On the gauge-invariant orbital angular momentum of vector optical vortices in the paraxial approximation and beyond
Abstract
In this paper we present a gauge-invariant formalism for describing the spin and orbital angular momenta of scalar and vector optical vortices. The correction term, arising from consistent incorporation of the transverse vector potential's nonlocality, restores gauge invariance and makes it possible to separate the total angular momentum into spin and orbital components. We propose a method for calculating the orbital and spin angular momenta of multimode vector vortex fields and show that the orbital angular momentum of such beams contains two qualitatively different components. The polarization-independent contribution to the orbital angular momentum is related to the topological charge that determines the order of the phase singularity, while the polarization-dependent one is proportional to the helical topological charge that determines the spatial inhomogeneity of the polarization. We also discuss the quantization procedure for fields with spatially inhomogeneous polarization in terms of modes with a helical topological charge, and examine the limits of applicability of the proposed formalism.
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BibTeX
@misc{maliutina2026gaugeinvariant,
title = {{On the gauge-invariant orbital angular momentum of vector optical vortices in the paraxial approximation and beyond}},
author = {E. V. Maliutina and E. A. Vashukevich and V. A. Leonov and D. D. Reshetnikov and T. Yu. Golubeva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40523},
eprint = {2610.40523},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40523},
}
RIS
TY - UNPB
TI - On the gauge-invariant orbital angular momentum of vector optical vortices in the paraxial approximation and beyond
AU - E. V. Maliutina
AU - E. A. Vashukevich
AU - V. A. Leonov
AU - D. D. Reshetnikov
AU - T. Yu. Golubeva
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40523
UR - https://arxiv.org/abs/2610.40523
AB - In this paper we present a gauge-invariant formalism for describing the spin and orbital angular momenta of scalar and vector optical vortices. The correction term, arising from consistent incorporation of the transverse vector potential's nonlocality, restores gauge invariance and makes it possible to separate the total angular momentum into spin and orbital components. We propose a method for calculating the orbital and spin angular momenta of multimode vector vortex fields and show that the orbital angular momentum of such beams contains two qualitatively different components. The polarization-independent contribution to the orbital angular momentum is related to the topological charge that determines the order of the phase singularity, while the polarization-dependent one is proportional to the helical topological charge that determines the spatial inhomogeneity of the polarization. We also discuss the quantization procedure for fields with spatially inhomogeneous polarization in terms of modes with a helical topological charge, and examine the limits of applicability of the proposed formalism.
ER -