Spectrally and Spatially Resolved Smith-Purcell Radiation in Plasmonic Crystals with Short-Range Disorder

Electrons interacting with plasmonic structures can give rise to resonant excitations in localized plasmonic cavities and to collective excitations in periodic structures. We investigate the presence of resonant features and disorder in the conventional Smith-Purcell effect (electrons interacting with periodic structures) and observe the simultaneous excitation of both the plasmonic resonances and the collective excitations. For this purpose, we introduce a new scanning-electron-microscope-based setup that allows us to probe and directly image new features of electron-photon interactions in nanophotonic structures like plasmonic crystals with strong disorder. Our work creates new possibilities for probing nanostructures with free electrons, with potential applications that include tunable sources of short-wavelength radiation and plasmonic-based particle accelerators.

Popular Summary

Electrons generate light when they pass over the surface of any periodic structure, such as a crystal or a diffraction grating. This phenomenon is known as the Smith-Purcell effect, and it depends critically on the quality, fidelity, and exact features of the sample. Significant progress in nanofabrication over the past decade has spawned a renewed interest in this effect as well as a variety of new phenomena and applications. Despite this progress, it has not been clear whether Smith-Purcell and other similar light emission phenomena could still occur in disordered structures, where light and other kinds of waves always become concentrated in spots rather than propagate freely. We find that the Smith-Purcell effect does occur in strongly disordered diffraction gratings, and we demonstrate it in plasmonic crystals, which are metal films that can trap light (and, generally, electromagnetic waves) along their surface.

We modified a scanning electron microscope (SEM) to observe the interaction of free electrons moving parallel to samples of silver that have periodic grooves or deposits. Our setup obtains direct optical images of the surface while simultaneously recording the spectrum of the emitted light. This allows us to not only record what kind of light is generated but where on the sample it comes from. We find that in addition to the traditional Smith-Purcell emission, light is also generated via a different mechanism near the edges and defects of the sample. Our modified SEM setup can simultaneously measure both mechanisms and distinguish between them.

A better understanding of how electrons interact with nanophotonic structures, where light is controlled and generated on nanometer scales, can lead to the development of tunable sources of terahertz, infrared, and visible radiation as well as new diagnostic tools.

Figure 1

Illustration of the experimental setup. The left part (shaded in blue) describes the modified stage inside the vacuum chamber of the SEM. The sample is held so that its surface is almost parallel to the path of the electron beam. The emitted light is collected by an objective, directing the emitted light into an enclosure box holding the rest of the optical setup. The right part (shaded in green) describes the optical collection setup, having a beam splitter (BS) that splits the optical beam to a fiber tip collector leading to a spectrometer (right of BS) and two CCD cameras (below the BS). Right before the spectrometer fiber, we place a polarizer. Lens 2 is used to image the surface of the sample on two CCDs. We choose between them with a flip mirror. We change among three CCDs: a visible CCD, a less-sensitive but color-visible CCD, and a near-infrared CCD.

Figure 2

The conventional Smith-Purcell effect. (a) Illustration of the interaction presenting the electrons as a black dashed arrow, passing near a grating (which is shown by its real SEM image). The colored wiggly arrows represent the emitted Smith-Purcell radiation. (b) Measured spectra for different kinetic energies. (The measurements are displaced vertically for clarity.) The dashed vertical lines are calculated according to the conventional Smith-Purcell theory, with the color corresponding to the same kinetic energies.

Figure 3

Direct imaging of enhanced and inhibited emission from line defect. (a,b) Illustration of the electron beam (dashed black arrow) interacting with line defects fabricated in the samples. (c–e) False color optical images of the light emission from the samples showing a clear enhancement (c,d) or inhibition (e) of the emission from the edge of the periodic structure and from the line defect. The samples are fabricated by either electron beam lithography with silver deposition (c,d) or by focused ion beam milling of trenches into a silver film (e). These techniques result in different cross sections to the electrons interacting with the gratings, as illustrated by the grating profiles between (a) and (b), leading to enhanced and inhibited emission, respectively. The electrons’ kinetic energy is 13 kV and 20 kV in (c) and (d,e), respectively.

Figure 4

Collective and resonant effects in the interaction of free electrons with a disordered plasmonic structure. (a) Illustration of the Smith-Purcell emission from the 2D plasmonic crystal with strong disorder. (b) Illustration of the emission from the localized plasmonic resonance of a single silver rod. In both (a) and (b), the electron beam is plotted with a dashed black line, and the emitted light is drawn as wiggly arrows. The semiperiodic structure itself is the SEM image of the real pattern. (c) Measuring the spectra for different kinetic energies with a polarizer that transmits light polarized along the $z$ axis. This shows a very good match to conventional Smith-Purcell theory [Eq. (1)], marked by dashed lines in the color corresponding to the same kinetic energies. (d) Measuring the spectrum with a polarizer that transmits light polarized along the $y$ axis. This shows a single plasmonic resonance at 730 nm, agreeing with simulations (see Fig. 6). Note that small features from the spectral peaks of (c) can be seen in (d) and vice versa. This is explained by the conventional Smith-Purcell radiation not being entirely $z$ polarized in this structure, in addition to imperfections in the polarization filtering. For comparison of the scales, the red peak in (c) is 2.4 times more intense than the red peak in (d).

Figure 5

The localized plasmonic resonance of a single silver rod. (a) The reflection of a normal incidence beam polarized along the $z$ ($y$) axis in blue (green), simulated for an exactly periodic plasmonic crystal, similar to the structure in Figs. 4 and 6. For reference, we plot in red the reflection from a silver surface without nanorods. (b) Total absorption (blue) and scattering (red) from a single silver nanorod (subtracting the background by simulating a silver surface without any feature). The results for $z$ ($y$)-polarized incidence are plotted by a dashed (solid) curve. (c) Electric-field amplitude (absolute value) for the resonance at about 600 nm. The field distribution makes it clear that this is a Bloch mode resonance. Indeed, this resonance disappears when simulating the structure with absorbing boundary conditions in (b) (perfectly matched layers—PMLs) instead of periodic boundary conditions in (a). (d) Electric-field amplitude (absolute value) of the localized plasmonic resonance at about 730 nm, which appears in both (a) and (b) as expected.

Figure 6

Collective contribution from a disordered structure. Simulation of the Smith-Purcell dispersion relation, plotting the far-field Poynting vector along the radial direction as a function of the polar angle in a disordered array (a,c) and a periodic array (b,d) with a pitch of 145 nm, which is the mean value for the disordered array. We choose the positions of the disordered array by image processing of the SEM image (e)—retrieving the positions of the rods marked by red circles overlaying the image. The illustration of the light emission is presented in (f), marking the polar angle of emission $\theta$. The noise robustness and the dispersion relation are independent of the azimuthal angle (taken to be zero in the simulation here).