Title page for ETD etd-04212010-110316


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 the

wavelength. 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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