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Optics Letters

Strong enhancement of magnetic dipole emission in a multilevel electronic system

Sinan Karaveli, Rashid Zia

Published Oct 8, 2010• 68 citations
Publisher

Abstract

The Purcell effect is commonly used to increase light emission by enhancing the radiative decay of electric dipole transitions. In this Letter, we demonstrate that the opposite effect, namely, the inhibition of electric dipole transitions, can be used to strongly enhance light emission via magnetic dipole transitions. Specifically, by exploiting the differing symmetries of competitive electric and magnetic dipole transitions in trivalent europium, we demonstrate a fourfold enhancement of the far-field emission from the (5)D(0)→(7)F(1) magnetic dipole transition in trivalent europium. We show that this strong enhancement is well predicted by a three-level model that couples the individual Purcell enhancement factors of competitive transitions from the same excited state.

DOI
10.1364/ol.35.003318

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We demonstrate that magnetic dipole transitions provide an additional degree of freedom for engineering emission spectra. Without the need for a high-quality optical cavity, we show how a simple gold mirror can strongly tune the emission of trivalent europium. We exploit the differing field symmetries of electric and magnetic dipoles to selectively direct the majority of emission through each of three major transitions (centered at 590, 620, and 700 nm), and present a model that accurately predicts this tuning from the local electric and magnetic density of optical states.

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Engineering the local density of states with nanophotonic structures is a powerful tool to control light-matter interactions via the Purcell effect. At optical frequencies, control over the electric field density of states is typically used to couple to and manipulate electric dipole transitions. However, it is also possible to engineer the magnetic density of states to control magnetic dipole transitions. In this work, we experimentally demonstrate the optical magnetic Purcell effect using a single rare earth ion coupled to a nanophotonic cavity. We engineer a new single photon emitter, Er$^{3+}$ in MgO, where the electric dipole decay rate is strongly suppressed by the cubic site symmetry, giving rise to a nearly pure magnetic dipole optical transition. This allows the unambiguous determination of a magnetic Purcell factor $P_m=1040 \pm 30$. We further extend this technique to realize a magnetic dipole spin-photon interface, performing optical spin initialization and readout of a single Er$^{3+}$ electron spin. This work demonstrates the fundamental equivalence of electric and magnetic density of states engineering, and provides a new tool for controlling light-matter interactions for a broader class of emitters.

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

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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 $4{f}^{\text{n}}$ 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.

arXiv:1208.2642•Physical Review B•Sep 5, 2012•253 citations
The Purcell effect is commonly used to increase light emission by enhancing the radiative decay of electric dipole transitions. In this Letter, we demonstrate that the opposite effect, namely, the inhibition of electric dipole transitions, can be used to strongly enhance light emission via magnetic dipole transitions. Specifically, by exploiting the differing symmetries of competitive electric and magnetic dipole transitions in trivalent europium, we demonstrate a fourfold enhancement of the far-field emission from the (5)D(0)→(7)F(1) magnetic dipole transition in trivalent europium. We show that this strong enhancement is well predicted by a three-level model that couples the individual Purcell enhancement factors of competitive transitions from the same excited state.
We demonstrate that magnetic dipole transitions provide an additional degree of freedom for engineering emission spectra. Without the need for a high-quality optical cavity, we show how a simple gold mirror can strongly tune the emission of trivalent europium. We exploit the differing field symmetries of electric and magnetic dipoles to selectively direct the majority of emission through each of three major transitions (centered at 590, 620, and 700 nm), and present a model that accurately predicts this tuning from the local electric and magnetic density of optical states.
Engineering the local density of states with nanophotonic structures is a powerful tool to control light-matter interactions via the Purcell effect. At optical frequencies, control over the electric field density of states is typically used to couple to and manipulate electric dipole transitions. However, it is also possible to engineer the magnetic density of states to control magnetic dipole transitions. In this work, we experimentally demonstrate the optical magnetic Purcell effect using a single rare earth ion coupled to a nanophotonic cavity. We engineer a new single photon emitter, Er3+^{3+}3+ in MgO, where the electric dipole decay rate is strongly suppressed by the cubic site symmetry, giving rise to a nearly pure magnetic dipole optical transition. This allows the unambiguous determination of a magnetic Purcell factor Pm=1040±30P_m=1040 \pm 30Pm​=1040±30. We further extend this technique to realize a magnetic dipole spin-photon interface, performing optical spin initialization and readout of a single Er3+^{3+}3+ electron spin. This work demonstrates the fundamental equivalence of electric and magnetic density of states engineering, and provides a new tool for controlling light-matter interactions for a broader class of emitters.
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].
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.
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.
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.