Quantifying and controlling the magnetic dipole contribution to $1.5-\mu \mathrm{m}$ light emission in erbium-doped yttrium oxide

We experimentally quantify the contribution of magnetic dipole (MD) transitions to the near-infrared light emission from trivalent erbium-doped yttrium oxide (Er${}^{3+}$:Y${}_2$O${}_3$). Using energy-momentum spectroscopy, we demonstrate that the ${}^4$I${}_{13/2}{\to }^4$I${}_{15/2}$ emission near 1.5 $\mu$m originates from nearly equal contributions of electric dipole (ED) and MD transitions that exhibit distinct emission spectra. We then show how these distinct spectra, together with the differing local density of optical states for ED and MD transitions, can be leveraged to control Er${}^{3+}$ emission in structured environments. We demonstrate that far-field emission spectra can be tuned to resemble almost pure emission from either ED or MD transitions and show that the observed spectral modifications can be accurately predicted from the measured ED and MD intrinsic emission rates.

Figure 1

Quantifying the near-infrared ED and MD transitions in Er${}^{3+}$:Y${}_2$O${}_3$ by energy-momentum spectroscopy. (a), (b) Experimental energy-momentum spectra obtained for $s$ and $p$ polarization, respectively. (c) Spectrally resolved emission rates, ${\Gamma }_0^{\mathrm{ED}}$ and ${\Gamma }_0^{\mathrm{MD}}$, obtained from fitting the experimental momentum cross sections at each wavelength. Inset shows a schematic of the measured sample. (d)–(f) Comparison of experimental data and theoretical fits for three peak wavelengths (1517, 1548, and 1564 nm) as highlighted by dashed lines in (c).

Figure 2

LDOS-based tuning of Er${}^{3+}$:Y${}_2$O${}_3$ emission near a gold mirror. (a) Normalized experimental spectra measured for different emitter-mirror separation distances, $d$; each spectra is normalized to its total integrated intensity [37]. (b) Normalized theoretical spectra predicted by the three-layer LDOS model using ED and MD intrinsic rates from Fig. 1. (c), (d) Comparison of experimental and theoretical spectra for $d=219$ nm and $d=441$ nm as indicated by dashed white lines in (a) and (b). Inset in panel (d) shows a schematic of the sample with different thickness spacer layers between the emitter layer and gold mirror.

Figure 3

Analysis of ED and MD contributions. (a), (b) Relative ED and MD contributions to the emission spectra as predicted by theoretical calculations for the $d=219$- and 441-nm cases. (c) Fractional contribution of the ED and MD transitions integrated over the full spectral range from 1450 to 1610 nm. (d) Comparison of the experimentally observed and theoretically predicted normalized intensity variations at three representative wavelengths: 1517 nm, 1548 nm, and 1564 nm as a function of relative path length, $N$. The intensity traces in panel (d) present vertical cross sections through Figs. 2 and 2, in which each cross section has been normalized to its maximum value to facilitate side-by-side comparison.