Analysis of rainbow scattering by a chiral sphere

“…To this end, the condition we now apply is an approximation based on the physical case of a molecule that is essentially isotropic, yet chiral. (The study of notionally chiral spheres is a subject that has itself attracted recent interest [24][25][26][27].) Applying this assumption means that we can write G g, α a, G α 3ag, α α 3a 2 , G αα 9a 2 g, α αα 9a 3 , G ααα 27a 3 g, α ααα 27a 4 , where a and g are isotropic electric-electric and electricmagnetic scattering scalars, respectively.…”

mentioning

confidence: 99%

Laser optical separation of chiral molecules

Bradshaw

Andrews

2015

Opt. Lett.

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The optical trapping of molecules with an off-resonant laser beam involves a forward-Rayleigh scattering mechanism. It is shown that discriminatory effects arise on irradiating chiral molecules with circularly polarized light; the complete representation requires ensemble-weighted averaging to account for the influence of the trapping beam on the distribution of molecular orientations. Results of general application enable comparisons to be drawn between the results for two limits of the input laser intensity. It emerges that, in a racemic mixture, there is a differential driving force whose effect, at high laser intensities, is to produce differing local concentrations of the two enantiomers. Trapping of this type usually relates to the interaction of the laser field with a transition electric dipole, as shown by Fig. 1(a). Interactions between the irradiating beam and a transition magnetic dipole are also possible, but the associated coupling strength is usually much smaller in magnitude, and the effects are generally ignored. However, when considering the possibility of chiral discrimination (in which input light of left-handed circular polarization offers different observables compared to right-handed polarization), the conventional trapping mechanism involving only electric dipole transition moments has to be extended to accommodate transition magnetic dipoles [7]. In fact, the forward-Rayleigh scattering events most relevant in chiral discrimination involve a mixture of magnetic and electric dipole interactions, as illustrated by Fig. 1(b), with one kind of coupling involved in the input photon annihilation and the other in the output photon release.To understand the energetics in greater detail, we note that the underlying mechanism for the optical trapping of molecules is based on the variation of intensity within the optical beam, which produces a position-dependent lowering of energy for the molecules it encounters: the alternating electric field of the radiation may be interpreted as producing a dynamic Stark shift to the molecular ground state energy. In terms of quantum electrodynamics, the energy shift (which is quadratically dependent on the electric field of the light) has to originate in forward-Rayleigh scattering, i.e., the concerted annihilation and creation of photons with identical energy and wave-vector. In such a case, the optical wavelengths will lie in a region of transparency for the irradiated molecule-the throughput laser beam therefore emerges unchanged. The primary physical determinant of optical trapping is the potential energy U, whose evaluation from quantum theory requires that the initial and final states (here denoted by I) are identical [8]. An expression for U per molecule is determined from second-order time-dependent perturbation theory, i.e.,where S is an intermediate state of the system comprising both molecule and radiation, E is the energy of the state denoted by its subscript, and H int is the dipolar interaction Hamiltonian given byHere, μ and m are the electric and...

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“…If, to further simplify Eq. (21) to a form involving fewer parameters, it is further assumed that the chiral molecules have essentially isotropic α and G tensors [51][52][53][54][55][56], the following is obtained:…”

Section: Orientational Effects Of the Input Beam A Ensemble Averagesmentioning

confidence: 99%

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

Andrews¹

2015

J. Opt. Soc. Am. B

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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 nonspherical, 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. As a consequence, optical trapping can be used as a means of achieving enantiomer separation.

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Analysis of rainbow scattering by a chiral sphere

Cited by 15 publications

References 23 publications

Improvements for scattering from a large-sized chiral cylinder at an oblique incidence

Improvements for scattering from a large-sized chiral cylinder at an oblique incidence

Laser optical separation of chiral molecules

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

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