Type of Document Dissertation Author Fortes, Santiago Prado Parentes Author's Email Address santiago@math.lsu.edu URN etd-04212010-110316 Title Power Series Expansions for Waves in High-Contrast Plasmonic Crystals Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title Lipton, Robert Committee Chair Shipman, Stephen Committee Co-Chair Wolenski, Peter Committee Member Litherland, Richard Committee Member Perlis, Robert Committee Member Sterling, Thomas Dean's Representative Keywords
- Bloch Waves
- Periodic Media
- Power Series Expansions
- Plasmonic Crystal
Date of Defense 2010-03-12 Availability unrestricted Abstract In this thesis, a method is developed for obtaining convergent power series expansions for dispersion relations in two-dimensional periodic media with frequency dependent constitutive relations. The method is based on high-contrast expansions in the parameter = 2d=, where d is the period of the crystal cell and is thewavelength. The radii of convergence obtained are not too small, on the order of 10��2. That the method applies to frequency dependent media is an important fact, since the majority of the methods available in the literature are restricted to frequency independent constitutive relations. The convergent series for the disper-
sion relation is used to defi ne an eff ective property valid for finite cell structure
sizes, as opposed to a quasi-static property, valid only in the limit ! 0.
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