Multimaterial Interfaces

The interaction of acoustic or electromagnetic waves with structured materials is often complicated by the fact that the scattering geometry involves domains where multiple media meet at a single point. Examples include the design of diffraction gratings, the development of high efficiency solar cells, and non-destructive optical inspection in semiconductor manufacturing (metrology). We have developed integral equation methods for the calculation of two-dimensional scattering from both compact and periodic structures. Our approach involves the modification of a standard integral representation, the use of adaptive refinement at geometric singularities, and (most recently) the development of a fast direct solver, which permits the rapid calculation of scattering from a fixed structures at multiple angles of incidence.

  • L. Greengard and J.-Y. Lee, Stable and accurate integral equation methods for scattering problems with multiple material interfaces in two dimensions , J. Comput. Phys., 231 , 2389-2395 (2012).
  • L. Greengard, K. L. Ho, and J.-Y. Lee, A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions , J. Comput. Phys., 258 , 738-751 (2014).
  • The figure shows two copies of an infinite array of scatterers arrange on the surface of a dielectric substrate. The upper half-space, the lower half-space and the trapezoidal-shaped domains all have different dielectric constants. The electromagnetic field is singular where they meet ("triple points"), causing convergence problems for standard numerical methods.