无散射完美反射在多通道单片高对比度光栅中的实现：直接-间接傅里叶谐波干涉与解集的维数

中文摘要 AI 辅助

单片高对比度光栅（MHCGs）尽管存在开放的更高阶衬底衍射通道，仍能表现出无散射的完美反射，但其潜在机制尚未被完全阐明。利用傅里叶谐波描述，我们证明在高折射率衬底中，所有开放的更高阶通道可以通过直接和间接源贡献所产生的辐射场之间的相消干涉被同时消除。相比之下，当调制引起的零阶场与入射波的背景透射场发生相消干涉时，零阶透射消失。这些消除机制共同在无损耗MHCGs中产生单位零阶反射率。内部场谐波的近不变性解释了这些条件对衬底折射率变化的显著稳定性。我们进一步表明，对称兼容的开放通道数量决定了完美反射解集的通用余维数。根据独立设计参数数量相对于该余维数的大小，解形成连续曲线、表现为孤立点，或通常不存在。当额外的衍射通道打开时，引入额外的几何参数可恢复孤立的完美反射解。相同的消除机制和通道计数适用于TE和TM两种偏振。

英文摘要

Monolithic high-contrast gratings (MHCGs) can exhibit scatter-free perfect reflection despite open higher-order substrate diffraction channels, but the underlying mechanism has not been fully clarified. Using a Fourier-harmonic description, we show that all open higher-order channels in the high-index substrate can be simultaneously extinguished through destructive interference between the radiation fields generated by the direct and indirect source contributions. By contrast, the zeroth-order transmission vanishes when the modulation-induced zeroth-order field interferes destructively with the background transmitted field of the incident wave. Together, these cancellations yield unit zeroth-order reflectance in lossless MHCGs. The near invariance of the internal field harmonics accounts for the remarkable stability of these conditions against changes in the substrate refractive index. We further show that the number of symmetry-compatible open channels determines the generic codimension of the perfect-reflection solution set. Depending on the number of independent design parameters relative to this codimension, the solutions form continuous curves, appear as isolated points, or are generically absent. Introducing an additional geometrical parameter restores isolated perfect-reflection solutions when an additional diffraction channel opens. The same cancellation mechanisms and channel counting apply to both TE and TM polarizations.

发表机构

• Kongju National University（公州国立大学）

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