Journal
SYMMETRY-BASEL
Volume 11, Issue 11, Pages -Publisher
MDPI
DOI: 10.3390/sym11111427
Keywords
electromagnetic helicity; conformal symmetry
Categories
Funding
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [258734477-SFB 1173]
- KIT through the Virtual Materials Design (VIRTMAT) project by the Helmholtz Association via the Helmholtz program Science and Technology of Nanosystems (STN)
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The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in momentum space, in (r,t) space, and in the time-harmonic (r,omega) space are obtained, featuring Riemann-Silberstein-like fields and potentials. The time-harmonic expressions can be directly evaluated using the outputs of common numerical solvers of Maxwell equations. The results are shown to be equivalent to the well-known volume integral for the average helicity, featuring the electric and magnetic fields and potentials.
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