Irreducible Cartesian Tensor Analysis of Harmonic Scattering from Chiral Fluids

Abstract

Symmetry principles of several distinct kinds are revealingly engaged in an analysis focussing on third harmonic scattering, a current focus of research on nonlinear optics in chiral media. Analysis in terms of irreducible Cartesian tensors elucidates the detailed electrodynamical origin and character of the corresponding material properties. Considerations of fundamental charge, parity and time reversal (CPT) symmetry reveal the conditions for an interplay of transition multipoles to elicit a chiral response using circularly polarised pump radiation, and the symmetry of quantised angular momentum underpins the associated selection rules and angular distribution. The intrinsic structural symmetry of chiral scatterers determines their capacity to exhibit differential response. Exploiting permutational index symmetry in the response tensors enables quantitative assessment of the boundary values for experimentally measurable properties, including circular intensity differentials.

Principles of fundamental symmetry in optical vortex interactions

“…It is interesting to observe that a prominent role has also been found for electric quadrupole interactions in the chiroptical discrimination exhibited in optical harmonic scattering from fluid suspensions of chiral nanoparticles. [50][51][52][53][54][55] One area for further exploration and extension of the principles elicited here is the growing topic of spatio-temporal optical vortices, [56][57][58][59][60] while other intriguing possibilities may arise in the chiral interactions of vector vortex beams with transverse-variable-polarization. [61][62][63][64][65][66][67] It will be interesting to see if novel features and enhanced chiral propensities will also emerge in these new connections.…”

Optical Activity in Third‐Harmonic Rayleigh Scattering: A New Route for Measuring Chirality

“…Drawing on fundamental electrodynamic and symmetry principles, theory has been developed to describe THRS from molecules, focusing on its detailed dependence on both polarization and on properties of the nonlinear optical susceptibility tensor for the scattering centres. [ 55 ] More recently, this analysis has been extended specifically to elicit mechanisms and features uniquely associated with chiral species, [ 56 ] here we extend the theory to the case of nanohelices.…”

Fundamental symmetry origins in the chiral interactions of optical vortices

“…Moreover, such a twisted beam lends a propensity for enhanced levels of sensitivity, as in the many cited studies where electric quadrupole interactions prove to contribute significantly to vortex chiroptical effects. It is interesting to observe that a prominent role has also been found for electric quadrupole interactions in the chiroptical discrimination exhibited in optical harmonic scattering from fluid suspensions of chiral nanoparticles 115–120 …”

“…It is interesting to observe that a prominent role has also been found for electric quadrupole interactions in the chiroptical discrimination exhibited in optical harmonic scattering from fluid suspensions of chiral nanoparticles. [115][116][117][118][119][120] While the presented analysis reveals necessary conditions for optical beams with circular (in fact any elliptical) state of polarization, and/or a twisted wavefront, to exhibit chiral discrimination, there are other experimental considerations. Numerous studies have identified constraints that must be satisfied for particular forms of chiral discrimination to be observable, many of these connected with the spatial extent of measured lightmatter interaction, and the degree of structural isotropy or anisotropy across that region.…”