Doctoral Dissertations

Keywords and Phrases

Correlated disorder; Random disorder; Wave transport


"Passive quasi-one-dimensional random media exhibit one of the three regimes of transport - ballistic, diffusive, or Anderson localization - depending on system size. The ballistic and diffusion approximations assumes particle transport, whereas Anderson Localization occurs when wave self-interference effects are dominant. When the system contains absorption or gain, then how the regimes can be characterized becomes unclear. By investigating theoretically and numerically the ratio of transmission to energy in a random medium in one dimension, we show this parameter can be used to characterize localization in random media with gain. Non-conservative media implies a second dimension for the transport parameter space, namely gain/absorption. By studying the relations between the transport mean free path, the localization length, and the gain or absorption lengths, we enumerate fifteen regimes of wave propagation through quasi-one-dimensional nonconservative random media. Next a criterion characterizing the transition from diffusion to Anderson localization is developed for random media with gain or absorption. The position-dependent diffusion coefficient, which is closely related to the ratio of transmission to energy stored in the system, is investigated using numerical models. In contrast to random structures, deterministic aperiodic structures (DAS) offer predictable and reproducible transport behaviors while exhibiting a variety of unusual transport properties not found in either ordered or random media. By manipulating structural correlations one may design and fabricate artificial photonic nanomaterials with prescribed transport properties. The Thue-Morse structure is a prime example of deterministic aperiodic systems with singular-continuous spatial Fourier spectra. The non-periodic nature of the system makes it notoriously difficult to characterize theoretically especially in dimensions higher than one. The possibility of mapping the two-dimensional aperiodic Thue-Morse pattern of micro-cavities onto a square lattice is demonstrated, making it amenable to the tight-binding description"--Abstract, page iv.


Yamilov, Alexey

Committee Member(s)

Story, J. Greg
Vojta, Thomas
Cao, Xu
Parris, Paul Ernest, 1954-



Degree Name

Ph. D. in Physics


National Science Foundation (U.S.)
United States. Veterans Administration


Missouri University of Science and Technology

Publication Date

Spring 2012

Journal article titles appearing in thesis/dissertation

  • Relation between transmission and energy stored in random media with gain
  • Classification of regimes of wave transport in quasi one-dimensional non-conservative random media
  • Near-field effects in wave transport through in disordered waveguides
  • Anderson localization as position-dependent diffusion in disordered waveguides
  • Mapping algorithm from the two-dimensional aperiodic Thue-Morse structure to the square lattice
  • 2D Thue-Morse array of optical cavities: tight-binding model


xiv, 158 pages

Note about bibliography

Includes bibliographical references (pages 144-157).


© 2012 Benjamin Henry Payne, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings


Thesis Number

T 10009

Print OCLC #


Electronic OCLC #


Included in

Physics Commons