• Login
    View Item 
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Application of Lie theory to optical resonators: The two dimensional master equation

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    azu_td_9972121_sip1_c.pdf
    Size:
    4.437Mb
    Format:
    PDF
    Download
    Author
    Triscari, Joseph Michael
    Issue Date
    2000
    Keywords
    Mathematics.
    Physics, Optics.
    Advisor
    Wyant, James
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    The goal of this dissertation is the derivation of a differential equation that describes the evolution of an electromagnetic field in a stable cavity that has no axial symmetry (a toroidal system). The approach uses concepts from the theory of Lie groups and Lie algebras. Since the mathematics may be unfamiliar to the general reader, before the derivation for toroidal systems is executed, the differential equation for an optical system with radial symmetry will be derived using the general mathematical approach. After some of the theorems and formalisms associated with toroidal systems are presented, a description of general toroidal systems and their actions on electromagnetic fields will be presented. The action of systems on electromagnetic fields will be shown to be a linear representation of a group (locally). Having established the preliminaries, the differential equation can be derived. The desired differential equation is derived in three steps. In the first step, a set of differential operators that appear in a simplified equation are derived by recognizing them as the basis of a Lie algebra representation associated with the local linear representation on electromagnetic fields. In the second step, coefficients for the reduced problem are derived. Finally, the complete differential equation is presented. Algorithms that allow one to implement the above results will be presented. These algorithms will be used to execute a computation in a numerical example. By way of verification, it will be shown that the results of this dissertation subsume previous work in several ways including the structure of modes in stable toroidal cavities and the prediction of angular momentum.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Optical Sciences
    Degree Grantor
    University of Arizona
    Collections
    Dissertations

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.