On X-ray waveguiding in nanochannels: Channeling formalism

Abstract

The question on X-ray extreme focusing (smallest reachable spot size) brings us to the idea for using the wave features of X-ray propagation in media. As known, wave features are revealed at propagation in ultra-narrow collimators as well as at glancing reflection from smooth flat and/or strongly curved surfaces. All these phenomena can be described within the general formalism of X-ray channeling.

Synchrotron-based spectroscopy of X-ray channeling through hollow capillary microchannels inside glass plates

“…Capillary optics is one of the fastest growing X-ray optical technologies (Pfeiffer et al, 2002;Sun et al, 2009) because of its superior capacity of generating high-flux-density beams in the micrometre and submicrometre range. The properties and peculiarities of X-ray beams formed by polycapillary optics have been intensively studied over the past 20 years (Kumakhov & Komarov, 1990;Bilderback et al, 1994;Dabagov et al, 1995;Dabagov & Uberall, 2007). Investigations of X-ray waveguides and microcapillary optics based on the phenomenon of multiple total external reflection (Dabagov, 2003) are devoted to ultrafocusing properties and partially coherent beams.…”

“…In microchannels the propagation features are defined by the interaction of radiation with a curved surface and characterized by the waves that propagate close to the capillary walls. A basic point of X-ray beam transportation in a capillary channel (as an X-ray waveguide) is the mode regime (Spiller & Segmuller, 1974;Dabagov, 2003;Bukreeva et al, 2010) associated in particular with the surface channeling of X-ray radiation, first determined by Dabagov (see Bellucci & Dabagov, 2003;Dabagov & Uberall, 2007).…”

X-ray waveguiding for micro- and nanofocusing

“…The estimations performed by means of Eqs. (17) and (18) have shown the one-order increase of a single mode intensity |P 1 | 2 for ultra narrow planar guide (d ≪ λ ⊥ ). The angular dependence of the normalized intensity |P 1 (ϑ)| 2 in respect to geometrical one is presented in Fig.…”

“…However, some fine features observed require solution of the wave equation of radiation propagation [13][14][15][16] and finally, can be explained in view of the radiation interference due to the various channel's curvatures. The latter occurs as trapped radiation propagation in the very vicinity of a surface [3,17].…”

Surface Channeling of Charged and Neutral Beams in Capillary Guides

“…To describe the radiation propagation into capillaries, it must be noted that in widely used capillary systems, the sizes of channels (micrometer-sizes) essentially exceeds the effective wavelength of the radiation that is transmitted. It allows the radiation dispersion at multiple-reflection propagation of the radiation down the capillary channel to be analysed within the ray optics approximation, which, in turn, for very small grazing angles, exposes the picture of whispering gallery modes (surface channeling modes) [100][101][102][103][104][105]. The modern technology for manufacturing capillary optical systems enables extremely small channel diameters (nanometer-sizes) to be reached at the drawing process [56,106].…”