Gratings for VUV to X-ray applications
Résumé
Gratings are widely used in an energy range going from VUV to soft X-rays to analyze or select the photon energy. These gratings typically have line densities ranging from ~200 l/mm to 2000 l/mm. A first revolution came around 1970 where mechanical ruling was replaced by holographic printing and lithography. Holographic gratings are more regular, free of “ghost” and show less scatter. However, only rectangular profiles (lamellar) are easy to produce with this technique, though asymmetric etching in silicon may provide blazed gratings. There is also a limit in the line period can be printed, somewhat over half the holographic wavelength, ie ~250 nm.
Classical metal coated gratings have decreasing performances with higher energies. Multilayer (ML) coatings offer the significant advantage of providing good reflectivity at much larger grazing incidence angle than simple metal coating at the same photon energy. However the incidence angle must be matched to the photon energy and multilayer period through the Bragg law. It implies that the deviation angle varies with the wavelength. However this deviation can be easily compensated by ML coated mirror of matched period. On the other hand, the fact that matching condition should be satisfied for both the grating and the multilayer period channels the diffraction into a single order the efficiency of which can reach high values. Use of ML gratings will be illustrated by the example of SOLEIL Sirius beamline
Classically, gratings are oriented so that grating line direction is perpendicular to the incidence plane. In such case all diffracted orders stay in the incidence plane. When the projection of the incident wave vector on the surface is parallel to the line directions, diffraction orders are distributed on a cone the axis of which is the line direction. The aperture angle of this cone is the incident glancing angle and can be freely chosen. Small glancing angles, combined with blazed profiles or ML coating, allow high efficiencies since there is no screening effect. However, the dispersion given by such a conical geometry is small. Improving it requires to increase the line density. Nano-fabrication techniques could offer an alternative to holography for manufacturing very dense grating. Properties of conical are used for instance in our design of the FAB10 beamline at ATTOLAB behind the HHG* source. They are also considered for spatial X-ray spectrometers.
Designing grating based instruments for the X-ray domain requires to be able to model the diffraction properties of simple and ML coated gratings. Since the considered photon frequencies are well above plasma frequencies, the grating is model as a thick structure with a periodic transverse modulation of the dielectric constant varying with the depth. Computations are somewhat similar to ML reflectivity ones, but propagating a vector of diffracted waves rather than a single one. Examples of computation will be given.