Theory of crossed-beam diffraction gratings

The operation of crossed-beam gratings is analyzed in terms of diffraction efficiency and beam quality, following Solymar's method's General solutions for arbitrary beam widths, general beam profiles, and illumination with two beams are derived. A scheme for improving the beam quality of these gratings is proposed. The analysis should be useful in integrated optics for designing beam expanders, beam contractors, and mirrors, and for analyzing waveguide interferometers.