Interference of surface plasmons and Smith-Purcell emission probed by angle-resolved cathodoluminescence spectroscopy

We investigate the interplay between geometrical lattice resonances and surface plasmons mediating the emission of Smith-Purcell visible light via angle-resolved cathodoluminescence spectroscopy. We observe strong modulations in the dispersion curves of Smith-Purcell radiation (SPR) when they intersect the surface plasmons of silver gratings using a 200-kV transmission electron microscope. The decay of the plasmons away from the grating is directly probed by controlling the electron-beam position relative to the sample surface with nanometer precision. Our measurements are in excellent agreement with numerical simulations, clearly revealing the presence of characteristic Fano profiles resulting from the interference of the light continuum and the discrete plasmon states for each direction of emission. The intensity anomaly in the SPR emission pattern can be well explained from the geometrical consideration of the intersections between the dispersion planes of the SPR and surface plasmon polariton (SPP). A strong and directional SPR beam can be realized under the condition that the SPR dispersion plane comes in contact with the band edge of the SPP dispersion plane.

Figure 1

(a) Illustration of a 1D silver grating and an aloof electron moving parallel to its surface with impact parameter $b$. (b) Geometry of the angle-resolved measurement of Smith-Purcell radiation using a parabolic mirror. The specimen faces the mirror with its surface normal oriented parallel to the paraboloid axis $z$. The electron beam is incident along $x$. The cathodoluminescence (CL) emission is collected as a function of emission direction defined by angles $\theta$ and $\phi$ through a moving pinhole mask.

Figure 2

(a)–(c) Angle and energy dependence of the CL differential intensity $d^{2}I/d\omega d\theta$ ($\phi =0^{\circ }$) originating from silver gratings of periods $d=500$, 600, and 800 nm. The 200-keV electron is passing $\sim 50\mathrm{nm}$ away from the metal surface. (d)–(f) Dispersion patterns $d^{2}I/d\omega d{k}_x$ obtained by changing the angle $\theta$ in (a)–(c) to the wave vector $k_x=(\omega /c)cos\theta$. (g)–(i) Calculated patterns corresponding to (d)–(f). Blue lines in (d)–(i) indicate the electron dispersion $k_x=v/c$ and its umklapp images displaced by an integral number of times $2\pi /d$ along $k_x$. The green curves represent the surface plasmon dispersion of flat silver and its umklapp images. The red line indicates the dispersion line of light (the light line). Insets to (e) and (h) show experimental and theoretical CL intensity profiles along the $AB$ segments of the density plots.

Figure 3

(a) Angle- and energy-resolved CL emission from the same $d=800\mathrm{nm}$ grating as in Fig. 2, taken with an electron beam located close to the surface. (b) Panchromatic map of the sample, revealing the metal surface and the depth of the grating ($\sim 350\mathrm{nm}$). (c) Wavelength dependence of the CL decay length with electron-surface separation. (d)–(f) Spectral images taken at fixed emission angles (d) $\theta ={135}^{\circ }$, (e) $\theta ={110}^{\circ }$, and (f) $\theta ={100}^{\circ }$, marked by vertical white lines in (a). The horizontal axis indicates the electron-beam position relative to the metal surface (vertical line). The data in (c) are obtained by analyzing (d) (squares), (e) (circles), and (f) (triangles).

Figure 4

(a)–(j) Monochromatic emission patterns from the $d=800$-nm grating taken at 200 keV by scanning the pinhole mask in the mirror image plane, presented at various photon energies from (a) 1.92 eV to (j) 2.8 eV. (k) The panchromatic emission pattern observed by the CCD camera under the same condition, together with the contour lines of the emission angles $(\theta ,\phi )$.

Figure 5

(a) Schematic representation of the dispersion plane ($h_n$ plane) of the $n\text{th}$ SPR in the $E-\mathit{k}$ space. The observable backward emission occurs on the dispersion plane inside the light cone indicated by a blue color. (b) The cone plane in the $\mathit{k}$ space formed by the SPR wave vectors with equal photon energy. (c) Emission directions of the SPR with equal photon energy in a real space. (d) The configuration of the SPR dispersion plane ($h_{-3}$ plane) and the SPP dispersion planes in the $E-\mathit{k}$ space. The intensity anomaly of the SPR arises along the intersection line (pink) and especially at the spots (red) on the band edge line (red) at the zone boundary. (e) Dispersion lines of the SPR and SPP on the $E-k_x$ cross-sectional plane in (d) for the $d=800$-nm grating and 200-keV incident beam.

Figure 6

(a)–(f) Panchromatic emission patterns (the upper row) from grating of period $d=800$ nm obtained by imaging the parabolic mirror using the CCD camera taken at various accelerating voltages. The lower row shows corresponding ARS patterns at $\phi =0^{\circ }$ acquired in the same way as in Fig. 2. The strong directional beam appears in (b) 110 keV and (d) 140 keV.

Figure 7

Dispersion patterns from the $d=800$-nm grating at (a) 110 keV and (b) 140 keV in $E-k_x$ plane transformed from the ARS patterns in Figs. 6 and 6. Intensity enhancement occurs near the crossing point of the two SPP dispersion lines, when the SPR dispersion plane comes in contact with the band edge at the crossing point.