Abstract
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.
Highlights
The optical helicity and the optical chirality are two quantities that are used to describe chiral electromagnetic fields
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
Summary
The volume integral of the helicity density is proportional to the difference in the number of left- and right-handed circularly polarised photons in the field [9], linking the concept to the particle physics notion of helicity as the component of spin angular momentum in the direction of propagation The inclusion of both the A and C potentials in the definition is important in order to ensure that the helicity is locally conserved [3, 6]. We consider the fields of an ‘optical centrifuge’, formed by two co-propagating circularly polarised pulses of opposite handedness, one positively and one negatively chirped [17] We find both features: that the measures disagree in sign, as for the unchirped plane waves, and that the helicity and chirality have different time dependencies, as for the chirped pulses. In all of the cases considered, the differences between the two measures of handedness can be understood by considering a frequency decomposition of the field, and the different frequency scaling of the measures
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