Optical tweezers have become standard tools in many interdisciplinary research domains due to the possibility of manipulating, sorting, separating, and trapping micro- and nanometer sized objects. Already in 1993, shortly after the development of the original approach in 1986 based on strong laser beam focusing using a high numerical aperture (NA) microscope objective [1], the first fiber-based optical tweezers were demonstrated [2]. Trapping was obtained by aligning the fibers of two pigtailed lasers using just a cover slip and a capillary. This first work already highlights the great simplicity and small footprint of optical fiber tweezers. It has already been demonstrated that trapping of small particles at low light power is possible using microstructured fibers [3–5]. Chemical etching [6–10] and mechanical grinding [11] are the most popular techniques to realize fiber tips used for trapping in single or dual fiber geometries. More complex methods such as focused ion beam etching [12–14] and self-guided photopolymerization [15] are also applied to realize beam shaping devices at the distal ends of optical fibers. Finally, 3D printing of diffracting elements presents a versatile technique for beam shaping [16] and imaging purposes [17]. Fresnel lenses obtained by this technique have recently been applied for very efficient optical trapping of 1 μm and 500 nm polystyrene beads [18].

A major motivation for the development of optical tweezers is the possibility to combine trapping experiments with other experimental tools such as optical spectroscopy [19–22]. As an example, one can cite the use of Raman tweezers for the identification of nanoplastics in seawater [23]. Moreover, photoluminescent nanoparticle trapping is of great interest due to potential applications in bio-imaging experiments [24]. For example, NaYF4 nanorods are biocompatible materials used as efficient hosts in optoelectronic devices [25,26]. NaYF4 has a relatively low phonon energy (300–400cm−1) [27], and the presence of yttrium allows straightforward substitution with other lanthanide ions [28]. The red-emitting Eu3+ ions show interesting anisotropic emission that is more prominent than Er/Yb or other lanthanide dopants [29,30]. Moreover, the europium emission features distinct electric dipole (ED) and magnetic dipole (MD) transitions [27,31,32].

Optical trapping and manipulation require recording the position of trapped particles by optical microscopy. Photoluminescence (PL) imaging allows for determination of the nanoparticle position, whereas in the case of nanorods with hexagonal crystal structure, the emission anisotropy is used to determine the nanorod orientation [30,33,34]. Nanorods with high aspect ratios tend to form clusters that cannot be resolved optically. Measuring the PL emission power [33] or the trap stiffness [35] allows us, however, to estimate the number of nanorods in a cluster.

In this paper, we report on optical trapping of NaYF4:Eu3+ nanorods using our recently developed Fresnel lens fibers [18]. These fibers produce focused beams with NA=0.5 and a focal length of 100 μm. Compared to former experiments using optical fiber tips [36,37], the nanorods are efficiently trapped at about 100 μm from the fibers, thus removing any mechanical or optical influence on the particle’s optical emission properties. Two specific aspects will be presented in detail: the optical trapping behavior of nanorods in the anisotropic trapping potential of our dual fiber tweezers and the spectroscopic investigation of the anisotropic europium emission.

The NaYF4:Eu3+ nanorods are synthesized by the hydrothermal process described in more detail in Ref. [37]. The process is based on a mixture of sodium hydroxide, ammonium fluoride, and rare earth chlorides in an oleic acid solution that is transferred into an autoclave and heated at 200°C for 24 h while stirring. The nanorods are obtained when cooling down to ambient temperature. After synthesis, particles are extensively washed by centrifugation to remove excess oleic acid, and surface oleate ligands are exchanged with citrates to ensure good dispersion. Just before optical trapping experiments, the nanorod solution is extensively diluted in water and sonicated for a few minutes to separate the nanorods. The nanorods are characterized by scanning electron microscopy (SEM) in which they are observed to have mean lengths and diameters of l=1.2μm and d=120nm, respectively [Fig. 1(a)].

A detailed description of the Fresnel lens fiber design and fabrication is given in Ref. [18]. The lenses are printed on standard, commercial single mode fibers (Nufern 780-HP) by femtosecond two photon lithography (Nanoscribe Photonic Professional GT) with commercial resist (Nanoscribe IP-Dip) [38]. The total writing time is 55 min for the lenses used in this work. To achieve a reasonable working distance at high NA, the optical fiber mode is expanded by propagation through a solid cylinder of 500 μm length [Fig. 1(b)]. The diffracting lens is modeled via a phase-function and geometrical ray-tracing based on the local grating approximation. The Fresnel lens fibers with NA=0.5 produce a tightly focused Gaussian shaped spot with a waist of 0.8 μm at a focal distance of f=97.5μm in water.

The schema of the optical fiber tweezers is displayed in Fig. 1(c). The 808 nm trapping laser (LU0808M250, Lumics) is separated into two equal arms using a polarizing beam splitter and a half-wave plate to control the relative light intensities in each arm. The light beam is coupled into the optical fibers using fiber launchers. The output power from each fiber is directly measured at its distal end in air, before and after each experiment. The power values given in this paper correspond to the emitted power of one fiber in air. The fibers are mounted on two sets of x,y,z piezoelectric translation stages for high precision position alignment (PI P-620 and SmarAct SLC-17 series). The trapping chamber consists of an O-ring placed in between two glass slides and cut in two parts to insert the fibers. All experiments are carried out at room temperature (T=290 K).

A homemade microscope, consisting of a long working distance microscope objective (Mitutoyo G Plan Apo 50×, NA = 0.55) and a CMOS camera (Hamamatsu ORCA FLASH 4.0 LT), is used for trapping visualization. Typical trapping videos contain 3000 frames recorded at frame rates of 200 fps (frames per second). The Eu-doped nanorods are optically pumped using a 393.5 nm laser with a bandwidth below 1.5 nm (OxxiusLBX-395-120-CSB-PPA). The pump laser is injected directly through the microscope objective using a dichroic mirror. The pump laser polarization is not controlled, thus being oriented in an arbitrary direction inside the xy plane. The typical pump laser power is 25 mW at the output of the microscope objective.

The recorded trapping videos are analyzed using a custom-written particle tracking algorithm, developed in the Scilab environment. This algorithm is based on two-dimensional Gaussian fitting of the ellipsoidal trapped nanorod PL image. It takes into account the time dependent particle orientation in the observation plane. Two complementary methods are applied to deduce the trap stiffness κ from the particle position records, assuming a harmonic optical trapping potential U(x)=12κx2 [6]. Both methods are used independently in the axial (x) and transverse (y) directions of the observation plane. In the Boltzmann statistics (BS) method, the probability P of finding the particle at position x can be described in the framework of the equipartition theorem by P(x)=1Ze−κ·x22kBT,(1)with Z the normalization factor and 2kBT the thermal energy. In power spectrum analysis (PSA), the power spectrum of the recorded position is fitted to the Lorentzian function: P(f)=2kBTγ(fc2+f2),(2)with fc=κ/2πγ the corner frequency and γ the friction coefficient. To take into account the nonspherical shape of the trapped nanorods, the model developed by Tirado et al. is applied [39]. Two distinct friction coefficients, perpendicular and parallel to the nanorod long axis, are defined by $$\begin{gathered} γ⊥=4π·llnp+Γ⊥·η, \\ γ||=2π·llnp+Γ||·η, \end{gathered}$$(3)with p=l/d the nanorod aspect ratio, η the dynamic viscosity [in water η(300K)=8.65×10−4N·s·m−2], and Γ a dimensionless correction coefficient depending on p. For the given aspect ratio (p=10), these coefficients are Γ⊥=0.86 and Γ‖=−0.11, resulting in friction coefficients of γ⊥=4.13×10−9N·s·m−1 and γ||=2.98×10−9N·s·m−1, respectively.

For the spectroscopic measurements, the trapped nanorods’ PL is collected through the microscope objective by introducing a mirror on a flip-mount. The emission is then directed onto either a spectrometer coupled to an EM-CCD camera (Princeton Instruments ProEM) or an avalanche photodiode (APD, Thorlabs APD440A) for lifetime measurements. A set of optical filters suppresses the trapping and pumping wavelengths. Moreover, a linear polarizer in front of the spectrometer allows us to record polarization-resolved emission spectra. The zero of the polarizer angle θ is experimentally calibrated to the direction parallel to the trapping fiber’s axis. The emission spectra are recorded with a slit width of 0.88 mm and an integration time of 10 s. For lifetime measurements, the pump laser is directly modulated at 11 Hz with a rectangular waveform. The overall response time of the laser and the APD is ≈20μs, well below the expected Eu3+ lifetime. The PL is acquired at the maximum APD gain of 2.65×109V/W and without any spectral filtering. The lifetime τ of the D50 level is obtained by fitting the normalized intensity to the single exponential function I(t)/I0=exp(−t/τ), with I0 the mean intensity at t<0. To exclude any influence of the experimental setup, the numerical fits are limited to the time range from 500 μs to 10 ms.

NaYF4:Eu nanorods are optically trapped in a counterpropagating geometry using two Fresnel lens fibers separated by 195 μm. Typical trapping powers are 11 mW to 32 mW. The PL image of the trapped nanorods shows elliptical bright spots with typical lengths and widths of 1.5 μm and 500–550 nm, respectively [Fig. 2(a)]. The spot width corresponds to the microscope resolution of ≈500nm and does not indicate the actual nanorod width.

During trapping experiments, we concurrently observe untrapped nanorods that are attracted into the optical trap. When entering the trap, they form indistinguishable nanorod clusters with the rod(s) that is already trapped. In general, nanorods with high aspect ratios tend to form clusters of aligned nanorods that cannot be resolved by optical means. To get an estimation of the number of trapped particles, we measure the PL increase of the trapped cluster when a new nanorod joins [Fig. 2(a)]. The observed emission intensity steps are linearly increasing with the increasing number of nanorods in the clusters. It is thus possible to characterize the trapping properties as a function of the trapped cluster size.

Figure 2(b) shows the x−y tracking record of clusters containing one, two, and three nanorods for a trapping laser power of 32.2 mW. As expected for counterpropagating two beam tweezers, the particles are more efficiently trapped in the direction transverse to the fibers, i.e., perpendicular to the laser beam axes. Moreover, the nanorods are mainly aligning parallel to the fiber axis. Finally, the trapping becomes more efficient with an increasing number of rods inside the cluster.

Depending on the number of nanorods in the trapped cluster, the trap stiffness is about 7 to 32 times higher in the transverse direction compared with the axial direction. This anisotropy increases significantly with the number of nanorods. In fact, the transverse trap stiffness for three rods is about 7.4 times higher than for a single rod, whereas the axial stiffness increase is limited to 1.6 times. Moreover, this dependency is quite different for the two directions (Fig. 4 insets). The increase is exponential in the transverse direction and exponentially converging towards a threshold in the axial direction.

The angular distribution width (σθ) is linearly decreasing with the number of particles [Fig. 2(c) and Table 1] and trapping power (not shown). The distribution width of 5.2° for one single rod at 32.2 mW trapping power is sufficiently low for the spectroscopic investigation of the anisotropic Eu3+ emission.

The emission studies are performed on single nanorods and at a trapping power of 33.2 mW to ensure stable trapping with low angular dispersion. The emission spectrum exhibits three strong emission bands in the 570 nm to 710 nm spectral region [Fig. 5(a)]. One specific feature of the Eu3+ emission is the simultaneous presence of ED and MD transitions. Moreover, all main transitions start form the D50 energy level: D50→F17 at 585–600 nm (MD590), D50→F27 at 603–621 nm (ED615), and D50→F47 at 683–705 nm (ED695). The first transition is an MD transition, whereas the other two are ED transitions. The D50→F37 can be distinguished at about 650 nm. However, its low intensity makes its further characterization difficult. The further, relatively weak band at 582 nm corresponds to the D51→F37 transition, the only one starting from the higher D51 level.

Each of the three main transition bands can be divided into three to four emission peaks with either π orientation (θ=0°, parallel to the fibers axis) or σ orientation (θ=90°, perpendicular to the fibers). As can be seen in Fig. 5, each transition band contains σ and π peaks. For example, the dominant contribution to the ED615 emission is of σ orientation with, however, a weak π oriented peak at 618 nm. In the case of the MD590 emission, two regions of similar intensity are distinguishable: π orientation below 590.5 nm and σ orientation for longer wavelengths. Finally, the ED695 band is of σ orientation at the low wavelength side and π orientation for longer wavelengths.

The emission spectra of trapped nanorods are compared to the emission of a single cluster of 15 to 20 nanorods on a glass substrate [Fig. 5(a) inset]. The linewidths of the emission peaks in the 575–630 nm range are identical for trapped and dispersed nanorods. The D51→F37 peak intensity is, however, more pronounced on the substrate. Moreover, the three MD590 peaks are better distinguishable, and the ED6151 peak at 610 nm is missing in the cluster emission on the substrate.

The experimental emission intensities are fitted to the orthogonal polar function: I=A·sin2(θ−φ)+B·cos2(θ−φ),(4)with I the intensity, θ the polarizer angle with θ=0° parallel to the trapping fibers’ axes, and φ an angular shift that indicates the actual nanorod orientation with respect to the optical fiber axis (Table 2). For all clearly polarization dependent transitions, the deviation of the nanorod orientation from the trapping beam’s axis is below 4°, in good agreement with the microscope observations.

ED and MD moments p and m are not perfectly parallel or perpendicular to the NaYF4c axis [34]. In the paraxial approximation, the angle α between the respective dipole moments and the c axis can be obtained from the fitting parameters A and B in Eq. (4) by using A=cos2α and B=(1/2)·sin2α for an MD transition and A=(1/2)·sin2α and B=cos2α for an ED transition [32]. In both cases, A and B have to be normalized using sin2α+cos2α=1. Modeling the nanorod emission, one has to consider three orthogonal dipoles parallel to the rods’ a, b, and c axes (parallel to the trap x, y, and z axes). As the emission is captured in the z direction only, half of the emission of the a and b dipoles is captured, leading to the factor 1/2 in front of A or B for ED and MD dipoles, respectively.

In the case of the MD transition, the two peaks MD5901 and MD5902 are of π orientation, whereas the MD5903 peak is of σ orientation. The MD of the MD5902 peak is orientated nearly parallel to the nanorod c axis (α=80.5°), resulting in a high B/A ratio and a narrow waist of its polar plot. On the other hand, the MD5901 dipole orientation of 63.2° results in a more oval polar plot, which shows, however, still a clear π orientation. The dipole orientation of the MD5903 peak (α=36.8°), well below 45°, reflects its σ orientation and results also in a clearly visible waist.

The ED615 emission band is dominated by the σ orientated peak ED6152 with a dipole angle of α=69.6°. The dipole orientation of the longer wavelength peak ED6153 of α=49.8° is close to 45°, leading to a nearly oval polar plot. The short wavelength side peak ED6951 does not show a clear orientation. Moreover, its fitted nanorod orientation angle of φ=−43.7° prohibits the determination of the dipole orientation.

The ED695 emission band is the only one fitted to four Gaussian peaks. The long wavelength peak ED6954 shows, however, no clear polarization behavior with φ=32.6°. Moreover, the strongest peak (ED6952) shows less pronounced polarization dependence with a dipole orientation of α=47.4°. The two side peaks ED6951 and ED6953 show, however, strong σ and π orientation dependence with dipole angles of α=80.0° and 30.8°, respectively.

The lifetime of the europium D50 level is measured using a trapped nanorod cluster estimated to consist of two or three nanorods. The trapping conditions are equal to the ones for spectroscopic measurements. The PL decay is a single exponential with a lifetime of τ=4.4ms (Fig. 7). No significant dependence on the pump power Ppump was observed in the 7–12 mW range. The PL emission power measured by the APD is linearly increasing with Ppump.

This PL decay of the trapped particles was compared to the already mentioned nanorod cluster on a glass slide. In this case, the decay is clearly a double exponential with short and long decay times of τ1=1.3ms and τ2=4.5ms, respectively. As for the trapped nanorods, no significant dependence is found between the pump power and the decay time, whereas the PL power increases linearly with Ppump.

Stable nanorod trapping is observed for fiber-to-fiber distances of about 200 μm and for light powers as low as 10 mW. As expected for dielectric nanorods, they align parallel to the beam/fiber axis, with a low angular distribution of σθ=4°−5°. The PSA suggests that the nanorod motion in the transverse and axial directions is not completely independent. In the transverse direction, the power spectra can be fitted to the Lorentzian function [Eq. (2)] only for frequencies above 2.5 Hz. At lower frequencies the power spectrum is not constant but approaches the value of the axial motion for frequencies of about 1 Hz. Taking into account the large aspect ratio of p=10, the presence of weak rotational modes can provoke the coupling of the two linear translation modes at low frequencies.

In general, BS and PSA are complementary methods with each having its own advantages and drawbacks. BS does not require one to know the Stokes’ friction coefficient. Slow mean trapping position shifts or two metastable trapping regions as observed for single rod trapping [Fig. 2(b)] result, however, in underestimated κ values. PSA allows one to neglect these drifts by fitting only to higher frequencies, but requires high frequency particle position recordings. In our case, the small nanorod PL signal limits video recordings to 200 fps. The linear slope of the PS above the corner frequency fc can, thus, only be partially resolved (Fig. 3). As a consequence, the PSA was not possible for all trapping videos. Finally, the trap stiffness obtained by PSA is in general higher than the BS one. However, the trap efficiency and the angular distribution are largely sufficient for the study of the nanorod emission properties.

The observed polarization features of the Eu3+ emission are related to the intrinsic crystalline anisotropy and symmetry of lanthanide sites. The effect of birefringence on the polarized emission can be estimated to less than 1% for highly anisotropic crystals under the given experimental conditions. Chacon et al. studied the NaYF4:Eu3+ emission by confocal microscopy on identical single nanorods, dispersed on a quartz substrate [32]. In accordance with our measurements on a glass substrate, they found a more intense D51→F37 transition peak at 583 nm and also three more pronounced peaks in the MD emission band. They determined the dipole orientations of the MD5901–3 peaks to α=65.7°, 68.9°, and 37.8°, respectively. Compared to our present work, the MD of the MD5902 peak was thus found to be about 10° smaller. The observed difference can be related to the influence of the quartz substrate on the Eu3+ emission properties.

In former work, we trapped NaYF4:Eu3+ nanorods using optical fiber tips [37]. In this configuration, the nanorods were attracted to the fiber tips and trapping was realized with contact to one fiber tip. At that time, the spectroscopic study was limited to the MD590 and ED615 bands. The emission spectra are very similar in both cases. Using Fresnel lenses, the nanorods are, however, better aligned to the fiber axis. For a more detailed comparison, we have applied our advanced data analysis to the former results. Similar to the already mentioned nanorods on a quartz substrate, the MD orientation of the MD5902 is found to be 5° smaller. Concerning the ED₆₁₅ band, the polarization dependence of the short-wavelength side peak ED6151 at 610 nm is less pronounced in the tip contact. The corresponding dipole angle of α=51° is very close to 45°. As already mentioned, this peak is absent for nanorods dispersed on a substrate (Fig. 5 and Ref. [32]), suggesting that this feature is due to the contact with the optical fiber tip.

The PL decay of trapped nanorods is a single exponential with a decay time of 4.4 ms. For the particle cluster on the glass substrate, an additional, shorter decay with τ1=1.3ms is observed. The appearance of this fast decay is not yet elucidated. It could be related to the stronger peak at 582 nm, which is the only observed emission line starting from the higher D51 state. Nonradiative decay routes make the PL decay rate of this state considerably faster than that of the lowest excited state D50 [27]. A further hypothesis could be dielectric influence of the substrate or even auto-fluorescence from the glass substrate.

Stable and reproducible trapping of europium-doped nanorods is studied in far-field, Fresnel lens dual fiber tweezers. High normalized trapping efficiencies κ˜ are observed for single nanorods or nanorod clusters containing two or three nanorods. PSA with distinct friction coefficients for the orthogonal directions parallel and perpendicular to the nanorod axis suggest slight coupling of the motion in these two directions.

Polarization-resolved spectroscopy allows us to specify the σ and π configurations of the ED and MD emission bands and to deduce the nanorod orientation. The Eu3+ emission decay time of 4–5 ms underlines the low phonon energy of the NaYF4 host matrix.

The presented results highlight the outstanding performance of our Fresnel lens fiber optical tweezers, permitting stable trapping of nanoparticles at low light power and large particle to fiber distance. The optical study of free, purely optically trapped, single nanoparticles is significantly facilitated. Moreover, the possibility to determine the nanorod orientation by fast spectroscopic means is of paramount interest for microrheologic experiments with anisotropic particles.

Acknowledgment. J.F acknowledges very fruitful discussions with G. Colas des Francs from ICB in Dijon, France. S.N.C. is grateful to Institut Néel for hosting her during the work. We thank also T. Pohl for his valuable help with graphics.