基于逆散射技术的光子带隙设计

D. Pommet, L. Malley, M. Fiddy
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摘要

相反的问题对于设备和应用程序开发尤为重要。对于非周期介质,可以进行近似,从而求得散射介电常数分布的估计。在过去的15年里,我们自己的工作[1,2,3]已经从试图解释这些近似中最严格但计算最简单的近似,线性化的first Born和Rytov近似,转移到可以应用于强散射介质以及非线性(例如χ3)结构的技术发展。我们还将这些方法应用于真实的实验数据和模拟案例,因为这些工作在医学和地球物理成像以及光学元件设计等不同领域具有广泛的用途。从这些研究中可以更清楚地了解如何将微分倒谱法(见Morris等人在本卷和[4]中的论文)和畸变波方法相结合,以合成既具有强散射又具有规定的光学可控散射模式的结构。差分倒谱滤波技术对远场散射数据的傅里叶反演恢复的函数进行处理,认为它代表了散射体积内介电常数分布和总场的乘积。这种滤波方法原则上可以应用于任意高介电常数的散射结构。
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Photonic band gap design based on inverse scattering techniques
The inverse problem is particularly important for device and application development. For non-periodic media, approximations can be made which allow estimates of the scattering permittivity distribution to be found. Our own work over the last 15 years [1,2,3] has moved from trying to interpret the most restrictive yet computationally simple of these approximations, the linearizing first Born and Rytov approximations, to the development of techniques which can be applied to both strongly scattering media as well as nonlinear (e.g. χ3) structures. We have also applied these methods to real experimental data as well as simulated cases, as such work has wide ranging uses in fields as diverse as medical and geophyiscal imaging, as well as the design of optical components. Emerging from these studies is a clearer understanding as to how the differential cepstral method (see paper by Morris et al in this volume and [4]) and distorted wave methods can be integrated in order to synthesize structures which are both strongly scattering and which have prescribed optically controllable scattering patterns. The differential cepstral filtering technique processes the function recovered by Fourier inversion of far-field scattering data, recognizing that it represents the product of the permittivity distribution and the total field within the scattering volume. This filtering method can be applied to scattering structures of arbitrarily high permittivity, in principle.
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