Efficient Computational Method for Multiply Layered Three-Dimensional Photonic Structures

Numerical methods play an important role in the design and optimization of photonicstructures and devices. General numerical methods for solving the Maxwell's equationsare applicable to most photonics problems, but special methods developed for a class ofstructures are often much more efficient. Many photonic devices are multiply layered, inthe sense that the structure consists of a few parts where each part is a layeredstructure (i.e., the material properties depend only on one spatial variable z). In thisproject, we develop an efficient numerical method for three-dimensional (3D) multiplylayered structures by coupling one-dimensional (1D) mode expansions and boundaryintegral equations for two-dimensional (2D) Helmholtz equations. Our methodeffectively reduces the original 3D problems to 2D problems. Compared with the classicalmode matching method (also called eigenmode expansion method or modal method), ourmethod is much more efficient, since it avoids the expensive step of solving 2Deigenvalue problems. The method developed in this project will be used to analyzepractical 3D photonic structures.