Optimal Diffractive Focusing of Vortex Beams
Abstract
We formulate diffractive ring focusing of paraxial beams carrying orbital angular momentum (OAM) through a finite circular aperture as a variational optimization problem. For a fixed topological charge, we determine the real-valued radial pupil that maximizes the intensity at a prescribed ring radius and propagation distance under a normalization constraint on the input field. The resulting problem admits an exact analytical solution: the optimal pupil combines the familiar Fresnel phase structure with an OAM-dependent Bessel radial modulation, and the associated eigenvalue yields a rigorous upper bound on the achievable ring intensity. We further analyze the lens-assisted configuration and derive a simple bound that allows direct comparison between diffractive and refractive vortex focusing. The theory also provides a quantitative framework for evaluating the performance of practical mask designs, including binary Fresnel-Bessel zone plates and amplitude-weighted pupils. We have experimentally tested our predictions in the optical domain by implementing the corresponding vortex beam pupils and comparing their propagation and focusing performance with the optimal solution. Our results establish the vortex-beam analogue of optimal amplitude-only focusing and identify the fundamental limits governing diffractive concentration of structured waves
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BibTeX
@misc{ghobadi2026optimal,
title = {{Optimal Diffractive Focusing of Vortex Beams}},
author = {Roohollah Ghobadi and Carrie Rodriguez and Lukas Scarfe and Maxim A. Efremov and Ebrahim Karimi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10842},
eprint = {2610.10842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10842},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal Diffractive Focusing of Vortex Beams
AU - Roohollah Ghobadi
AU - Carrie Rodriguez
AU - Lukas Scarfe
AU - Maxim A. Efremov
AU - Ebrahim Karimi
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10842
UR - https://arxiv.org/abs/2610.10842
AB - We formulate diffractive ring focusing of paraxial beams carrying orbital angular momentum (OAM) through a finite circular aperture as a variational optimization problem. For a fixed topological charge, we determine the real-valued radial pupil that maximizes the intensity at a prescribed ring radius and propagation distance under a normalization constraint on the input field. The resulting problem admits an exact analytical solution: the optimal pupil combines the familiar Fresnel phase structure with an OAM-dependent Bessel radial modulation, and the associated eigenvalue yields a rigorous upper bound on the achievable ring intensity. We further analyze the lens-assisted configuration and derive a simple bound that allows direct comparison between diffractive and refractive vortex focusing. The theory also provides a quantitative framework for evaluating the performance of practical mask designs, including binary Fresnel-Bessel zone plates and amplitude-weighted pupils. We have experimentally tested our predictions in the optical domain by implementing the corresponding vortex beam pupils and comparing their propagation and focusing performance with the optimal solution. Our results establish the vortex-beam analogue of optimal amplitude-only focusing and identify the fundamental limits governing diffractive concentration of structured waves
ER -