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arXiv:1208.2642 · Physical Review B

Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths

Christopher M. Dodson, Rashid Zia

Published Sep 5, 2012• 253 citations
arXivHTMLPDF

Abstract

Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the $4{f}^{\text{n}}$ configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.

DOI
10.1103/physrevb.86.125102

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Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the 4fn4{f}^{\text{n}}4fn configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.
Summary form only given. Although it is often assumed that all light-matter interactions at optical frequencies are mediated by electric dipole transitions, strong optical-frequency magnetic dipoles do exist. In fact, we see magnetic dipole emission every day from the many lanthanide ions (such as erbium, europium, and terbium) that help to illuminate everything from fluorescent lighting to telecom fiber amplifiers. Higher-order processes such as magnetic dipole and electric quadrupole transitions also play an important part in the light emission from transition metal ions and semiconductor quantum dots. Nevertheless, most applications have overlooked the device implications of these electric-dipole-forbidden transitions throughout the visible and near-infrared regime, and their contributions to many important emitters have not been fully characterized.In this presentation, we will experimentally characterize the "forbidden" transitions in a range of solid-state emitters and investigate their applications and implications for nanophotonics. We will examine the electric dipole approximation commonly used to describe light-matter interactions and discuss naturally occurring systems that exhibit higher-order magnetic dipole and electric quadrupole emission. We will illustrate how these nanoscale quantum transitions can provide both a new way to probe magnetic light-matter interactions and a new degree of design freedom for active electronic and photonic devices. Specifically, we will demonstrate how the different symmetries of multipolar transitions can be exploited to identify, quantify, and control light emission, even at sub-lifetime scales. Despite similar radiation patterns, magnetic and electric dipole emitters have different symmetries with respect to polarization and phase. Thus, in an inhomogeneous environment, we can tailor interference effects and the local density of optical states to selectively enhance either electric or magnetic dipole emission [1,2]. To examine the scope of such higher-order transitions, we will present quantum mechanical calculations that identify all the magnetic dipole and electric quadrupole emission lines in the trivalent lanthanide series in the visible to near-infrared spectrum [3]. Then, we will present an energyand momentum-resolved spectroscopy technique to directly quantify the electric and magnetic dipole contributions from any mixed transition. [4] Using energy-momentum spectroscopy, we will experimentally examine the higher order transitions in lanthanide ions [4,5], transition metal ions [6], and epitaxial quantum dots [7]. If time permits, we will then show how the symmetry differences between magnetic and electric dipoles can be used to address specific electronic states [6] and to dynamically tune emission spectra at sub-lifetime-scales [8].
Tremendous advances in the study of magnetic light-matter interactions have recently been achieved using man-made nanostructures that exhibit and exploit an optical magnetic response. However, naturally occurring emitters can also exhibit magnetic resonances in the form of optical-frequency magnetic-dipole transitions. Here we quantify the magnetic nature of light emission using energy- and momentum-resolved spectroscopy, and leverage a pair of spectrally close electric- and magnetic-dipole transitions in trivalent europium to probe vacuum fluctuations in the electric and magnetic fields at the nanometre scale. These results reveal a new tool for nano-optics: an atomic-size quantum emitter that interacts with the magnetic component of light. Light-matter interactions are generally dominated by electric fields and electric-dipole transitions. This study, however, quantifies magnetic contributions to light emission and so exploits the strong natural magnetic-dipole transitions in lanthanide ions to measure optical-frequency magnetic fields.
Mie resonances in dielectric particles can increase the local optical density of states (LDOS) associated with either electric or magnetic transition rates in nearby quantum emitters without ohmic losses. Their rather large quality factors compensate their low field confinement as compared to the plasmon resonances of metallic nanostructures for which nonradiative decay channels dominate. We show theoretically that near-infrared quadrupolar magnetic resonances in silicon particles can preferentially promote magnetic versus electric radiative deexcitation in trivalent erbium ions at 1.54 $\ensuremath{\mu}$m. The distance dependent interaction between magnetic (electric) dipole emitters and induced magnetic or electric dipoles and quadrupoles is derived analytically and compared to quasiexact full-field calculations based on Mie theory. We discuss how near-field coupling between nearby particles can further enhance the magnetic LDOS and compensate for the weak refractive index contrasts between dielectric particles and a typical host matrix for the lanthanide ions.
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., 5D0^{5}\mathrm{D}_{0}5D0​ level of Eu3+{\mathrm{Eu}}^{3+}Eu3+) 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, 103{10}^{3}103, and 104{10}^{4}104, respectively.
Naturally occurring magnetic dipole resonances can be used as optical sources in metamaterials and optical nanostructures to engineer light emission with applications in energy harvesting, biological imaging, and other photonic devices. Here, we use energy-momentum spectroscopy to quantify the electric and magnetic dipole emission rates of near-infrared transitions in Dy3+ and Tm3+ doped Y2O3. Of these emission lines, we find that the overlapping 4F9/2 → 6F11/2 and 4F9/2 → 6H9/2 transitions in Dy3+ and the overlapping 1G4 → 3H5 and 3H4 → 3H6 transitions in Tm3+ exhibit the greatest MD emission and thus offer the most direct pathway for integration with magnetic modes in resonant nanostructures.