Determining the 3D Orientation of Optically Trapped Upconverting Nanorods by in situ Single-particle Polarized Spectroscopy

An approach to unequivocally determine the three dimensional orientation of optically manipulated NaYF4:Er3+,Yb3+ upconverting nanorods (UCNRs) is demonstrated. Long-term immobilization of individual UCNRs inside single and multiple resonant optical traps allow for stable single UCNR spectroscopy studies. Based on the strongly polarization dependent upconverted luminescence of UCNRs it is possible to unequivocally determine, in real time, their three dimensional orientation when optically trapped. In single-beam traps, polarized single particle spectroscopy has concluded that UCNRs orientate parallel to the propagation axis of the trapping beam. On the other hand, when multiple-beam optical tweezers are used, single particle polarization spectroscopy demonstrated how full spatial control over UCNR orientation can be achieved by changing the trap-to-trap distance as well as on the relative orientation between optical traps. All these results show the possibility of real time three dimensional manipulation and tracking of anisotropic nanoparticles with wide potential application in modern nanobiophotonics.


Introduction
Rare earth doped Upconverting Nanoparticles (hereafter UCNPs) have being emerged during last years as useful fundamental building blocks in modern photonics. UCNPs are being extensively used in a large variety of research fields including solar energy, nanomedicine and bioimaging, among many others. [1][2][3][4][5][6][7][8] UCNPs show the unique capability of producing visible (VIS) luminescence under near-infrared (NIR) optical excitation by a multiphoton excitation process known as upconversion. 6,9 When compared to other nanomaterials also capable of NIR-to-VIS optical conversion (such as metallic nanoparticles and semiconductor nanocrystals), UCNPs present several remarkable advantages including long-term photochemical stability, narrow emission lines, long luminescence lifetimes, and size-independent spectral shape of their luminescence bands. [10][11][12][13][14] Recent works also pointed out that, since in UCNPs the multiphoton excitation is assisted by real electronic states, large NIR-to-VIS efficiencies could be achieved upon cw excitation without requiring the use of expensive, ultrafast, high power laser sources (as is the case when using gold nanoparticles or semiconductor nanocrystals). 9 This fact boosted the use of UCNPs for optical conversion in solar cells as well as in the development of cost-effective bioimaging equipment. [15][16][17] In the particular field of fluorescence bioimaging, UCNPs are nowadays considered as one of the most promising in vitro luminescence probes because of the low autofluorescence generated by continuous wave NIR optical excitation. 18 Moreover, recent works demonstrated that some UCNPs are not only capable of in vitro imaging but, in addition, they can also be used as intracellular thermal and chemical sensing units. [19][20][21][22] In addition, intracellular studies based on single UCNP are nowadays a real possibility as the synthesis of ultra-small (< 10 nm in diameter) UCNPs showing large NIR-to-VIS optical conversion efficiencies has been, indeed, recently demonstrated. 23 As a consequence, UCNPs are being also considered as promising optical probes for experiments at single-cell and single-particle level. As a result of the intensive research carried out on UCNPs during last years, a wide range of UCNPs consisting of different host lattices and dopants have appeared into scene. 4,24,25 Modifying the different synthesis parameters different emission bands 12 , particle sizes 23 and morphologies 3, 4, 13, 26-28 could be achieved. Among all of them, Erbium and Ytterbium codoped NaYF 4 UCNPs are considered as the reference combination of dopants and host material. 13,23 In particular, the recently demonstrated possibility of synthesizing NaYF 4 :Er 3+ ,Yb 3+ upconverting nanorods (hereafter NaYF 4 :Er 3+ ,Yb 3+ UCNRs) appears to be specially interesting as they constitute an unique system that could be used in a wide range of applications including security inking, cell tracking, cell manipulation, and bottom-up fabrication of nanofluidic and optical devices. 14,26,29,30 However, the full exploration of the potential applications of techniques have been demonstrated to be capable of remote manipulation and assembly of different nanorods. These include the application of electric and magnetic fields as well as the use of laminar flows in microfluidic channels. [31][32][33] Despite the good results obtained so far by these techniques, they lack the ability to provide real time three-dimensional spatial control. Optical tweezers are an appealing tool for real three dimensional manipulation of nanosized objects in aqueous environments. 34,35 Firstly demonstrated by Askhin and co-workers, Optical Trapping (OT) of sub-micrometric structures is based on the gradient force created in the surroundings of a tightly focused laser beam. 36,37 When a nanoparticle is randomly moving close to the laser focus, optical electric field polarizes the nanoparticle so that it behaves as an electric dipole in a non-homogenous electric field. As a consequence, the polarized nanoparticle is pushed towards the beam focus. OT and remote manipulation of a great variety of different nanostructures (including metallic nanoparticles, semiconductor nanowires, semiconductor quantum dots (QDs) and, more recently, UCNPs) have been already demonstrated. [37][38][39][40][41][42][43] In previous experiments, the characterization of the dynamics of trapped nanostructures has been limited to accurate measurements of both trapping force and particle incorporation rates. Nevertheless, practical applications require a deep understanding of the exact orientation of the optically trapped nanoparticles inside the optical trap. This is a challenging task since conventional approaches cannot be used: the trapped particle size is well below the resolution provided by optical microscopy. Thus, the design and development of non-direct strategies for nanoparticle tracking inside optical traps become necessary. As an example, Jauffred et al. determined the position distribution curve of optically trapped QDs by accurate tracking of their two-photon excited emission. 37 In the case of highly asymmetric nanoparticles (such as nanorods) not only the position inside the trap is relevant but also their intra-trap orientation needs to be known. Such knowledge has been achieved in the case of optically trapped Gold Nanorods (GNRs) and niobates nanowires by the real time analysis of luminescence and by polarized Second Harmonic Generation, respectively. These pioneer experiments demonstrated that orientation of asymmetric nanoparticles inside optical traps is far from being easy to predict. 39,44 Niobates nanowires were found to align along the trapping beam axis whereas GNRs orientated parallel to the polarization vector of the trapping laser beam. It also worth mention that, a part from the particle material, the characteristics of the trapped particle, such as its length in the case of nanorods, deeply affect the way it is trapped. 45 Fig S1). Moreover, the low density of distilled water facilitates NaYF 4 :Er 3+ ,Yb 3+ UCNR manipulation when trapped since no strong optical forces are needed in order to overtake the drag force. At this point, we should note that distilled water shows a nonnegligible absorption coefficient at the trapping wavelength (980 nm). This could lead to the appearance of thermal effects in the surroundings of the trap. According to previous works, in our experimental conditions, we had estimated that the temperature increment induced by the focused laser radiation is lower than 5 o C.
We state that such reduced heating does not affect the optical trapping experiments. 47 Optical trapping experimental setup.
Single-beam optical tweezers setup is depicted in Fig 1a. The 980 nm laser radiation coming from a single-mode fiber-coupled laser diode is collimated by a mounted rochester aspheric lens (Thorlabs, A230TM-B) and then expanded by a 2X beam expander (Thorlabs, BE02M). This laser radiation is used for both optical trapping and to excite NaYF 4 :Er 3+ ,Yb 3+ UCNRs luminescence. All the experiments were performed by using the maximum laser power provided by the laser (60 mW). For multiple-beam optical trapping experiments, the single-beam optical trapping setup was modified as it is schematically illustrated in Figure S2. We experimentally observed that the total laser power provided by the 980 nm laser diode was insufficient to form two highly stable optical traps by itself. A second 1064 nm laser beam (Nd:YAG laser, Ventus, Laser Quantum, Photonic Solutions) was used to create two additional traps perfectly overlapping with the 980 nm ones. The 1064 nm beam was made collinear with the 980 nm beam using a beamsplitter (Thorlabs, BS020) to combine the two beams (as seen in Fig S2). Then, the collinear laser beams were both split into two by using a second beamsplitter, and then reflected off by plane mirrors to recombine them as shown in Fig S2. By slightly changing the alignment of either of the plane mirrors it was possible to create a slight angular difference in the propagating beams, resulting in two separate optical traps when focused through a high numerical aperture microscope objective. The laser power at any of these two traps (80 mW) is the sum of the overlapping 980 and 1064 nm laser powers. The extra contribution of the 1064 nm laser beam lead to two stable optical traps. In summary, in this configuration, each optical trap is composed of the 1064 nm beam and the 980 nm laser beam; the more powerful laser operating at 1064 nm used to provide the power for stable optical trapping, while the 980 nm radiation is needed for exciting NaYF 4    non-radiative energy transfer process.

Dried sample experiments.
It is possible to find in the literature numerous examples revealing that highly anisotropic nanoparticles could generate a highly polarized luminescence. [48][49][50] This was firstly demonstrated in nonspherical QDs that show well differentiated polarization states in their luminescence when their aspect ratio (length to diameter ratio) exceed 2. 48 Later, a strong polarization anisotropy was discovered in codoped Tm 3+ and Yb 3+ NaYF 4 nanorods with aspect ratios close to 7. 49 The exact origin of the polarization anisotropy in rare earth doped NaYF 4 UCNRs is still unclear and, up to now, it is far from being fully understood.  Fig S4 in the Supporting Information). The large induced polarization variation (fivefold) in the intensity ratio reveals the R 652/660 coefficient as a reliable and precise parameter to determine the relative orientation of NaYF 4 :Er 3+ ,Yb 3+ UCNRs by polarized single-particle spectroscopy. A tentative explanation of the polarized luminescence of NaYF 4 :Er 3+ ,Yb 3+ UCNRs can be given based on the recently published  work of Ping Chen et al. 51 In this work, authors demonstrated that the polarized luminescence of Erbium doped NaYF 4 nanodisks is due to the deterministic orientation of the crystallographic optical axis inside the nanoparticle. They claim that the optical axis in their nanostructures is perpendicular to the hexagonal (largest) face, so that the luminescence recorded along this direction do not show any polarization dependence. On contrary, when measuring perpendicularly to this direction, due to the existence of an anisotropic crystal field, the luminescence becomes strongly polarized dependent due to the appearance of polarization induced forbidden and allowed transitions. 52 We state at this point that, very likely, the optical axis of our NaYF 4 :Er 3+ ,Yb 3+ UCNRs lies parallel to their longest dimensions (i.e. optical axis coincides with the geometrical axis of the UCNRs). This would lead to a non-polarized luminescence when measured along the longest dimension (as it is observed later in optical trapping experiments) and to a strongly polarized luminescence when spectra are recorded perpendicularly to the longest dimension of the UCNR (see Fig 3).  This has been accomplished by performing polarized spectroscopy on a single optically trapped NaYF 4 :Er 3+ ,Yb 3+ UCNR. The emission spectra generated by an optically trapped NaYF 4 :Er 3+ ,Yb 3+ UCNR were systematically analyzed for different polarization states. At variance with the experimental results included in Fig 3, we observed that the luminescence spectra generated along the trapping direction was only slightly polarization dependent. This is evidenced in Fig 4a that includes the emission spectra generated by a single optically trapped NaYF 4 :Er 3+ ,Yb 3+ UCNR as obtained for two arbitrary orthogonal polarizations. Within experimental error, they have been fund to be virtually the same. In the emission spectra included in Fig 4a, the 660 nm line clearly dominates over the 652 nm peak, being this behavior independent of the polarization state as shown in the two dimensional map where emission intensity of the red band is represented as a function of the emission polarization angle. According to data included in Fig 3, Fig S2). Such a setup allowed for an accurate control over distance and relative position between two optical traps. Two different situations were found to take place. When optical traps are separated a distance longer than one micron (approximately), they behave as two independent single-beam  Fig 6). Rotation of the optically trapped Evolution of the emitted spectra of a trapped NaYF4:Er 3+ ,Yb 3+ UCNR when the distance between traps is reduced. The recorded emission polarization angle is fixed to that indicated by white arrows. It can be seen that the emission spectra changes from that attributed to perpendicular polarization (a-c) to that for the parallel polarization state UCNR. Note that the data included in Fig 5 and 6 does not only reveal the possibility of accurate three dimensional optical manipulation of single UCNRS but also the continuous monitoring of their three dimensional orientation by single particle spectroscopy.

Conclusions
In summary, resonant stable optical trapping of NaYF 4  ,Yb 3+ upconverting nanorod whose three dimensional orientation was unequivocally determined by the analysis of the polarization state of their single particle luminescence. The possibility, demonstrated here, of applying simple experimental approaches to achieve three dimensional manipulation of upconverting nanorods, whilst knowing their exact position and orientation, open up a new avenue into their use in numerous applications ranging from biology to nanofluidics. Evolution of the emitted spectra when rotating the longitudinal axis of the NaYF4:Er 3+ ,Yb 3+ UCNR. Emission polarization angle is fixed to that indicated by white arrows. Perpendicular polarization is measured when NaYF4:Er 3+ ,Yb 3+ UCNR axis happen to be perpendicular to the emission polarization angle (lower panel). An intermediate state is observed when NaYF4:Er 3+ ,Yb 3+ UCNR axis form approximately 45º with the emission polarization angle and both polarization states are measured (middle panel). Scale bar corresponds to 1 µm in all images.