Analysis of superimposed holographic gratings

Several recent applications of diffractive optical elements utilize superimposed holographic gratings. These applications include: associative storage, optical interconnect, multiple beam generation and combining, color displays and filtering, beam shaping, and wavelength multiplexing. Almost all previous work on grating diffraction analysis, however, is for single grating structures. In this work, the rigorous coupled-wave approach for grating diffraction (developed by the author) has been extended to two (or more) superimposed gratings of arbitrary periodicity, slant, modulation, and thickness and for incident light of arbitrary wavelength, angle of incidence, and polarization. The analysis is applied to several grating structures produced by the typical configurations for sequentially recording two superimposed holograms. They are (1) common reference beam (common Bragg angle), (2) common object beam direction (the beam diffracted by one grating is at the Bragg angle of the other grating), (3) recording medium rotation, (4) two recording light wavelengths and common reference and object beam directions, and (5) mixed transmission and reflection gratings. The angular dependence of the diffraction characteristics of these structures on the grating modulation, thickness, and polarization is presented. It is shown that in addition to direct diffraction of the incident beam at or near the Bragg angle of one grating and the associated crosstalk diffraction by the second grating, cross diffraction may occur if the beam diffracted by the one grating is at or near the Bragg angle of the other grating (common object beam recording configuration).