Research ArticlePHYSICS

Observation of electron-induced characteristic x-ray and bremsstrahlung radiation from a waveguide cavity

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Science Advances  22 Jan 2021:
Vol. 7, no. 4, eabd5677
DOI: 10.1126/sciadv.abd5677
  • Fig. 1 X-ray generation in waveguides.

    (A) An e-beam (e) impinges onto a planar waveguide consisting of cladding layer (CL), guiding layer (GL), and a central fluorescent metal layer (FL). The electron impact excites atoms, which emit characteristic x-rays and bremsstrahlung into the waveguide. Angle- and energy-resolved detection is implemented by scanning an SDD detector. To increase the angular resolution, the SDD can be replaced by the MÖNCH detector. For excitation with x-rays: The e-beam (e) is replaced by a focused x-ray beam (a) impinging the waveguide in grazing incidence. Here, the detection is in an angle of 90° to the primary x-ray beam. Both beams (e) and (a) can be scanned in Δz to change the propagation length of the generated x-rays inside the waveguide. (B) Detailed view on the x-ray generation with electron impact. Characteristic x-rays are emitted into waveguide modes with mode numbers m. The x-rays exit the channel either through the thinned top cladding by evanescent waves (r) or directly at the end of the channel (g). (C) Detected far-field emission of characteristic x-rays generated inside the waveguide shows sharp emission peaks at the structure’s horizon.

  • Fig. 2 Simulation of propagation and modal emission.

    (A) Propagation of the electric field inside a single Mo/C waveguide, when a plane wave is incident under the angle θPW as given in the inset. The main direction of propagation is along the z direction [see (C)]. The propagation is based on finite-difference simulations. (B) Intensity of the propagated field as a function of θPW in the center of the guiding layer and at a distance of Δz = 400 μm to the side edge. The colored stars mark the positions in (A) and (B). According to the reciprocity theorem, we now change directions: If an atom in the center of the guiding layer and at a distance of Δz = 400 μm emits x-rays, then the intensity measured at an angle θf = θPW is given by (B). Scale bars (A), 10 nm in y and 100 μm in z. The color in (A) scales with the normalized intensity of the electric field on a logarithmic scale.

  • Fig. 3 Characteristic radiation in the Co/Cu waveguide.

    Far-field intensity of the characteristic Kα lines, exhibiting modal peaks as a function of angle θf with respect to the waveguide horizon. Intensities measured with an SDD detector excited with electron impact and, for comparison, fluorescence excited with a laboratory x-ray tube. The right ordinate shows the Kα radiant flux Φp per e-beam power for the characteristic (e-beam excited) radiation. (A) Co-Kα radiation excited in the central ∂-layer. (B) Cu-Kα radiation excited in the cladding. Peak positions match the simulated intensities.

  • Fig. 4 Synchrotron-excited fluorescence inside the Fe/Ni multiwaveguide.

    Modification of Fe-K fluorescence intensity IFe by the waveguide modes, measured by scanning a focused synchrotron beam close to the side face of the waveguide. (A) Detector image of IFe shows strong modulations as a function of θf, whereas IFe is constant along the lateral direction θ. Radiation exits through both interfaces: the exit face of the waveguide θf ≃ 0 and the top cladding. The intensity at negative θf is damped by absorption in the substrate. (B) IFef) is obtained after integration along θ of the detected intensity. The simulated intensity is shown for comparison. The zoom in the inset shows Fano-like line shapes. (C) The variation of fluorescence intensity close to the exit side IFef, Δz), with each column of the matrix corresponding to an intensity profile such as in (B). Pronounced oscillations show that the emission of fluorescence oscillates with distance to the exit of the waveguide. (D) Simulated intensity. The arrows indicate Δz of the profiles shown in (B). The color scales with the intensity in arbitrary units on a linear scale (A) and logarithmic scale (C and D).

  • Fig. 5 Characteristic radiation of the Mo/C multiwaveguide.

    Variation of characteristic Mo-K intensity when scanning the e-beam toward the truncated side of the waveguide array. (A) IMo as a function of the exit angle θf and the distance Δz between the e-beam position and the waveguide edge. For better visibility of the interference effects of the radiation exiting through the side edge, the intensity map IMof, Δz) has been corrected for the damping of the waveguide, by a division with Φpfit (see below). (B) Total radiant flux Φp per incident e-beam power of Mo-K radiation exiting through the side face of the waveguide, i.e., between the angular range ∣θf∣ ≤ 2.9 mrad [green rectangle in (A)]. The least square fit Φpfit of a biexponential decay to the radiant flux Φp yields two characteristic decay lengths (1/e-lengths), a slow decay Δz1/e = 622(11) μm and a faster decay Δz1/e = 82(2) μm, which can be attributed to the 0th and 1st mode, respectively. The right ordinate shows the Mo-K brilliance per e-beam power of the radiation leaving through the side edge. The color in (A) scales with the intensity in arbitrary units on a logarithmic scale.

  • Fig. 6 E-beam–excited characteristic and bremsstrahlung radiation in the Fe/Ni multiwaveguide system.

    The x-ray spectrum is measured with the SDD detector as a function of exit angle θf. The mode pattern for each of the characteristic emission lines—Fe-Kα, Fe-Kβ, Ni-Kα, and Ni-Kβ—is observed as horizontal lines with the local maxima at the angles of the waveguide modes. The bremsstrahlung background in between the horizontal lines of characteristic radiation also shows the modulation of the waveguide’s mode pattern. The inset shows the theoretical positions of the modes for the characteristic radiation (dots) and for the bremsstrahlung continuum (lines), with mode numbers m = 0 to 6 (from left to right). The color scales with the intensity in arbitrary units on a logarithmic scale.

  • Fig. 7 Increasing the brilliance of the Mo/C waveguide with elongated e-beam spots.

    The brilliance B of the characteristic Mo-K radiation generated inside the Mo/C waveguide system can be increased substantially by expanding the e-beam spot on top of the waveguide along the z direction. The area power density of the e-beam is kept constant at the value used in the experiments pe = 4kW/mm2. We calculated the brilliance by numerical integration of the data in Fig. 5B. The integration limits of the e-beam are from z0 to z1 = z0 + ze (see inset). Note that the effective x-ray spot size of the modes leaving the waveguide through the side face does not change with a variation of ze. The e-beam power P(ze) is given on the upper abscissa.

  • Fig. 8 X-ray source based on direct emission into waveguide modes.

    (A) A source can, for example, be realized by exchanging the conventional diamond-supported W layer in transmission targets with a diamond-supported waveguide structure. The waveguide anode emits into a narrow radiation cone (dark red) with increased brilliance in comparison to the emission cone of a conventional anode (light red). The diamond forms the vacuum window and, at the same time, supports the waveguide structure, which can consist of cylindrical (B) or planar guides (C).

  • Table 1 Waveguide samples.

    The layer composition of the three samples is listed from top to bottom.

    Cu, 40 nmNi, 30 nmMo, 30 nm
    Cr, 10 nm
    Pulsed laser

Supplementary Materials

  • Supplementary Materials

    Observation of electron-induced characteristic x-ray and bremsstrahlung radiation from a waveguide cavity

    Malte Vassholz and Tim Salditt

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