Soft-X-Ray Vortex Beam Detected by Inline Holography

We demonstrate inline holography with a soft-x-ray vortex beam having an orbital angular momentum. A hologram is recorded as an interference pattern between a Bragg-diffracted wave from a fork grating and a divergent wave generated by a Fresnel zone plate. The images obtained exhibit fork-shaped interference fringes, which confirm the formation of a vortex beam. By analyzing the interference images, we successfully obtain a spiral phase distribution with a topological charge $\ell =\pm 1$. The results demonstrate that the inline-holography technique may be an effective probe for the characterization of topological defects in magnetic textures.

Figure 1

(a) Schematic illustration of a fork grating with $b=1$. (b) Scanning-electron-microscopy image of the central part of the fork grating used in this study. $\mathrm{Ta}$ metal (gray) is deposited on a membrane of ${\mathrm{Si}}_3{\mathrm{N}}_4$. (c) Experimental setup for coherent soft-x-ray inline holography. Incident x rays are focused using a Fresnel zone plate (FZP). The first-order diffraction from the FZP is selected by an order-sorting aperture (OSA) placed at the focal point. The zeroth-order direct beam is stopped by center stops on the FZP and the OSA. Bragg-diffracted waves, which occur at the fork grating located downstream of the focal point, interfere with waves transmitted outside the grating. (d) Diffraction pattern from fork grating without interference, which shows diffraction up to the fourth order.

Figure 2

(a) Experimental results for inline holography of the diffraction of a vortex beam interfering with the transmitted reference beam. The dashed circles indicate fork-shaped patterns appearing in the Bragg diffractions with $\ell =-1$ and $\ell =+1$. The length of the scale bar represents an angle of 5 mrad measured from the fork grating. (b) Simulated interference pattern from a fork grating with $b=1$; the pattern from a rectilinear grating ($b=0$) is shown in the inset.

Figure 3

(a),(b) Contours of the absolute value of $I_n^{\mathrm{\prime }}$ obtained in the way described in the text for the Bragg diffractions with (a) $\ell =-1$ and (b) $\ell =+1$, which are shown in Fig. 2. (c),(d) Spiral phase distribution for vortex diffraction waves with (c) $\ell =-1$ and (d) $\ell =+1$.

Figure 4

Simulation of inline holography for a hexagonal SkL (a) and a SkL with a dislocation in the skyrmions (b). We calculate the corresponding interference diffraction patterns (second column), the absolute values of $I_n^{\mathrm{\prime }}$ (third column), and the phase distribution (fourth column) of the diffracted waves, indicated by red arrows in the second column. The insets in the second column represent images of the $z$ component of the magnetic moment in the corresponding SkLs. The images of SkLs shown in the first column are visualized using the Spirit framework [29].