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.
| Identifer | oai:union.ndltd.org:LSU/oai:etd.lsu.edu:etd-07062016-130759 |
| Date | 02 August 2016 |
| Creators | Abeynanda, Gayan Shanaka |
| Contributors | Delzell, Charles, Litherland, Richard, Davidson, Mark, Lipton, Robert, Shipman, Stephen, Webster, Elizabeth |
| Publisher | LSU |
| Source Sets | Louisiana State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lsu.edu/docs/available/etd-07062016-130759/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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