Reflectionless excitation of arbitrary photonic structures: a general theory
Reflectionless excitation of arbitrary photonic structures: a general theory
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DOI：
10.1515/nanoph-2020-0403
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发表时间：
2020-10
期刊：
影响因子：
7.5
通讯作者：
A. Stone;William R. Sweeney;C. Hsu;Chia Wei Hsu;Kabish Wisal;Zeyu Wang
中科院分区：
文献类型：
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作者：
A. Stone;William R. Sweeney;C. Hsu;Chia Wei Hsu;Kabish Wisal;Zeyu Wang
摘要本文概述和解释了最近发展起来的任意一维有限光子结构的阻抗匹配或无反射激发理论。该理论包括导波和自由空间激励的情况。它描述了完全无反射激励成为可能的必要和充分条件，并指定了必须调整多少物理参数才能实现这一点。在没有几何对称性的情况下，例如宇称和时间反演、宇称和时间反演的乘积或旋转对称性，至少一个结构参数的调谐将是实现无反射激发所必需的。该理论采用最近确定的一组复频率解的麦克斯韦方程组作为起点，其定义为具有零反射到一组选定的输入通道，并被称为R-零。为了将R零点移动到真实的频率轴，调谐通常是必要的，在那里它成为物理稳态阻抗匹配解决方案，我们将其称为无反射散射模式（RSM）。此外，除了在单通道系统中，RSM对应于特定的输入波前，并且任何其他波前通常不是无反射的。将该理论视为谐振器临界耦合概念的推广是有用的，但它适用于任意维度，任意数量的通道，甚至当谐振不是光谱隔离时。在具有宇称和时间反演对称性（真实的介电函数）或具有宇称-时间对称性的结构中，通常R零点的子集具有真实的频率，并且无反射状态存在于离散频率处而无需调谐。然而，它们并不存在于每个光谱范围内，因为它们在法布里-珀罗或双镜谐振腔的特殊情况下，由于两个RSM相遇时的自发破缺现象。这样的破环跃迁对应于一种新的特殊点，只是最近才发现，在反射和透射共振线型的形状是平坦的。给出了一维多镜腔、二维多波导结和多模波导理想模式转换器的响应面的数值例子。讨论了两种求R零点和RSM的方法。第一个是一个简单的概括复杂的缩放或完全匹配层的方法，并适用于一些重要的情况下，第二个涉及模式特定的边界匹配方法，最近才被证明，并可以适用于所有的几何形状的理论是有效的，包括自由空间和多模波导问题的类型在这里解决。
Abstract We outline and interpret a recently developed theory of impedance matching or reflectionless excitation of arbitrary finite photonic structures in any dimension. The theory includes both the case of guided wave and free-space excitation. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible and specifies how many physical parameters must be tuned to achieve this. In the absence of geometric symmetries, such as parity and time-reversal, the product of parity and time-reversal, or rotational symmetry, the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex frequency solutions of the Maxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real frequency axis, where it becomes a physical steady-state impedance-matched solution, which we refer to as a reflectionless scattering mode (RSM). In addition, except in single-channel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. It is useful to consider the theory as representing a generalization of the concept of critical coupling of a resonator, but it holds in arbitrary dimension, for arbitrary number of channels, and even when resonances are not spectrally isolated. In a structure with parity and time-reversal symmetry (a real dielectric function) or with parity–time symmetry, generically a subset of the R-zeros has real frequencies, and reflectionless states exist at discrete frequencies without tuning. However, they do not exist within every spectral range, as they do in the special case of the Fabry–Pérot or two-mirror resonator, due to a spontaneous symmetry-breaking phenomenon when two RSMs meet. Such symmetry-breaking transitions correspond to a new kind of exceptional point, only recently identified, at which the shape of the reflection and transmission resonance lineshape is flattened. Numerical examples of RSMs are given for one-dimensional multimirror cavities, a two-dimensional multiwaveguide junction, and a multimode waveguide functioning as a perfect mode converter. Two solution methods to find R-zeros and RSMs are discussed. The first one is a straightforward generalization of the complex scaling or perfectly matched layer method and is applicable in a number of important cases; the second one involves a mode-specific boundary matching method that has only recently been demonstrated and can be applied to all geometries for which the theory is valid, including free space and multimode waveguide problems of the type solved here.