DETERMINING THE SHAPE OF ARBITRARY-SHAPED NANOELEMENTS FROM EM WAVE SCATTERING

Abstract

Precise determination of nanoscale structures is a key issue in nanotechnology and materials science. Conventional approaches to nano-element characterization usually rely on simplifying assumptions and idealized geometries, whose practical applicability is seriously restricted when dealing with real, arbitrarily shaped nano-objects. In this project, the inverse, generally ill-posed, problem of shape determination of arbitrary nano-elements by scattered electromagnetic waves is considered. A computationally efficient framework was developed using scattering data of appropriate resolution, which will enable the identification and accurate reconstruction of nano-element shapes. We begin by formulating the relevant scattering problem in an isogeometric-analysis-based boundary element method setting and subsequently employ hybrid optimization techniques to solve the inverse scattering problem. Regularization methods have been used to alleviate the inherent ill-posedness, while global and local optimization algorithms have been incorporated for appropriately addressing the shape reconstruction problem in different stages. The numerical approach is verified against both simple and complex shapes with known and unknown geometrical characteristics, which demonstrates the capacity of the implemented approach to accurately identify nanoscale geometries in a widely range of settings. The achieved results show that the developed method facilitates the identification and reconstruction of simple or complex shapes remarkably without sacrificing accuracy or computational efficiency. It is also demonstrated that the developed methodology holds the potential to be extended to handle different kinds of nanoscale elements as well as significantly larger structures. This fact permits its extension to object/signal identification for military applications, non-intrusive inspection, remote sensing, and many more. Such examples of shape identification with a limited range of the scattering signal are included in this work to demonstrate the applicability of the developed approach to inverse problems found in real-life applications.