Identifier

etd-04212010-110316

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

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 _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_ 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_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.

Date

2010

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Lipton, Robert

DOI

10.31390/gradschool_dissertations.2884

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