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Imaging and Sensing (Waves) Seminar

September 27, 2022 - 3:00pm

Room: ACS 362B

Speaker: Elsie Cortes

Title: Boundary Integral Equation Methods for Optical Cloaking Models

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

[1] Kress, R. Boundary integral equations in time-harmonic acoustic scattering. 1991. Mathematical and Computer Modelling.

[2] Sun Q., Klaseboer E., Khoo B. C., and Chan D. Y. C. 2015. Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.