X-ray Echo Spectroscopy

Abstract

X-ray echo spectroscopy, a counterpart of neutron spin-echo, is being introduced here to overcome limitations in spectral resolution and weak signals of the traditional inelastic x-ray scattering (IXS) probes. An image of a point-like x-ray source is defocused by a dispersing system comprised of asymmetrically cut specially arranged Bragg diffracting crystals. The defocused image is refocused into a point (echo) in a time-reversal dispersing system. If the defocused beam is inelastically scattered from a sample, the echo signal acquires a spatial distribution, which is a map of the inelastic scattering spectrum. The spectral resolution of the echo spectroscopy does not rely on the monochromaticity of the x-rays, ensuring strong signals along with a very high spectral resolution. Particular schemes of x-ray echo spectrometers for 0.1-0.02-meV ultra-high-resolution IXS applications (resolving power > 10 8 ) with broadband 5-13 meV dispersing systems are introduced featuring more than 10 3 signal enhancement. The technique is general, applicable in different photon frequency domains.

Aberration-free imaging of inelastic-scattering spectra with x-ray echo spectrometers

“…It predicts aberrationfree imaging, provided ideal (perfectly focusing and nonabsorbing) parabolic x-ray lenses are used, which make sure that the collimating and focusing elements form a truly imaging optical system. This conclusion is also supported by computational wave propagation studies [7] performed with SRW code [8] for a 0.1-meV-resolution x-ray echo spectrometer with the parameters from [1].…”

“…The main components of the defocusing and refocusing systems are the dispersing elements D D and D R and focusing elements F, F 1 , and F 2 . The dispersing elements are characterized by the cumulative angular dispersion rates D ∪ D and D ∪ R , cumulative asymmetry parameters b ∪ D and b ∪ R , and spectral bandwidths ∆E D and ∆E R , respectively, see [1,6] for details. The focusing elements are characterized by the focal lengths f , f 1 , and f 2 .…”

“…The focusing elements are characterized by the focal lengths f , f 1 , and f 2 . These parameters determine [1,6] the linear dispersion rate G D and the magnification factor A D of the defocusing system…”

“…D. Description of the sample, a secondary source for the refocusing system X-rays scattered from the sample are seen by the refocusing system as emanating from a secondary threedimensional source. Studies [1,6,7] show that the performance of the refocusing system is relatively insensitive to the secondary source position along the optical axis. In particular, the tolerance on the position variation is at least a few millimeters in the present case of the 0.1-meV spectrometer.…”

“…The theory of x-ray echo spectrometers developed in [1,6] is based on paraxial analytical ray tracing, which uses ray transfer matrix analysis. It predicts aberrationfree imaging, provided ideal (perfectly focusing and nonabsorbing) parabolic x-ray lenses are used, which make sure that the collimating and focusing elements form a truly imaging optical system.…”