Chiral discrimination in optical trapping and manipulation

Abstract

When circularly polarized light interacts with chiral molecules or nanoscale particles powerful symmetry principles determine the possibility of achieving chiral discrimination, and the detailed form of electrodynamic mechanisms dictate the types of interaction that can be involved. The optical trapping of molecules and nanoscale particles can be described in terms of a forward-Rayleigh scattering mechanism, with trapping forces being dependent on the positioning within the commonly non-uniform intensity beam profile. In such a scheme, nanoparticles are commonly attracted to local potential energy minima, ordinarily towards the centre of the beam. For achiral particles the pertinent material response property usually entails an electronic polarizability involving transition electric dipole moments. However, in the case of chiral molecules, additional effects arise through the engagement of magnetic counterpart transition dipoles. It emerges that, when circularly polarized light is used for the trapping, a discriminatory response can be identified between left-and righthanded polarizations. Developing a quantum framework to accurately describe this phenomenon, with a tensor formulation to correctly represent the relevant molecular properties, the theory leads to exact analytical expressions for the associated energy landscape contributions. Specific results are identified for liquids and solutions, both for isotropic media and also where partial alignment arises due to a static electric field. The paper concludes with a pragmatic analysis of the scope for achieving enantiomer separation by such methods.

Laser optical separation of chiral molecules

“…From this general result, it emerges that at one extreme, when the electric field of the input beam is very small, i.e., β → 0, the isotropic result of hU L−R i −2GI∕ε 0 c 2 is obtained, in agreement with previous work [7]. In contrast, at the other extreme where E is very large-namely, cases with strong orientation effectsthe following expression is found from Eq.…”

“…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.…”

Chiral discrimination in optical binding

“…[71] It has also been shown, through an application of QED theory, that discriminatory optical trapping forces -though smallcan act as a mechanism to separate left-and right-handed molecules. [38,72] In conclusion, although it is likely to prove difficult to implement these discriminatory effects in the direct pursuit of enantiomer separation, there may be scope to develop a means of identifying chirality in optically bound systems, using conventional laser optical instrumentation. It is interesting to consider a possible experimental strategy.…”

“…iR R e e j kR ij kR (35) Therefore, the overall phased average result for equation (31) is: (36) A similar analysis for the second term in curly brackets of (30) gives the result; (37) which gives the overall phase-averaged energy shift for (30) as: (38) Finally, averaging the remaining three terms of equation (21), expanding the spherical Bessel functions and using double angle formulae gives the total phased-averaged energy as: …”

“…[37] In contrast, an optical force arises when both the initial and final states are identical, such as where discriminatory effects have recently been shown to occur in optical trapping. [38,39] The discriminatory effect in chiral entities can be attributed to their low symmetry, where selection rules allow at least some electronic transitions to include contributions from not only electric dipole, but also other electric and magnetic multipole moments. Although small in comparison to electric-dipole forces, the leading term dependent on the handedness of each molecule typically arises from electric-magnetic dipole couplings, and these are the source of the chiral discrimination.…”