A Fast 3D Full-Wave Solver for Nanophotonics
by
Lei Zhang
B.Eng., Electrical Engineering University of Science and Technology of China (2003) M.Eng., Electrical Engineering National University of Singapore (2005) Submitted to the School of Engineering in partial fulllment of the requirements for the degree of Master of Science in Computation for Design and Optimization at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2007 c Massachusetts Institute of Technology 2007. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School of Engineering May 11, 2007 Certied by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jacob K. White Professor of Electrical Engineering Thesis Supervisor Accepted by. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jaime Peraire Professor of Aeronautics and Astronautics Co-Director, Computation for Design and Optimization Program
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A Fast 3D Full-Wave Solver for Nanophotonics by Lei Zhang
Submitted to the School of Engineering on May 11, 2007, in partial fulllment of the requirements for the degree of Master of Science in Computation for Design and Optimization
Abstract
Conventional fast integral equation solvers seem to be ideal approaches for simulating 3D nanophotonic devices, as these devices are considered to be open structures, generating elds in both an interior channel and in the innite exterior domain. However, many devices of interest, such as optical ring resonator lters or waveguides, have channels that can not be terminated without generating numerical reections. Therefore, designing absorbers for these channels is a new problem for integral equation methods, as integral equation methods were initially developed for problems with nite surfaces. In this thesis we present a technique to eliminate reections, making the channel volume conductive outside the domain of interest. The surface integral equation (SIE) method is employed to take advantage of the piecewise homogeneous medium. The Poggio-Miller-Chang-Harrington-Wu (PMCHW) formulation is formed and the boundary element method is employed to construct and solve a linear system. Moreover, the block Toeplitz matrix property and using FFT helps reduce memory requirement, and accelerate the circulant matrix vector product. Numerical experiments are presented to demonstrate that this method can effectively reduce reections to 1%, and is easily incorporated in an fast integral equation solver. Thesis Supervisor: Jacob K. White Title: Professor of Electrical Engineering

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