Theory of reflectionless scattering modes
Theory of reflectionless scattering modes
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DOI：
10.1103/physreva.102.063511
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发表时间：
2019-09
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影响因子：
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通讯作者：
William R. Sweeney;C. Hsu;A. Stone
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文献类型：
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作者：
William R. Sweeney;C. Hsu;A. Stone
我们发展了一种特殊类型的散射态的理论，在这种散射态中，一组渐近通道被选择为输入，互补集作为输出，并且输入通道的反射为零。一般来说，在离散复频率处存在无限多个这样的解。我们的结果适用于线性电磁波和声波散射，也量子散射，在所有的维度，任意几何形状，包括散射体在自由空间中，并为任何选择的输入/输出集。当这种状态出现在实频率轴之外时，我们将其称为反射零（R-零），而当它被调谐到真实的频率作为稳态解时，我们将其称为无反射散射模式（RSM）。这种无反射行为需要特定的单色输入波前，由具有本征值零的滤波散射矩阵的本征向量给出。稳态RSM可以通过不破坏通量守恒的指数调谐或通过增益-损耗调谐来实现。通量守恒腔的响应面是双向的，而非通量守恒腔的响应面一般是单向的。具有${\cal PT}$-对称性的腔在复共轭对中具有单向R-零点，这意味着对于小的增益-损耗参数，无反射状态自然地出现在真实的频率处，但是在自发的${\cal PT}$-破缺跃迁之后移动到复频率平面中。数值例子的RSM给出了一维腔的增益/损耗，一个${\cal PT}$腔，一个二维的多波导结，和一个二维的变形介质腔在自由空间。我们概述并实现了一个通用的技术来解决这些问题，这表明有希望设计光子结构是完美的阻抗匹配的特定输入，或可以完美地转换输入从一组模式的互补集。
We develop the theory of a special type of scattering state in which a set of asymptotic channels are chosen as inputs and the complementary set as outputs, and there is zero reflection back into the input channels. In general an infinite number of such solutions exist at discrete complex frequencies. Our results apply to linear electromagnetic and acoustic wave scattering and also to quantum scattering, in all dimensions, for arbitrary geometries including scatterers in free space, and for any choice of the input/output sets. We refer to such a state as reflection-zero (R-zero) when it occurs off the real-frequency axis and as an Reflectionless Scattering Mode (RSM) when it is tuned to a real frequency as a steady-state solution. Such reflectionless behavior requires a specific monochromatic input wavefront, given by the eigenvector of a filtered scattering matrix with eigenvalue zero. Steady-state RSMs may be realized by index tuning which do not break flux conservation or by gain-loss tuning. RSMs of flux-conserving cavities are bidirectional while those of non-flux-conserving cavities are generically unidirectional. Cavities with ${\cal PT}$-symmetry have unidirectional R-zeros in complex-conjugate pairs, implying that reflectionless states naturally arise at real frequencies for small gain-loss parameter but move into the complex-frequency plane after a spontaneous ${\cal PT}$-breaking transition. Numerical examples of RSMs are given for one-dimensional cavities with and without gain/loss, a ${\cal PT}$ cavity, a two-dimensional multiwaveguide junction, and a two-dimensional deformed dielectric cavity in free space. We outline and implement a general technique for solving such problems, which shows promise for designing photonic structures which are perfectly impedance-matched for specific inputs, or can perfectly convert inputs from one set of modes to a complementary set.