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3D finite-difference frequency-domain method for plasmonics and nanophotonics [electronic resource]

The finite-difference frequency-domain (FDFD) method is a conceptually simple method to solve time-dependent differential 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 significantly 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.

Sp14-EE-256-01 : Numerical Electromagnetics. 2014 Spring

Principles and applications of numerical techniques for solving practical electromagnetics problems. Finite-difference time-domain (FDTD) method and finite-difference frequency-domain (FDFD) method for solving 2D and 3D Maxwell?s equations. Numerical analysis of stability, dispersion, and dissipation. Perfectly matched layer (PML) absorbing boundaries. Total-field/scattered-field (TF/SF) method. Interaction of electromagnetic waves with dispersive and anisotropic media. Homework assignments require programming and the use of MATLAB or other equivalent tools. Prerequisite: 242 or equivalent.

Neurological disorders and imaging physics. Volume 4, Application to attention deficit hyperactivity disorder

Attention deficit hyperactivity disorder (ADHD) is a common neurological disorder that impacts focus, self-control, and other skills important in daily life. Caused by differences in brain anatomy and wiring, it is known to be one of the most common conditions in childhood. As ADHD plays a serious role in how children function in school and in their everyday life, having a deep understanding of this neurological condition is critical. This book explores recent advances in neuroimaging techniques, methods, applications and machine learning algorithms

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