We derive the magnetic dipole selection rules and the magnetic dipole absorption rate for a spherical semiconductor quantum dot. We find that electric dipole and magnetic dipole transitions are exclusive and therefore can be spectrally distinguished. The magnitudes of electric and magnetic absorption rates are compared for excitation with a strongly focused azimuthally polarized beam. It turns out that spatial optical resolution can be increased by detection of the ratio of magnetic and electric absorption rates. Resolution is limited only by the purity of the laser mode used for excitation.
We derive the magnetic dipole selection rules and the magnetic dipole absorption rate for a spherical semiconductor quantum dot. We find that electric dipole and magnetic dipole transitions are exclusive and therefore can be spectrally distinguished. The magnitudes of electric and magnetic absorption rates are compared for excitation with a strongly focused azimuthally polarized beam. It turns out that spatial optical resolution can be increased by detection of the ratio of magnetic and electric absorption rates. Resolution is limited only by the purity of the laser mode used for excitation.
High Resolution Image Download MS PowerPoint Slide At optical frequencies, interactions of the electric field component of light with matter dominate, whereas magnetic dipole transitions are inherently weak and challenging to access independently of electric dipole transitions. However, magnetic dipole transitions are of interest, as they can provide valuable complementary information about the matter under investigation. Here, we present an approach which combines structured light irradiation with tailored sample morphology for enhanced and high-contrast optical magnetic field excitation, and we test this technique on Eu 3+ ions. We generate spectrally tunable, narrowband, polarization-shaped ultrashort laser pulses, which are specifically optimized for the spectral and the spatial selective excitation of magnetic dipole and electric dipole transitions in Eu 3+:Y 2 O 3 nanostructures integrated into a metallic antenna. In the presence of the metallic antenna, the excitation with an azimuthally polarized beam is shown to provide at least a 3.0–4.5-fold enhancement of the magnetic dipole transition as compared to a radially polarized beam or a conventional Gaussian beam. Thus, our setup provides new opportunities for the spectroscopy of forbidden transitions.
We use the magnetic field distribution of an azimuthally polarized focused laser beam to excite a magnetic dipole transition in Eu^{3+} ions embedded in a Y2O3 nanoparticle. The absence of the electric field at the focus of an azimuthally polarized beam allows us to unambiguously demonstrate that the nanoparticle is excited by the magnetic dipole transition near 527.5 nm. When the laser wavelength is resonant with the magnetic dipole transition, the nanoparticle maps the local magnetic field distribution, whereas when the laser wavelength is resonant with an electric dipole transition, the nanoparticle is sensitive to the local electric field. Hence, by tuning the excitation wavelength, we can selectively excite magnetic or electric dipole transitions through optical fields.
The electromagnetic-vacuum-field fluctuations are intimately linked to the process of spontaneous emission of light. Atomic emitters cannot probe electric- and magnetic-field fluctuations simultaneously because electric and magnetic transitions correspond to different selection rules. In this Letter we show that semiconductor quantum dots are fundamentally different and are capable of mediating electric-dipole, magnetic-dipole, and electric-quadrupole transitions on a single electronic resonance. As a consequence, quantum dots can probe electric and magnetic fields simultaneously and can thus be applied for sensing the electromagnetic environment of complex photonic nanostructures. Our study opens the prospect of interfacing quantum dots with optical metamaterials for tailoring the electric and magnetic light-matter interaction at the single-emitter level.
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].
Optical frequency magnetic dipole (MD) transitions follow different selection rules from those invoked by the coupling of light to the electric dipole (ED) moment giving valuable complementary spectral information about the system under investigation. However, MD interactions contribute to the optical spectrum by approximately two orders of magnitude less than the ED transitions, therefore remaining concealed in traditional optical spectroscopy. To allow the unperturbed direct detection of the magnetic-field-MD interactions a novel type of magneto-optical spectroscopy is proposed. To this end, spatial separation of the electric and the magnetic field (EF & MF) components of the light can be achieved by means of azimuthally polarised beams (APB) [1]. Under external focusing, the APB develops a doughnut-shaped intensity profile exhibiting a longitudinal MF component at the centre of the beam while the polarisation of the EF oscillates along the beam perimeter. Another way to discern between ED and MD transitions is through spectral selectivity. For example, Eu3+ ions exhibit a MD-allowed transition at 527.5 nm and an ED-allowed one at 532 nm [2].
One of the central assumptions in quantum electrodynamics is to invoke the dipole approximation because (quantum) emitters are much smaller than the wavelength of light. The main consequence is that only the electric dipole plays a role in light-matter interactions at optical frequencies. In this paper we show that semiconductor quantum dots possess large magnetic-dipole and electric-quadrupole moments, which can be accessed with light. Moreover, quantum dots are capable of mediating electric-dipole, magnetic-dipole and electric-quadrupole interactions on dipole-allowed transitions and therefore are fundamentally different than atoms.