18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005
Author(s)Johnson, Steven G., 1973-
Topics in Applied Mathematics: Mathematical Methods in Nanophotonics
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Topics vary from year to year. Topic for Fall: Eigenvalues of random matrices. How many are real? Why are the spacings so important? Subject covers the mathematics and applications in physics, engineering, computation, and computer science. From the course home page: Course Description This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.
linear algebra, eigensystems for Maxwell's equations, symmetry groups, representation theory, Bloch's theorem, numerical eigensolver methods, time and frequency-domain computation, perturbation theory, coupled-mode theories, waveguide theory, adiabatic transitions, Optical phenomena, photonic crystals, band gaps, anomalous diffraction, mechanisms for optical confinement, optical fibers, integrated optical devices