X-ray back diffraction from monolithic two silicon crystal plates of 25-150 µm thick and a 40-150 µm gap using synchrotron radiation of energy resolution ∆E = 0.36 meV at 14.4388 keV shows clearly resonance fringes inside the energy gap and the total-reflection range for the (12 4 0) reflection. This cavity resonance results from the coherent interaction between the X-ray wavefields generated by the two plates with a gap smaller than the X-ray coherence length. This finding opens up new opportunities for high-resolution and phase-contrast X-ray studies, and may lead to new developments in X-ray optics.PACS numbers: 41.50.+h,07.60.LyLasers of long wavelength, ranging from visible spectra to soft X-rays, have had a great impact on the development of sciences and led to diverse applications in physics, chemistry, biology, material sciences, engineering, etc. In the case of shorter wavelength hard X-rays, X-ray lasers, including free-electron lasers, have long been anticipated to provide a coherent X-ray source for probing structures of matter, periodic and non-periodic, in sub-atomic scales, including the structures of nanoparticles, quantum dots, and single biological molecules. One of the components for making lasers is the optical resonator, like the Fabry-Perot resonators [1]- [3]. However, an X-ray resonator for X-ray lasers has never been realized, although it has long been proposed [4]-[6] and pursued [7]-[14] from time to time for more than three decades. In fact, the difficulty in realizing X-ray resonators with observable resonance fringes arises mainly from the required experimental conditions on coherence are not easily attainable, aside from the many well documented theoretical studies of X-ray cavity resonance [3]- [12] reported in the literature. Recent experiments of Liss et al [13] and Shvyd'ko et al [14] have observed storage of X-ray photons in a few tens back-and-forth reflection cycles in two-plate crystals with continuously decaying reflectivities in time-resolved experiments. The latter have also showed the beating of two Pendellösung fringes [15] on the tails of diffraction profiles in photon energy scans, mainly due to crystal thickness effects. Although these results are useful for X-ray optics and time-resolved experiments, they did not show observable cavity resonance fringes, mainly because the required coherence conditions were not satisfied and the insufficient energy resolution used washed out resonance fringes (see later discussion).An unambiguous way to demonstrate the cavity resonance is, under appropriate coherent conditions, to show resonance interference fringes inside the total reflection range and inside the energy gap of a back diffraction • .) for back diffraction. Multiple reflections take place within the crystal gap and generate forward-transmitted and back-reflected beams. The coherent interaction among the transmitted and the reflected beams inside the crystal plates and within the gap leads to cavity resonance. [7,11,12]. Moreover, images of concentric interference ri...
We employ angle-resolved photoemission to study the electronic structure of atomically uniform films of Ag grown on Ge(111). A new kind of quantum well state is observed near a specific emission direction away from the surface normal. In contrast with the usual quantum well state arising from electron confinement by specular reflections at the surface and interface of the film, the new kind involves retroreflections, or umklapp reflections, at the interface. It requires four reflections, instead of the usual two reflections, to complete a coherent interference path.
We report on the trapping of 14keV photons in periods of 1.11–1.67ps by the 12 4 0 backdiffraction in two- and multiplate silicon single-crystal cavities of a few hundred micrometer size. The formation of standing waves inside the cavities ensures better coherence for the x rays. We anticipate that the transmitted x rays through this type of cavities can be used as a quasicoherent x-ray source for probing the dynamic structures of solids, liquids, and biological substances.
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