Abstract
The angular momentum content and propagation of linearly polarized Hermite-Gaussian modes are analyzed. The helicity gauge invariant continuity equation reveals that the helicity and flow in the direction of propagation are zero. However, the helicity flow exhibits nonvanishing transverse components. These components have been recently described as photonic wheels. These intrinsic angular momentum terms, depending on the criterion, can be associated with spin or orbital momentum. The electric and magnetic contributions to the optical helicity will be shown to cancel out for Hermite-Gaussian modes. The helicity ϱAC here derived is consistent with the interpretation that it represents the projection of the angular momentum onto the direction of motion.
Highlights
Electromagnetic fields are capable of carrying angular momentum and transferring it to matter
The former has been associated with the spin angular momentum (SAM) whereas the latter has been associated with the orbital angular momentum (OAM) of light
Polarized Hermite-Gauss modes do not carry angular momentum in the direction of propagation. They carry a transverse angular momentum that arises from terms like E × A, usually associated with SAM
Summary
Electromagnetic fields are capable of carrying angular momentum and transferring it to matter. The electromagnetic field’s linear momentum is given by Poynting’s vector p → E × H, where E and H represent the electric and magnetic fields, respectively. This approach has the baffling prediction that the AM in the direction of propagation must be zero, since it must be perpendicular to r and p [4]. The helicity conservation equation is the angular momentum analogue to Poynting’s theorem, where energy is the scalar quantity and linear momentum its corresponding flow.
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