Limitations of a superchiral field

Recently, Tang and Cohen [Y. Tang and A. E. Cohen, Science 332, 333 (2011)] proposed and demonstrated the use of superchiral electromagnetic fields to enhance optical enantioselectivity. Their work generated much excitement as enantioselective signals are typically quite small, and it appeared that the enhancement factor could be extremely large. In this paper we explicitly show the limitations of such fields by including the magnetic susceptibility term. This term is small and is ignored in most cases compared to the electric polarizability term. However, for the fields used, the enhancement was obtained at the electric field energy node. Due to conservation of field energy, the magnetic field energy is then maximum, and the magnetic susceptibility contribution can no longer be ignored. This then is what limits the enhancement of the optical enantioselectivity. For a counterpropagating left- and right-circularly polarized light field, as used in the aforementioned experiment, we show that this fundamentally limits the enhancement to one or two orders of magnitude in general, determined by the ratio of the magnetic susceptibility to the electric polarizability of the material used. We also generalize the dissymmetry factor to include optical rotation effects present in chiral media, as opposed to fields being in vacuum. In the process, we generalize Lipkin's Z(000) zilch (or optical chirality) to that for a linear medium. This generalization shows that chirality of the material cannot be completely separated from chirality of the field and that opposite enantiomers are symmetric in terms of the dissymmetry factor enhancement. Finally, an analogy between ellipsometric chiroptical signal enhancement and enhanced optical enantioselectivity using a standing wave chiral field is discussed. Our analysis and generalization can be used as a guide for future searches of locally enhanced chiral fields. DOI: 10.1103/PhysRevA.86.063834