PIMS-SFU Computational Math Seminar: Kthim Imeri

Abstract: Metasurfaces are surfaces with microscopic objects on top, which can yield unexpected physical properties like, bending of light, relocating sound peaks, flat lenses, color printing, holograms and cloaking devices. In this talk we consider two metasurfaces. The first uses so-called Helmholtz resonators, these can be any cavities provided they have an opening. We use those resonators to achieve an abrupt phase change, a full absorption and a full reflection of incident sound waves. With the second metasurface we want to form a two dimensional optical device made of scattering objects of circular form, such that we can solve a linear system of equations by letting light scatter in the metasurface and collecting the scattered wave. This idea has been realized in a physics paper. The issue now is to find the scattering objects in an efficient way. To this end we consider a new method to solve the Helmholtz equation, this is a particular PDE, by inflating the scattering objects up to its full size and solving the PDE in every step using a particular asymptotic expansion. This idea originates from the explicit Euler method. We numerically show that this method is more efficient than the Boundary Element Method in its simplest form.