Date of Award

1-1-2001

Thesis Type

Masters

Document Type

Thesis

Divisions

Faculty of Science

Department

Department of Physics

Institution

Universiti Malaya

Abstract

In recent studies, the generalized eikonal equation and the equation of continuity had been shown able to describe wave phenomena, which cannot be obtained by simple geometrical optics. The time dependent generalized eikonal equation, derived from the time dependent Maxwell wave equation, is able to describe dispersion and soliton effects. This method was exten4ed to include diffraction, self-trapping and self-focusing in linear and non-linear media for stationary waves. For cases that have no analytical solution, the generalized eikonal equation and the equation of continuity are solved numerically. The solutions are in good agreement with the solutions obtained from the Fresnel-Kirchhoff integral. The question remains whether the generalized eikonal equation, as a non-linear equation, can be used to show a linear effect, that is, the linear superposition of two beams. In this study, it will be shown that the generalized eikonal formalism self consistently satisfies the superposition principle and allows interference effects. First, it will be shown, theoretically, to comply with the superposition principle. Numerically, it will also be shown that the formalism satisfies the linear superposition of two beams, thus giving interference effects. For this purpose, a general numerical program was developed to solve the generalized eikonal equation and the equation of continuity. The forward time centred space (ITCS) scheme used had a stability problem that was overcome by the application of an implicit method to the scheme. The implicit method stabilizes the ITCS scheme and shows an improvement in accuracy. The results obtained by this scheme agree with those obtained by the numerically solved Fresnel integral with a relative error of the order of 10⁻⁵ at 1 meter away from the origin. By using this scheme, point by point ray tracing of wave effects in the diffraction and interference of two and more beams were carried out. These results closely match those calculated by the Fresnel integral. The generalized eikonal formalism has thus been verified both theoretically and numerically to satisfy the superposition principle enabling the interference of two or more light waves to be described.

Initial

snms

Additional Information

Dissertation (M.A) -- Faculty of Science, Universiti Malaya, 2001.

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