First Observation of New Flat Line Fano Profile via an X-Ray Planar Cavity

A new Fano profile of a flat line is achieved experimentally by manipulating the relative amplitude of the continuum path, when $q$ takes the pure imaginary number of $-i$ in the x-ray regime. The underlying mechanism is that the interference term in the scattering will cancel the discrete term exactly. This new Fano profile renders only an observable continuum along with an invisible response to the discrete state of atomic resonance. The results suggest not only a different strategy to invisibility studies which provides a possible tool to identify weaker structures hidden by the strong white line, but also a new scenario to enrich the manipulations of two-path interference and nonlinear Fano resonance.

Figure 1

(a) The two-path interferometer is built by an x-ray planar cavity with an embedded ultrathin atomic layer. In the present Letter, three cavity samples with different $t_{\mathrm{top}}$ values of 0, 1.0, and 2.2 nm are prepared [44]. The inset shows the energy levels of atom W, $E$ is the incident x-ray energy and $E_0=10208\mathrm{eV}$ is the transition energy of the W atom. (b) Conception of the two-path interference mechanism. $\varphi$ is the relative phase of the two paths. If $\varphi \ne \pi /2$, $q$ is a complex number. The Fano interference spectra are the asymmetric lines, as shown at the top. The orange and purple lines correspond to positive and negative $\mathrm{Re}(q)$, respectively. If $\varphi =\pi /2$, the parameter $q$ is a pure imaginary number, and generally symmetric Lorentz line or window resonance is observed. However, when $\mathrm{Im}(q{)}^2=1$, the spectrum becomes a flat line (the red solid line in the right inset), which is equal to the intensity of the continuum path.

Figure 2

(a) Numerical reflectivity as a function of energy at different amplitudes of $c^{\prime }$. (b) A numerical 2D map of the reflection spectrum vs the energy and $\mathrm{Im}(q{)}^2$ ($c^{\prime }$). The reflectivity becomes a constant when $\mathrm{Im}(q{)}^2=1$ $(c^{\prime }=1.351)$. Herein, ${\gamma }_0=7.2$, ${\gamma }_c=7.6$, and $E_0=10208\mathrm{eV}$ are used from the sample of $t_{\mathrm{top}}=1.0\mathrm{nm}$ (Supplemental Material, Table S2 [44]). (c) and (d) The cavity properties of Pt $(t_{\mathrm{top}})/\mathrm{C}$ (19.8 nm)/${\text{WSi}}_2$ (2 nm)/C (20.2 nm)/Pt (15.0 nm)/Si (substrate) simulated by the Parratt formalism with $t_{\mathrm{top}}$ varying from 0.0 to 2.2 nm (more details are shown in Fig. S5 and Supplemental Material, Sec. III [44]). (c) The fitted $\kappa$ and ${\kappa }_R$ as a function of $t_{\mathrm{top}}$ and (d) the $c^{\prime }$ derived from (c).

Figure 3

The 2D maps of the reflectivity spectra vs the energy and angle offset. (a)–(c) Reflectivity spectra of the samples with $t_{\mathrm{top}}$ values of 0, 1.0, and 2.2 nm. The zero angle offsets of the y-axis are located at 0.222°, 0.216°, and 0.216°. Panels (d)–(f) show the experimental results of (a)–(c), with the absorption edge being subtracted. Panels (g)–(i) show the calculations by the quantum optics model with the experimental parameters in Table S2 [44] used. From the left to the right panels, the conversion from valleys to peaks is clearly observed at the corresponding mode angles (dashed lines).

Figure 4

(a)–(c) The experimental and fitted reflectivity spectra at model angles of the three samples with different $t_{\mathrm{top}}$ as a function of incident photon energy. The dots are the experimental results, and the pink solid lines are the fitted results. (d)–(f) The extracted results after discarding the contributions of the absorption edge.