Periodic photonic lattices constitute a fundamental pillar of physics supporting a plethora of scientific concepts and applications. The advent of metamaterials and metastructures is grounded in a deep understanding of their properties. Based on Rytov’s original 1956 formulation, it is well-known that a photonic lattice with deep subwavelength periodicity can be approximated with a homogeneous space having an effective refractive index. Whereas the attendant effective medium theory (EMT) commonly used in the literature is based on the zeroth root, Rytov’s closed-form transcendental equations possess, in principle, an infinite number of roots. Thus far, these higher-order solutions have been totally ignored; even Rytov himself discarded them and proceeded to approximate solutions for the deep-subwavelength regime. In spite of the fact that Rytov’s EMT models an infinite half-space lattice, it is highly relevant to modeling practical thin-film periodic structures with a finite thickness as we show. Therefore, here, we establish a theoretical framework to systematically describe subwavelength resonance behavior and to predict the optical response of resonant photonic lattices using the full Rytov solutions. Expeditious results are obtained because of the semianalytical formulation with direct, new physical insights available for resonant lattice properties. We show that the full Rytov formulation implicitly contains refractive-index solutions pertaining directly to evanescent waves that drive the laterally propagating Bloch modes foundational to resonant lattice properties. In fact, the resonant reradiated Bloch modes experience wavelength-dependent refractive indices that are solutions of Rytov’s expressions. This insight is useful in modeling guided-mode resonant devices including wideband reflectors, bandpass filters, and polarizers. For example, the Rytov indices define directly the bandwidth of the resonant reflector and the extent of the bandpass filter sidebands as verified with rigorous simulations. As an additional result, we define a clear transition point between the resonance subwavelength region and the deep-subwavelength region with an analytic formula provided in a special case.

中文翻译：

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Rytov的完全有效中等形式主义对共振形表面的物理描述和设计的适用性

周期性光子晶格构成物理学的基本支柱，支持大量科学概念和应用。超材料和元结构的出现是建立在对它们的特性的深刻理解的基础上的。基于Rytov最初的1956年公式，众所周知，可以用具有有效折射率的均匀空间来近似具有深亚波长周期性的光子晶格。文献中常用的伴随有效介质理论（EMT）基于第零个根，而Rytov的闭式先验方程式原则上具有无限个根。到目前为止，这些高阶解决方案已被完全忽略。甚至Rytov本人也将其丢弃，并开始对深亚波长体制进行近似求解。尽管Rytov的EMT对无限的半空间晶格进行建模，但与我们对有限厚度的实用薄膜周期性结构进行建模非常相关。因此，在这里，我们建立了一个理论框架来系统地描述亚波长共振行为，并使用完整的Rytov解预测共振光子晶格的光学响应。由于半分析配方具有直接的，新的物理见解，可用于共振晶格特性，因此获得了快速的结果。我们表明，完整的Rytov公式隐含地包含直接与e逝波有关的折射率解决方案，e逝波驱动基于共振晶格特性的横向传播的Bloch模式。事实上，共振辐射的Bloch模式经历了与波长有关的折射率，这是Rytov表达式的解。这种见解对建模包括宽带反射器，带通滤波器和偏振器的导模谐振设备很有用。例如，Rytov指数直接定义了谐振反射器的带宽以及通过严格仿真验证的带通滤波器边带的范围。作为附加结果，我们通过特殊情况下提供的解析公式定义了谐振子波长区域和深子波长区域之间的清晰过渡点。Rytov指数直接定义了谐振反射器的带宽，以及经过严格模拟验证的带通滤波器边带的范围。作为附加结果，我们通过特殊情况下提供的解析公式定义了谐振子波长区域和深子波长区域之间的清晰过渡点。Rytov指数直接定义了谐振反射器的带宽以及通过严格模拟验证的带通滤波器边带的范围。作为附加结果，我们通过特殊情况下提供的解析公式来定义谐振子波长区域和深子波长区域之间的清晰过渡点。