Doctor of Philosophy (PhD)
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 _x0011_ = 2_x0019_d=_x0015_, where d is the period of the crystal cell and _x0015_ is the wavelength. The radii of convergence obtained are not too small, on the order of _x0011_ _x0019_ 102. 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_x000C_ne an eff_x000B_ective property valid for _x000C_finite cell structure sizes, as opposed to a quasi-static property, valid only in the limit _x0011_ ! 0.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Fortes, Santiago Prado Parentes, "Power series expansions for waves in high-contrast plasmonic crystals" (2010). LSU Doctoral Dissertations. 2884.