Chirality and angular momentum in optical radiation

Abstract

This paper develops, in precise quantum electrodynamic terms, photonic attributes of the "optical chirality density", one of several measures long known to be conserved quantities for a vacuum electromagnetic field. The analysis lends insights into some recent interpretations of chiroptical experiments, in which this measure, and an associated chirality flux, have been treated as representing physically distinctive "superchiral" phenomena. In the fully quantized formalism the chirality density is promoted to operator status, whose exploration with reference to an arbitrary polarization basis reveals relationships to optical angular momentum and helicity operators. Analyzing multi-mode beams with complex wave-front structures, notably Laguerre-Gaussian modes, affords a deeper understanding of the interplay between optical chirality and optical angular momentum. By developing theory with due cognizance of the photonic character of light, it emerges that only the spin angular momentum of light is engaged in such observations. Furthermore, it is shown that these prominent measures of the helicity of chiral electromagnetic radiation have a common basis, in differences between the populations of optical modes associated with angular momenta of opposite sign. Using a calculation of the rate of circular dichroism as an example, with coherent states to model the electromagnetic field, it is discovered that two terms contribute to the differential effect. The primary contribution relates to the difference in left- and right- handed photon populations; the only other contribution, which displays a sinusoidal distance-dependence, corresponding to the claim of nodal enhancements, is connected with the quantum photon number-phase uncertainty relation. From the full analysis, it appears that the term "superchiral" can be considered redundant

Point source generation of chiral fields: measures of near- and far-field optical helicity

“…For the given system, only diagonal components of the V tensor yield non-zero electric contributions to the field, whilst for the U tensor, non-zero components arise only for i ≠ j, and neither index can represent the z-component, given that Rk = Rz. Utilizing equation (4) now produces an S3 parameter whose far-zone limit proves identical in form to equation (12). The non-physical nature of the near-zone result, noted earlier, therefore emerges as a reflection upon the short-range validity of the Stokes parameter, rather than any issue between a classical or quantum field formulation.…”

“…In the corresponding quantum field formulation, in which both of these fields are elevated to operator status and cast as Fourier series, it is not immediately apparent that the result is Hermitian, as should befit a quantum observable. However, on performing a mode expansion the helicity emerges in an obviously Hermitian form simply cast in terms of the number operators for left and right circular polarizations,ˆL N and ˆR N respectively: [12] …”

“…[9,10] Moreover it emerges that these each of these quantities, expressed in photonic terms, has a direct dependence on the relative occupancy of optical modes with opposing helicity -a feature that is most readily apparent when left-and right-handed modes are used as the basis. [11,12] To further address in detail the specific relationships between various practical measures of optical chirality, it is appropriate to consider the very simplest system: the optical field associated with spontaneous, circularly polarized emission from an isolated point source. Focusing on quantitative analytical measures of optical helicity, the development of electrodynamic theory leads to expressions for three distinct observables, each of which has a connection with optical helicity.…”

Expanded horizons for generating and exploring optical angular momentum in vortex structures

“…One feature that has aroused considerable recent interest is the rediscovered quantitation of 'optical chirality' and its associated flux for classical and quantum optical fields [22][23][24][25]. These conserved quantities were originally extracted from Maxwell's equations with an application of Noether's Theorem, with the earliest reporter being surprisingly dismissive of the results, surmising that they could have no physical significance [26].…”

Optical manipulation of matter-wave vortices: An analog of circular dichroism

“…This has triggered new research on interaction of matter with laser beams having certain spatial profiles, like, LG or Bessel profile [3,4]. From extensive theoretical [5][6][7] and experimental works [8,9] it has been believed that the OAM of LG beam does not play a role in CD. On the contrary, here we prove that the matter-wave vortex of a Bose-Einstein condensate (BEC) interacting with an LG beam can lead to CD-like effects, i.e., the light absorption becomes sensitive to the handedness of the field OAM.…”