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Effective permittivity of finite inhomogeneous objects

机译：有限不均匀物体的有效介电常数

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摘要

A generalization of the S-parameter retrieval method for finite three-dimensional inhomogeneous objects under arbitrary illumination and observation conditions is presented. The effective permittivity of such objects may be rigorously defined as a solution of a nonlinear inverse scattering problem. We confirm analytically and observe numerically effects that were previously reported in the one-dimensional strongly inhomogeneous slabs: the nonuniqueness of the effective permittivity and its dependence on the illumination and observation conditions, and the geometry of the object. Moreover, we show that, although the S-parameter retrieval of the effective permittivity is scale free at the level of problem statement, the exact solution of this problem either does not exist or is not unique. Using the results from the spectral analysis we describe the set of values of the effective permittivity for which the scattering problem is ill-posed. Unfortunately, real nonpositive values, important for negative refraction and invisibility, belong to this set. We illustrate our conclusions using a numerical reduced-order inverse scattering algorithm specifically designed for the effective permittivity problem.
机译：给出了在任意光照和观察条件下有限三维非均匀物体S参数检索方法的一般化。可以将这些物体的有效介电常数严格定义为非线性逆散射问题的解决方案。我们通过分析确认并观察到先前在一维强烈非均匀平板中报告的数值效应：有效介电常数的非唯一性及其对照明和观察条件以及物体几何形状的依赖性。而且，我们表明，尽管有效介电常数的S参数检索在问题陈述的层次上是无标度的，但该问题的精确解决方案不存在或不是唯一的。使用频谱分析的结果，我们描述了散射问题不适当地解决的有效介电常数的值集。不幸的是，对于负折射和隐形性很重要的真实非正值属于该集合。我们使用专门针对有效介电常数问题设计的数值降阶逆散射算法来说明我们的结论。

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