On the differences between helicity and chirality

The optical helicity and the optical chirality are two quantities that are used to describe chiral electromagnetic fields. In a monochromatic field, the two quantities are proportional to one another, and the distinction between the two is therefore largely unimportant. However, in a polychromatic field, no such proportionality holds. This paper explicitly examines both the helicity and chirality densities in various polychromatic fields: the superposition of two circularly polarised plane-waves of different frequencies, a chirped pulse of circularly polarised light, and an "optical centrifuge" consisting of two oppositely chirped circularly polarised beams of opposite handedness. Even in the simplest case there can be significant qualitative differences between the two quantities -- they may have opposite signs, or one may be zero while the other is not. The origin of these differences lies in the different frequency scaling of the two quantities, which is made relevant by the presence of multiple frequency components in the fields