Identifier

etd-07062016-130759

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

Certain universal features of photonic resonant scattering systems are encapsulated in a simple model which is a resonant modification of the famous Lamb Model for free vibrations of a nucleus in an extended medium. We analyze this "resonant Lamb model" to garner information on dynamic resonant scattering of near-monochromatic fields when an extended system is weakly coupled to a resonator. The transmitted field in a resonant scattering process consists of two distinct pathways: an initial pulse (direct transmission) and a tail of slow decay (resonant transmission). The resonant Lamb model incorporates a two-part scatterer attached to an infinite string with a continuous spectrum. The non-resonant part of the scatterer is associated with direct scattering; and the resonant part is associated with field amplification and delayed transmission. We provide a mathematical characterization of the "direct transmission" and the "resonant transmission" by analyzing the pole structure of the resolvent operator of the system. The coupling constant (gamma), the proximity of resonance to the central frequency of incidence (eta) and the spectral width (sigma) of the incident pulse are three distinguished parameters that are small and affect resonance in the high-Q and near-monochromatic regime. The main objectives of this work are to analyze resonant amplification and transmission anomalies in the simultaneous High-Q and near-monochromatic regime as they depend on the three aforementioned parameters and to quantify the accuracy of coupled mode theory in that same regime.

Date

2016

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Shipman, Stephen

DOI

10.31390/gradschool_dissertations.2672

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