this, and based on our exact analytical findings, we show that the near-field <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi mathvariant="italic">f</i:mi><i:mi>CD</i:mi></i:msub></i:math> factor can be related to magnitudes that can be computed in the far field, i.e., the scattering cross-section and the helicity expectation value. Strikingly, we show that in the case of lossless cylindrically symmetric samples, the near-field <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi mathvariant="italic">f</k:mi><k:mi>CD</k:mi></k:msub></k:math> factor can be inferred experimentally only from two far-field measurements at specific scattering angles. Our contribution paves the way for the experimental characterization of devices capable of enhancing molecular CD spectroscopy from far-field measurements.