光和质量扩散的隐形和变形
Cloaking and anamorphism for light and mass diffusion
摘要：
我们首先回顾了电磁波的隐身和海市蜃楼效应的经典结果。然后，我们表明，变换光学允许掩蔽的对象或产生海市蜃楼的扩散制度。为了实现这一点，我们考虑在转换坐标中的漫射光子密度的方程，这是有效的散射介质中的漫射光。更确切地说，推广转换为星域中介绍的[Diatta和Guenneau，J. Opt. 13，024012，2011]的物质波，我们数值证明，不同形状的无限导电物体散射漫射光完全相同的方式。我们还提出了一个设计的外部光扩散斗篷空间变化的符号移位参数，隐藏一个有限大小的散射斗篷外。接下来，我们分析在[Guenneau和Puvirajesinghe，R. Soc.Interface 10，20130106，2013]，并且提出使用克服该问题的非线性变换。最后，我们研究了其他形式的不变变换扩散方程在时域中，并触及共形映射和非欧几里德伪装应用于扩散过程。
英文摘要：
We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we consider the equation for diffusive photon density in transformed coordinates, which is valid for diffusive light in scattering media. More precisely, generalizing transformations for star domains introduced in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we numerically demonstrate that infinite conducting objects of different shapes scatter diffusive light in exactly the same way. We also propose a design of external light-diffusion cloak with spatially varying sign-shifting parameters that hides a finite size scatterer outside the cloak. We next analyse non-physical parameter in the transformed Fick's equation derived in [Guenneau and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a non-linear transform that overcomes this problem. We finally investigate other form invariant transformed diffusion-like equations in the time domain, and touch upon conformal mappings and non-Euclidean cloaking applied to diffusion processes.
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