We present an analytical method involving the nonlinear polarizability tensor for calculating the second harmonic generation (SHG) intensity for a nonlinear sandwich metasurface. The theoretical model is that a nonlinear meta-atom can be considered as a nonlinear electric- and magnetic-dipole, which allows the nonlinear polarizability tensors to be calculated from the far-field of the scattered SHG. The results suggest that the simultaneous excitation of electric and magnetic plasmonic resonances improves the SHG intensity, which is quantitatively consistent with the ones by the finite-difference time-domain method. Therefore, various nonlinear metasurfaces can be designed for applications in nonlinear micro-nano photonic devices.

中文翻译：

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非线性极化率张量法确定非线性夹层超表面的二次谐波生成

我们提出了一种涉及非线性极化率张量的分析方法，用于计算非线性夹层超表面的二次谐波产生（SHG）强度。理论模型是，可以将非线性亚原子视为非线性电偶极子和磁偶极子，从而可以从散射SHG的远场计算出非线性极化率张量。结果表明，电和磁等离子体共振的同时激发提高了SHG强度，这与通过时域有限差分法定量地一致。因此，可以设计各种非线性超表面，以用于非线性微纳光子器件。