Mechanism of volume diffraction effect: Modulation of soft x-rays by high-resolution zone plates
Phys. Rev. Applied 26, 014082 – Published 27 July, 2026
DOI: https://doi.org/10.1103/mjkj-lp1k
Abstract
This work investigates the modulation of x-rays by high-resolution zone plates (ZPs), challenging the limitations of traditional phasor-based theory when volume diffraction effects (VDE) dominate. Using the beam propagation method (BPM), we simulated the optical field dynamics and identified three key causes of efficiency degradation in traditional ZPs with rectangular profiles: amplitude-type modulation, focal spot displacement, and phase mismatch. Experimental validation using a 15 nm outermost-zone ZP fabricated via e-beam lithography and tested at Shanghai Synchrotron Radiation Facility (SSRF) confirms the superior accuracy of BPM over phasor-based theory. Furthermore, slant zone plates incorporating Bragg diffraction mitigate VDE-induced losses, achieving near-ideal phase modulation. Finally, a waveguide-based interpretation provides physical insight into VDE mechanisms, highlighting the potential of geometric innovations to overcome current limitations.
