a Generalized Analysis of Acousto-Optic and Holographic Bragg Gratings and Beam Transformation Filters.

A general plane wave transfer function and integral formalism for moving and stationary grating diffraction at arbitrary Bragg and incident angles is developed based on a modified multiple plane wave scattering technique. A computer holography type encoding technique for designing beam transformation filters is proposed. Some useful tools for measuring the performance of holographic optical interconnections are examined and suggested. In the first case, for an incident optical beam with an arbitrary profile, a general integral formalism for acousto-optic and holographic Bragg diffraction is developed. The formalism is applicable to dynamic gratings created by sound waves as well as static (holographic) gratings of any modulation strength over a wide range of Bragg angles. Numerical results for light beams incident on moving gratings are obtained for three different profiles by employing this formalism. Straightforward extensions to the case of holographic gratings with or without tilt, are also presented, and the results are compared, wherever feasible, with other known approaches. The case of a beam transformation is treated by employing computer generated hologram technique. These beam transformation filters are intended to convert planar optical beams with arbitrary field distributions into beams with desired profiles. The transmission coefficient of such a filter is encoded as computer generated holograms by employing a detour phase technique. A few illustrative examples are presented to demonstrate the feasibility of the encoding scheme. Based on this technique, the case of the design of a spatial filter for Gaussian to Bessel beam transformation is also introduced. In the second case, diffraction efficiencies of holographic optical interconnects are first evaluated for varying grating constants, angles of incidence (normal, exact Bragg-, and twice Bragg angles), and angles of tilt. Then, the effects of wavelength change as well as input angular misalignment on the direction of the diffracted (first) order of light are examined for untilted as well as tilted holograms. In the presence of angular misalignments, a compensational relationship intended to stabilize the desired direction of the output beam by tuning the input wavelength is also derived quantitatively. Finally, the crosstalk between adjacent channels in a transmission type hologram is quantitatively analyzed in terms of above parameters.