微扰单向隐形
Perturbative Unidirectional Invisibility
摘要：
我们概述了一个一般的微扰方法评估散射功能的有限范围内的复杂的潜力，并使用它来检查复杂的矩形势垒扰动。在光学中，这些对应于$n(x)=n_0+f(x)$形式的调制折射率分布，其中$n_0$是实数，$f(x)$是复数值，而$|f(x)|\ll1\leq n_0$是复数值。我们给出了一个全面的描述这种媒体的单向不可见的现象，证明了五个一般定理，其实现在${\cal PT}$对称和非${\cal PT}$对称材料。特别是，我们建立了单向不可见的${\cal PT}$对称的样品，其折射率具有恒定的实部的不可能性，并显示如何一个简单的缩放变换的单向不可见的${\cal PT}$对称的指数分布与$n_0=1$可用于生成一个层次的单向不可见的${\cal PT}$对称的指数分布与$n_0>1$。有关$n_0>1$的单向不可见性的结果开辟了这种现象在各种活性材料的实验研究的方式。作为我们的一般结果的应用，我们表明，与$n(x)=n_0+ζe^{iK x}$，$ζ$和$K$实数，和$|ζ|\ll 1$的介质可以支持单向不可见性只有$n_0=1$。然后，我们构建了$n(x)=n_0+\sum_\ell z_\ell e^{iK_\ell x}$形式的单向不可见折射率分布，其中包括$z_\ell$复合物、$K_\ell$实数、$|z_\ell|\ll 1$和$n_0>1$。
英文摘要：
We outline a general perturbative method of evaluating scattering features of finite-range complex potentials and use it to examine complex perturbations of a rectangular barrier potential. In optics, these correspond to modulated refractive index profiles of the form $n(x)=n_0+f(x)$, where $n_0$ is real, $f(x)$ is complex-valued, and $|f(x)|\ll1\leq n_0$. We give a comprehensive description of the phenomenon of unidirectional invisibility for such media, proving five general theorems on its realization in ${\cal PT}$-symmetric and non-${\cal PT}$-symmetric material. In particular, we establish the impossibility of unidirectional invisibility for ${\cal PT}$-symmetric samples whose refractive index has a constant real part and show how a simple scaling transformation of a unidirectionally invisible ${\cal PT}$-symmetric index profile with $n_0=1$ may be used to generate a hierarchy of unidirectionally invisible ${\cal PT}$-symmetric index profiles with $n_0>1$. The results pertaining unidirectional invisibility for $n_0>1$ open up the way for the experimental studies of this phenomenon in a variety of active material. As an application of our general results, we show that a medium with $n(x)=n_0+ζe^{iK x}$, $ζ$ and $K$ real, and $|ζ|\ll 1$ can support unidirectional invisibility only for $n_0=1$. We then construct unidirectionally invisible index profiles of the form $n(x)=n_0+\sum_\ell z_\ell e^{iK_\ell x}$, with $z_\ell$ complex, $K_\ell$ real, $|z_\ell|\ll 1$, and $n_0>1$.
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