3d Finite-difference Frequency-domainmethod for Plasmonics and Nanophotonics a Dissertation Submitted to the Department of Electrical Engineering and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

The finite-difference frequency-domain (FDFD) method is a conceptually simple method to solve time-dependent dišerential equations for steady-state solutions. In solving Maxwell’s equations in three-dimensional (3D) space, however, the FDFD method has not been a popular method due to the slow convergence of iterative methods of solving a large system of linear equations Ax = b constructed by the FDFD method. In this dissertation, we show that the convergence speed can be greatly accelerated for plasmonic and nanophotonic systems by carefully modifying the properties of A. First, we make the matrix A signicantly better-conditioned by using the stretched-coordinate perfectly matched layer (SC-PML) rather than the more commonly used uniaxial PML (UPML) as an absorbing boundary. Second, we eliminate the high multiplicity of near-zero eigenvalues of A by utilizing the continuity equation. By combining these two techniques, we achieve 300-fold acceleration in the convergence of iterative methods for an example 3D plasmonic system. We also demonstrate successful application of the acceleration techniques to a real-world engineering problem of designing novel integrated optical circuit components, namely broadband sharp 90-degree bends and T-splitters, in plasmonic coaxial waveguides.