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Physical Review A

Model for partial coherence and wavefront curvature in grating interferometers

Benjamin J. McMorran, Alexander D. Cronin

Published Jul 1, 2008• 29 citations
Publisher

Abstract

We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam's initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.

DOI
10.1103/physreva.78.013601

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We analyze time-domain Talbot–Lau interferometry of organic cluster beams that are exposed to pulsed photodepletion gratings in the vacuum ultraviolet. We focus particularly on the analysis of the complex (phase and absorption) character of the optical elements. The discussion includes the role of wavefront distortions due to mirror imperfections on the nanometer level and the effect of finite coherence in the diffraction gratings. This improved understanding of the interferometer allows us to extract new information on optical properties of anthracene and ferrocene clusters and to define conditions for future matter-wave experiments.
Paths of particles, emitted from distributed sources and passing out through slits of two gratings, G0G_{0}G0​ and G1G_{1}G1​, up to detectors, have been computed in details by the path integral method. The slits are represented by Gaussian functions that simulate fuzzy edges of the slits. Waves of matter be computed by this method show perfect interference patterns both between the gratings and behind the second grating. Coherent and noncoherent the distributed particle sources reproducing the interference patterns are discussed in details. Paraxial approximation stems from the wave function when removing the distributed sources onto infinity. The more hard-edged slits of the grating G1G_{1}G1​ are examined by simulating those slits by a superposition of more hard the Gaussian functions. As for the particles here we consider fullerene molecules. De Broglie wavelength of the molecules is adopted equal to 5 pm.
A generalized description of Talbot-Lau interference with matter waves is presented, which accounts for arbitrary grating interactions and realistic beam characteristics. The dispersion interaction between the beam particles and the optical elements strongly influences the interference pattern in this near-field effect, and it is known to dominate the fringe visibility if increasingly massive and complex particles are used. We provide a general description of the grating interaction process by combining semiclassical scattering theory with a phase space formulation. It serves to systematically improve the eikonal approximation used so far, and to assess its regime of validity.
Matter-wave near-field interferometric experiments require interference contrast as high as possible in order to extract information from the interference patterns. One of the tasks to accomplish this requirement is to align the distances between gratings and detection. We present here a method for this precision alignment. An electron beam as a matter-wave source, a diffraction grating, and mask grating were used in this study. The simulations show that the longitudinal scanning of the mask grating with the detection can specify the exact location of the near-field or so-called Talbot distance with the condition of using the gratings with small open fractions. Therefore, the various open fractions were done in the calculation. Due to the lack of commercial gratings with small open fractions, a technique of two overlapping gratings can be applied for changing arbitrary grating shapes and open fractions. We conclude that smaller open fraction of the gratings gives better longitudinal alignment. The results show that the Talbot distance is located at the highest throughput behind the gratings. The present study can provide a method for implementing matter-wave diffraction experiments in the future.