X-Ray Resonance in Crystal Cavities: Realization of Fabry-Perot Resonator for Hard X Rays

Abstract

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...

Reaction intermediates in the catalytic Gif-type oxidation from nuclear inelastic scattering

“…The NIS experiments were carried out at the ID18 beamline of the European Synchrotron Radiation Facility using a high-resolution monochromator of the +m, −n, −n, +m type [14,15] (first pair of crystals: Si (4 4 0), second pair of crystals: Si (10 6 4)) yielding an overall energy resolution of about 1.0 meV (8 cm −1 ) for the measurements at 70 K and 1.2 meV (9.6 cm −1 ) for the measurements at 20 K and ensuring high spectral flux [16].…”

Coherent Control of Nuclei and X-Rays

“…Moreover, several upgrades of the XFEL are already commissioned and produce fully coherent x-ray laser [20]. Apart from the new light sources like the XFEL [21][22][23][24][25][26], detectors with a better energy resolution [27] and the improved optics elements for hard x-rays [28][29][30][31] contribute to the breakthrough. The totality of all these technology realizations may lead us into an entirely new era of studying the interaction between nuclei and radiation, i.e., nuclear quantum optics.…”

“…In the past, the main impediment for this type of study were the poor x-ray optics elements, making a high energy photon rather a tool instead of an easily manipulated subject. Due to significant technological advances, modern optics elements were significantly improved for low energy γ-rays (hard x-rays), e.g., the development of diamond mirrors with more than 99% reflectivity [28,35], hard x-ray waveguides [29,30] and the Fabry-Pérot resonator [31,36,37]. Hence the road for studying single hard xray photons is paved.…”

“…Such a task requires mastery of x-ray optics and powerful control tools of single-photon wave packet amplitude, frequency, polarization and phase [122]. The development of x-ray optics elements has made already significant progress with the realization of x-ray diamond mirrors [28,35,60] and cavities [123], hard x-ray waveguides [29,30] and the Fabry-Pérot resonator [31,36,37]. Efficient coherent photon storage for photon delay lines and x-ray phase modulation, preferably even for single-photon wave packets, are next milestones yet to be reached.…”

Realizing in-plane surface diffraction by x-ray multiple-beam diffraction with large incidence angle

“…[11][12][13] For g 1 ¼ 004, this principle gives two parasitic reflection pairs (202, 202) and (022, 022), with the corresponding reciprocal lattice points G 2 , G 3 , G 4 , and G 5 all located on the equator of the 004 back-reflection Ewald sphere in Fig. 1(b), i.e., exact 004 back reflection is a six-beam diffraction configuration.…”