Electromagnetic trapping of chiral molecules: Orientational effects of the irradiating beam

The photonic interaction generally responsible for the electromagnetic trapping of molecules is forward-Rayleigh scattering, a process that is mediated by transition electric dipoles connecting the ground electronic state and virtual excited states. Higher order electric and magnetic multipole contributions to the scattering amplitude are usually negligible. However, on consideration of chiral discrimination effects (in which an input light of left-handed circular polarization can present different observables compared to right-handed polarization, or molecules of opposite enantiomeric form respond differently to a set circular polarization), the mechanism must be extended to specifically accommodate transition magnetic dipoles. Moreover, it is important to account for the fact that chiral molecules are necessarily non-spherical, so that their interactions with a laser beam will have an orientational dependence. Using quantum electrodynamics, this article quantifies the extent of the energetic discrimination that arises when chiral molecules are optically trapped, placing particular emphasis on the orientational effects of the trapping beam. An in-depth description of the intricate ensemble-weighted method used to incorporate the latter is presented. It is thus shown that, when a mixture of molecular enantiomers is irradiated by a continuous beam of circularly polarized light, a difference arises in the relative rates of migration of each enantiomer in and out of the most intense regions of the beam. In consequence, optical trapping can be used as a means of achieving enantiomer separation.