Abstract We report on the numerical demonstration of enhanced second harmonic generation (SHG) originating from collective resonances in plasmonic nanoparticle arrays. The nonlinear optical response of the metal nanoparticles is modeled by employing a hydrodynamic nonlinear Drude model implemented into Finite-Difference Time-Domain (FDTD) simulations, and effective polarizabilities of nanoparticle multipoles in the lattice are analytically calculated at the fundamental wavelength by using a coupled dipole–quadrupole approximation. Excitation of narrow collective resonances in nanoparticle arrays with electric quadrupole (EQ) and magnetic dipole (MD) resonant coupling leads to strong linear resonance enhancement. In this work, we analyze SHG in the vicinity of the lattice resonance corresponding to different nanoparticle multipoles and explore SHG efficiency by varying the lattice periods. Coupling of electric quadrupole and magnetic dipole in the nanoparticle lattice indicates symmetry breaking and the possibility of enhanced SHG under these conditions. By varying the structure parameters, we can change the strength of electric dipole (ED), EQ, and MD polarizabilities, which can be used to control the linewidth and magnitude of SHG emission in plasmonic lattices. Engineering of lattice resonances and associated magnetic dipole resonant excitations can be used for spectrally narrow nonlinear response as the SHG can be enhanced and controlled by higher multipole excitations and their lattice resonances. We show that both ED and EQ–MD lattice coupling contribute to SHG, but the presence of strong EQ–MD coupling is important for spectrally narrow SHG and, in our structure, excitation of narrow higher-order multipole lattice resonances results in five times enhancement.

中文翻译：

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具有多极共振耦合的超表面中的二次谐波产生

摘要我们报告了源自等离子体纳米颗粒阵列中的集体共振的增强型二次谐波产生 (SHG) 的数值演示。金属纳米粒子的非线性光学响应是通过采用在有限差分时域 (FDTD) 模拟中实现的流体动力学非线性 Drude 模型进行建模的，并且通过使用耦合的基本波长，在基本波长处分析计算了晶格中纳米粒子多极子的有效极化率偶极-四极近似。在具有电四极 (EQ) 和磁偶极 (MD) 共振耦合的纳米颗粒阵列中激发窄集体共振导致强烈的线性共振增强。在这项工作中，我们分析了对应于不同纳米粒子多极的晶格共振附近的 SHG，并通过改变晶格周期来探索 SHG 效率。纳米粒子晶格中电四极杆和磁偶极子的耦合表明对称性破坏和在这些条件下增强 SHG 的可能性。通过改变结构参数，我们可以改变电偶极子 (ED)、EQ 和 MD 极化率的强度，可用于控制等离子体晶格中 SHG 发射的线宽和幅度。晶格共振和相关磁偶极子共振激发的工程可用于窄谱非线性响应，因为 SHG 可以通过更高的多极激发及其晶格共振来增强和控制。我们表明 ED 和 EQ-MD 晶格耦合都有助于 SHG，