Generation of nearly pure and highly directional magnetic light in fluorescence of rare earth ions

TL;DR

This paper analyzes how to generate nearly pure, highly directional magnetic light emission from rare-earth ions in dielectric spheres, achieving significant enhancements in directivity, decay rates, and fluorescence.

Contribution

It identifies specific configurations of dielectric spheres and emitter positions that maximize magnetic dipole emission dominance and enhancement.

Findings

Branching ratio of MD transition approaches one.

Magnetic light directivity increases by over 25 times.

Fluorescence enhancement exceeds 10,000 times.

Abstract

A thorough analysis of the emission via the magnetic dipole (MD) transition, called magnetic light below, of trivalent rare-earth ions in or near dielectric homogeneous spheres has been performed. In the search for enhancement of fluorescence from magnetic light, one faces the difficult task of identifying the regions where the combined fluorescence due to multiple electric dipole (ED) transitions becomes negligible compared to the fluorescence of the MD transition. We have succeeded in identifying a number of configurations with dielectric sphere parameters and a radial position of a trivalent rare-earth emitter wherein the branching ratio of the MD transition approaches its limit of one, implying that transitions from a given initial level (e.g., $^5$D$_0$-level of Eu$^{3+}$) are completely dominated by the MD transition. The dimensionless directivity of the MD emission, the radiative decay rates, and the fluorescence of the magnetic light can be increased by a factor of more than $25$, $10^3$, and $10^4$, respectively.