Abstract There have been many studies on model characteristics of optical fibers since 1970. In the past twenty years we have seen changes in the index profiles and operating parameters (such as the carrier wavelength and fiber dispersion) of the fibers. We shall expect some change in the future as well. In this thesis we propose a 2nd-order coupled transverse magnetic field ordinary differential equations and associated boundary conditions for analyzing fiber modes with complex index profiles. Using finite-difference approximation, we convert the equations into matrix eigenvalue-eigenvector equations. These are then numerical solved (suing many commercial numerical softwares such as Matlab) to obtain propagation constants and field distribution inside the fibers. We shall show that our method do not require the use of cylindrical functions nor will the computation increase due to the increase of complexity in the index profile. In addition to finite-difference approximation, we may expand the model solutions in terms of elementary functions. In this thesis we computed many commercially available optical fibers such as 8/125, 9/125 step index fibers and 50/125, 62.5/125 graded index fibers. We compared our results against exact solution (the step index case) and found that we have converging solutions as we reduce the fiber sampling grid size £Gx. The difference in propagation constant is less than 0.1% when £Gx is < £f/6 .

Thesis (doctoral)--Grossherzoglich-Hessische Ludwigs-Universität zu Giessen, 1917. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Michigan, 1931. / Cover title. Thesis note in foot-note on p. [102]. "Reprinted from the Annals of mathematical statistics, May, 1931."

Thesis--Syracuse University, 1918. / "Presented before the American mathematical society, Oct. 28, 1916. Sept. 5, 1917, and Sept. 5, 1918"--P. [3], foot-note. "This investigation is a continuation of published work of Professor E.D. Roe, Jr."--P. [3]. "The tables of coefficients which belong with this paper will be published in atlas form"--P. 48, foot-note.

Thesis (Ph. D.)--University of Pennsylvania, 1914.

Thesis (Ph. D.)--University of Michigan, 1931. / Cover title. Thesis note in foot-note on p. [102]. "Reprinted from the Annals of mathematical statistics, May, 1931."

Thesis--Syracuse University, 1918. / "Presented before the American mathematical society, Oct. 28, 1916. Sept. 5, 1917, and Sept. 5, 1918"--P. [3], foot-note. "This investigation is a continuation of published work of Professor E.D. Roe, Jr."--P. [3]. "The tables of coefficients which belong with this paper will be published in atlas form"--P. 48, foot-note.

Thesis (Ph. D.)--University of Pennsylvania, 1914.

Thesis--Catholic University of America, 1951. / Includes bibliographical references.

Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald polynomials interpolate between the symmetric and nonsymmetric types. We begin developing theory for these partially-symmetric polynomials, and prove results including their stability, an integral form, and a Pieri-like formula for their multiplication with certain elementary symmetric functions. / Doctor of Philosophy / There are two well-understood types of polynomials known as the nonsymmetric Macdonald polynomials and symmetric Macdonald polynomials. We define a new form of Macdonald polynomials, which we call partially-symmetric, that are somewhere between the symmetric and nonsymmetric versions. We examine properties of these new partially-symmetric polynomials, including what happens when adding additional symmetric variables, how to multiply them by a constant to clear out denominators in their coefficients, and what happens when multiplying them by another symmetric polynomial.