Focusing Hard X Rays to Nanometer Dimensions by Adiabatically Focusing Lenses

We address the question of what is the smallest spot size that hard x rays can be focused to using refractive optics. A thick refractive x-ray lens is considered, whose aperture is gradually (adiabatically) adapted to the size of the beam as it converges to the focus. These adiabatically focusing lenses are shown to have a relatively large numerical aperture, focusing hard x rays down to a lateral size of $2\mathrm{n}\mathrm{m}$ (FWHM), well below the theoretical limit for focusing with waveguides [C. Bergemann et al., Phys. Rev. Lett. 91, 204801 (2003)].

Figure 1

Adiabatically focusing x-ray lens. The lens is composed of a large number of individual (aspherical) refractive lenses, whose aperture is matched to the converging beam size, increasing the refractive power per unit length along the lens.

Figure 2

Characteristic aperture $a=\frac{4\sqrt{{\delta }^{\prime }}}{\sqrt{\pi }{\mu }^{\prime }}$ as a function of x-ray energy for different lens materials.

Figure 3

(a) Intensity distribution of monochromatic x rays propagating through an AFL. (b) Intensity distribution behind the lens. The lateral beam size in the focus is $4.74\mathrm{n}\mathrm{m}$ (FWHM). (c) Intensity distribution behind a nanofocusing lens [5] (lateral beam size $14.2\mathrm{n}\mathrm{m}$). Distances along the optical axis in (b) and (c) are measured from the exit of the lens.

Figure 4

(a) Kinoform profile of one side of an individual lens and resulting intensity distribution of x rays propagating through a kinoform AFL with five segments. (b) Intensity distribution behind the lens. The lateral beam size is $2.21\mathrm{n}\mathrm{m}$ (FWHM).

Figure 5

Lateral beam profiles for a nanofocusing lens, an adiabatically focusing lens, and two kinoform AFLs with three and five segments, respectively.