Figure 2: Quantifying the ED and MD transitions in Eu³⁺:Y₂O₃ by energy-momentum spectroscopy.

(a,b) Experimental energy- and momentum-resolved BFP spectra for s- and p-polarization, respectively. (c) Integrated energy spectrum showing the total observed emission (N, black line) decomposed into the contributions from ED (N_ED, blue line) and MD (N_MD, red line) transitions. (d,e) Theoretical BFP spectra for s- and p-polarization, respectively, produced using fits to equation (1). (f) Spectrally resolved intrinsic emission rates, A_ED (solid blue line) and A_MD (solid red line), deduced from this fitting analysis together with their 95% confidence intervals (dashed lines). (g) Momentum cross-sections for three representative wavelengths showing strong agreement between experimental data (solid lines) and theoretical fits (dashed lines) for both s-polarization (blue) and p-polarization (red). Emission at 592 nm shows a concave up p-polarized cross-section that is consistent with MD emission, and fitting confirms that this transition is predominantly magnetic (MD=90.8±2.0%). In contrast, 612-nm emission shows a concave down p-polarized cross-section with a local maxima at k_||=0, and the fit shows that emission at this wavelength is almost purely electric (ED=99.0±1.0%). Emission at 624 nm shows a less-pronounced maxima, and fitting reveals that this is a more mixed line (ED=88.4±0.7%).