Focusing Analysis of Single-Mode Photon Sieve with Equal-Diameter Pinholes Working in "Water Window" Band

As processing technologies become mature, and the requirement for spatial resolution increases, pinholes on the photon sieve get smaller and smaller. For pinholes with different sizes on the photon sieve, the incident uniform plane wave can excite one or more waveguide modes, which results in the inter-modal dispersion and phase difference. Even if there is only single-mode transmission in the pinholes, the effective refractive index of the fundamental mode is related to the size of the pinhole, which leads to different phases of pinholes with different diameters at the exit. To eliminate these phase differences, the single-mode photon sieve with equal-diameter pinholes is proposed. The focusing effect of the photon sieve in the "water window" band is studied, and the corresponding Gaussian far-field diffraction model is established. In addition, the distribution of the Gaussian mode field is confirmed based on the numerical simulation through the finite element software, and the effectiveness of the far-field model is verified by calculating the Fresnel diffraction integral.