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Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry
Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry
LSU Doctoral Dissertations
In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical …
A New Method In Distribution Theory With A Non-Smooth Framework, Yunyun Yang
A New Method In Distribution Theory With A Non-Smooth Framework, Yunyun Yang
LSU Doctoral Dissertations
In this work, we present a complete treatment of the theory of thick distributions and its asymptotic expansion. We also present several applications of thick distributions in mathematical physics, function spaces, and measure theory. We also discuss regularization using different surfaces. In the last chapter we present some recent applications of distributions in clarifying the moment terms in the heat kernel expansion, and in explaining the relation between the heat kernel expansion and the cylinder kernel expansion.
A Discrete Model Of Guided Modes And Anomalous Scattering In Periodic Structures, Natalia Grigoryevna Ptitsyna
A Discrete Model Of Guided Modes And Anomalous Scattering In Periodic Structures, Natalia Grigoryevna Ptitsyna
LSU Doctoral Dissertations
We study a discrete prototype of anomalous scattering associated with the interaction of guided modes of a periodic scatterer and plane waves incident upon the scatterer. The transmission anomalies arise because of the non-robustness of a guided mode, a mode that exists only at a specific frequency and wave number pair. The simplicity of the discrete prototype allows one to make certain explicit calculations and proofs, and to examine details of important resonant phenomena of the open wave guides. The main results are (1) a formula for transmission anomalies near a non-robust guided mode with rigorous error estimates that extends …