Coupled Wave Description Of The Diffraction By Zone Plates With High Aspect Ratios

A coupled-wave description of zone plates with high aspect ratios is given. The concept of optical thickness is used to consider the change in the diffraction properties of a high resolution micro zone plate with increasing radius. The change of the diffraction behavior from the Raman-Nath regime in the center of the zone plate to the Bragg regime towards its edge is discussed. Due to increasing sensitivity to deviations from the Bragg condition with increasing optical thickness, satisfaction of the Bragg condition is shown to be the most critical demand for achieving high diffraction efficiencies. Basic equations that describe the diffraction by a zone plate of arbitrary aspect ratio are presented. Numerical results for high resolution zone plates with a sinusoidal grating profile are discussed, considering pure phase gratings as well as zone plates built with an absorbing material. Calculations both for Bragg and off-Bragg devices are given. The decrease of the local diffraction efficiency due to deviations from the Bragg condition is shown, as well as an increase that occurs if the zones are tilted toward the optical axis. The influence of absorption in the grating on the diffraction efficiency is discussed.