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Fresnel zone
About: Fresnel zone is a research topic. Over the lifetime, 2337 publications have been published within this topic receiving 37650 citations.
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TL;DR: It is shown that simple analytical models describe the tilt sensitivity of thin zone plates and the thickness at which volume diffraction must be considered, and the performance of example zone plates for soft x-ray focusing at 0.5 keV and hard x-rays focusing at 10 keV is examined.
Abstract: Fresnel zone plates are frequently used as focusing and imaging optics in x-ray microscopy, as they provide the ease of use of normal incidence optics. We consider here the effects of tilt misalignment on their optical performance, both in the thin optics limit and in the case of zone plates that are sufficiently thick so that volume diffraction effects come into play. Using multislice propagation, we show that simple analytical models describe the tilt sensitivity of thin zone plates and the thickness at which volume diffraction must be considered, and examine numerically the performance of example zone plates for soft x-ray focusing at 0.5 keV and hard x-ray focusing at 10 keV.
9 citations
TL;DR: Flexible, lightweight, four- and eight-level phase photon sieves with 25.8% and 49.7% transmission efficiency, respectively, up to five times greater than that of any other photon sieve reported thus far are presented.
Abstract: Over the past several decades, the need for high-resolution, high-efficiency, lightweight, high-contrast focusing optics has continued to increase due to their applications in fields such as astronomy, spectroscopy, free-space optical communications, defense, and remote sensing. In recent years, photon sieve planar diffractive optics, which are essentially Fresnel zone plates with the rings broken into individual “pinhole” apertures, have been developed on flexible, lightweight polyimide substrates. However, transmission efficiencies have continuously been very low (∼1%–11%) until this work, thus impeding the widespread use of photon sieves in practical applications. Here, we present flexible, lightweight, four- and eight-level phase photon sieves with 25.7% and 49.7% transmission efficiency, respectively, up to five times greater than that of any other photon sieve reported thus far. Additionally, these sieves were fabricated via a single step pulsed laser ablation method. The total time to fabricate a ∼3 cm2 photon sieve via the single-step fabrication was tens of seconds, giving the technique a significant advantage over traditional photolithography used to generate multilevel structures. Analytical analysis of the photon sieve was carried out via the finite-difference time-domain (FDTD) method and was in very good agreement with experimental results. We have also calculated via FDTD modeling the behavior of higher-level photon sieves for further enhanced efficiencies, and analytically show an estimated upper bound on photon sieve efficiency of 70% within the first focal plane null in the limit of increasing step number, and the data presented herein provide a relationship between efficiency and step number. Additionally, this process of multilevel diffractive lens fabrication can be extended to multilevel Fresnel zone plates, which have not previously been demonstrated by this process. The results presented in this work represent a new step in high-resolution diffractive optics, showing efficiencies suitable for widespread applications in addition to drastically reducing the cost and complexity of fabricating multilevel focusing elements.
9 citations
TL;DR: In this paper, the concept of Fresnel zones for modes is introduced, which is analogous to the usual Fresnel zone introduced for rays, and the analysis of mode scattering at large-scale and random inhomogeneities of a medium in waveguides is simplified.
Abstract: The notion of Fresnel zones for modes is introduced, which is analogous to the usual Fresnel zones introduced for rays. It is shown that using Fresnel zones for modes one can simplify the analysis of mode scattering at large-scale and random inhomogeneities of a medium in waveguides. Simple formulae to calculate fluctuations of mode amplitudes are obtained. They are similar to well-known formulae of geometrical optics and to those of the Rytov method used to calculate fluctuations of ray complex amplitudes. Relations deduced can be used for calculating field fluctuations both at regular waveguide points and at caustics.
9 citations
TL;DR: In this paper, the Fourier transform method was used to solve the Fresnel-Kirchhoff integral problem for coherent and partially coherent illumination of a wave-front phase step.
9 citations
TL;DR: In this paper, the optical matching characteristics of undulator radiation with some condenser zone plates were investigated in the soft X-ray region using an undulator beamline at the Photon Factory.
Abstract: Optical matching characteristics of undulator radiation with some condenser zone plates were investigated in the soft X-ray region using an undulator beamline at the Photon Factory. It was confirmed that the monochromatization of the first harmonic of the undulator radiation was made by meams of a system consisting of a zone plate and a pinhole, but the transmission efficiency and the wavelength resolution of the system were lower than expected. Analyses show that the results can be attributed to the finite source size of the undulator radiation which is determined by the present storage ring operation and also to the longer focal lengths of the zone plates used. It was also found that the virtual source point of the undulator radiation should be assigned at the position of the undulator itself.
9 citations