X-ray guided modes produced by Bragg reflections of multilayers: an analytical treatment

Abstract

It is analytically shown that X‐ray Bragg reflections from periodical multilayer structures can be used for the excitation of guided modes. The X‐ray guided modes in (i) a guiding film embedded in a periodical multilayer and (ii) an air gap between two space‐separated multilayers have been considered. In the former case, analytical expressions have been obtained which describe a resonant X‐ray intensity enhancement taking place inside the guiding film under the guided mode excitation. Optimal parameters of the waveguide have been found, which are needed to achieve a maximum intensity gain. In the latter case, eigen guided modes arising in the air gap have been determined. Properties of the eigen modes have been studied.

Advanced x-ray multilayer waveguide optics

“…Generally speaking, these advantages of the novel WGA result in enhancement of the waveguide performance [26,29,32,33], being at the same time a coherence filter and a secondary quasi-focusing device.…”

“…It is well known that a multilayer structure based on Bragg theory can increase the guided intensity [32,33]; also the choice of materials plays an important role: Introducing two Mo layers into a Ge/C /Ge structure can increase the transmission significantly [29] by reducing absorption of the evanescent wave in the cladding.…”

“…Tapered waveguides channels with an exit size down to 16.5 nm × 14.6 nm have been reported recently [23]. In [30,31], the single guiding film was generalized to an array of planar wavguides, and in [32,33], the cladding was generalized to a multilayer structure.…”

“…With thin film deposition techniques, notably 8 nm [27,28] for the given material could be reached in a planar thin film waveguide with an optimized cladding material (Mo/C /Mo structure embedded in Ge wafers [29]). Furthermore, the single guiding film [30,31] or the cladding film [32,33] can be generalized to a multilayer structure. Therefore, for purposes of the highest beam confinement or to exploit novel geometries as in this thesis, waveguiding in only one dimension as in an array of thin planar films, is suitable and attractive, owing to a better control of layer sequences.…”

“…In these experiments, the collimated synchrotron beam was coupled into the array of waveguides via the so-called resonant beam coupling scheme through the top of the multilayer structure. In other applications [32,33], the cladding layer instead of the guiding layer was generalized to a multilayer, while keeping only a single guiding layer. In this way, the internal reflection angles of guided beams could be increased.…”