This thesis descibes a theoretical study of nonlinear self-focusing as applied to the metrology of the nonlinear optical parameters of a medium. It also studies the phe- nomenon of optical power limiting which utilizes self-focusing e ects. As an analytical tool, a mode decomposition method which uses an orthogonal and complete set of Gaussian-Laguerre modes as a basis set is used to treat these problems. Nonlinear media both in the thin and thick limits are investigated. For thin media, a closed form expression is derived which describes the optical eld of an initally Gaussian beam that is perturbed by a thin nonlinear material which exhibits nonlinear absorption as well as nonlinear refraction. This result is valid for any regime of nonlinearity in the thin medium approximation. Thick media are treated using a numerical extension of the Gaussian-Laguerre Mode Decomposition technique. Spatial scanning techniques such as the Z-scan that rely on self-focusing e ects and that are used to measure the nonlinear optical parameters of a material are studied in detail. Optical limiting in both thick and thin media is also investigated.

This thesis descibes a theoretical study of nonlinear self-focusing as applied to the metrology of the nonlinear optical parameters of a medium. It also studies the phe- nomenon of optical power limiting which utilizes self-focusing e ects. As an analytical tool, a mode decomposition method which uses an orthogonal and complete set of Gaussian-Laguerre modes as a basis set is used to treat these problems. Nonlinear media both in the thin and thick limits are investigated. For thin media, a closed form expression is derived which describes the optical eld of an initally Gaussian beam that is perturbed by a thin nonlinear material which exhibits nonlinear absorption as well as nonlinear refraction. This result is valid for any regime of nonlinearity in the thin medium approximation. Thick media are treated using a numerical extension of the Gaussian-Laguerre Mode Decomposition technique. Spatial scanning techniques such as the Z-scan that rely on self-focusing e ects and that are used to measure the nonlinear optical parameters of a material are studied in detail. Optical limiting in both thick and thin media is also investigated.