This dissertation includes three separate studies of related waveguide grating phenomena. These studies deal with a numerical improvement of the integral method of diffraction grating theory, the theoretical analysis of waveguide gratings, and fabrication techniques for photoresist grating masks. The first topic addresses the acceleration of the convergence of the integral kernels. To improve the performance of the integral method for calculating diffraction grating efficiencies, the convergence of the integral kernels is studied. A nonlinear sequence transformation, Levin's u-transformation, is successfully applied to accelerate the convergence of the integral kernels. The computer execution time saving is significant. The application details and many numerical examples are given. The second subject is the ray optics theory of waveguide grating analysis. To establish a linkage between the analysis of diffraction gratings and the analysis of waveguide gratings, a new rigorous ray optics theory is developed. It takes into account phase changes on diffraction, multiple diffraction processes, depletion of the incident guided wave, and lateral shifts. A general characteristic equation that determines the waveguide grating attenuation (coupling) coefficient is derived. The symmetry properties of grating diffraction are applied to waveguide grating analysis for the first time. Lateral shifts of optical rays at a periodically corrugated interface similar to the Goos-Haenchen shift at a planar interface are suggested. The third subject is the in situ control of the development of photoresist grating masks. The existing method for monitoring and modeling photoresist grating development are modified and extended to monitoring and modeling photoresist grating mask development. Experimental examples, detailed theoretical considerations, and computer simulations are presented.

The properties of photo-induced gratings in germania doped glass fibers were studied. Permanent phase gratings in a fiber core were fabricated by the mixing of two contra propagating waves. Experiments are described and results are presented which show that the strength of a photoinduced grating is strongly dependent on the writing power as well as the laser writing wavelength. A rigorous development of linear coupled mode theory for the contra propagation geometry is given and used to model the experimentally observed grating responses as a function of fine tuning frequency of probing light. Measurements have been done of the amplitude and phase response of the grating structure and compared with theoretical models of uniform and chirped gratings. The theoretically predicted negative group velocity dispersion in fiber grating was observed interferometrically and described in detail. The nonlinear coupled mode theory has been fully implemented in a computer program and some numerical results are given in the second part of this thesis. The dynamics of a pulse propagating in the fiber grating is simulated and the results show its dependence on pulse energy, frequency detuning, and the type of grating geometry. A limitation is found in the dispersion property of a constant amplitude fiber grating so that the pulse compression ratio and the width of a compressible pulse is strictly limited to ≅250 picoseconds.

The problem of recovering a wavefront or surface deviation from a fringe pattern image is investigated. The data sets generated in sampling a fringe pattern are considered in the frequency domain and errors that arise in analyzing the pattern are given an aliasing interpretation. Uniform sampling is shown to be superior to other sampling schemes. A variety of techniques for locating fringe centers are reviewed and three synchronous convolution methods are demonstrated that do not require the location of fringe centers. For the latter, direct phase measurements are obtained from fringe pattern photographs over a uniform grid with an accuracy comparable to temporal heterodyne interferometry. Two microprocessor-based video systems are described in which the traditional and synchronous convolution methods were implemented.

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