Title page for ETD etd-07062016-130759


Type of Document Dissertation
Author Abeynanda, Gayan Shanaka
Author's Email Address gabeyn1@lsu.edu
URN etd-07062016-130759
Title Dynamic Resonant Scattering of Near-Monochromatic Fields
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Shipman, Stephen Committee Chair
Davidson, Mark Committee Member
Delzell, Charles Committee Member
Lipton, Robert Committee Member
Litherland, Richard Committee Member
Webster, Elizabeth Dean's Representative
Keywords
  • Resonant Pathway
  • Resonant Lamb Model
  • Resonant transmission
  • Dynamic Resonance
  • Near-monochromatic
  • Dynamic Resonant Scattering
  • Coupled Mode Approximation
  • Asymptotic Nature of Resonance
Date of Defense 2016-06-29
Availability unrestricted
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.
Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
  Abeynanda_Diss.pdf 747.90 Kb 00:03:27 00:01:46 00:01:33 00:00:46 00:00:03

Browse All Available ETDs by ( Author | Department )

If you have questions or technical problems, please Contact LSU-ETD Support.