Titre : Carlos Pérez Arancibia (Pontificia Universidad Católica de Chile). Toward accurate and efficient boundary integral equation methods for metasurface design
Contact : Maryna Kachanovska
Date : 15/04/2021
Lieu : 14h, visioconférence
Abstract. We consider a class of electromagnetic scattering problems arising in the design of optical metasurfaces. Metasurfaces are planar metamaterial slabs of subwavelength thickness consisting of a pattern made up of a large number of subwavelength optical elements(typically, nanorods or nanopillars), that are engineered to manipulate the direction, amplitude, phase, and polarization of light. The massive size and multiple-scale complexity of the computational domains involved in these problems pose major challenges to general-purpose PDE solvers, hence opening up exciting research opportunities for the development of efficient physics-informed numerical approximations and/or for the improvement of specializedMaxwell/Helmholtz solvers. In the first part of the talk, we present a PDE-constrained adjoint-based optimization framework for metasurface inverse design that relies on a fast but low-order scattering approximation—known as a thelocally-periodic approximation(LPA)—which is used to avoid fully solving the governing Maxwell equations at each step of the iterative optimization solver. Examples of practical interest demonstrate both the capabilities and limitations of the LPA. Indeed, examples of metasurfaces are shown in which the LPA fails to provide accurate enough solutions and where difficult-to-compute higher-order corrections are needed to properly account for the relevant physics. These examples reveal, in part, that despite the success of the LPA in some settings, provably accurate full-wave solutions are still very valuable either for validation of optimized designs, for the training of surrogate models, or for optimization(provided an appropriate balance between accuracy and speed is considered).In the second part of the talk, we present an efficient high-order boundary integral equation(BIE) method for the full-wave numerical solution of metasurface scattering problems. We first frame them as classical locally perturbed two-layer media scattering problems and we justify the use of BIE methods for their solution (over finite difference and finite element methods). Emphasis is given on the salient limitations of standard layered media BIE methods based on Sommerfeld integrals that (arguably) render metasurface scattering problems intractable by them. We then introduce a fast, flexible, and easy-to-implement BIE method based on the windowed Green function (WGF) method which does not involve the evaluation of computationally expensive Sommerfeld integrals and exhibits high-order (super-algebraic)convergence as the size of the truncated surface increases. A variety of examples demonstrate the applicability, accuracy, and efficiency (as compared to the Sommerfeld-integral approach)of the proposed methodology based on both spectrally accurate Nystrom and boundary element methods. Promising results are shown, where, to the best of the author’s knowledge, a full-wave 3D BIE solver has for the first time been used to compute the electromagnetic scattering off of a small-size light-focusing all-dielectric metasurface. This work has been done in collaboration with Rapha ̈el Pestourie (MIT), Steven G. Johnson(MIT), Oscar P. Bruno (Caltech), and Rodrigo Arrieta (PUC Chile).