Quantifying and controlling the magnetic dipole contribution to 1.5 $mu$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 (LDOS) 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.