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arXiv · 2608.19054

Transversality Locks Longitudinal Gradients in Structured-Light Quadrupole Transitions

Kayn A. Forbes·Dale Green·Abdullah F. Alharbi·Akbar Salam
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Abstract

Electric quadrupole absorption is driven by optical field gradients, not by field amplitudes alone. This distinction is crucial for structured light, where a paraxially small longitudinal field can generate a leading-order longitudinal gradient. For fully vectorial Laguerre-Gaussian modes, Maxwell transversality locks this longitudinal gradient to the transverse structured gradient of the leading paraxial field. This locking is therefore a general electromagnetic constraint, not a focusing-dependent correction that can be removed independently. Decomposing the symmetric-traceless optical field-gradient tensor into spherical components reveals a strongly channel-selective response: the $\Delta m=0$ transition requires the longitudinal gradient at the retained order, the $\Delta m=\pm1$ channels receive scalar and vectorial nonparaxial corrections on top of the carrier-scale longitudinal derivative of the transverse field, and the $\Delta m=\pm2$ channels remain transverse at the same order. These results show that longitudinal optical structure can enter structured-light quadrupole transitions as an indispensable leading-gradient contribution, even when the longitudinal field amplitude itself is paraxially small.

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Kayn A. Forbes, Dale Green, Abdullah F. Alharbi, Akbar Salam. 2026-08-19. Transversality Locks Longitudinal Gradients in Structured-Light Quadrupole Transitions. https://arxiv.org/abs/2608.19054

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