Date of Award
Doctor of Philosophy
Dr. Arthur R. McGum
Dr. Clement A. Burns
Dr. Lisa Paulius
Dr. Sung Chung
We have studied four examples of periodicity and disorder in nature and the phenomena associated with them.
In the first chapter of the dissertation we present an introduction to this work.
In the second chapter, the photonic band structures of two types of zinc blend structures are computed using the plane wave expansion method. Both structures are formed from an array of dielectric spheres in a vacuum background. In a first type zinc blend structure the spheres have the same size but different dielectric constants. In a second type of structure we keep the dielectric contrast of the spheres the same but change their radii. The lowest frequency band gaps are studied as a function of the dielectric constant ratio in the first structure and as a function of the radii ratio in the second type of structure.
In the third chapter a numerical algorithm is used to generate two-dimensional randomly rough surfaces. The results are used to compute the probability density that the nearest maximum (minimum) to a given maximum (minimum) is at a certain distance. Results are presented for random surfaces defined by surface height correlation function specified by Gaussian, Lorentzian and a novel type of statistics. Results are also presented for a recently proposed one-dimensional random surface.
In the fourth chapter we study the effects of disorder on magnetic superiattices. We have presented two methods to calculate the dispersion relation for electromagnetic waves propagating through stochastically modulated superiattices. The first method is self-consistent method and the second one is based on the Green’s functions approach.
In the fifth chapter a new Reverse Monte Carlo method for the determination of the surface profile statistics from differential reflection data for scattering of electromagnetic radiation from surface is presented. The method is used to extract the power spectrum of the surface profile from scattering data recently measured and from data generated by computer. Excellent agreement between the original and retrieved data was found.
In the sixth chapter we present the conclusions of this dissertation.
Simeonov, Simeon D., "Periodicity and Disorder" (1999). Dissertations. 1534.