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Improved emission of SiV diamond color centers embedded into concave plasmonic core-shell nanoresonators András Szenes 1, Balázs Bánhelyi 2, Lóránt Zs. Szabó 1, Gábor Szabó 1, Tibor Csendes 2, Mária Csete

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Improved emission of SiV diamond color centers embedded into concave plasmonic core-shell nanoresonators András Szenes 1, Balázs Bánhelyi 2, Lóránt Zs. Szabó 1, Gábor Szabó 1, Tibor Csendes 2, Mária Csete 1,* 1 Department of Optics and Quantum Electronics, University of Szeged, Dóm tér 9, Szeged, H-6720, Hungary. 2 Institute of Informatics, University of Szeged, Árpád tér 2, Szeged, H-6720, Hungary Abstract Configuration of three different concave silver core-shell nanoresonators was numerically optimized to enhance the excitation and emission of embedded silicon vacancy (SiV) diamond color centers simultaneously. According to the teoff between the iative rate enhancement and quantum efficiency (QE) conditional optimization was performed to ensure ~2-3-4 and 5-fold apparent cqe enhancement of SiV color centers with ~10% intrinsic QE. The enhancement spectra, as well as the near-field and charge distribution were inspected to uncover the physics underlying behind the optical responses. The conditionally optimized coupled systems were qualified by the product of the iative rate enhancements at the excitation and emission, which is nominated as P x factor. The optimized spherical core-shell nanoresonator containing a centralized emitter is capable of enhancing considerably the emission via bonding dipolar resonance. The P x factor is 529-fold with 49.7% cqe at the emission. Decentralization of the emitter leads to appearance of higher order multipolar modes, which is not advantageous caused by their noniative nature. Transversal and longitudinal dipolar resonances of the optimized ellipsoidal core-shell resonator were tuned to the excitation and emission, respectively. The simultaneous enhancements result in P x factor with 50.6% cqe at the emission. Rod-shaped concave core-shell nanoresonators exploit similarly transversal and longitudinal dipolar resonances, moreover they enhance the fluorescence more significantly due to their antenna-like geometry. P x factor of enhancement is achievable while the cqe is 50.3% at the emission. The enhancement can result in fold P x factor, when the criterion regarding the minimum QE is set to 20%. 1. Introduction Metal nanoparticles are capable of coupling light into collective electron oscillations at their resonance frequencies, which phenomenon is nominated as localized surface plasmon resonance (LSPR). The LSPR is of great interest due to the accompanying strong EM-field localization into regions significantly smaller than the illuminating wavelength, which can be exploited in different application areas including high sensitivity biosensing and photothermal cancer therapy [1, 2]. Metal nanoshells on dielectric cores are interesting plasmonic structures, since they have widely tunable spectral and near-field properties, which have been already described in the literature [3]. Metal nanoshells on their boundary can support primitive sphere- and cavity plasmons, hybridized modes as well as higher order multipoles by leaving the quasistatic limit i.e. when the particle size is smaller than λ/10, where λ is the wavelength in the surrounding medium [4, 5]. It is an intriguing property of core-shell particles that the same dipolar mode can appear in case of different geometries, however these dipolar modes are accompanied by different number of multipoles, and surprisingly larger scattering cross-section can be achieved via thicker shells [4]. Geometrical tuning of different multipolar modes into specific wavelength intervals was realized, and the differences in the far-field patterns were analyzed [5]. The geometrical tuning is ensured by the hybridization of primitive plasmons supported by the core-shell type nano-objects. The simplest hybridization of primitive sphere and cavity plasmons results in a lower energy resonance with a symmetric charge distribution and in a higher energy resonance with an antisymmetric charge separation, which are also referred as bonding and antibonding modes, analogously to the molecular orbital theory [5, 6, 7]. Many works have been presented about, how the energy of these plasmon modes depends on the dielectric properties of the embedded core and the surrounding medium, as well as on the ratio of the core ius and the full composite nanoparticle ius, which is nominated as the generalized aspect ratio (AR) [8, 9]. In a homogeneous dielectric medium the energy of a nanoshell plasmon resonance is determined solely by the AR in the quasistatic limit [8]. Namely, increase of the AR strengthens the interaction between the primitive plasmons, which red-shifts the symmetric mode-, while blue-shifts the antisymmetric mode-related resonance peak. In general, increase of the permittivity of the surrounding medium promotes the appearance of higher order multipolar modes at larger wavelengths and red-shifts the already existing plasmon resonances. Since the plasmon peak shift is linearly proportional to the refractive index modification of the embedding medium, bio-sensing applications have been developed [5, 10]. In core-shell design considerations it is important to note, that an embedding medium with higher permittivity makes the resonances more sensitive to AR changes. Modification of the core s permittivity has similar spectral effect to that of the surroundings, however the symmetric bonding mode is more sensitive to the embedding medium, while the antisymmetric antibonding mode exhibits larger sensitivity to the changes of the core s medium [9]. Interestingly, in case of nanoshells the larger particle ius does not lead essentially to a stronger scattering. It is especially true for the core-shell particles consisting of multiple dielectric and metal layers, e.g. for the so-called nanomatryoskas, where modification of the middle dielectric layer thickness makes it possible to control the scattering efficiency [11, 12]. All these phenomena can be explained based on the hybridization model with some restrictions, and experiments also prove that by modifying the surroundings and core s dielectric properties or the AR of the nanoshell, the plasmon resonances can be tuned from IR through the UV [5-7]. The near-field enhancement accompanying the LSPR on various nanoparticles has important applications. Several works have been devoted to exploit the LSPR to enhance fluorescence of different emitters [13-15]. All these efforts are based on that the absorption and scattering cross-sections of plasmonic nanoresonators can be detuned via a properly designed geometry. Simple metal nanorods are especially promising candidates for fluorescence enhancement due to their co-existent longitudinal and transversal LSPR occurring at wavelengths tunable by the geometry [16]. In our previous study we have shown those precisely tunable properties, which make the noble metal nanorods capable of enhancing the emission and excitation simultaneously [17]. Nanoshells can also support various multipolar resonances due to the plasmon hybridization, which leads to distinct peaks on their extinction spectra [4, 5]. Elongated nanoshells also show distinct plasmon resonances according to the symmetry breaking stem from different axes and to the hybridization of the corresponding primitive modes [18-20]. Moreover, nanoshells with reduced symmetry could also sustain various plasmonic resonances [21-23]. However, still a few studies have been realized to use them as fluorescence enhancing particles [24]. This is caused by the retardation effects and the electron scattering phenomenon, which limits the resonator quality properties of larger core-shell particles [25, 26]. Accordingly, there is a great demand for core-shell resonators capable of approaching the materials related limits. Diamond color centers are stable single-photon sources and possess unpaired electron spin functioning as a qubit at room temperature hence they are important for quantum information processing (QIP) applications. Among them, silicon vacancy centers (SiV) are the most promising novel diamond defects for QIP and quantum cryptography applications due to their advantageous relaxation time, stability, uniquely narrow spectral lines and the rare orthogonality of dipoles corresponding to the transition moments of excitation and emission [27-29]. In this paper, we present results about the fluorescence enhancement of silicon vacancy diamond color centers via various concave core-shell type nanoresonators. To enhance the fluorescence of SiV centers, diamond cores were embedded into silver nanoshells, and their optical response was optimized via geometry tuning. The purpose was to enhance the iative rate at the excitation and emission wavelengths simultaneously. The intuitive expectation is that the QE of the coupled system could be enhanced with respect to that of the silver nanorod enhanced SiV centers inspected previously, according to the reduced amount of the absorbing metal [17]. Optimization of different types of concave core-shell nano-resonators illumination configuration has been performed to demonstrate their special advantages and to uncover the underlying nanophotonics. 2. Methods Calculations were realized via the commercially available COMSOL Multiphysics RF module, by applying our previously developed optical response readout methodology [17]. The fluorescent color center is approximated by a pure point-like electric dipole embedded into a diamond dielectric environment and the P dipole power iated towards the far-field and the P non- power dissipated as a heat inside the metal, acting as an inhomogeneous environment, were calculated. The quantities characterizing the coupled SiV center - core-shell nanoresonator system are the Purcell factor of the dipole [30, 31] and QE quantum efficiency of the core-shell nanoresonator, as well as the product of them, which equals to the R iative rate enhancement with respect to vacuum, i.e. is identical with the fluorescence rate enhancement [17]: P P non R Purcell QE, (1) non P0 P P P0 where P 0 is the power emitted by the point-like electric dipole in vacuum. During the numerical computations the emitter was treated as a lossless dipole, hence the QE 0 ~ 10% intrinsic quantum efficiency of SiV centers at their emission wavelength has been taken into account during the post-analysis. Accordingly, the ideal QE has been corrected to determine the corrected cqe at the emission as follows: cqe P P P non 1 QE QE 0 0 P. (2) The QE apparent quantum efficiency enhancement of SiV centers is also presented for each coupled systems, which is the ratio of the cqe corrected quantum efficiency and the intrinsic QE 0. According to reciprocity theorem the R excitation excitation and R em ission emission rate enhancement can be calculated with the same method. Similarly to our previous paper, a conditional optimization has been performed, by taking into account that the Purcell factor and QE of the coupled dipole nanoshell resonator systems are inversely proportional [17]. The criterion set regarding the iative rate enhancement at the excitation was that it has to be larger than R excitation unity, while a cqe larger than a specific value, namely % was demanded at the emission. These cqe values correspond to approximately fold QE apparent quantum efficiency enhancement of SiV centers. The objective function was the product of iative rate enhancements at the excitation and emission wavelengths, which is nominated as P x factor: P R R (3). x excitation The in-house developed GLOBAL optimization algorithm was implemented into COMSOL [32, 33]. The configuration of four different coupled systems has been optimized: 1. Centralized spherical core-shell (CSCS): The dipole was exactly in the center of a spherical silver nanoshell and the fluorescence enhancement in the 2D parameter space of the r 1 core ius and t shell thickness was inspected. One can expect only one single resonance peak in CSCS case in the inspected wavelength interval, because of the significant damping of the higher energy anti-bonding asymmetrical resonance. 2. Decentralized spherical core-shell (DSCS): A decentralized dipole is embedded into a spherical nanoresonator composed of a silver nanoshell. According to the symmetry breaking of illumination, multiple plasmonic resonances are expected, which can be precisely tuned to the desired wavelengths simultaneously. 3. Decentralized ellipsoidal core-shell (DECS): A decentralized dipole is embedded into an ellipsoidal coreshell nanoresonator composed of a silver nanoshell, which was elongated along one of its axes. Breaking the spherical symmetry of the concave nanoresonator inherently leads to multiple resonances, therefore it is expected that resonances with appropriate energy difference can be finely tuned to the desired wavelengths simultaneously. 4. Decentralized rod-like core-shell (DRCS): Deforming the ellipsoid into a rod-shaped nanoshell improves the antenna features of the concave nanoresontor, therefore it is expected that the optimized DRCS may lead to a larger iative rate enhancement. The far-field iative rate enhancement spectra are presented for each type of core-shell resonators. To extract the wavelength dependent iative rate enhancement, the frequency of the monochromatic dipole was swept in the [400 nm, 900 nm] interval. For further analyses the scattering cross-sections of nanoresonators were also determined via plane wave illumination in the same [400 nm, 900 nm] interval. The surface charge distribution on the nanoshell is also presented to uncover the type of underlying plasmonic resonances involved into the fluorescence enhancement. In addition to this, the spatial distribution of the E-field enhancement is presented as well. Although, in case of an experimental realization the parameters including the r 1 core ius and t shell thickness, i.e. the AR, as well as the (x, y) dipole position and (, ) orientation have relatively large uncertainties, our results are presented with 0.1% accuracy, according to the high numerical stability of the finite element model computation. The optimized coupled SiV center - core-shell resonator systems are ranked based on the product of the excitation and R emission emission P R excitation emission rate enhancements, namely on the P x factor. In the main text, we present the optimized coupled systems determined with 50% cqe criterion, which have approximately 5-fold δqe apparent quantum efficiency enhancement, whilst further optimization results are provided in the Supplementary material. 3. Results 3.1. Centralized dipole in optimized spherical concave core-shell nanoresonator Figure 1. Optical response of an optimized spherical core-shell nanoresonator containing a centralized dipole. (A) Purcell factor i.e. total decay rate enhancement and quantum efficiency (B) iative rate enhancement and scattering cross-section spectra of the optimized configuration corresponding to excitation (dashed lines) and emission (solid lines), inset: zoomed spectra around 600 nm. (C) Distribution of the surface charge density in arbitrary units and the normalized E-field enhancement with respect to vacuum on a logarithmic scale at the SiV excitation (top) and emission (bottom). The simplest inspected configuration is, when a centralized dipole is embedded into a spherical core-shell nanoresonator closed by a silver nanoshell. Here only the r 1 core ius and t shell thickness were varied and the optimization resulted in a core-shell with aspect ratio (AR=r 1/(r 1+t)), which exhibits a resonance and corresponding Purcell factor peak exactly at the SiV emission (Fig. 1A and B). Based on that the spectral position of the plasmon resonance is dependent mainly on the aspect ratio of a core-shell structure close to the quasistatic limit, one could expect that by tuning the AR it is possible to tune the plasmonic resonance to the SiV excitation and hence to enhance the fluorescence via excitation rate enhancement (SFig. 1). However, caused by the criterion set during optimization regarding that the cqe must approach 50% at the emission, the optimization resulted in a coupled system exhibiting a large iative rate enhancement at SiV emission, which is in accordance with Eq (2). R emission The coupling of the centralized SiV color center to the spherical core-shell resonator results in large 482-fold emission rate enhancement, while the 1.1-fold iative rate enhancement at the wavelength of excitation is only slightly larger than unity. The product of iative rate enhancements is P x=529 in case of the optimized CSCS (STable 1). An important advantage of the centralized spherical core-shell configuration is that the QE is high (73.2% and 49.7%) both at the excitation and emission wavelengths. Accordingly, the spherical core-shell nanoresonator enhances the intrinsic QE of the centralized SiV by a factor of In case of this simple coupled system the results obtained by the in-house developed optimizing algorithm were verified by a parametric sweep above the r 1 core ius and t shell thickness space (SFig. 1 and 2). It was also revealed that a gually increasing QE can be obtained by increasing the core ii at the excitation wavelength, while there is a narrow optimal parameter region capable of maximizing the cqe at the emission. However, the parameter region appropriate to enhance the iative rate is governed by the Purcell factor at both wavelengths (SFig. 1 and 2). R Due to the rotational symmetry of the spherical core-shell nanoresonator the optical response is independent of the spatial orientation of the electric dipole, accordingly the optical responses take on the same values in excitation and emission configurations. Consequently, only dipolar plasmonic modes can be excited both at the excitation and emission wavelengths. Detailed inspection of the charge and near-field distribution shows that the dipolar charge distributions on the CSCS are perpendicular to each other, but the resonance is exclusively cavity and partially sphere plasmon like and the corresponding E-field enhancement is very weak and significantly stronger at the excitation and emission, respectively (Fig. 1C, top and bottom). At both wavelengths along the dipole oscillation direction a well-defined E-field depletion is observable around the dipole in the resonator and inside the shell with respect to that in a homogeneous environment. The near-field is the weakest inside the metal shell, where the strongest charge accumulation with the same sign is observable on the inner and outer interface, in accordance with the literature [5]. The near-field is enhanced along the dipole oscillation direction in the close vicinity of the metal shell due to the evanescent field of the LSPR, while the enhancement farther on outside perpendicularly to the dipole oscillation direction corresponds to the far-field iation pattern of the coupled dipole-nanoresonator system. The strength of the E-field enhancement correlates with the iative rate enhancement values. R The selection rules of plasmon hybridization predict that two types of localized resonances could appear, however the charge distributions show that only the lower energy bonding resonance is at play in SiV fluorescence enhancement, while the higher energy anti-bonding resonance is out of the inspected wavelength interval (Fig. 1C). The absence of anti-bonding resonance is caused by the moderate charge separation, which is limited by the small size of the optimized spherical core-shell resonator. This explains that the Purcell factor and R iative rate enhancement of the optimized CSCS configuration shows one single peak originating from bonding resonance causing that an efficient resonant coupling occurs only at the wavelength of emission (Fig.1A). Although, the scattering cross-section for plane wave illumination indicates a peak close to SiV excitation, the centralized dipole is not capable of resulting in a charge separation, which could

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