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Full-Text Articles in Physical Sciences and Mathematics
Bloch Spectra For High Contrast Elastic Media, Jayasinghage Ruchira Nirmali Perera
Bloch Spectra For High Contrast Elastic Media, Jayasinghage Ruchira Nirmali Perera
LSU Doctoral Dissertations
The primary goal of this dissertation is to develop analytic representation formulas and power series to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lame' system inside phononic crystals. Then we obtain convergent power series for the Bloch wave spectrum using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the inclusion array and the Dirichlet spectra of the inclusions. Sufficient conditions for the separation of spectral branches of the dispersion …
Spectral Properties Of Photonic Crystals: Bloch Waves And Band Gaps, Robert Paul Viator Jr
Spectral Properties Of Photonic Crystals: Bloch Waves And Band Gaps, Robert Paul Viator Jr
LSU Doctoral Dissertations
The author of this dissertation studies the spectral properties of high-contrast photonic crystals, i.e. periodic electromagnetic waveguides made of two materials (a connected phase and included phase) whose electromagnetic material properties are in large contrast. A spectral analysis of 2nd-order divergence-form partial differential operators (with a coupling constant k) is provided. A result of this analysis is a uniformly convergent power series representation of Bloch-wave eigenvalues in terms of the coupling constant k in the high-contrast limit k -> infinity. An explicit radius of convergence for this power series is obtained, and can be written explicitly in terms of the …