Explorer Microcavity-Modified Emission from Rare-Earth Ion-Based Molecular Complexes

Despite the remarkable optical properties of rare-earth ion materials, their applications as light sources and in quantum technologies are often hindered by their long lifetimes and weak emission


INTRODUCTION
Rare-earth elements, including lanthanides, scandium and yttrium, have been widely used in a diverse field of technologies such as lighting, telecommunication, and bioimaging [1][2][3] due to their stable and narrow emission bands that span ultraviolet to near-infrared wavelengths.Unique to rare-earth ions, their partially filled 4f shells are shielded from the surrounding environment by the filled 5s 2 and 5p 6 outer electron shells, thus rendering extraordinary optical and spin coherence properties of the rare-earth ions. 4,5 hese advantageous features, combined with the optically addressable spin states, have made rare-earth ions one of the most compelling candidates for qubit and quantum memory applications. 6wever, accompanying these sharp, atomic-like optical transition features of rare-earth ions is their extremely weak oscillator strength.The resultant record long optical lifetimes lead to faint photoluminescence (PL), thus posing severe obstacles for their applications as light sources 2,3 and optical addressability for quantum information science. 7From a materials perspective, great strides have been made to overcome the limited oscillator strength of rare-earth ions, most notably by sensitizing them with highly absorbing antenna ligands. 2,8 his strategy can effectively increase the absorption coefficients of the rare-earth ions by 4 -5 orders of magnitude without significantly affecting their emission qualities.Moreover, the versatility of these molecular complexes, facilitated by the easily tunable chemical and electronic structures of the surrounding ligands, [8][9][10][11] may provide opportunities for tailor-made quantum systems with minimal nuclear spins and high brightness.Recent demonstrations of long-lived spectral holes in such molecular complex ensembles 12 attest the potential to establish light-spin interfaces in these materials, making them interesting alternative platforms beyond rare-earth ion doped macroscopic bulk materials.
Rare-earth ion molecules are also natural systems for integration into photonic cavities and optoelectronic devices.To further enhance the brightness of the rare-earth ion molecules and provide necessary control over their optical properties that would be beneficial for optical and optoelectronic devices, as well as quantum devices that can ultimately operate at the single ion level, 13,14 we leverage the natural combability of the molecular complexes with photonic structures and increase their photoluminescence by coupling them to optical microcavities.To illustrate the influence of the photonic cavities, we incorporate a small ensemble of the rare-earth ion molecules into a fully tunable planar Fabry-Pérot cavity.The tunability of the planar cavity allows us to monitor in situ the PL intensities and decay rates of the rare-earth ion molecules when the resonance frequency of the Fabry-Pérot cavity is tuned across the PL emission wavelength of the molecules.An increase in the decay rate by two orders of magnitude accompanied by an enhancement factor of 30 in the PL intensity can be achieved when the Fabry-Pérot cavity is tuned into resonance with the molecular complex emission.The negligible Purcell effect of the microcavity and the superlinear dependence of the PL intensity on the excitation power suggest that the cavity-induced PL enhancement and decay rate acceleration are cause by amplified spontaneous emission.These results suggest the high compatibility of the rare-earth ion molecular complexes with photonic platforms and signify the easy tunability and high efficiency of the approach demonstrated here for modulating the rare-earth ion emission.

RESULTS AND DISCUSSION
The rare-earth ion molecular complex used in this study is a triply-ionized europium complex, ([Eu(TTA)3(DPEPO)]), due to the efficient ligand sensitization and well understood energy levels of this material. 9,15,16 T synthesize the [Eu(TTA)3(DPEPO)] complexes, briefly, 2theoyltrifluoroacetone is dissolved in ethanol and in situ deprotonated by one equivalent of aqueous solution of NaOH.Subsequently, the ethanol solution is heated to 60 0 C and a stoichiometric quantity of EuCl3⸳H2O aqueous solution is added dropwise to the hot solution, followed by the addition of DPEPO ethanol solution in drops (see Methods for details).The absorption spectrum of the Eu(III) complexes is dominated by that of the ligands at below 400 nm (Fig. 1a).The corresponding energy states involved are depicted in Fig. 1b.Ligand sensitization is manifested as efficient energy transfer from the ligands to the Eu(III) ions.Upon excitation of the ligands at 3.3 eV, sensitized Eu(III) ion emission can be detected with characteristic spectral features corresponding to the 5 D0  7 FJ (J = 0 -3) transitions (Fig. 1a).Among these, the 5 D0  7 F2 transition at around 2.02 eV is the most prominent due to its high sensitivity to the ligand environment.A weak 5 D0  7 F0 transition at 2.15 eV is also detected due to the partially allowed electric dipole transition caused by the ligand-field.
To facilitate versatile control of the PL emission from the Eu(III) complexes, we integrate them into a highly flexible open Fabry-Pérot cavity that allows full in situ tunability over the resonance modes of the microcavity (Fig. 1d). 17,18 he cavity consists of two parallel mirrors fabricated by depositing thin layers of Au onto quartz substrates.The bottom mirror, which is coated with 5 nm thick alumina as the spacer, is subsequently spin coated with a dense film of the Eu(III) complexes (Fig. 1d).During the measurements, the excitation and collection using an optical objective occur through this bottom mirror.To complete the planar cavity, a top mirror is brought close to the bottom one using a piezoelectric actuator mounted on a three-dimensional micromanipulator.The small incremental step size of the piezoelectric actuator allows us to fine tune the resonance frequency of the planar cavity in situ via adjusting its cavity length.To add more flexibility to the system and allow access to smaller cavity lengths, we partially polish away the top mirror surface until only a raised plinth that is around 200 μm x 300 µm in size and 100 µm in depth is left in the middle (Fig. 1e).In this way, the open Fabry-Pérot cavity is formed between the bottom mirror and the plinth in the top mirror (Fig. 1f).This configuration yields more maneuver and allows the distances between the two cavity mirrors to be reduced to sub-10 µm.We demonstrate later that this reduction in the cavity length is instrumental in effectively increasing the PL intensity and the decay rate.
The whole cavity is built on top of a Fourier imaging setup which enables the detection of k-vector resolved optical signals from the samples (Fig. 1c).The emission or reflection patterns of the samples can be discerned using this approach, in which every point in the image plane corresponds to a distinct emission or reflection angle θ (Fig. 1d). 19,20 hen resolved energetically using a spectrometer, this translates into in-plane photon momentum-resolved optical spectra, with the inplane photon momentum defined as  ‖ =   sin .The k-vector dependent reflectivity spectrum of an empty cavity shows clear cavity resonance modes (Fig. 2a).The planar cavity leads to photon quantization in the vertical direction (perpendicular to the sample plane, Fig. 1d) while the in-plane photon states are unaffected.Collectively this leads to the photon dispersion inside the cavity shown in Fig. 2a, which can be approximated as parabolic due to the small  ‖ range (see Supporting Information S1 for the detailed calculation method). 21We can further extract the reflection spectrum at  ‖ = 0, as shown in Fig. 2b, as well as the corresponding quality factor Q of the cavity.For the specific cavity configuration presented in Fig. 2a and 2b, a Q value of around 40 is obtained from Q = E/ΔE, where E is the resonance peak energy and ΔE the corresponding linewidth, respectively.This value is in good agreement with our transfer-matrix simulation results, from which we derive a Q value of 80 and a cavity length L of 1.8 μm (see Methods for details).Upon integrating the Eu(III) complexes into the cavity, the quality factor Q reduces slightly to 35.Most notably, in the k-vector resolved PL spectra, the originally evenly distributed PL intensity at various in-plane momentum values (Fig. 2c) exhibits enhanced intensities at certain  ‖ values, presumably caused by the coupling of the Eu(III) complex emission with the cavity modes (Fig. 2d).Fitting the cavity photon dispersion using the parabolic model yields a cavity length L of 1.8 μm, agreeing well with the value we derived from the reflection spectra shown in Fig. 2a and 2b.
To systematically investigate the cavity enhanced PL intensity, we take advantage of the unique configuration of the Fabry-Pérot cavity to tune the cavity length over a wide range so as to change the cavity mode volume.When the top mirror slowly approaches the bottom one, the momentumresolved PL spectra is simultaneous monitored.By the accompanied reduction in the cavity length, we are able to sweep the resonance energy of the Fabry-Pérot cavity across the emission energy of the Eu(III) complexes.Figure 3a clearly demonstrates the k-vector resolved PL spectra of the system when a cavity resonance mode crosses the PL emission energy (see Supporting Information S2 for more data).Due to photon quantization in the vertical direction of the cavity, nearly parabolic dispersion can be observed for the PL coupled into the cavity modes, and the corresponding PL intensities at these  ‖ values are evidently higher than the uncoupled areas.To quantify the cavity-induced PL spectral changes, we plot the PL spectra of the Eu(III) complexcavity system at k|| = 0 as a function of the corresponding cavity length that we derive from the transfer-matrix method.Fig. 3b and 3c show the PL spectra of the cavity at k|| = 0 when the cavity length is adjusted to be around 16.4 µm (Fig. 3b) and 1.2 µm (Fig. 3c).A strong enhancement in the PL intensity can be observed as the cavity mode is tuned in resonance with the optical transition energies.By defining the PL intensity of the system at when the cavity mode is out of resonance with the emission energy as the reference, we are able to derive the PL enhancement factors at various cavity lengths.Fig. 3d and 3e show the PL enhancement factors of the most prominent 5 D0  7 F2 transition at around 2.02 eV (indicated by the white lines in Fig. 3b   and 3c).The peaks and valleys represent the cases when the cavity modes are tuned in and out of resonances with the emission energy.We obtain a maximum PL enhancement factor of around 5 for cavity length of around 16.4 µm, and 30 when the cavity is narrowed to only around 1.2 µm.
The detected PL intensity  is determined by the collection efficiency of the setup , the quantum yield QY and absorption cross section  of the Eu(III) complex-cavity system collectively, i.e.,  ∝  • QY • .Since no significant changes in the collection efficiency  and absorption cross section  are expected upon tuning the cavity mode into resonance with the emission energy, the increase in the PL intensity at certain cavity lengths is most likely caused by an increase in the spontaneous emission rate  , which subsequently affects the quantum yield of the system by QY = , under the assumption that the intrinsic nonradiative decay rate  of the Eu(III) complexes is purely determined by the complexes' intrinsic properties and unaffected by the tuning of the cavity resonance modes.Therefore, to gain a direct insight into the cavity-induced PL enhancement, the determination of the cavity-induced changes in the spontaneous emission rate  is essential.
We measure the PL decay curves of the Eu(III) complex-cavity system to determine changes in the spontaneous emission rates when the PL emission is coupled ( ) and uncoupled ( ) to the cavity modes.Fig. 4a shows the PL decay curves of the Eu(III) complexes when the top mirror of the cavity is removed (blue curve), and when in a cavity with a cavity length of 16.4 (red curve) and 1.2 µm (green curve), respectively.The decay curve measured for the Eu(III) complexes out of resonance with the cavity (specially, when the top mirror is removed) exhibit mono-exponential characteristics, yielding an average decay rate  =  +  of around 1/473.7 µs -1 , consistent with previously reported values of similar systems. 9In stark contrast, the Eu(III) complexes coupled to the cavities display bi-exponential features in their decay curves.While the long components of the Eu(III) complexes in both cavities (termed as  ) have PL decay rates comparable to these outside the cavity (  = 1/511 µs -1 for the 16.4 µm cavity and 1/513 µs -1 for the 1.2 µm), the short components (termed as  ) yield drastically faster decay rates.For the 16.4 and 1.2 µm cavities, we obtain  of 1/9.8 µs -1 and 1/4.5 µs -1 , respectively.We assign the long components in the decay curves originating from the Eu(III) complexes that are not coupled to the cavity modes, and the complexes could be due to spatial mismatches between some of the emitters and the cavity modes, as shown in Fig. 2d (the dim emission regions where the in-plane photon momentum mismatches with the cavity dispersion curve), and/or polarization mismatch between the cavity modes and the optical transition dipole orientations of the Eu(III) ions.We determine the quantum yield, QY, of the Eu(III) complexes outside the cavity to be around 82% (see Methods).Taken together, we can derive the spontaneous emission rate enhancement factors,  / , of the Eu(III) complexes coupled to the 16.4 and 1.2 µm long cavities to be around 64 and 140, respectively.These drastic increases in the spontaneous emission rates result in near unity QYs of the Eu(III) complexes that are coupled to the cavities (QY = 99.6% and 99.9% for the 16.4 and 1.2 µm long cavities, respectively), signifying the negligible contributions from nonradiative decay channels.
7][28] We first evaluate the influence of the Purcell effect by estimating the Purcell factor,  , of the system, which can be derived theoretically 29 from  = ( / ) , where  is the emission wavelength,  the refractive index at the position of the emitter,  the cavity mode volume, and  the quality factor of the cavity.We extract the  values of the cavities to be around 35 from the reflection spectrum at  ‖ = 0.The cavity mode volume  is calculated by adapting a previously reported model for planar cavities: 30,31  = , where L is the cavity length, and R is the reflectivity of the gold mirrors.Based on these equations, we obtain a Purcell factor of 0.015 for a 1.8 µm long cavity.This minimal Purcell effect is quite unlikely to be the main cause of the observed PL changes upon coupling to the microcavity.
To further identify the underlying mechanism leading to the enhanced PL intensity and increased decay rate, we systematically perform pump-power dependent PL measurements of the Eu(III) complex-cavity system.Fig. 4b shows the integrated PL intensities of the Eu(III) complexes as a function of the pump power.The PL intensity, I, of the Eu(III) complexes outside cavity exhibit linear dependence on the pump power (Fig. 4b, blue dots and line).In contrast, the PL intensity of the cavity-coupled complexes demonstrates a superlinear dependence on the pump power.By assuming the pump power to be proportional to the number of the excited molecular complexes, N, we obtain a power law dependence I ~ N α with an exponent of α = 1.4.(Fig. 4b, red dots and curve).Both amplified spontaneous emission and superradiance have superlinear dependence on the pump power, although a major difference in their exponent indices could be expected: superradiance typically exhibits explicit quadratic pump power dependence (I ~ N 2 ), [26][27][28] while amplified spontaneous emission could show superlinear dependence with any exponent indices, depending on the specific carrier dynamics and electronic properties of the gain media. 24,25,32 W would like to note that although a previous theoretical study 33 has predicted that in low quality cavities with large dissipation rates, superradiance with α < 2 could occur when the number of emitters is small (N < 10 6 ), we expect this not to be the case in our study due to the large quantities of molecules coupled to the cavities (N > 10 8 , estimated by assuming only a single layer of molecules covering the bottom mirror).Combining this I ~ N 1.4 superlinear pump-power dependence of the PL intensity, with the PL enhancement and spontaneous emission rate increase, we tend to ascribe the cavity-induced modifications in the PL to amplified spontaneous emission.

CONCLUSION
In summary, we demonstrate PL enhancement and lifetime reduction of rare-earth ion molecular complexes by coupling them into photonic cavities.Utilizing a highly flexible Fabry-Pérot cavity with full tunability in its cavity length and hence cavity resonance modes, we are able to effectively tune the cavity modes into and out of resonance with the rare-earth ion emission.By resolving the PL emission in the momentum space using Fourier imaging and spectroscopy measurements, we are able to accurately determine the corresponding PL enhancement factors, which achieve a maximum value of 30 when the cavity length is reduced to 1.2 µm.The corresponding spontaneous emission rate is increased by a factor of 140.Through pump-power dependent measurements, we reveal that the major mechanism leading to the cavity-induced PL enhancement and lifetime reduction is the amplified spontaneous emission.These findings evidence the natural compatibility of the rare-earth ion molecular complexes with photonic cavities.Combined with their easily tunable molecular and electronic structures, rare-earth ion molecules may serve as promising alterative candidates for lighting, optoelectronic and quantum-related applications.

METHODS
Material synthesis.The quantum yield of the synthesized Eu(TTA)3(DPEPO) complexes was measured according to the approach described by Demas and Crosby 34 using tris(bipyridine)ruthenium(II) chloride (Ru(bpy)3Cl2) as the standard.A Hamamatsu C9920-02 measurement system and an integrating sphere purged with nitrogen were used for measuring the PL quantum yield of films.
Fabrication of the optical cavities.The bottom mirror of the tunable Fabry-Pérot cavity consists of a quartz substrate coated with a 50 nm gold film.To prevent energy and charge transfers between the gold film and the Eu(TTA)3(DPEPO) complex film, the bottom mirror is further deposited with 5 nm alumina before spin coating the Eu(TTA)3(DPEPO) complex film onto it.The top mirror with a raised plinth in the middle is fabricated by polishing a quartz substrate using a dicer until a 200 μm x 300 μm plinth is left in the middle.The plinth is around 100 μm in depth.
This geometry allows us to reduce the length of the Fabry-Pérot cavity to less than 10 μm, which is hardly achievable using two parallel mirrors of similar sizes.The fabricated quartz substrate is then deposited with 50 nm gold to serve as the top mirror.To allow fine tuning of the cavity length, the top mirror is attached to a piezoelectric actuator that is mounted on a three-dimensional micromanipulator.
Optical measurements.The Fabry-Pérot microcavity is mounted onto a 4f Fourier imaging setup that is built on an inverted optical microscope.For momentum-resolved reflectivity measurements, white light from a lamp is focused onto the bottom mirror of the cavity using a 60x oil objective with a NA of 1.4 (Olympus, PlanApo).For momentum-resolved PL measurements, the white light is replaced by laser pulses from a 375 nm diode laser.Reflected white light or PL emission is collected by the same objective and focused onto the entrance slit of a 300 mm spectrometer equipped with a EMCCD camera (Princeton Instruments, PhotonMax).For time-resolved measurements, the PL emission was focused onto a single photon avalanche diode (PicoQuantum, MPD).The repetition rate of the diode laser was set to be 1 or 4 kHz using a function generator.
Numerical simulations.To simulate the reflectivity of the bare microcavities and extract the cavity lengths and quality factors, transfer-matrix calculations were performed.The structure is formed by a glass substrate covered by 50 nm of Au and 5 nm of alumina, mimicked as a multilayer system with infinite interfaces between the abovementioned different media, with corresponding thicknesses and refractive indices.The gap between the two halves of the cavity is filled with air and its thickness is varied to fit the experimental cavity modes.Plane waves at the emission wavelengths are used as the light sources to illuminate the cavities at a normal incidence angle.
ASSOCIATED CONTENT Supporting Information.
The following files are available free of charge: Calculation of photon dispersion inside the cavity; cavity length-dependent, momentum-resolved PL spectra.

Figure 2 :
Figure 2: (a) k-vector dependent reflectivity spectrum of an empty cavity with parabolic fitting

Figure 3 :
Figure 3: (a) BFP images of the emitter-cavity system at cavity length L of 1.26 µm (left) and 1.2

Figure 4 :
Figure 4: (a) Decay curves in a 1 ms scale for Eu-molecules in free space (blue), coupled to a