The numerical solution of frequency-domain acoustic and electromagnetic periodic scattering problems

Larry (Yuxiang) Liu

Physics Department, Dartmouth College

The control of waves using periodic structures is crucial for modern optical, electromagnetic and acoustic devices such as diffraction gratings, filters, photonic crystals and meta-materials, solar cells, and absorbers. We present a high-order accurate boundary-based numerical solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic lattice of objects. We focus on the case of axisymmetric objects, and handle both the acoustic and electromagnetic cases. We combine the method of fundamental solutions with a new periodizing scheme, and with various fast algorithms such as the fast multiple method, and so-called "skeletonization". Our scheme has exponential convergence property, avoids singular quadratures, periodic Green's functions, and lattice sums, and its convergence rate is unaffected by resonances within obstacles. We also discuss new methods for handling corner singularities.

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