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Abstract
Trapping of NaYF4:Er/Yb/Gd nanorods using an original optical fiber-tip tweezers is reported. Depending on their length, nanorods are reproducibly trapped in single or dual fiber tip configurations. Short rods of 600 nm length are trapped with two fiber tips facing each other. In contrary, long rods (1.9 μm) can be stably trapped at the apex of one single fiber tip and at a second stable trapping position 5 μm away from the tip. The up-conversion emission of trapped long nanorods is studied as a function of the position on the nanorod and in three orthogonal directions. The experimental results are discussed using numerical simulations based on exact Maxwell Stress Tensor approach.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the last years optical tweezers became widely used and a great amount of work was published on optical trapping or manipulation of objects of various compositions [1, 2], sizes [3, 4], and shapes [5,6]. Trapping of anisotropic nanoparticles was realized and results on various objects such as silicon or semiconductor nanowires [7], carbon nanotubes [8], or metallic rods [9] were presented.
Besides the initial approach of laser beam focusing tweezers, based on high N.A. microscope objectives, complementary approaches have been developed such as optical fiber tweezers [10,11]. Optical trapping with single fiber and dual fiber geometries were realized. In the single fiber case, the trapped particles are either in contact with the fiber tip or specially structured fibers are used for realizing a focal point at a finite distance from the tip end [12,13]. In the dual fiber approach the radiation pressure of the two counter-propagating light beams vanishes at an equilibrium point, thus allowing efficient optical trapping at relatively low light intensities. Asymmetric light distributions can be engineered to control the particle position or the orientation of non-spherical particles such as nanowires [14] or biological cells [15].
Among all possible luminescent nano-emitters, rare earth-doped nanoparticles have attracted a lot of attention [16, 17]. In particular, erbium - ytterbium co-doped hexagonal NaYF4 crystals exhibit interesting optical properties such as high up-conversion efficiency [18, 19]. Moreover, these particles are investigated and considered for their versatility and numerous applications [20–22], because of their chemical and physical properties [23], large anti-stokes shifts, and low toxicity. Optical trapping of these nanorods was reported using beam focusing optical tweezers [17,24].
In this paper we report optical trapping and the spectroscopic study of trapped NaYF4 nanorods using our fiber tip optical tweezers [4,25]. Special consideration will be given to the nanorod length dependent trapping behavior and the particle emission study with directional and spatial resolution.
2. Experimental section
2.1. Nanorods elaboration
Lanthanide-doped nanorods with three different sizes are prepared by adapting the processes reported by Wang and coworkers [16,26]. The synthesis is based on the solvothermal reaction (typically at 200°C for 24h) between metal and fluoride salts in a mixture of ethanol, water, and oleic acid. These previous studies evidenced the drastic impact of the particles composition on the nanorods aspect ratio, especially considering the substitution of various amounts of Y3+ by other rare earths such as Gd3+ [16] or Y3+ [26] among others. Adapting the process reported in [16], we were able to produce the NR06 and NR09 samples having lengths of 0.640 and 0.940 μm and aspect ratios of 6.4 and 5.9, respectively. Significant changes of the protocol had to be found for reaching a significantly higher length, and we found it efficient to remove all Gd3+ and reduce significantly the Yb3+ content. This led to the NR19 sample exhibiting an average length of 1.9 μm and an aspect ratio of 23.8.
Following these synthesis procedures, the particles may crystallize either in the cubic (α) or the hexagonal (β) polymorphs of NaYF4, that can be easily recognized from their morphology: the cubic phase corresponds to small nanocubes, whereas the hexagonal phase exhibit the desired nanorod shape. In almost all our samples, a small amount of the cubic phase could be observed in the TEM images mixed with the nanorods. Size selective centrifugation of the colloidal suspensions was achieved in order to remove excess oleic acid and to separate the nanorods from the small α-NaYF4 nanocubes. In a last step, surface oleate ligands are exchanged with citrates to ensure a good dispersion of the nanorods in water. Finally, three stock solutions of aqueous nanorods dispersions are obtained (NR06, NR09, and NR19) with a volumic concentration of about 1% [Table 1, Fig. 1(a)].
Table 1. Main parameters of the studied nanorods (with l length, d diameter, and AR the aspect ratio).
Fig. 1 (a) SEM picture of the nanords. (b) Powder X-Ray diffraction pattern of NR19. (c) Illustration of the β-NaYF4 crystalline structure.
The quality of the samples is confirmed by powder X-Ray diffraction pattern, showing only the hexagonal pattern [Fig. 1(b)]. A detailed analysis of the diffraction patterns allows us to confirm the P63/m crystalline structure of the nanorods [Fig. 1(c)]. This crystalline structure presents only one site for the Er3+ ions. This site present a (Wyckoff notation of the site: d) with its main axis along the c axis. This implies specific selections rules for the electric and magnetic dipoles as detailed in [27].
2.2. Optical tweezers set-up
The NaYF4 nanorods are trapped in suspension using our optical fiber tip tweezers, based on chemically etched straight fiber tips. The emitted Gaussian beams have an emission angle of 8° in water and a minimal beam waist of 900 nm [25]. Each fiber tip is mounted on a set of piezoelectric translation stages allowing easy fiber alignment with sub-micrometer precision [Fig. 2]. The trapping wavelength was chosen to 808 nm, by reason of the low optical absorption of water at this wavelength and the possibility of direct excitation of the trapped ebium-doped particles. The tweezers’ optical system consists of two symmetric arms allowing independent coupling of light into both fiber tips. The relative light intensities of the trapping laser in the two fiber tips and, thus, the trapped particle equilibrium position, is controlled by a half wave plate and a polarized beam-splitter.
Fig. 2 Scheme of the optical fiber tip tweezers set-up. Left inset: geometry of the dual fiber tip trap. Right inset: geometry and microscopy slide of the single fiber tip trap including the auxiliary fiber tip used for particle emission recording as used for the NR19 rods.
Particle trapping is observed by visualizing the NRs up-conversion emission using a home-made microscope based on a ×50 long working distance objective (N.A.= 0.55) and a CMOS camera. Trapping videos contain 3000 to 5000 frames, typically recorded at 200 or 325 fps. The Er/Yb-doped particles are directly excited by the trapping laser at 808 nm through the Er3+ 4I15/2 → 4I9/2 transition. Experiments with a supplementary 980 nm pump laser beam injected through the microscope objective does not significantly modify the emission properties of the trapped particles.
A dedicated particle tracking algorithm was developed in the free Scilab environment [28]. In this algorithm, the particle position is determined by fitting a two-dimensional Gaussian function resulting in an improved spatial resolution with respect to the camera resolution of 80 nm/pixel. The particle positions in axial and transverse directions with respect to the fiber axis are recorded. The particles anisotropy can be clearly observed for the 1900 nm long NRs. In this case the tracking algorithm allows us to determine separately the two half axis of the spatial emission ellipsoid and thus the particle orientation.
The trap stiffness κ is determined in axial and transverse directions with respect to the fiber axis, using Boltzmann statistics and power spectra analysis as described elsewhere in details [25]. Boltzmann statistics does not require the knowledge of the particle shape, whereas for power spectra analysis the particle anisotropy enters into the Stokes friction coefficient γ0. Different corrections, depending on the aspect ratio, are suggested for anisotropic particles. In this paper we will use [29]:
with l and d the nanorod length and diameter, respectively, and η the dynamic viscosity of the surrounding media (water).Our optical tweezers set-up allows us to record the trapped particle emission in three orthogonal directions using distinct methods [Fig. 2]: through the microscope objective, coupling into the trapping fiber tip, and coupling into a further fiber tip. The possibility to record the emission in the three orthogonal directions is of paramount interest for anisotropic particles. Moreover, each of the three methods has its specific characteristics. The signal through the microscope lens is relatively intense, but do not allow any spatially resolved measurements. The signal recorded by the trapping fiber tip is automatically aligned on the trapped particle. Finally, the auxiliary fiber tip allows measurements with spatial resolution by scanning the fiber tip relative to the trapped particles. The signal recorded by the fiber tips is, however, significantly lower with respect to the microscopy lens.
In all three cases, the up-conversion emission is recorded using a spectrometer coupled to an EM-CCD camera. In the case of the objective a mirror is insert to direct the emission to the spectrometer, whereas in the case of the trapping fiber a dielectric mirror allows to separate the trapping laser from the emission. Finally, the auxiliary fiber tip, which is identical to the trapping fiber tip and orientated perpendicularly to the trapping fiber, is fixed on a piezoelectric x − y − z translation stage in order to allow position scanning. The captured emission is guided to the spectrometer using a standard fiber-coupling device.
2.3. Modelisation
The fiber tip tweezers are numerically simulated using 3D finite element method [4]. The tapered silica fiber (optical index 1.45) presents an input diameter Din = 1 μm, a tapered full angle of 15° and the radius of curvature of the output is fixed at 50 nm. The whole system is immersed in water (optical index 1.33) and the entrance of the fiber is excited with the linearly polarized fiber mode HE11 (injected power Pin = 1 W). In order to avoid parasitic reflections at the borders of the window, we used scattering boundary conditions. The diameter of the NaYF4 nanorod is 100 nm and its optical index is 1.48 [30].
The (time-averaged) optical force acting on the nanorod is computed thanks to the Maxwell Stress Tensor (MST) formalism and expresses [31]:
with T̿ the MST, S a surface enclosing the trapped particle and n⃗ refers the the surface normal vector. In addition, the electromagnetic field also exerts an optical torque on the elongated nanorod. If the pivot point is at r⃗0, the torque writes:3. Nanorod trapping
3.1. Dual fiber tip trapping
Stable and reproducible trapping is observed for the shortest particles (l = 640 nm, NR06) for a fiber tip-to-tip distance of 4 μm and light powers in the range from 1.5 to 4.0 mW at each fiber tip [Fig. 3]. As expected for sub-wavelength-sized luminescent particles, the NR06 appear as a bright, circular spots with about 500 nm radius, corresponding to the microscope resolution.
Fig. 3 Trapping of NR06 and NR09 nanorods: (a) Trapping stiffness along the transverse and axial directions as a function of the trapping power, (b, c) Microscopic photoluminescence image of trapped particles, and (d) Boltzmann statistics.
Boltzmann statistics and power spectra analysis give coherent results with stiffness values of up to 0.55 pN · μm−1 in transverse direction [Fig. 3]. The higher stiffness in transverse direction with respect to the axial one is consistent with our trap geometry [25]. Boltzmann statistics shows that the trapping potential is harmonic in transverse direction. However in axial direction the shoulder on the right side suggests the presence of interference fringes as already observed for spherical nanoparticles [4].
Trapping of the mean sized NR09 rods is significantly less stable with respect to the NR06. In axial direction, the NRs are oscillating in between the two fiber tips, prohibiting any evaluation of the experimental results. In transverse direction we have applied Boltzmann statistics and power spectra analysis to evaluate the trap stiffness. The obtained very low values and the flat power dependence show, however, that the standard harmonic trap model cannot be applied.
Finally, the long NR19 could not be trapped in the two fiber tips geometry. In fact, they are efficiently attracted by the fiber tips, and stable trapping at the apex of one of the two tips is observed. They are leaving this position immediately after switching off the laser, thus excluding any influence of adhesion forces. The results of single tip trapping will be presented in details in the next section.
For small dipolar particles, the optical forces in axial direction can be decomposed in two forces with opposite direction: the gradient force and the scattering force. The gradient force attracts the nanorods towards the tips, whereas the scattering force pushes the nanorods away from the tips. For larger particles, it is no more possible to separate the gradient and scattering forces but using MST formalism (see section 2.3), we can calculate the total force in axial direction (Fz) for a nanorod situated close to the fiber tip (170 nm) [Fig. 4]. For the short rods, Fz is repulsive, whereas it is attractive for the long rods with a sign change near the intermediate length rods. Thus, for the short NR06, the scattering force is prevailing, whereas the gradient force is dominant for the long NR19s. In the intermediate case of the NR09, the competition between the two forces results in a weak efficient force, thus explaining the unstable trapping.
Fig. 4 (a) Electric field map in the presence of a 2 μm long rod placed at 170 nm from the fiber tip. (b) Optical force acting on a rod as a function of its length. The rod diameter is fixed to 100 nm. The injected power is 1 W. (c) Microscope picture of a NR19 trapped by a single fiber tip.
Non-spherical nanorods inside an anisotropic trapping potential are expected to be trapped with a preferential orientation. However, the small particle size of the NR06 and the low trapping efficiency of the NR09 does not allow to detect their orientation or to study the oscillation of the particle between different metastable orientations. The case of the longest particles will be discussed below.
3.2. Single fiber tip trapping of long nanorods
In the case of trapping the long nanorods with only one single fiber tip, two stable trapping positions can clearly be distinguished: one in close vicinity to the fiber tip and one at 5 – 6 μm from the fiber tip. Trapping near the fiber tip is characterized by two distinct regimes with a clear threshold [Fig. 5]. For high intensities, above 36.5 mW, the nanorods are in contact to the tip. For lower intensities the particles are oscillating in axial direction over a distance of about 1 micron. For lowest intensities one can even observe one metastable position at about 0.9 μm from the tip. The intensity threshold is confirmed by power spectra analysis of the trapped nanorod angular orientation fluctuations. The corner frequency fc and the low frequency limit a0 show a clear threshold which can be visualized by fitting to a Fermi-type function [Fig. 5]. At low intensity, we are close to our resolution limit. At high power the nanorod is attracted by the tip so that the mechanical contact limits it movement. These features explain the constant regime of fc before and after the threshold.
Fig. 5 (a) Position ensemble transverse (X) vs axial (Y) occupied by a trapped NR19 for several trapping powers. (b) Axial position statistics and (c) power spectra for 3 different powers 32.0, 36.5, and 54.9 mW. (d) Corner frequency fc and low frequency value a0 as a function of light intensity.
The second stable trapping position of the NR19 is situated at about 5 to 6 μm [Fig. 6]. Simultaneous trapping at the fiber tip of a second particle is also possible but not necessary. Compared to trapping near the fiber tip, trapping is less stable, but particles remain, however, several minutes. The trap stiffness obtained by Boltzmann statistics and power spectra analysis are in good agreement. The measured normalized trapping stiffness from both methods are about 4 and 0.8 pN·μm−1·W−1 in axial and transverse directions, respectively. These values are averaged over the particle orientation dependent trapping stiffness. In fact, the trapping efficiency is too low to keep the particle orientation constant over a time span long enough for resolving stiffness measurements for distinct orientations. The trapping videos clearly show the fast nanorod rotation around the trap equilibrium position.
Fig. 6 Single fiber tip, simultaneous trapping of two NR19 rods in the near vicinity and at d = 6.8 μm from the tip, respectively: (a) microscope image, (b) tracking curves, (c) Boltzmann statistics, (d) Typical trap stiffness for the different powers and distances to the tip, and (e) power spectra of the upper nanorod.
The calculated electric field map of the single fiber tip geometry is displayed in Fig. 7. For a bare trap, without particle near the fiber tip, we observe a secondary focus point at approximately 7 μm away from the fiber tip in agreement with the observed nanorod trapping at few microns of the fiber tip. This spot is maintained when a first rod is trapped perpendicularly to the fiber axis, hence second trapping is possible. However, this secondary spot is canceled when the first rod is trapped parallel to the fiber axis, thus releasing the second trap position.
Fig. 7 Calculated electric field map: without rod (a), when a first rod is optically trapped perpendicularly (b) or parallel (c) to the trap axis. Same scale bar of 1 μm for all figure and intensity scale between 0 et 2.75 × 107 V·m−1 Red circles emphases the second focus point visible far from the tip in (a) and (b). Microscope images of (d) a single NR19 particle trapped far from the tip and (e) two trapped NR19 particles.
4. Spectroscopy of trapped Nanorods
4.1. Spatial emission distribution
The long NaYF4 Nanorods are reproducibly and stably trapped for light intensities above ≈ 30 mW. In order to efficiently reduce the residual Brownian movement during spectroscopic measurements, we applied the maximum laser power of 50 mW. Under these conditions, the nanorods are strongly trapped and their movement range is below 100 nm. The microscopy image clearly indicates a nanorod orientation parallel to the fiber tip axis i.e. the trapping laser beam. The emission spot size observed by the microscope is 2 × 0.5 μm2, limited by the microscope resolution of about 500 nm.
Using the second optical fiber tip, the spatial distribution of the nanorods up-conversion emission was measured by scanning the fiber tip in longitudinal (x) and transverse (z) directions [Figs. 2 and 8(a)]. The step size was fixed in both directions to 200 nm. The recorded spectra show the expected shape of the typical erbium up-conversion process. No significant variations of the spectral shape was detected for the different positions.
The spatial intensity distribution is of Gaussian shape in both directions. Along x, a Gaussian fit reveals a width of around . Along z, the Gaussian fit of the profile give typical values of . The comparison of this value with the nanorod width of w = 80 nm allows to estimate the experimental resolution to 550 nm, in good agreement with fiber tip emission measurements [25].
Compared to optical near-field characterization methods, such as scanning near-field optical microscopy (SNOM), the observed spatial resolution is certainly lower. However, it allows to characterize free, only optically trapped particles. Moreover, the capturing fiber tip does not perturb the nanorod emission and the captured emission intensity is high enough to realize a good spectroscopic resolution. Moreover, we expect near-field imaging possible with our setup.
In a second measurement series, a different longitudinal emission profile with two distinct peaks was observed [Fig. 8(a) inset], whereas the emission spectra remained unchanged. The profile can be fitted to a double-Gaussian function, represented as a dashed line on the figure. The two corresponding maxima are separated by a distance of 2.4 μm. As the repartition of the doping ions is mostly constant along the nanorod, it cannot explain the observed emission variation. In contrast, the possibility of trapping a aggregate of few aligned nanorods can explain the experimental observation.
Fig. 8 (a) Spatial profile of the PL at λem = 539.6nm respectively in z and x directions with a Gaussian fit in red. Inset: emission of a nanorod cluster (b) Dispersion curves of a circular nanowire. The effective index is represented as a function of the wire radius at the emission wavelength λ = 540 nm. The NaYF4 wire (optical index n = 1.48) is in water (nw = 1.33). Insets shows the fundamental HE11 mode intensity profile for diameters of 250 nm and 600 nm.
To underline this assumption, we simulate the guided modes dispersion for a cylindrical NaYF4 nanowire immersed in water [Fig. 8(b)]. For diameters below 650 nm, the nanowire is monomodal and supports only the fundamental HE11 mode. For the diameter of the trapped nanorods (d ≈ 80 nm), the optical index of this mode is very close to the optical index of water. The mode is thus largely extending outside the nanorod. In contrast, for larger diameters the same mode is well confined inside the rod. The Er3+ emission can therefore couple into the guided mode. We estimate the corresponding coupling efficiency β = ΓHE11/(ΓHE11 + Γother) by integrating over the wire cross-section and considering a random orientation of the dipole moment [32,33]. The efficiency is below 0.1% for a 100 nm diameter wire and slightly increases to 5% for a diameter of 600 nm (corresponding to a maximum coupling efficiency of 10% at the center). For still larger diameters, which would correspond to nanorod clusters, the wire supports higher order modes to which the luminescence can couple, further increasing the β−factor.
The efficient coupling to guided modes inside a nanorod cluster would explain the appearance of two emission maxima at the cluster extremities. The light emitted inside the cluster could be guided along its longitudinal axis and diffused at the ends. This effect was already observed by confocal microscopy investigation of similar rods presenting micrometric diameters [34,35].
Nanorods with a high aspect ratio tend to form aggregates. In trapping experiments it is quite difficult to distinguish single nanorods or to estimate the actual number of trapped rods. It was shown that counting the steps of the recorded emission intensity allows to determine the number of nanorods [17].
4.2. Emission directionality
In a further step we compare the spectra collected in three orthogonal directions [Fig. 9]. All three spectra present three bands corresponding to the transition lines 2H11/2 → 4I15/2 between 513 and 530 nm, 4S3/2 → 4I15/2 between 530 and 570 nm and 4F9/2 → 4I15/2 between 640 and 675 nm. The maximum intensity is in the three conditions around 539 nm. However, the shape of the three bands change significantly depending on the collection method.
This difference can be explained by the emission properties of the Er3+ ions in a P63/m structure. This environment impose some selection rules on the polarization and the direction of the emitted light [27]. The most obvious difference is for the transition lines 2H11/2 → 4I15/2 between 513 and 530 nm. The peak at 519 nm is visible with the objective and the lateral fiber but not with the axial fiber. Then the emission colinear with the c axis is reduced in this part of the spectrum. This means that the PL is emitted orthogonally to the c direction (σ or π emission). But only few transitions are not allowed in this direction. Then we can associate the emission peak at 519 nm to a transition between crystal-field levels both with a symmetry of Γ11,12, the only transition with no emission in the c axis [27].
5. Conclusions
In conclusion, optical trapping of NaYF4:Er/Yb/Gd nanorods with different aspect ratios and lengths in between 640 nm and 1.9 μm is presented. The actual behavior of trapped nanorods is found to be strongly dependent on the particle size. Particles with a length of 640 nm are trapped in the dual fiber tip tweezers with trap stiffnesses in transverse direction of up to 135 pN·μm−1·W−1. The longest NR19 rods are strongly attracted by one single fiber tip and two stable trapping positions are observed, one at the fiber tip and a second at about 6 μm form the tip. The up-conversion emission of trapped nanorods was recorded with spatial and directional resolutions, allowing us for example to verify the emission selection rules for these anisotropic particles.
The presented results clearly show the interest of our optical fiber tip tweezers for the optical investigation of anisotropic fluorescent particles.
Funding
French National Research Agency (ANR) FiPlaNT and SpecTra (ANR-12-BS10-012, ANR-16-CE24-00-01).
Acknowledgments
Calculations were performed using HPC resources from DSI-CCuB (Université de Bourgogne).
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