Search for: All records

Optical cloaking refers to making an object invisible by preventing the light scattering in some directions as it hits the object. There is interest in cloaking devices in radar and other applications. Developing a model to accurately capture cloaking comes with numerical challenges, however. We must determine how light propagates through a medium composed by multiple, thin layers of materials with different electromagnetic properties. In this paper we consider a multi-layered scalar transmission problem in 2D and use boundary integral equation methods to compute the field. The Kress product quadrature rule is used to approximate singular integrals evaluated on boundaries, the Boundary Regularized Integral Equation Formulation (BRIEF) method [1] with Periodic Trapezoid Rule (PTR) is employed to treat nearly singular ones (off boundaries) appearing in the representation formula. Numerical results illustrate the efficiency of this approach, which may be applied to N arbitrary smooth layers. 

The study of scattering by a high aspect ratio particle has important applications in sensing and plasmonic imaging. To illustrate the effect of particle’s narrowness (that can be related to parity properties) and the need for adapted methods (in the context of boundary integral methods), we consider the scattering by a penetrable, high aspect ratio ellipse. This problem highlights the main challenge and provides valuable insights to tackle general high aspect ratio particles. We find that boundary integral operators are nearly singular due to the collapsing geometry to a line segment. We show that these nearly singular behaviors lead to qualitatively different asymptotic behaviors for solutions with different parities. Without explicitly taking this into account, computed solutions incur large errors. We introduce the Quadrature by Parity Asymptotic eXpansions (QPAX) that effectively and efficiently addresses these issues. We demonstrate the effectiveness of QPAX through several numerical examples. 

We consider acoustic binding of particles resulting from radiation forces created through multiple scattering. This problem has potential for developing methods for assembling novel meta-materials. A key consideration in acoustic binding is when two or more particles are closely situated to one another and form a cluster. For that case, the near-field scattering by the particles becomes important. Here, we study multiple scattering by two closely-situated sound-hard spheres. Using boundary integral equation (BIE) methods, we find that a close evaluation problem arises leading to a nearly singular system of BIEs governing the surface fields. An asymptotic analysis of the problem reveals that this nearly singular behavior will lead to large error in the numerical solution unless it is explicitly addressed. 

When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified representations of the problem’s solution. Similar to Gauss’s law used to modify Laplace’s double-layer potential, we use modified representations of Laplace’s single-layer potential and Helmholtz layer potentials that avoid the close evaluation problem. Some techniques have been developed in the context of the representation formula or using interpolation techniques. We provide alternative modified representations of the layer potentials directly (or when only one density is at stake). Several numerical examples illustrate the efficiency of the technique in two and three dimensions. 

The concept of “cloaking” an object is a very attractive one, especially in the visible (VIS) and near infra-red (NIR) regions of the electromagnetic spectrum, as that would reduce the visibility of an object to the eye. One possible route to achieving this goal is by leveraging the plasmonic property of metallic nanoparticles (NPs). We model and simulate light in the VIS and NIR scattered by a core of a homogeneous medium, covered by plasmonic cloak that is a spherical shell composed of gold nanoparticles (AuNPs). To consider realistic, scalable, and robust plasmonic cloaks that are comparable, or larger, in size to the wavelength, we introduce a multiscale simulation platform. This model uses the multiple scattering theory of Foldy and Lax to model interactions of light with AuNPs combined with the method of fundamental solutions to model interactions with the core. Numerical results of our simulations for the scattering cross-sections of core-shell composite indicate significant scattering suppression of up to 50% over a substantial portion of the desired spectral range (400 - 600 nm) for cores as large as 900 nm in diameter by a suitable combination of AuNP sizes and filling fractions of AuNPs in the shell.