Mirror-Constrained Optical Hall Rectification in Asymmetric Gold Gratings:\\ Edelstein Conversion and a Phase-Seeded Kerr Four-Wave Mixing Instability
Abstract
Transverse optical rectification has been reported in a one-dimensional asymmetric Au grating even though an ideal profile h(x) retains the xz mirror Me:y→−y. Because Jy is odd under Me, whereas the p-polarized bilinears |Ex|2, |Ez|2, and Re(ExEz*) are even, the transverse dc current requires a distinct mirror-odd factor Lamy. We formulate a symmetry-complete effective model combining the origin-independent cell invariant Astr=Im(h12h2*), Drude--Edelstein spin polarization, and spin--orbit conversion. We then propose a dynamical realization of Lamy for a finite-width device. A driven pump-like plasmonic mode at ky≃0 generates a mirror pair of transverse surface-plasmon-polariton quasinormal modes (Kx,± qy) through the same third-order susceptibility that produces self- and cross-Kerr shifts. Four-wave mixing creates the pair and locks its phase sum but, by itself, cannot change the pair-population difference. Weak coherent backscattering makes the relative drive phase observable; a small phase difference from incident ky, spot displacement, edges, or disorder then unfolds a Kerr directional instability and deterministically selects its sign. The resulting population imbalance supplies the dynamical mirror-odd factor Ldyn=ληη in the structure-dependent AstrLamy⟨ jxsy⟩t side-jump-like channel, which vanishes for the centered symmetric grating because Astr=0. We give the complete three-mode equations, the pump-only and saturated-state Bogoliubov problems, the imperfect-pitchfork reduction, and a validated normalized numerical realization. The normalized equations exhibit a robust supercritical pitchfork with an approximately one-half critical exponent and phase-reversed branch selection.
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BibTeX
@misc{leuenberger2026mirrorconstrained,
title = {{Mirror-Constrained Optical Hall Rectification in Asymmetric Gold Gratings:\\ Edelstein Conversion and a Phase-Seeded Kerr Four-Wave Mixing Instability}},
author = {Michael N. Leuenberger and Richard M. Osgood III},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05761},
eprint = {2610.05761},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05761},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mirror-Constrained Optical Hall Rectification in Asymmetric Gold Gratings:\\ Edelstein Conversion and a Phase-Seeded Kerr Four-Wave Mixing Instability
AU - Michael N. Leuenberger
AU - Richard M. Osgood III
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05761
UR - https://arxiv.org/abs/2610.05761
AB - Transverse optical rectification has been reported in a one-dimensional asymmetric Au grating even though an ideal profile h(x) retains the xz mirror Me:y→−y. Because J_y is odd under Me, whereas the p-polarized bilinears |E_x|^2, |E_z|^2, and Re(E_xE_z^*) are even, the transverse dc current requires a distinct mirror-odd factor Lamy. We formulate a symmetry-complete effective model combining the origin-independent cell invariant Astr=Im(h_1^2h_2^*), Drude--Edelstein spin polarization, and spin--orbit conversion. We then propose a dynamical realization of Lamy for a finite-width device. A driven pump-like plasmonic mode at k_y≃0 generates a mirror pair of transverse surface-plasmon-polariton quasinormal modes (K_x,± q_y) through the same third-order susceptibility that produces self- and cross-Kerr shifts. Four-wave mixing creates the pair and locks its phase sum but, by itself, cannot change the pair-population difference. Weak coherent backscattering makes the relative drive phase observable; a small phase difference from incident k_y, spot displacement, edges, or disorder then unfolds a Kerr directional instability and deterministically selects its sign. The resulting population imbalance supplies the dynamical mirror-odd factor Ldyn=λ_ηη in the structure-dependent AstrLamy⟨ j_xs_y⟩_t side-jump-like channel, which vanishes for the centered symmetric grating because Astr=0. We give the complete three-mode equations, the pump-only and saturated-state Bogoliubov problems, the imperfect-pitchfork reduction, and a validated normalized numerical realization. The normalized equations exhibit a robust supercritical pitchfork with an approximately one-half critical exponent and phase-reversed branch selection.
ER -