Abstract
Here, we describe a systematic derivation of the general form of the optical helicity density of ellipticaly polarized
paraxial Laguerre–Gaussian modes LG`; p; . The treatment incorporates the contributions of the longitudinal field
components for both the paraxial electric E and magnetic B fields, which satisfyMaxwell’s self-consistency condition
in the sense that E is derivable from B and vice versa. Contributions to the helicity density to leading order in
.k2w2
0/1 (where k is the axial wavenumber and w0 the beam waist) include terms proportional to optical spin
and topological charge `, aswell as a spin-orbit j`j term.However, evaluations of the space integrals leading to the
total helicity confirmthat the space integral of the `-dependent termin the density (which is due entirely to the longitudinal
fields) vanishes identically for all ` and p, so that, in general, only determines theHopf index, with the
optical vortex LG` p character featuring only in the action constant.
paraxial Laguerre–Gaussian modes LG`; p; . The treatment incorporates the contributions of the longitudinal field
components for both the paraxial electric E and magnetic B fields, which satisfyMaxwell’s self-consistency condition
in the sense that E is derivable from B and vice versa. Contributions to the helicity density to leading order in
.k2w2
0/1 (where k is the axial wavenumber and w0 the beam waist) include terms proportional to optical spin
and topological charge `, aswell as a spin-orbit j`j term.However, evaluations of the space integrals leading to the
total helicity confirmthat the space integral of the `-dependent termin the density (which is due entirely to the longitudinal
fields) vanishes identically for all ` and p, so that, in general, only determines theHopf index, with the
optical vortex LG` p character featuring only in the action constant.
Original language | English |
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Pages (from-to) | 459-466 |
Number of pages | 8 |
Journal | JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS |
Volume | 39 |
Issue number | 2 |
DOIs | |
Publication status | Published - 10 Jan 2022 |