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Europium-Doped NaYF4 Nanocrystals as Probes for the Electric and Magnetic Local Density of Optical States throughout the Visible Spectral Range

Absorption and emission in the ultraviolet, visible, and infrared spectral range are usually mediated by the electric-field component of light. Only some electronic transitions have significant “magnetic-dipole” character, meaning that they couple to the magnetic field of light. Nanophotonic control over magnetic-dipole emission has recently been demonstrated, and magnetic-dipole transitions have been used to probe the magnetic-field profiles of photonic structures. However, the library of available magnetic-dipole emitters is currently limited to red or infrared emitters and mostly doped solids. Here, we show that NaYF4 nanocrystals doped with Eu3+ have various electric- and magnetic-dipole emission lines throughout the visible spectral range from multiple excited states. At the same time, the colloidal nature of the nanocrystals allows easy handling. We demonstrate the use of these nanocrystals as probes for the radiative electric and magnetic local density of optical states in a planar mirror geometry. A single emission spectrum can reveal enhancement or suppression of the density of optical states at multiple frequencies simultaneously. Such nanocrystals may find application in the characterization of nanophotonic structures or as model emitters for studies into magnetic light–matter interaction at optical frequencies.


Spectroscopic experiments
Excitation: The mirror samples were loaded on a Nikon Ti-U inverted microscope equipped with a 100× air objective with a numerical aperture of 0.9. Measurements in tetradecane solution were done using a thin microscope coverslip with a droplet of NCs in tetradecane (diluted 10× from the stock solution) and an oil immersion objective with a numerical aperture of 1.3. The Eu 3+ ions of the sample were excited at 395 nm and 20 kHz (or at 100 Hz for Figure 1d in the main text) using the output of a Spectra-Physics Spirit-OPA optical parametric amplifier pumped by a Spectra-Physics Spirit solid state laser (520 nm). For the mirror experiments, the laser power was 45 μW at the position of the sample, focussed to a spot of approximately 1 μm diameter. Assuming that the absorption cross-section of Eu 3+ at 395 nm is 10 −20 cm 2 (Ref. S4), this would correspond to an excitation rate of approximately 0.1 ms −1 .
Detection: The emitted light was collected using the same objective, and dispersed on an Andor Shamrock 303i imaging spectrograph, using a 150 lines/mm grating blazed at 500 nm and a 100 μm entrance slit. The emission spectrum was detected on an Andor iXon 888 Ultra electron multiplying charge-coupled device camera (EMCCD) cooled to −75 • C and operated at an electron multiplying gain of 1000. The central ∼60 rows on the CCD image were then integrated in the vertical direction to obtain the emission spectrum (Figure 1e,f and Figure 2e in the main text). For the fits ( Figure 3 in the main text) we took into account the 20% lower detection efficiency of the setup for the near-infrared emission at 690 nm, as determined by comparison to a calibrated spectrometer. The photoluminescence decay traces of Figure 1d in the main text were detected on a Excelitas SPCM-AQRH-14-TR avalanche photodiode, and recorded on a PicoQuant PicoHarp 3000 time-correlated single photon counting module operated in time-tagging mode.

Calculating the radiative decay rate of ED and MD emitters
On top of a mirror: We consider a three-layer mirror geometry as depicted in Figure 2a of the main text: layer 0 is air with dielectric constant ε0 = 1 containing NCs with refractive index n = 1.48 (Ref. S5) doped with emitters, layer 1 is Al2O3 with dielectric constant ε1 = 2.82, and layer 2 is Ag with frequency-dependent dielectric constant ε2 (Ref. S3). The radiative decay rate for a MD or ED transition in this geometry is: S6,S7 Here γ bulk ED , γ bulk MD are the radiative decay rates in the corresponding bulk material, nNC = 1.48 is the refractive index of the NC host material, χ ED = 3/(2 + n 2 NC ) and χ MD = 1 are the local-field factors for ED and MD transitions, k0 = 2π/λ is the free-space wavevector of the light emitted in the transition, and l0 = −i √ 1 − u 2 . The dependence of the radiative decay rates on the spacer thickness d is contained in the reflection coefficients rs and rp: where r 01 s,p and r 12 s,p are the reflection coefficients for the separate interfaces air/Al2O3 and Al2O3/Ag, respectively, which are given by The upper limit of integration can be set to u * = NA to calculate the rate γ det of radiative decay into photon modes that can be collected by an objective with finite numerical aperture (NA), or to u * = ∞ for the total rate γ tot of radiative decay including energy transfer to the metal, plasmons and photons that are not collected by the objective.
Dispersed in a solvent: The radiative decay rate of ED and MD transitions for NCs dispersed in a homogeneous solvent of refractive index n (where we use tetradecane with n = 1.429 in the main text) is: S8 where χ ED (n) = 3n 2 /(2n 2 + n 2 NC ) and χ MD = 1 are the local-field factors. For this situation, since the emission is isotropic, there is a constant factor between γ tot and γ det that does not depend on emission wavelength or dipole character of the transition but only on the experimental geometry.
The fitting procedure: A model equation for the branching ratios was generated using Equation 2 of the main text, by evaluating the integrals of Equations S1 and S2 in Wolfram Mathematica. This yields model expressions for the branching ratios β model J→J ′ as a function of the bulk decay rates (where J and J ′ are labels for the 5 DJ excited states and the 7 F J ′ ground states). Next, a best fit with the experiment is found by minimizing with respect to the bulk decay rates Several excitation lines are observed in the visible range of the spectrum from the lowest-energy 7 F 0 state or from the thermally populated 7 F 1 state, to the 5 D J excited states. Some excitation lines have MD character, S8 as indicated with an asterisk. e excitation transitions to the 5 D 1 state are used in Ref. S9 (labeled in yellow). e UV spectral range shows several excitation lines close to each other occur, corresponding to a series of closely-spaced excited states. e strongest excitation line, for the transition to the 5 L 6 excited state, lies at 395 nm and is used to excite for the experiments presented in the main text. is measurement was done on a Edinburgh Instruments FLS980 spectro uorometer equipped with a 450 W Xe arc lamp.
Diffraction angle (deg) 20 40 60 Intensity (arb. units) Figure S1 | e X-ray di raction pattern of NaYF 4 :Eu 3+ NCs. e X-ray di raction pattern of NaYF 4 :Eu 3+ NCs synthesized according to our method (but not the exact same batch as used for the spectroscopic experiments), recorded using a Co Kα source (λ = 1.79 Å). e crystal structure matches the reference data for hexagonal β-NaYF 4 (JCPDS 00-028-1192; red bars).  Figure S4 | e independent electric and magnetic local density of optical states. eoretical radiative decay rates of (a) the electric-dipole transitions, and (b) the magnetic-dipole transitions of NaYF 4 :Eu 3+ NCs. Solid lines: the decay rate γ det into 'detectable' photon modes that can be collected by our microscope objective (NA 0.9), as a function of separation from the Ag mirror as in the geometry of Figure 2a in the main text. Dashed lines: the total decay rate γ tot , including photon emission at angles grazing over the mirror surface, plasmon emission, and energy transfer to the metal. Circles: γ det (closed symbols), and γ tot (open symbols) for NCs in vacuum, NCs in tetradecane, and bulk NaYF 4 :Eu 3+ . All decay rates are normalized to the total decay rate γ tot of the transition in NCs in vacuum. Excitation power (normalized) 10 -3 10 -2 10 -4 10 -1 10 0 Intensity (normalized) 1.0 1.5 2.0 Figure S5 | e emission intensity from higher-energy excited states of Eu 3+ in NaYF 4 NCs. e fraction of Eu 3+ emission coming from the 5 D 1 excited state (yellow) and the 5 D 2 excited state (green) as a function of excitation power at 395 nm, and normalized to the lowest power. e NCs are dispersed in tetradecane. e emission is collected with an oil-immersion objective (NA 1.3) to allow more accurate detection of the intensity from the 5 D 2 and 5 D 1 states at low excitation power. 5 D 1 5 D 2