Proceedings PaperDiffraction efficiency of multiple-grating holographic fan-out elements
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The performance of optically mastered holographic fan-out elements is considered, in the limit, as the angular separation between output beams becomes small. This type of element consists of a number of superimposed gratings, each recorded with a common reference and a distinct signal beam. On replay with the reference beam, in addition to the expected zero and first orders, a large number of spurious orders are observed. These are produced by multiple grating diffraction processes and can contain significant power. By considering an infinite set of spurious orders, operator expressions are derived for the power in each of the significant diffraction orders. These expressions are analogous to the two wave solution for a single grating but with the coupling constant replaced by a coupling operator. In the cases of two and three gratings expansion of the operator expressions yields simple and analytical formulae. For the general case a pure recurrence relationship is derived linking all the diffraction orders. The validity of the results is demonstrated by comparison with a direct numerical solution of the coupled wave equations. Excellent agreement is obtained for angular separations of up to 1 degree(s) and for holograms of moderate thickness up to 5 degree(s).