Design and applications of volume holographic optical elements

Volume gratings were studied both theoretically and experimentally in order to design and analyze practical volume holographic optical elements. The diffraction of finite (Gaussian) beams by transmission gratings is investigated. A closed form solution for the off-Bragg profiles is obtained, and the distortion in the resulting profiles is analyzed. Criteria for when the finiteness of the beam has a minimal effect on the angular selectivity response are given. A model is developed to investigate the cross talk in multiplexed gratings. Experimental verification in LiNbO₃ and PTR glass is demonstrated. The diffraction efficiency and output profiles of finite beams diffracted from reflection gratings on and off-Bragg are investigated. Using these beams decreases the diffraction efficiency, and the diffracted profiles are shown to be distorted, with higher distortion off-Bragg. The fidelity is shown to improve with increasing grating strength. The output profiles of diffraction by overlap gratings is investigated. Lateral shift and beam distortion are observed. When the diffraction efficiency reaches 83% the diffracted beam is shown to split into multiple sections. A method is given to obtain a diffracted beam with any desired profile. It is shown that most of the previously mentioned effects can be corrected, however the splitting of the beam at 83% cannot. Multiplexing in reflection gratings is also investigated. A narrow transmission peak is shown to occur midway between the Bragg wavelengths of the individual gratings. By adding more gratings, additional peaks are obtained. Similar devices are designed using thin film stacks. These devices have many advantages, including simpler scaling and no sidelobes. The number of transmission peaks is found using multi-mirror Fabry-Perot interferometer theory, and expressions are given for their location and width. The effects of including the variation in average index when modeling gratings recorded in the presence of absorption is presented. These effects are seen to increase as the grating type goes from un-slanted transmission to un-slanted reflection. Finally, the characteristics of plane waves incident on over-modulated transmission gratings are investigated. It is shown that they will experience one of three types of off-Bragg behavior.