Quantitative Analysis of Second-Harmonic Generation in Plasmonic Nanowires: Symmetry Breaking and a Topological Defect
Abstract
This paper develops a quantitative theory of second-harmonic generation (SHG) in hollow plasmonic nanowires, distinguishing geometric symmetry breaking from cavity effects. We consider a centrosymmetric material with a concentric circular cavity and a slightly perturbed outer boundary. Relative to the solid nanowire in~\cite{liu2026quantitative}, the cavity introduces a topological defect by changing the cross-section from a disk to a doubly connected domain, whereas the outer-boundary perturbation breaks geometric symmetry. Local inversion-symmetry breaking at the interfaces induces nonlinear surface polarization. Using layer potentials and boundary-perturbation asymptotics, we derive explicit leading- and first-order formulas for the fundamental and second-harmonic fields. For a circular outer boundary, the leading-order second-harmonic field is purely quadrupolar; its amplitude differs from the solid-wire case by O(γ2) as γ=ri/re→0 and decays as O(re−ri) in the nonresonant thin-shell limit. For perturbations proportional to cos(nθ), n≥3, the first-order second-harmonic correction contains only modes n−2, n, and n+2, yielding dipolar, quadrupolar, or higher-order radiation for n=3, n=4, or n≥5, respectively, provided the lowest-order modal coefficient is nonzero. We derive plasmonic resonance conditions at both frequencies and estimate the singular orders of single and simultaneous resonances, including possible higher-order singularities from coincident resonance factors. Thus geometric symmetry determines the multipolar modes, whereas the cavity radius controls their amplitudes and resonant enhancement.
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BibTeX
@misc{lei2026quantitative,
title = {{Quantitative Analysis of Second-Harmonic Generation in Plasmonic Nanowires: Symmetry Breaking and a Topological Defect}},
author = {Qi Lei and Hongyu Liu and Zhi-Qiang Miao and Guang-Hui Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35307},
eprint = {2610.35307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35307},
}
RIS
TY - UNPB
TI - Quantitative Analysis of Second-Harmonic Generation in Plasmonic Nanowires: Symmetry Breaking and a Topological Defect
AU - Qi Lei
AU - Hongyu Liu
AU - Zhi-Qiang Miao
AU - Guang-Hui Zheng
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35307
UR - https://arxiv.org/abs/2610.35307
AB - This paper develops a quantitative theory of second-harmonic generation (SHG) in hollow plasmonic nanowires, distinguishing geometric symmetry breaking from cavity effects. We consider a centrosymmetric material with a concentric circular cavity and a slightly perturbed outer boundary. Relative to the solid nanowire in~\cite{liu2026quantitative}, the cavity introduces a topological defect by changing the cross-section from a disk to a doubly connected domain, whereas the outer-boundary perturbation breaks geometric symmetry. Local inversion-symmetry breaking at the interfaces induces nonlinear surface polarization. Using layer potentials and boundary-perturbation asymptotics, we derive explicit leading- and first-order formulas for the fundamental and second-harmonic fields. For a circular outer boundary, the leading-order second-harmonic field is purely quadrupolar; its amplitude differs from the solid-wire case by O(γ^2) as γ=r_i/r_e→0 and decays as O(r_e−r_i) in the nonresonant thin-shell limit. For perturbations proportional to cos(nθ), n≥3, the first-order second-harmonic correction contains only modes n−2, n, and n+2, yielding dipolar, quadrupolar, or higher-order radiation for n=3, n=4, or n≥5, respectively, provided the lowest-order modal coefficient is nonzero. We derive plasmonic resonance conditions at both frequencies and estimate the singular orders of single and simultaneous resonances, including possible higher-order singularities from coincident resonance factors. Thus geometric symmetry determines the multipolar modes, whereas the cavity radius controls their amplitudes and resonant enhancement.
ER -