Spontaneous emission dynamics of Eu³⁺ ions coupled to hyperbolic metamaterials

Thanks to the screening of their partially filled 4f orbitals, rare-earth (RE) ions are found to exhibit atom-like optical transitions, often insensitive to the choice of the host matrix. This behavior is best illustrated in crystals such as Y₂SiO₅, where Eu³⁺ ions are seen to feature optical linewidths as narrow as ∼400 Hz in the visible region of the spectrum.¹ Because 4f electrons are often unpaired, they also exhibit large magnetic moments that can be typically polarized and manipulated with high fidelities. These properties have prompted interest for applications in quantum information processing,^2–5 particularly as quantum memories, with nuclear-spin-based coherent storage times exceeding several hours.⁶ 

A main consequence of their narrow optical linewidths, however, is that the fluorescence from RE emitters is intrinsically faint, hence complicating the isolation of single-ions and their spin manipulation.^7–9 In an attempt to overcome these limitations, recent work has demonstrated enhanced detection via coupling to photonic crystal cavities based on Purcell enhancement of the spontaneous emission.^9–11 Nonetheless, the fixed resonance modes dictated by the cavity structure and the complexity of the required nanofabrication techniques hinder the practicality of this approach.

Alternatively, hyperbolic metamaterials (HMMs), usually constructed by sub-wavelength stacking of metal and dielectric interfaces, result in a broadband divergence of the photonic density of states (PDOS).^12–14 This phenomenon stems from their hyperbolic dispersion in momentum space, supporting the propagation of high-k electromagnetic waves that are, otherwise, evanescent.^13,15 Additionally, this characteristic broadband response in HMMs can be conveniently tuned based on the choice of the metal/dielectric interface and the corresponding metal fill factor, all of which can be leveraged so as to gain control on the spontaneous emission of multi-level systems.^14–16 

Here, we investigate the emission dynamics of a set of Eu³⁺(NO₃)₃·6H₂O nanoparticles overlaid on an HMM structure formed by a hexagonal array of Ag nanowires grown within a porous Al₂O₃ matrix.¹⁷ Compared to particles on a bare SiO₂ substrate, we observe a 2.4 fold increase in the Eu³⁺ spontaneous emission rate near the HMM, accompanied by an enhancement of the fluorescence from the ⁵D₀ → ⁷F₂ Eu³⁺ transition. With the help of finite-difference time-domain (FDTD) simulations, we show that this response is consistent with that expected for HMM-coupled Eu³⁺ ions. Further, our calculations suggest that there is much room for improvement, provided that the HMM geometry is revised to match the emission properties of Eu³⁺ more closely. As a whole, these observations highlight intriguing opportunities on the use of HMMs to tailor the emission properties of rare-earth ions for applications in quantum information processing and nanoscale metrology.

We focus on the luminescence properties of Eu³⁺ ions in crystals of Eu³⁺(NO₃)₃·6H₂O (europium nitrate hexahydrate or ENHH for short). A schematic of the atomic structure is shown in Fig. 1(a), along with a simplified version of the energy-level diagram for Eu³⁺ under 532 nm excitation. In this case, crystal-field interactions cause the Eu^{3+ 7}F level to split into its j = 0–6 components. 532 nm illumination (green arrow) results in excitation above the ⁵D₀ level, which is mostly followed by a nonradiative decay into ⁵D₀ followed by emission from one of the ⁵D₀ → ⁷F_j radiative transitions (red arrows).^18–20 In some cases, direct radiative decay from ⁵D₁ is non-negligible and can result, for example, in overlap with some of the ⁵D₀ → ⁷F_j transitions.^21,22 The ⁵D₁ → ⁷F_j transitions, however, are usually much faster than those stemming from ⁵D₀ and can, thus, be identified via time-resolved (TR) measurements.^20,21

Our glass substrate includes a region of porous alumina (Al₂O₃) inside which a hexagonal array of 75 nm silver (Ag) diameter nanowires is grown to form the HMM [white square in Fig. 1(b), upper-left panel]. A scanning electron microscopy (SEM) image of a small section of the HMM is shown in Fig. 1(b) (green square, upper-right panel). From the SEM scan, we estimate an inter-wire distance of 125 nm, resulting in a fill factor of 0.32.

To bring the RE ions in close contact with the HMM structure, we start by atomizing a low-concentration solution (0.018 M) of ENHH (Sigma Aldrich) in ethanol onto the HMM substrate to create particles of variable size. Rapid evaporation of the solvent produces a collection of crystals distributed throughout the substrate. The lower panel in Fig. 1(b) shows a fluorescence image of an area that includes the HMM section of the substrate: selection of ethanol as the solvent proved critical to deposit enough droplets on the HMM, suggesting electrostatic charging (see below). AFM imaging of the ENHH particles [Fig. 1(c)] reveals that while some nanoparticles are isolated and uniformly distributed, others group to form flat particle aggregates or poly-crystalline films, with an average height between 30 and 50 nm.

An important aspect of this study is to ensure that the fluorescence from Eu³⁺ ions lies within the hyperbolic dispersion regime of the HMM. To characterize this, we employ effective medium theory.²³ Figure 1(d) shows the real part of the parallel (magenta) and perpendicular (blue) components of the permittivity tensor for a 75 nm Ag nanowire/Al₂O₃ HMM with a fill factor of 0.32 (inset structure). We find that this structure supports HMM modes (green-shaded regions) within 350–405 nm (type-II HMM) and above 500 nm (type-I HMM). Within these regions, anisotropies of the effective permittivity tensor result in hyperbolic iso-frequency surfaces in momentum space (inset hyperbolas).¹² 

In our experiments, we use a 100×, 1.30 NA oil-immersion objective (Nikon, Plan Fluor) to excite the Eu³⁺ ensembles via a 532 nm continuous-wave (CW) laser [Fig. 2(a)]. The collected fluorescence is then filtered out via a dichroic mirror (DM) combined with a long-pass filter (LPF). We carry out time-resolved (TR) spectroscopy measurements using an acousto-optic modulator (AOM) to time the laser excitation and a pulse controller to gate the avalanche photo-detector (APD, Excelitas) over a pre-defined, short time window Δt (20 μs). Fluorescence decay curves emerge from gradually varying the delay of the acquisition interval Δt relative to the end of the excitation laser pulse.

Confocal fluorescence images reveal strong luminescence from individual ENHH clusters both outside and inside the HMM area [lower left-/right-side panels in Fig. 2(a)]. Optical spectroscopy from these sites indicates Eu³⁺ emission from the⁵D₀ → ⁷F_j radiative transitions [inset of Fig. 2(b)]. A comparison between the emission spectra from particles outside or inside the HMM does not expose major differences although the latter tend to show broader features (likely deriving from heterogeneous shifts in the emission wavelengths, see below). On the other hand, fluorescence lifetime measurements over a similarly large particle set show that, on average, the decay time of Eu³⁺ ions is shorter within the HMM region. This is shown in Fig. 2(c) where we observe differences between the characteristic decay rates by up to a factor 1.3. The histogram in Fig. 2(d) captures these changes more quantitatively: In both cases, we observe broad, skewed distributions of time constants although the maximum is shifted to lower values for particles sitting within the HMM structure. Overall, this shift corresponds to an excited state lifetime reduction of about 20%.

Interestingly, the above findings do not necessarily correlate with changes in fluorescence intensity, which, as shown in Fig. 2(b), responds differently depending on the emission wavelength. For example, while the emission peak at 620 nm (⁵D₀$→$⁷F₂ transition) experiences a growth of ∼20%, virtually no change is observed at shorter wavelengths (transitions ⁵D₀ → ⁷F₀ and ⁵D₀ → ⁷F₁); further, despite the shorter lifetimes (observed even for spectrally selective measurements, not shown for brevity), the emission brightness decreases for the ⁵D₀ → ⁷F₄ transition at longer wavelengths (see emission peaks at 695 nm).

To characterize possible size effects on the overall luminescence properties, we now turn our attention to small-radius ENHH particles (<1 μm lateral size). Emission spectra from these nanoparticles [left-side panel in Fig. 3(c)] circled in Fig. 3(a) and [left-side panel in Fig. 3(d)] circled in Fig. 3(b) reveal marked differences in the luminescence properties of Eu³⁺ ions. For example, direct comparison between each spectrum set and a spectrum representative of larger-radius particles (>2 μm lateral size), identified as “Ref” in Figs. 3(c) and 3(d) reveals substantial broadening of identified transitions, both inside and outside the HMM region, along with varying peak-intensity ratios.

As expected, we also find a size-related effect on the effective Purcell enhancement of the Eu³⁺ ions. For instance, in the case of small-radius particles inside the HMM, we find an average enhancement of 2.5 times in the emission rate on the HMM (8.1 kHz) compared to the outside (3.4 kHz on average). In contrast, for larger-radius particles, the enhancement in the Purcell factor is negligible (∼1.3). These observations are consistent with previous measurements²⁴ and FDTD simulations and stem from the reduction of averaged contributions over ions located farther away from the active HMM surface (where the effective Purcell factor is ∼1).

To better understand the interplay between Eu³⁺ emission and the HMM structure, we use the FDTD method to calculate the Purcell factor for a point dipole as a function of the distance Z to the HMM surface, the emission wavelength λ, and the HMM's fill factor ϕ. The presence of closely spaced Ag nanowires within the Al₂O₃ matrix creates a strong birefringence and results in a hyperbolic dispersion that profoundly changes the PDOS both inside the HMM and near its surface.^{13–15,17,25} Placing an emitter in close proximity to the HMM, thus, leads to a broadband enhancement of spontaneous emission and a corresponding increase in the decay rate through the Purcell effect.^24,26,27

Figure 4(a) shows a 2D color map of the calculated Purcell factor for a point dipole parallel to the HMM surface as a function of the distance and wavelength. We first consider the case ϕ = 0.32, close to the experimental value. Near the HMM, we find the broadband response anticipated for hyperbolic media. Our calculations indicate maximum Purcell enhancement within the 400–500 nm window even though the HMM impact extends to the range of longer wavelengths overlapping with the Eu³⁺ emission spectrum. Naturally, the enhancement decreases quickly with the increasing distance, meaning that the observed changes in a given particle derive from the fraction of emitters in close contact with the HMM. Figure 4(b) shows an average Purcell factor of dipoles placed above the HMM surface based on the particle-size distribution as extracted from AFM imaging [inset of Fig. 4(b)]. For Z <5 nm, the average Purcell factor shows enhancements of 37 and eight around 430 nm and 640 nm, respectively, with a Purcell factor of ∼8 in a wide wavelength range due to the broadband divergence of the PDOS in HMMs.

The experimental results summarized in Fig. 2(b) indicate an increase (decrease) in emission intensities for the 620 nm (690 nm) transitions. To explain these observations, we extract the Purcell factor as a function of distance from the HMM surface for transitions centered at 620 nm and 690 nm [two of those identified in Fig. 4(a)]. As shown in Fig. 4(c), the Purcell factor is slightly higher at 620 nm than at 690 nm, indicating a stronger enhancement. Therefore, for our HMM structure, we expect an asymmetric effect on the ⁵D₀ → ⁷F₂ and ⁵D₀ → ⁷F₄ transitions in Eu³⁺, with a net increase in the photon count for the former transition, consistent with our observations.

Better adapting the HMM structure to the emission range of Eu³⁺ could potentially increase the effective fluorescence enhancement in the visible range.¹⁴ For instance, Fig. 4(d) describes the Purcell factor for a dipole located 20 nm from the HMM surface, as a function of ϕ and emission wavelength. This distance of 20 nm corresponds to half the average height (dipole central position) obtained from the ENHH particle size distribution in Fig. 4(b). We find that by tuning the fill factor between 0.08 and 0.25, one could further increase the effective Purcell factor for the wavelength range that accommodates all the ⁵D₀ → ⁷F_j transitions in Eu³⁺.

In summary, we investigated the effects of HMM on the luminescence properties of Eu³⁺ ions in Eu³⁺(NO₃)₃·6H₂O particles. Upon 532 nm excitation, we observe strong photoluminescence with well-defined ⁵D₀ → ⁷F_j (j = 0–4) transitions at room temperature. For small-radius particles (<1 μm), where the effect of the HMM is more pronounced, we observed 2.4 times enhancement in the spontaneous emission rate. From FDTD simulations, we find that the net decay rate enhancement of Eu³⁺ ions could be substantially increased by tuning ϕ between 0.05 and 0.3 for the HMM structure.

M.L. and V.M.M. acknowledge support from the National Science Foundation through Grant No. NSF-1906096; C.A.M. acknowledges support from the Department of Energy through Grant No. BES-DE-SC0020638. All the authors acknowledge access to the facilities of the NSF CREST IDEALS, Grant No. NSF-HRD-1547830. V.M.M. and J.K.B. also acknowledge the program Scheme for the Promotion of Academic and Research Collaboration (SPARC), Ministry of Human Resources Development (MHRD), India, for supporting travel between India and the U.S. to foster international collaboration. We thank Daniela Pagliero and Artur Lozovoi for assistance with the experimental setup. We are also indebted to Fernando Meneses for useful discussions on the HMM structure.