Thin grating sequential diffractions for the analysis of Bragg diffractions by superimposed transmission phase gratings

We present a thin grating sequential diffraction technique on analyzing Bragg diffractions by superimposed transmission phase gratings. It can account for diffractions by any number of superimposed gratings with symmetric and asymmetric diffraction geometries. The angular and wavelength selectivity curves are found to depart from the (sine)² functional dependence of single-grating diffraction cases owing to the energy coupling among all diffracted and undiffracted beams. The calculation results match well with those calculated using thin-grating decomposition technique. The simple computation technique should be suitable for design engineers to establish grating index combinations prior to experimental implementation of optical beam splitting components.