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Steven G. Johnson. Oskooi, Ardavan F Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program 2008-12-11T16:56:17Z 2008-12-11T16:56:17Z 2008 2008 http://hdl.handle.net/1721.1/43738 261492471 Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 41-45). Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness. by Ardavan F. Oskooi. S.M. 45 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Computation for Design and Optimization Program. An investigation of the perfectly matched layer for inhomogeneous media Investigation of the PML for inhomogeneous media Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="941b6b49-75cb-427f-8973-0523d2a7a536"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>An investigation of the perfectly matched layer for inhomogeneous media</Title> <Subtitle>Investigation of the PML for inhomogeneous media</Subtitle> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2008</PublicationDate> <Authors> <Author> <DisplayName>Oskooi, Ardavan F</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Computation for Design and Optimization Program.</Keyword> <Abstract>Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>