Scattering of electromagnetic waves by multiple superposed gratings

Problems requiring the accurate evaluation of waves diffracted by periodically modulated media have been treated most recently by using coupled-wave techniques. However, in terms of computability and physical insight, the coupled-wave approach has provided only limited effectiveness in dealing with diffraction involving many superposed gratings. By developing a field representation in terms of multiply scattered waves, we provide here an alternative approach which is particularly effective for situations involving many such superposed volume gratings. In this approach, the pertinent scattered waves are easily described by flow graphs which serve as templates for algorithms that quantify any diffracted order of interest. Furthermore, the flow-graph procedure provides a straightforward physical interpretation of the scattering process by indicating how each diffracted order is constructed. For weakly modulated media, this approach is very accurate even if all backward scattering is neglected, in which case the multiple-scattering approach leads to a simpler construction for the pertinent diffracted orders. However, we found that backward-scattered contributions must be retained when dealing with strongly modulated media. The multiple-scattering approach was therefore developed to also include backward scattering whenever necessary. In fact, we could thus systematically solve problems that may not be easily handled by coupled-wave methods.;By using this novel multiple scattering formalism, we have specifically investigated crosstalk effects in volume holographic interconnections involving superposed gratings. In that context, we have explored the nature of interconnection crosstalk and evaluated its dependence on various design parameters, such as dynamic range, minimum angular separation between interconnections, etc. The multiple-scattering approach has thus revealed considerable qualitative and quantitative advantages by providing insights into the crosstalk mechanism which are not readily available by using coupled-wave or other methods.