수학과

제목: Integral equation methods for simulating waves in layered media

초록:

Waves in layered media have diverse applications in Optics and Electromagnetics. Numerical simulation plays an important role in the design and optimization of modern devices like diffraction grating and solar cells. In this talk, an integral equation method for the Helmholtz equation for simulating wave scattering from layered media will be discussed. In the case of periodically patterned layered media in both two and three dimensions, the solution of the Helmholtz equation is expressed as a sum of near and distant fields using the free-space Green’s function rather than quasi-periodic Green’s function. Subsequently, by enforcing  boundary conditions on this solution, we derive a set of integral equations for the N layers. The resulting linear system can be reduced to a block-tridiagonal matrix using the Schur complement and it can be solved efficiently with linear computational complexity in a number of layers. This approach overcomes slow convergence and Wood anomaly issues associated with the quasi-periodic Green’s function, making it capable of handling a large number of layers. The effectiveness of this method is demonstrated through numerical examples.