Furthermore, under the above-mentioned condition, resolved diffraction peaks have been observed from micro-fabricated reflection-gratings [ref]. Figure 1a and 1b show the schematics of matter-wave scattering from a transmission grating with the period of 100 nm and a square-wave grating whose period is 400 um, respectively. For the sake of convenience, the incidence angle \(\theta_{in}\) and the diffraction angle \(\theta_n\) of the nano-transmission grating are defined with respect to the normal line while those are determined by the angle between the incident beam and the grating-surface plane at the square-wave grating. A sign of the diffraction order is defined in a way that diffraction angles of positive orders are larger than negative orders./// In order to see the difference between two gratings, \(n\)-th-order diffraction angles over certain ranges of incidence angles from each grating are calculated by grating equation [2008-19] in Fig 1c and 1d, respectively. Here, matter-wave de Broglie wavelength is fixed at 136 pm. Assuming the angular resolution of the atomic beam is around 100 urad, up to 5th order diffraction peaks can be observed at grazing incidence angles from the micro-fabricated reflection-grating as it can be from a nano-transmission grating at a normal incidence condition. Considering the fact that the reflection and diffraction efficiencies are increased as incidence angle goes smaller from the reflection-type grating, diffraction efficiencies from square-wave gratings are expected to be higher as much as those efficiencies from transmission grating. Therefore, micro-fabricated structures can act as a matter-wave-grating and it appears important for the generality of matter-wave elements due to its lower price and size-limit than nano-fabricated structures like the nano-transmission grating. Thus, micro-fabricated solid structures can be a good candidate for practical matter-wave optical instruments as exploiting grazing incidence condition. 
// Giant Quantum Reflection of Neon Atoms from a Ridged Silicon Surface
he intensity of the direct beam was used to calibrate the absolute reflectivity, while the angle of the reflection was calculated from the distance between the image of the reflected atoms and that of the direct beam.