Dual-Symmetrized Construction of Electromagnetic Beams Beyond the Paraxial Approximation with an Explicit Separation of Scalar and Vectorial Corrections
Abstract
We develop a perturbative framework for constructing the fields of electromagnetic beams beyond the paraxial approximation, in which the vectorial correction is shared symmetrically between the electric and magnetic fields and separated from the isotropic scalar correction. The method is based on a direct iterative derivation from Maxwell equations and combines complementary electric-first and magnetic-first constructions, thereby removing the construction-dependent assignment of the vectorial correction to either the electric or magnetic field. In addition, the scalar envelope correction is obtained independently from the isotropic co-polar contribution to the solutions of the higher-order Helmholtz equation. The resulting corrected fields apply to an arbitrary paraxial envelope and input Jones polarization.
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BibTeX
@misc{alharbi2026dualsymmetrized,
title = {{Dual-Symmetrized Construction of Electromagnetic Beams Beyond the Paraxial Approximation with an Explicit Separation of Scalar and Vectorial Corrections}},
author = {Abdullah F. Alharbi and Kayn A. Forbes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.26776},
eprint = {2608.26776},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26776},
}
RIS
TY - UNPB
TI - Dual-Symmetrized Construction of Electromagnetic Beams Beyond the Paraxial Approximation with an Explicit Separation of Scalar and Vectorial Corrections
AU - Abdullah F. Alharbi
AU - Kayn A. Forbes
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2608.26776
UR - https://arxiv.org/abs/2608.26776
AB - We develop a perturbative framework for constructing the fields of electromagnetic beams beyond the paraxial approximation, in which the vectorial correction is shared symmetrically between the electric and magnetic fields and separated from the isotropic scalar correction. The method is based on a direct iterative derivation from Maxwell equations and combines complementary electric-first and magnetic-first constructions, thereby removing the construction-dependent assignment of the vectorial correction to either the electric or magnetic field. In addition, the scalar envelope correction is obtained independently from the isotropic co-polar contribution to the solutions of the higher-order Helmholtz equation. The resulting corrected fields apply to an arbitrary paraxial envelope and input Jones polarization.
ER -