Symmetry and Quantum Features in Optical Vortices

Abstract

Optical vortices are beams of laser light with screw symmetry in their wavefront. With a corresponding azimuthal dependence in optical phase, they convey orbital angular momentum, and their methods of production and applications have become one of the most rapidly accelerating areas in optical physics and technology. It has been established that the quantum nature of electromagnetic radiation extends to properties conveyed by each individual photon in such beams. It is therefore of interest to identify and characterize the symmetry aspects of the quantized fields of vortex radiation that relate to the beam and become manifest in its interactions with matter. Chirality is a prominent example of one such aspect; many other facets also invite attention. Fundamental CPT symmetry is satisfied throughout the field of optics, and it plays significantly into manifestations of chirality where spatial parity is broken; duality symmetry between electric and magnetic fields is also involved in the detailed representation. From more specific considerations of spatial inversion, amongst which it emerges that the topological charge has the character of a pseudoscalar, other elements of spatial symmetry, beyond simple parity inversion, prove to repay additional scrutiny. A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables. The analysis supports a persistence in features of significance for the material interactions of vortex beams, which may indicate further scope for suitably tailored experimental design.

Poincaré Rotator for Vortexed Photons

“…A Poincaré rotator is also useful to control the orbital angular momentum of photons [51]. The left and right vortexed states are orthogonal each other, such that they form SU (2) states [51][52][53][54][55][56][57][58][59]. A superposition states with these vortices can be controlled by a Poincaré rotator by adjusting the phase and amplitudes [51].…”

Fundamental symmetry origins in the chiral interactions of optical vortices

“…They, too, possess relatively few symmetry elements; according to their topological charge l, their irreducible representations only arising from features in C ∞h , C l and D l groups. 24 Although helicity and chirality are directly related only for radiation that is precisely monochromatic, 25 attention often focuses upon the latter, measured in terms of fields representing a local density and flux of optical chirality, χ and φ, respectively. These are two of the less familiar properties conserved by any freely propagating optical field (beyond the well-known cases of electromagnetic energy and linear momentum) [26][27][28] :…”

“…Helicity is also a feature of the azimuthal phase associated with any simple optical vortex, where structural symmetry is afforded by the helical wavefront and phase symmetry. They, too, possess relatively few symmetry elements; according to their topological charge l , their irreducible representations only arising from features in C ∞ h , C l and D l groups 24 …”

Principles of fundamental symmetry in optical vortex interactions

“…As has recently been discussed in considerable detail elsewhere, 49 attention therefore focuses upon the azimuthal phase term, exp(il). Once again, we can apply the operation P as reflection followed by  rotation.…”