# Optical Helicity and Chirality: Conservation and Sources
## 5 Concluding Remarks  
We have examined in detail the construction of the helicity density (1) in a vacuum and discussed the merits of using this quantity to characterise chiral light. Alongside this, we examined the chirality density (2) of the free electromagnetic field and pointed out cases in which the two quantities are trivially related. Only the conservation of helicity, however, generates a physically-meaningful symmetry transformation of the system. We used this to construct a continuity equation of the helicity of the free field, before extending the method to examine cases under which this symmetry is broken and helicity is no longer conserved. We have identified four distinct types of helicity sources. The first results from a non-constant value of \(\epsilon/\mu\), taking the form of the right-hand side of (27). The second helicity source has the general form of (16) [17] and can be understood in its simplest form in terms of a coupled electric-magnetic dipole system. The third results from the non-reciprocity parameter \(\alpha\) in the constitutive relations, of the form (38). The final type of source examined in this article results from a dual-symmetric object embedded in a chiral medium, expressible as an energy source multiplied by the chirality parameter \(\beta\), as given by (41).  
Categorisation of the distinct sources of helicity in this way provides insight into the electromagnetic response of different types of matter and is achieved by exploiting the inherent symmetry of the Maxwell equations. The distinction between the microscopic and macroscopic sources results from the non-tractable nature of the problem of determining the electromagnetic response of large volumes (\(\gg\)than the size of individual molecules) of helicity sources. In order to bridge this gap, we can perhaps look to experiments in which chiral objects are embedded into a dielectric host, forming an artificial composite chiral medium [50; 51]. In recent work, such methods have been used to verify that a chiral nanostructure is in fact able to sense the orbital, as well as the spin angular momentum of an impinging light beam [52; 53]. Theoretical study on this subject continues to reveal insight into the significance of twisted light beams in chiral light-matter interactions [54; 55], paving the way for new methods in the detection and manipulation of chiral matter. The importance of helicity in the characterisation of both natural and engineered chiral nanostructures is indeed becoming increasingly apparent: [PERSON] et al. [56] show that using structured light with maximised helicity leads to a direct measure of the chirality of such an object, which does not require knowledge of the helicity or energy densities of the field. It is also evident that both the helicity of the incident fields and the dual-symmetry (or helicity preserving nature) of a photonic structure are essential in circular dichroism enhancement effects [57]. Reconciling our understanding of both microscopic and macroscopic sources of helicity in a general theoretical model, however, is an ongoing topic of investigation.  
**Author Contributions:** This paper was built on original ideas by each of the authors, and each author performed some of the calculations. All authors contributed to the writing and editing of the manuscript.  
**Funding:** This research was funded by The Royal Society under Grant Numbers RP/EA/180010 and RP/150122 and the Engineering and Physical Sciences Research Council under Grant Number EP/N509668/1.  
**Conflicts of Interest:** The authors declare no conflicts of interest.