Abstract
Analytical forms of the optical helicity and optical chirality of monochromatic Laguerre–Gaussian optical vortex beams are derived up to second order in the paraxial parameter . We show that input linearly polarised optical vortices which possess no optical chirality, helicity or spin densities can acquire them at the focal plane for values of a beam waist via an orbital (OAM) to spin (SAM) angular momentum conversion which is manifest through longitudinal (with respect to the direction of propagation) fields. We place the results into context with respect to the intrinsic and extrinsic nature of SAM and OAM, respectively; the continuity equation which relates the densities of helicity and spin; and the newly coined term ‘Kelvin’s chirality’ which describes the extrinsic, geometrical chirality of structured laser beams. Finally, we compare our work (which agrees with previous studies) to the recent article (Köksal et al 2021 Optics Communications 490 126907) which shows conflicting results, highlighting the importance of including all relevant terms to a given order in the paraxial parameter.
Highlights
A stationary object is chiral if it cannot be superimposed onto its mirror image
Chiroptical and optical activity spectroscopies – using differential light-matter interactions – are widely used techniques to study the structures and functionalities of chiral molecules, biomolecules, metamaterials and nanostructures, as well as achiral objects such as atoms [1,2,3,4,5,6,7,8,9,10,11,12]. The observables in these spectroscopies are either time-even pseudo scalars or timeodd axial vectors; the former often referred to as true chirality on the account that these effects require chiral material structures, the latter false chirality as they can be supported by achiral media such as atoms as in magnetic circular dichroism [13]
In this work we study the optical helicity density explicitly as it is a more fundamental quantity, in the knowledge that the optical chirality gives an analogous result for the system we are studying
Summary
A stationary object is chiral if it cannot be superimposed onto its mirror image. Material chirality is a consequence of the geometric position of atoms in molecules and nanostructures. Chiroptical and optical activity spectroscopies – using differential light-matter interactions – are widely used techniques to study the structures and functionalities of chiral molecules, biomolecules, metamaterials and nanostructures, as well as achiral objects such as atoms [1,2,3,4,5,6,7,8,9,10,11,12].
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