We present a theoretical study of second-harmonic generation from a singular metasurface. The singular metasurfaces strongly interact with the incident light, where the large field enhancement forms an intense surface polarization that generates the second-harmonic field. By using transformation optics, the calculation of nonlinear optical response is converted from the metasurface frame to that of a simple slab geometry, largely reducing the complexity of the problem. In addition, the singular metasurface exhibits a weak dependence on the incident angle of light, which can be potentially used as an all-angle device for harmonic generations. Finally, we study the symmetry dependence of second-harmonic generation in the far field for the singular metasurface and show how to enhance the conversion efficiency under normal incidence by breaking the surface inversion symmetry.

中文翻译：

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从奇异超表面产生二次谐波

我们提出了从奇异超表面产生二次谐波的理论研究。奇异超表面与入射光强烈相互作用，其中大场增强形成强烈的表面极化，产生二次谐波场。通过使用变换光学，非线性光学响应的​​计算从超表面框架转换为简单的平板几何，大大降低了问题的复杂性。此外，奇异超表面对光的入射角表现出弱依赖性，可以潜在地用作谐波产生的全角度装置。最后，