Cathodoluminescence Enhancement Mechanisms in Silica Microspheres

TL;DR

This work analyzes cathodoluminescence in silica microspheres that function both as optical resonators for whispering-gallery modes and as high-NA collimators for external emission. By leveraging spectral, angular, and spatial data across multiple sphere sizes and electron-beam energies, the authors decompose CL into photon generation, radiative leakage, and material absorption, revealing surface-localized generation at the sphere boundary. They identify two emission regimes—WGM-dominated and collimated output—and quantify quality-factor components ($Q_{tot}$, $Q_{rad}$, $Q_{mat}$), demonstrating how geometry and material losses govern CL efficiency. The demonstrated collimation and mode selectivity enable applications in quantum measurements, fiber coupling, and studies of surface electronic excitations, advancing CL-based spectroscopy and potential electron–photon entanglement experiments.

Abstract

Cathodoluminescence (CL) enables optical-frequency analysis of samples with nanometer resolutions, originating from the interaction of a focused electron beam with radiative electronic states, or directly with the optical modes of the sample. Here we decompose the various mechanisms underlying CL generation and emission from an archetype spherical resonator using its spectral, angular and spatially resolved features. We investigate radiation of optical whispering-gallery modes in regimes of coherent and incoherent luminescence. The use of different experimental regimes allows us to disentangle the different contributions to the CL in spheres, namely, photon absorption, generation and radiative leakage, and conclude that the photon generation occurs precisely on the sphere's surface. In addition, the spheres serve as high-NA collimating lenses for CL, resulting in mode quality unprecedented for CL in free space. We believe that such collimated and directed CL in free space will enhance existing quantum measurements of CL and facilitate new ones, such as high-rate electron-photon entangled pairs, CL from quantum emitters, and homodyne analysis of CL.

Figures (5)

• Figure 1: Schematic of the measurement setup. (a) An electron beam is focused onto the sample, generating CL photons, which are collimated through a parabolic mirror. A slit before the grating maps the spectrum vs. the polar angle $\theta$, around $\phi=0^\circ$. (b) The inset shows CL enhancement by excitation of a resonant WGM (right) and by geometrical beam collimation (left).
• Figure 2: Angular-resolved CL spectrum. (a)–(b) SEM images of silica microspheres with diameters of 2.1 $\mu m$ , 4.4 $\mu m$, respectively. The electron-beam positioning is marked by a gray square circled in orange. (c) SEM image of a 62 $\mu m$ diameter sphere fabricated from a tapered optical fiber. (d) $\theta$-resolved CL spectrogram from the 2.1 $\mu$m sphere, showing peaks of the sphere's WGMs with a spatially varying background. (e) CL spectral count rate extracted from (d), summed over a low-background range $-70^\circ\leq\theta_{CL}\leq-10^\circ$ (purple) and a high-background range $-79.4^\circ \leq \theta_{CL} \leq -77.6^\circ$ (orange)
• Figure 3: Angular correlations of CL emission with electron impact coordinate. (a) CL emission peak angle $\phi_{CL}$ as function of the beam impact angle $\psi_e$, shows an emission trend to the opposing angle due to the rotation invariance and the sphere. (b) Expanded view of the marked segment, with added error bars. (c) A grid of impact positions of the electron beam, overlaid on a 2.1 $\mu m$ sphere. (d)-(e) 2D maps showing the CL angular distribution for electron excitation at $\psi_e = 320^\circ , r_e = R_{sphere}$ (d) and $\psi_e = 320^\circ, r_e = 0.2 R_{sphere}$ (e).
• Figure 4: Detected CL emission peak angle $\theta_\text{CL}$ as function of the electron beam radial distance from the center of the sphere $r_e$, shown for three different $\psi_e$ angles. The sphere radius is indicated by the black dashed line.
• Figure 5: Quality factor decomposition of silica microspheres. (a) Spectrum of the 4.4 $\mu m$ sphere and (b) 2.1 $\mu m$ sphere. The linewidth of the peaks in (a) was used to extract the material-loss quality factor, $Q_{mat}$. (c) Radiation quality factor, $Q_{rad}$, derived from the experimental linewidth of the peaks in (b) for TE (open circles) and TM polarized (filled circles). The x-markers are the radiative quality factors from the simulated whispering-gallery loss. The dashed line is a guide to the eye. The filled squares (right axis) are the linewidth ratio of TE- vs. TM-polarized modes.