ON THE DIFFRACTION PROPERTIES OF MULTILAYER COATED PLANE GRATINGS

Multilayercoated laminar gratings are examined in the kinematic approximation with refraction corrections to derive the relationships between wavelength and diffraction angle that determine when constructive interference occurs. Two cases are considered: the amplitude grating and the laminar grating. For each Bragg order of the multilayer we find the grating orders to be nearly linearly arrayed about the grating zero order which occurs at the multilayer Bragg angle and energy. Each reflection carries wavelengths given approximately by the multilayer bandwidth, but dispersed according to the grating equation with its central energy deviating approximately linearly in grating order about the Bragg energy. We are also able to demonstrate the extent to which the device behaves as an X-ray prism, maintaining a constant dispersion angle (given by the Bragg equation) for each diffracted energy. For the laminar grating we derive bar-height relationships for constructive and destructive interference at all grating orders and show that they are commensurate so that odd orders are maximized by the same height that cancels zero order. Finally we present a "two-crystal" monochromator design, using a grating and a non-parallel multilayer, which transmits the wavelength of choice parallel to the incoming beam while passing specularly reflected light into a beam stop at an offset angle. © 1990.