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

Abstract

To consider the relationship between different measures of chirality in an optical field, the simplest case is considered: direct spontaneous emission of circularly polarized light by a point source. In the electromagnetic fields radiated from a suitably chiral source, such as a low-symmetry chiral molecule undergoing radiative decay, optical helicity is exhibited in the extent of a difference in left-and right-handed circular polarization components. There are several practical measures for quantifying the emergence of ensuing optical helicity, exhibiting different forms of dependence on the properties of the emitter and the positioning of a detector. By casting each measure in terms of an irreducible helicity density, connections and distinctions can be drawn between results expressible in either classical or quantum form.

Optical Helicity and Chirality: Conservation and Sources

“…where B is the magnetic induction, is sometimes used as a measure of the total electromagnetic helicity [27,28], as, when time averaged, it is equivalent to the volume integral of (1). There is a sense in which the helicity is only meaningful when integrated over all space: the appearance of the gauge potentials in the definition implies that the helicity density at a point is explicitly gauge-dependent.…”

“…As an illustration of how charges and currents can act as a source of helicity, we consider a point source consisting of an oscillating electric and a magnetic dipole, with electric and magnetic dipole moments p(t) and m(t), as has been examined by Leeder et al [28]. This can be thought of as a simple model of a radiating chiral molecule, as the optical activity of chiral molecules ultimately arises from the simultaneous induction of electric and magnetic dipole moments through the electric-dipole magnetic-dipole polarisability tensor G [9] (see Chapter 3, §5.4).…”

“…We now consider what happens when a local current density is placed inside a chiral medium. Inserting the constitutive relations (28) into ∇ × E = −Ḃ and ∇ × H =Ḋ + j leads to:…”

“…The Tellegen contribution, proportional to α, is identical to the helicity source in an absence of currents or charges, as given in (38). Consider a chiral, reciprocal material described by (28) with α = 0. From (41), we would expect that an emitter that in free space emits no net helicity, such as a single oscillating electric dipole, may act as a source of helicity when placed inside a chiral medium.…”

Chirality and Chiroptical Effects in Metal Nanostructures: Fundamentals and Current Trends

“…on page 29 of the originally published article is not correct, in the sense that a nearfield quantum electrodynamic (QED) theory has indeed been developed in earlier works. [1] The authors regret this mistake in the article and take the chance to add further references for the readers who might want to go deeper in the subject. [2,3] However, to the best of our knowledge, it is yet unclear to which extent the optical chirality of a field influences the dissymmetry of a chiroptical system in a way that enhances measurable quantities such as circular dichroism (CD), or plasmon resonance shifts in QED frameworks.…”