Wide-Angle Energy-Momentum Spectroscopy

Publication Type:

Journal Article


Opt. Lett., Volume 39, p.3927–3930 (2014)




Emission, Materials and process characterization, Rare-earth-doped materials, Transition-metal-doped materials


Light emission is defined by its distribution in energy, momentum, and polarization. Here, we demonstrate a method that resolves these distributions by means of wide-angle energy-momentum spectroscopy. Specifically, we image the back focal plane of a microscope objective through a Wollaston prism to obtain polarized Fourier-space momentum distributions, and disperse these two-dimensional radiation patterns through an imaging spectrograph without an entrance slit. The resulting measurements represent a convolution of individual radiation patterns at adjacent wavelengths, which can be readily deconvolved using any well-defined basis for light emission. As an illustrative example, we use this technique with the multipole basis to quantify the intrinsic emission rates for electric and magnetic dipole transitions in europium-doped yttrium oxide (Eu3$+$:Y2O3) and chromium-doped magnesium oxide (Cr3$+$:MgO). Once extracted, these rates allow us to reconstruct the full, polarized, two-dimensional radiation patterns at each wavelength.