Diffraction Analysis of Multiplexed Holographie Gratings

Optical diffraction by periodic structures are of increasing importance in an expanding variety of engineering applications [1]. Diffraction of electromagnetic waves by spatially periodic media has been analyzed by numerous authors over the last fifty years [1]. In almost all previous analyses, only diffractive structure with one single grating (and its harmonics) were considered. Recent applications for holographic optical elements include associative storage, optical computing, multiple holographic storage, beam coding, multiple beam generation and combining, multi-color displays, multi-color filtering, beam shaping, synthetic lenses, interlaced elements, and multifrequency beam mixing. In these applications, two or more gratings of arbitrary spatial frequency and slant exist simultaneously within the diffractive element. Case [2] developed a couple-wave analysis for Bragg-angle diffraction of light by two superimposed thick phase holographic gratings. Alferness and Case [3], utilizing a thin grating decomposition method, examined both the direct and the cross coupling among the incident beam and the two first diffracted orders in such a structure.