Feasibility of X-ray beam nanofocusing with compound refractive lenses.

V G Kohn,M S Folomeshkin

doi:10.1107/s1600577520016495

Abstract

A more general analytical theory of X-ray beam propagation through compound refractive lenses (CRLs) than the earlier study by Kohn [(2003). JETP, 97, 204-215] is presented. The problem of nanofocusing with CRLs is examined in detail. For a CRL with a relatively large aperture the focusing efficiency is limited by the radiation absorption in the lens material. The aperture does not affect the focusing process and it is replaced by the effective aperture. The X-ray transverse beam size at the focus is then by a factor of γ = β/δ times smaller than the transverse beam size just behind the CRL. Here, δ and β are the real and imaginary parts of the CRL material refractive index n = 1 - δ + iβ. In this instance, to improve focusing efficiency, it is advantageous to decrease the CRL aperture and increase the photon energy E. However, with increasing photon energy, the material absorption decreases, which results in the CRL aperture impact on the transverse beam size. The latter leads to the fact that with a proper CRL length the beam size is independent of both the aperture and photon energy but depends only on the CRL material electron density andis approximately equal to wc = λ/(8δ)1/2, where λ denotes the radiation wavelength, as predicted by Bergemann et al. [(2003). Phys. Rev. Lett, 91, 204801].

Highlights

The complex refractive index for hard X-rays with photon energies from 5 to 100 keV may be written as n = 1 À + i where = 0 + 1
Where = hc/E is the wavelength of X-ray radiation, h is the Planck constant, c is the speed of light, E is the photon energy, e and m are the electron charge and mass, and N is the number of electrons per material unit volume
We can deduce that weak absorption slightly reduces the intensity but has almost no effect on the curve full width at half-maximum (FWHM), which for zero absorption is determined as follows, wf. This equation is valid for any photon energy E and is virtually the same as the one for the thin lens, except that for the long compound refractive lenses (CRLs) the distance rf is measured from its end and can be small

Summary

Introduction

Such sources may produce X-ray beams with very small lateral sizes, and even refractive lenses with relatively small effective apertures may be beneficial. A method of microstructuring (microfabrication) technology on a silicon surface, which is widely applied in the computer industry, has been developed since 2001 for manufacturing one-dimensional planar lenses (Grigoriev et al, 2001; Schroer et al, 2003) Microstructuring technology makes it possible to produce CRLs with relatively small curvature radius and aperture, and with small size along the beam path. It is these lenses that are currently capable of focusing X-rays to nanometre dimensions. The fourth section describes an iterative calculation method and the theory refinement for the case when the CRL aperture influences the result of beam focusing

Ray trajectories and main approximations of the theory

Analytical theory of focusing X-rays by the continuously refractive lens

Conclusion