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.

中文翻译：

---

任意光子结构的无反射激发：一般理论

摘要 我们概述并解释了最近发展的阻抗匹配或任意维度中任意有限光子结构的无反射激发的理论。该理论包括导波和自由空间激发的情况。它描述了实现完美无反射激发的必要和充分条件，并指定了必须调整多少物理参数才能实现这一目标。在没有几何对称性（例如奇偶校验和时间反转、奇偶校验和时间反转的乘积或旋转对称性）的情况下，需要调整至少一个结构参数以实现无反射激发。该理论采用麦克斯韦方程组最近确定的一组复频率解作为起点，它们的定义是在选定的一组输入通道中具有零反射，并且被称为 R-zeros。为了将 R-zero 移动到实际频率轴，调整通常是必要的，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，任何其他波前通常都不是无反射的。将该理论视为表示谐振器临界耦合概念的概括是有用的，但它适用于任意维度、任意数量的通道，甚至当谐振不是频谱隔离时。在具有奇偶和时间反转对称性（实介电函数）或奇偶时间对称的结构中，通常，R-zeros 的一个子集具有真实频率，并且无反射状态存在于离散频率而无需调谐。然而，由于当两个 RSM 相遇时自发的对称性破坏现象，它们并不存在于每个光谱范围内，就像它们在 Fabry-Pérot 或双镜谐振器的特殊情况下一样。这种破坏对称性的转变对应于一种新的例外点，最近才发现，在该点反射和传输共振线的形状变平。给出了用于一维多镜腔、二维多波导结和用作完美模式转换器的多模波导的 RSM 的数值示例。讨论了寻找 R-zeros 和 RSM 的两种求解方法。第一个是复杂缩放或完美匹配层方法的直接概括，适用于许多重要情况；第二个涉及一种模式特定的边界匹配方法，该方法最近才得到证明，可以应用于该理论适用的所有几何结构，包括此处解决的类型的自由空间和多模波导问题。