The aim of this project was to develop a passive optical compensating arrangement that would allow the formation and continued stability of interference patterns over a long timescale and also to investigate optical wave scattering in thick gratings at extreme angles of scattering. A novel passive arrangement based on a Sagnac interferometer is described that produces interference patterns more stable than those produced by a conventional arrangement. An analysis of the arrangement is presented that shows it to be an order of magnitude more stable than an equivalent conventional approach. The excellent fringe stability allowed holographic gratings with small periods (~ 0.5 μm) to be written in photorefractive lithium niobate with low intensity writing fields (~mW/cm2) produced by a He:Ne laser, despite long grating fabrication times (~ 1000 s). This was possible because the optical arrangement compensated for phase shifts introduced by translational and rotational mirror motion caused by environmental perturbations. It was shown that the rapid introduction of a phase shift in one of the writing fields can change the direction of energy flow in the two-wave mixing process. It was found that the improvement in stability of the modified Sagnac arrangement over a conventional interferometer decreased when the crossing angle was increased and that the point about which the mirrors are rotated greatly affects the stability of the arrangement. For a crossing angle of 12 degrees, the modified Sagnac arrangement is more than twice as stable when the mirrors are rotated about their midpoints, rather than their endpoints. Investigations into scattering in the extremely asymmetrical scattering (EAS) geometry were undertaken by scattering light from a 532nm Nd:YAG laser off gratings written in photorefractive barium titanate and lithium niobate. Despite the difficulties posed by background noise, there was very good agreement between the observed scattered field and that predicted by a previously established theoretical model. Thus, this work represents the first experimental observation of EAS in the optical part of the spectrum.

This thesis fills in the gaps in the existing theory of wave phenomena in thick diffraction gratings at extreme angles of scattering, i.e. when the scattered wave propagates parallel or almost parallel to the grating boundaries. A consistent theory of a new type of Bragg scattering of bulk and guided optical modes in thick uniform and non-uniform, dissipative and non-dissipative, slanted periodic gratings has been developed. This type of scattering is called extremely asymmetrical scattering (EAS). One of the main distinctive features of EAS is the strong resonant increase of the scattered wave amplitude compared to the amplitude of the incident wave. Several unique combinations of strong resonances shaping a complex multi-resonant pattern of EAS in different types of gratings have been predicted and investigated theoretically and numerically. This includes the prediction of a new resonant wave effect in non-uniform gratings with varying phase – double-resonant EAS, the discovery of several sharp and strong resonances with respect to scattering angle in gratings with the scattered wave propagating almost parallel to the grating boundaries (grazing-angle scattering (GAS)) for the case of second-order scattering, and the prediction of a new type of eigenmode in gratings with second-order scattering (especially in gratings with large amplitude). In addition, several other important practical problems that may be crucial for the experimental observation and application of EAS and GAS have been solved. These are the determination of the tolerance of EAS to small grating imperfections, e.g., fluctuations of the grating amplitude, prediction of unusually high sensitivity of second-order EAS to small variations of mean structural parameters, determination of the effect of weak dissipation on EAS, etc. Physical reasons for the predicted resonances and effects are explained. In particular, the crucial role of the diffractional divergence for EAS and GAS has been revealed, especially for non-uniform gratings. Methods of analysis involve the approximate and rigorous approaches. The approximate method is based on understanding the role of the diffractional divergence in the geometry of EAS and the two-wave approximation (valid for any types of waves). The rigorous approach is based on the rigorous coupled-wave analysis (RCWA) and, in particular, the known enhanced T-matrix algorithm (by Moharam, et al.) that is numerically stable for narrow and wide gratings with arbitrary amplitude (valid only for bulk electromagnetic waves).