Figure 1

Energy dependence of the reflectivity (a),(b), and transmissivity (${\mathrm{a}}^{\prime }$),(${\mathrm{b}}^{\prime }$), of x rays at normal incidence to the (0 0 0 30) atomic planes of $\alpha \mathrm{\text{−}}{\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ single crystals used as the interferometer mirrors: (a),(${\mathrm{a}}^{\prime }$): mirror 1, $d_1=63.0(1)\mu \mathrm{m}$; (b),(${\mathrm{b}}^{\prime }$): mirror 2, $d_2=58.6(2)\mu \mathrm{m}$ thick. $E_0=14.315\mathrm{k}\mathrm{e}\mathrm{V}$. Red lines are theoretical fits by using the dynamical theory of x-ray diffraction in exact backscattering. In the fit, the 2 meV energy width of the incident radiation is taken into account.Reuse & Permissions

Figure 2

Top: schematic of an x-ray Fabry-Pérot interferometer with $\alpha \mathrm{\text{−}}{\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ mirrors as in Fig. 1 separated by a gap of $d_{\mathrm{g}}=50\mathrm{m}\mathrm{m}$. Center and bottom: the appearance of the Fabry-Pérot resonances on the x-ray energy scale in reflection (left), and transmission (right). The central parts on an expanded scale are shown in the bottom graphs.Reuse & Permissions

Figure 3

Left: time response of the interferometer. The sharp green peaks are theoretical fits, without convolution with the time instrumental function. Right: energy dependence of the reflectivity of a single $\alpha \mathrm{\text{−}}{\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ mirror (red lines and dots) and the spectrum of incident x-ray photons (black line) normalized to the peak value of the reflection curve. The center of the spectral distribution $E$ of the incident radiation pulses is detuned (a) $E-E_0=10\mathrm{m}\mathrm{e}\mathrm{V}$ off the peak reflectivity, (b) $E-E_0=5\mathrm{m}\mathrm{e}\mathrm{V}$, and (c) tuned to the peak reflectivity of the mirrors: $E-E_0=0$, respectively. The spectral width of the incident radiation pulses is 2 meV; pulse duration is 100 ps. The 0.86-ns-decay constant in (c) corresponds to $0.76\mathrm{\text{−}}\mu \mathrm{e}\mathrm{V}$-broad transmission Fabry-Pérot resonances.Reuse & Permissions

Figure 4

Energy dependence of the reflectivity (a),(b), and transmissivity (${\mathrm{a}}^{\prime }$),(${\mathrm{b}}^{\prime }$), of the two-crystal interferometer. X rays are at normal incidence to the first crystal. (a),(${\mathrm{a}}^{\prime }$) The atomic planes of both crystals are adjusted parallel to better than $0.35\mu \mathrm{r}\mathrm{a}\mathrm{d}$. The solid red lines are theoretical spectra calculated by the theory of x-ray Fabry-Pérot interferometers [12, 5, 13] and averaged over the 2 meV bandwidth of the incident radiation. The dashed line in (${\mathrm{a}}^{\prime }$) is the product of the transmissivities through the mirrors 1 and 2, i.e., describes the transmissivity through a system of two noninteracting mirrors in Bragg backscattering. (b),(${\mathrm{b}}^{\prime }$) Mirror 2 is tilted by $3\mu \mathrm{r}\mathrm{a}\mathrm{d}$ from the parallel state. The red solid line in (${\mathrm{b}}^{\prime }$) is the same as in (${\mathrm{a}}^{\prime }$). Vertical dashed lines indicate the nodes of beatings in (a).Reuse & Permissions