View Article Online View Journal
Nanoscale Accepted Manuscript
This article can be cited before page numbers have been issued, to do this please use: J. Decombe, F. Valdivia-Valero, G. Dantelle, G. Leménager, T. Gacoin, G. Colas des Francs, S. Huant and J. Fick, Nanoscale, 2016, DOI: 10.1039/C5NR07727C.
This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains.
www.rsc.org/nanoscale
Page 1 of 9
Nanoscale View Article Online
Luminescent nanoparticle trapping with far-field optical fiber-tip tweezers Jean-Baptiste Decombe,a† Francisco J. Valdivia-Valero,b Géraldine Dantelle,a Godefroy Leménager,c Thierry Gacoin,c Gérard Colas des Francs,b Serge Huant,a and a Jochen Fick ∗
We report stable and reproducible trapping of luminescent dielectric YAG:Ce3+ nanoparticles with sizes down to 60 nm using far-field dual fiber tip optical tweezers. The particles are synthesized by a specific glycothermal route followed by an original protected annealing step, resulting in significantly enhanced photostability. The tweezers properties are analyzed by studying the trapped particles residual Brownian motion using video or reflected signal records. The trapping potential is harmonic in the transverse direction to the fiber axis, but reveals interference fringes in the axial direction. Large trapping stiffnesses of 35 and 2 pN·μm−1 ·W−1 are measured for a fiber tip-to-tip distance of 3 μm and 300-nm and 60-nm particles, respectively. The forces acting on nanoparticles are discussed within the dipolar approximation (gradient and scattering force contributions) or exact calculations using the Maxwell Stress Tensor formalism. Prospects for trapping even smaller particles are discussed.
1
Introduction
Trapping and manipulation of micro- and nanoparticles were introduced in 1986 by A. Ashkin 1 . This noninvasive instrument has developed many interesting applications, e.g. in biology where it is used for cell manipulation with high precision and free of any mechanical contact. Besides the historical approach of strong focused laser beam tweezers, a great variety of optical fiber-based tweezers was developed. Optical fiber tweezers are very flexible and easy to use as they do not use bulky high N.A. microscope objectives and require little alignment. Moreover, controlled nano-structuring of the optical fiber allows to transform the fiber guided modes into advanced beam types such as non-diffracting and self-healing quasi-Bessel beams 2 , 3D bottle beams 3 or optical vortices 4 . In most cases the nano-structuring relies on relatively fast and competitive techniques such as wet chemical etching 3–8 or photopolymerization 9,10 . Optical tweezing with single fiber and dual fiber geometries
a
Univ. Grenoble Alpes, Inst NEEL, 38000 Grenoble, France CNRS, Inst NEEL, 38000 Grenoble, France. b Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRSUniversité Bourgogne Franche-Comté, 21078 Dijon, France. c Physique de la Matière Condensée, CNRS UMR 7643, Ecole Polytechnique, 91128 Palaiseau, France. † Present address: Louisiana State University, Baton Rouge, USA. ∗ Fax: +33 476 887988; Tel: +33 456 387148; E-mail: jochen.fi[email protected]
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 focus point at a certain distance to the tip end 5,11 . In the dual fiber approach, with two equally illuminated fiber tips facing each other, the radiation pressure vanishes at equilibrium 12 . Efficient trapping can thus be obtained at relatively low light intensities. Moreover, asymmetric radiation pressure distributions can be engineered to control the particle position or the orientation of non spherical particles such as nano-wires 8 or biological cells 13 . In addition, trapping one nanoparticle far from the probe opens the door to the investigation of its optical properties at the single particle level in absence of perturbation by the surroundings. In a different approach, cleaved optical fibers or fiber tips can be used as a support to metallic nano-structures for plasmonic trapping 14–16 . These sorts of optical near-field tweezers are well adapted for dielectric nanoparticle or single molecule trapping. Their excitation efficiency and flexibility were significantly enhanced by using a fibered approach. Their main drawback, however, is in the need for cost and time intensive clean room nanostructuring technology. A further problem is that the trapped particle is most likely in contact with the metallic structure, what can strongly modify its optical properties. In this context, we have demonstrated stable and reproducible trapping of 1 μm dielectric particles using dual fiber tip tweezers with Gaussian 17 and quasi-Bessel beams 18 . In the present pa1–9 | 1
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Nanoscale
Page 2 of 9 View Article Online
DOI: 10.1039/C5NR07727C
2 2.1
ally detectable during hours whereas single raw particles become undetectable after few minutes due to photobleaching, in agreement with previous observations of nanoparticle powder 20 .
Methods Nanoparticle elaboration
YAG:Ce3+ particles with high luminescence quantum yield, excellent photostability and well-defined size distribution are elaborated using a glycothermal synthesis in combination with an original protected annealing procedure 19,20 . Yttrium acetate hydrate (7.425 mmol, 1.976 g), cerium acetate hydrate (0.15 mmol, 47.6 mg for a 2 at.% doping) and aluminium isopropoxide (12.5 mmol, 2.55 g) are mixed together with 53 mL of butanediol and poured into a 75-mL autoclave (Parr, Series 4740 High Pressure Vessel). The autoclave is heated at 300◦ C for 3 hours and then cooled down to room temperature. The obtained mixture is washed three times in ethanol by successive centrifugations (11000 rpm for 10 minutes). The resulting yellowish solution is a suspension of YAG:Ce nanoparticles in ethanol. Size selection is performed using short and fast centrifugation steps. A short centrifugation (1 min at 11 000 rpm) allows retrieving the smallest particles. A Dynamic Light Scattering (DLS) measurement gives an average size for the particles in suspension of 60 ± 40 nm (Fig.1.a.) The biggest particles can be retrieved by performing several centrifugations (11000 rpm, 1 min) and considering only the particles at the bottom. After 3 centrifugations, the particles at the bottom are redispersed into ethanol. Their averaged size is 300 ± 100 nm, determined by DLS and confirmed by SEM observations. In order to improve the optical properties of the as-made YAG:Ce nanoparticles, the obtained colloidal solutions (containing either the 60-nm or 300-nm nanoparticles) are mixed with a silica sol according to the procedure reported in 20 . After drying, the composite is grounded and then heated at 1000◦ C for 12 hours. A second annealing is performed (600◦ C for 12 hours under a Ar/H2 reductive atmosphere) to maintain the cerium ions into a +III oxidation degree. The last step of this process is to remove the silica matrix by a HF dissolution, consisting in adding a 2.5 vol.% HF solution to the composite and stirring the mixture for 3 hours. The obtained annealed nanoparticles are redispersed in water. Their size (60 nm or 300 nm) is preserved thanks to this protected annealing process. Particle absorption and emission spectra before and after the protected annealing are presented in Fig.1.b. Two excitation peaks are observed at 340 and 450 nm, associated with the Ce3+ 4f ⇒ 5d(2 B1g ) and 4f ⇒ 5d(2 A1g ) transitions, respectively. An intense and wide emission peak is obtained in the visible range due to 5d ⇒ 4f transitions. The main absorption peak is narrower for annealed particles because of the enhanced uniformity of the Ce3+ environment. The most important point is, however, their exceptional photostability. Annealed particles are individu2|
1–9
Fig. 1 (a) Statistical size distribution of the synthesized 60-nm YAG:Ce3+ particles. Inset : TEM image of the corresponding particles. (b) Absorption and emission spectra of the YAG colloidal solution before and after the protected annealing. Inset : Ce3+ energy diagram.
2.2
Optical tweezers set-up and characterization methods
The core of the used optical tweezers is made of two optical fiber tips facing each other (Fig. 2). Each tip is mounted on a set of x − y − z piezoelectric translation stages, allowing for easy fiber alignment with sub-micrometer precision 17 . The fiber tips are elaborated by chemical wet etching from standard single mode optical fibers. Their full tip angle is about 15◦ with apex sizes in the order of 60 nm. The emitted beam is of Gaussian shape with an 8◦ emission angle in water and a minimal beam waist of 900 nm. The trapping laser intensity is directly measured at each fiber tip in air and corrected for emission in water. The relative light intensities of the 808 nm trapping laser in the two fiber tips is controlled by an half-have plate and a polarized beam splitter. In each arm, a 90/10 beam splitter allows to record the light intensity which is back-reflected from the fiber tip. This back-reflection consists of the sum of the reflections from the fiber tip and the trapped particle together with the transmitted light
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
per we show that our far-field approach allows to trap dielectric nanoparticles as small as 60 nm without any need for metallic plasmonic structures. This is a large step forward compared to previous works which mainly deal with trapping of micrometersize objects. Furthermore, our approach offers the prospect for trapping even smaller particles, which is of interest for cell biology or sensor applications.
Page 3 of 9
Nanoscale View Article Online
DOI: 10.1039/C5NR07727C
2.3 Modelisation of the fibered optical tweezer We have performed 3D numerical simulations using a finite element method (FEM) 23 . The model is described in Fig. 3.a. It consists of two tapered silica fibers (optical index 1.45) with an input diameter Din = 1 μm, and a tapered full angle 2α = 15◦ . The radius of curvature of the output is fixed to 50 nm. The whole system is immersed in water and the input port of the fiber is excited with the linearly polarized fiber mode HE11 (effective index Ne f f = 1.3888 at λ = 808 nm). The input power is fixed to Pin = 1 W. In order to avoid parasitic reflexions at the borders of the window, we are using perfectly matched layers (PML). The mode propagation within the fibers is clearly visible in Fig.3.b. The interference pattern (interfringe of λ /2nw = 304 nm) originates from the two counter-propagating waves exiting from the elongated fibers. Fig. 2 Scheme of the optical nano-tweezers set-up.
from the second opposite fiber tip. Particle trapping is visualized by a homemade microscope using an x50 large working distance objective. A CMOS camera allows video recording at rates of up to 300 fps. The Ceriumdoped nanoparticles are excited through the microscope using a second laser emitting at 457 nm and a dichroic mirror. Different particle tracking algorithms were developed to obtain particle position records from the trapping videos. The particle positions in axial and transverse directions with respect to the fiber axis are distinguished. Two complementary methods are used to study the trapping properties: Boltzmann statistics 21 and power spectrum analysis 22 . The first method is based on the fact that the probability density P(x) of finding the particle in the potential well U(x) at a certain position x can be described using Boltzmann statistics. In the case of an harmonic trapping potential U(x) = κ/2 · x2 , the stiffness can be directly obtained by fitting P to the Gaussian function P(x) = exp(−κx2 /2kB T ), with κ the trap stiffness, kB the Boltzmann constant, and T the temperature. Generally, Boltzmann statistics works for any type of trapping potential. The definition of the trap stiffness κ becomes, however, irrelevant for a non-harmonic potential. In the second method, the oscillation power spectrum of the residual Brownian motion of the trapped particle is approximated by the Lorentzian function : P( fk ) =
kB T 2π 2 γ0 ( fc2 + fk2 )
(1)
with fc = κ/2πγ0 the corner frequency, γ0 = 6πηa the Stokes friction coefficient, η the dynamic viscosity of the host media, and a the particle radius. In practice, the trap stiffness is obtained by numerical fitting (in the log/log space) of the entire experimental spectra to Eq. 1. This method only works for harmonic potentials.
Fig. 3 (a) Calculation scheme for the silica nano-tips facing each other, immersed in water (dielectric constant εbg = n2bg = 1.77), and separated by dsep . The geometrical parameters are indicated on the figure. (b) Map of the electric field norm (in V/m) in the axial direction for a 300-nm particle between the tips separated by dsep = 2.5 μm. Each fiber is excited with Pin = 1 W HE11 fiber mode.
3
Results and discussion
3.1 Nanoparticle trapping 3.1.1 300-nm particles Stable and reproducible trapping of 300-nm YAG:Ce3+ is realized for light intensities (at the end of the fiber tips) down to 4 mW and for tip-to-tip distances up to 8 μm. The trapping properties are systematically studied by varying the injected light intensities 1–9 | 3
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
Moreover, the Stokes coefficient has to be known. The main advantage consists of its applicability to the video position records and to the back-reflected signal.
Nanoscale
Page 4 of 9 View Article Online
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
and the fiber tip-to-tip distances for trapping of one single particle. The shape and strength of the trapping potential is different in the axial and transverse directions. In the transverse direction, the position distribution statistics clearly indicates a harmonic potential (Fig. 4.a). The trap stiffness linearly increases with light intensities for all fiber tip-to-tip distances. This feature confirms the fact that particle trapping is only due to optical forces. Any influence from the fiber tips can be neglected. Furthermore, one can define a normalized trapping constant. For example a high value of κ˜ tr. = 35 pN·μm−1 ·W−1 was measured for a tip-to-tip distance of 3 μm. The reference power is taken at the end of a single fiber 17 .
Fig. 4 (a) Transverse position distribution of a 300 nm YAG:Ce3+ trapped particle for several fiber tip-to-tip distances. Inset: Fluorescence microscopy image of a trapped 300-nm particle (b) Axial position distribution for orthogonal (blue) and parallel (red) polarizations. Bold line are best Gaussian fits; In b), the thin red line is a guide to the eye for peak position visualization.
For the axial direction, the position distribution statistic is more complex (Fig. 4.b). Depending on the relative polarization of the two counter-propagating light beams, we observe some substructures. The distribution is fitted to series of equidistant Gaussian peaks with 350 nm spacing. This distance is of the order of half the trapping laser wavelength in water (304 nm). The subpeaks progressively disappear when annihilating the interference fringes by turning the relative polarization of one of the input beams. Additionally, this modification has no influence on the 4|
1–9
transverse trapping properties. This feature can only be observed for the 300-nm particles, i.e. particles of similar size than the interference fringe spacing. Larger micro-particles "feel" more than one (typically two or three) fringe at a time, resulting in averaging of the effect. As will be shown below, the Brownian motion of smaller (60 nm) particles is too large to resolve this substructure. The fiber tip-to-tip distance dependency of the trapping properties are studied in the 2 to 6 μm range and for a light intensity of 47 mW. The relative polarization is chosen to cancel the interference fringes. The trap stiffness is calculated applying Boltzmann statistics (Fig. 4) and power spectra method. In the later case video observation records and back-reflection signals (Fig 5.a) are used.
Fig. 5 Power spectra from the back-reflection (a) and normalized trapping stiffness along transverse direction (b) of a 300 nm YAG:Ce3+ as a function of fiber tip-to-tip distances. Inset : Stiffness along axial direction.
As expected, the trap stiffness deduced from all three methods is increasing with decreasing distance (Fig. 5.b). The experimental error was estimated to 15% from different sets of identical measurements (not shown here.) The values from Boltzmann statistics and back-reflection signals are in very good agreement. Values from the power spectra analysis of the video records are, however, diverging at short tip-to-tip distances. This difference can be explained by the camera readout frequency limitation. In
Nanoscale Accepted Manuscript
DOI: 10.1039/C5NR07727C
Page 5 of 9
Nanoscale View Article Online
order to clearly observe the weak photoluminescence of 300-nm particles, the camera integration time was fixed at 10 ms, thus limiting the resulting power spectra cutoff frequency to 50 Hz. On the other hand, the corner frequency of the trapped particle ( fc = κ/2πγ0 ) is about 90 (20) Hz for 2 (6) μm tip-to-tip distances. Consequently, the numerical fitting to Eq. 1 becomes inaccurate for small tip-to-tip distances. The higher readout frequency (≈ 5 kHz) of the back-reflection makes this method a better choice. Its main drawback consists, however, in the difficulty to distinguish the contributions from the particle position oscillations in transverse and axial directions (Fig. 5.a). In the case of 1 μm particles, we observe two distinct corner frequencies (not shown here) corresponding to the transverse and axial cases, respectively. For the present 300-nm particles, the power spectra are dominated by the contribution of the transverse oscillation. The inflection of the axial trapping contribution at low frequencies cannot be resolved. 3.1.2 60-nm particles In order to evaluate the limits of our far-field tweezers approach we are trapping 60-nm particles. Stable trapping is observed for tip-to-tip distances between 2 and 6 μm. In the case of these very small particles, trapping is, however, only possible for high light power of 46 mW. This remains, however, a remarkable result as stable and reproducible nanoparticle trapping using a far-field approach with micrometer-size beams is not straightforward. For the small particles the possibility to calculate the trap stiffness by the power spectra analysis of the back-reflection signals is of paramount interest. In fact, the low luminescence level of the 60-nm YAG:Ce3+ requires to increase the camera integration time, thus limiting its frequency to 20 fps. The estimated corner frequencies are in the 10 to 30 Hz range. Thus, the actual video frequency is too low for precise particle position tracking. Consequently, Boltzmann statistics and power spectra analysis of the recorded videos are not feasible anymore. The power spectra of the back signal (recorded at 5 kHz) show clearly the expected Lorentzian shape (Fig. 6.a, log-log scale). Such as in the case of the 300-nm particles, the power spectra are, however, dominated by the transverse trapping properties. Thus only the transverse stiffness constant can be measured. A value of κ˜ tr. = 2 pN·μm−1 ·W−1 is calculated for a tip-to-tip distance of 3 μm. This value is about 20 times smaller compared to the 300-nm particles. Trapping stiffness comparison with different tweezers approaches is not straightforward. Only few work is reported for the intermediate particle size of 60 to 300 nm. Beam-focusing and plasmonic tweezers are mainly dealing with micrometer or small nanometer particles, respectively. Moreover the comparison is complicated as some approaches does not allow straightforward trap stiffness intensity normalization or are measuring directly the optical forces. In this context the trap stiffness of 2.3 and 0.1 pN/μm (transverse / axial directions) measured with 300 nm particles are comparable with 2.5 and 8.3 pN/μm measured for 500 nm polystyrene particles trapped by a silicon nanocavity 24 . Considering a recently published comparison of plasmonic
Fig. 6 Power spectra from the back-reflection (a) and deduced normalized trap stiffness (b) of a 60-nm YAG particle as a function of fiber tip-to-tip distances. Inset : Fluorescence microscopy image of a trapped 60-nm YAG particle.
tweezers 25 , comparable values of 13 pN·μm−1 ·W−1 were measured for trapping 200 nm particles with a nano pillar approach 26 . Higher values have, however, been measured plasmonic nano block pairs (4000 pN·μm−1 ·W−1 ; 100 nm particles 27 ) or double nano-holes (100 pN·μm−1 ·W−1 ; 10 nm particles 28 ). However, compared to plasmonic tweezers, our approach does not require any clean-room elaboration techniques and one has also to take into account that our tweezers approach is contactless. 3.2 Theoretical discussion In order to understand the physical origin of the optical trap, we first discuss the case of a fiber tip-to-tip distance of 0.5 μm in the framework of the dipolar approximation. This configuration leads to one spot between the two tips which is associated to a single stable trapping position. The dipolar response of the dielectric nanoparticle (radius a, dielectric constant ε p ) is described by the effective polarisability: αe f f =
α0
n k3
bg 0 1 − i 6πε α0 0
(2)
1–9 | 5
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Nanoscale
Page 6 of 9 View Article Online
DOI: 10.1039/C5NR07727C ε −ε
where α0 = 4πε0 ε p ε pp+2εbgbg a3 is the quasi-static polarisability of n k3
In the dipolar approximation, the optical force can be separated in two contributions 29 : a conservative gradient force Fgrad that derives from a potential energy U pot and a scattering optical force Fscat along the beam propagation direction. These two (time-averaged) forces express: < Fgrad >
=
−∇U pot
(3)
< Fscat >
=
σnbg < S > cnbg
(4)
where U pot = −(1/4)ℜ{αrad }|E|2 is the potential energy of the dipolar particle in the presence of the electric field scattered at the tip end, σnbg = (nbg k0 /εbg ε0 )ℑ{αrad } the particle scattering cross } the time-averaged Poyntsection, and < S >= (1/2)ℜ{E ∧ H c ing vector. cnbg = nbg is the speed of light in the background medium. Finally, the resulting optical force acting on the particle < Ftotal >=< Fgrad > + < Fscat > can be attractive or repulsive depending on the ratio between the (attractive) gradient force and the (repulsive) scattering force associated to the EM field near the fiber extremity. Due to the symmetry of the configuration, the scattering force pushes the particle towards the center between the two tips and cancels at the center. The gradient force, estimated to about 22 fold higher than the scattering force, also traps the particle in the middle between the two tips. The potential energy and optical forces acting on a 300 nm YAG:Ce3+ (n = 1.82) are represented on Figs.7.a-b in the transversal plane equidistant from both tips. The gradient force also traps the particle in the center of the transverse plane whereas the scattering force is zero at the center and along the electric field polarization but is repulsive moving away from the trap center perpendicularly to the field polarization (Fig.7.b). We estimate the transverse stiffness constant associated to the gradient force. A harmonic fit to the potential energy leads to stiffness constants of 317 and 281 pN·μm−1 ·W−1 in the direction along and perpendicular to the electric field polarization, respectively (Fig.8.a). We also observe a harmonic behavior in the axial direction (stiffness ≈ 104 pN·μm−1 ·W−1 ) (Fig.8.b). Overall, the maximum magnitude of the total force in the axial direction is reached near each tip apex F 496 pN. In the transverse plane, the total force is F 25 pN (attractive) and 8 pN (repulsive) at 80 nm away from the center in direction parallel and perpendicular to the electric field polarization, respectively. As a consequence, the centered position is a stable equilibrium except for displacements perpendicular to the field polarization due to the scattering force. The particle size (300 nm) overcomes, however, the dipolar approximation so that exact calculation of the optical forces necessitates to use the Maxwell Stress Tensor (MST) formalism 30 . Practically, the optical force cannot be separated in a gradient and scattering contributions as in the dipolar approximation but 6|
1–9
Fig. 7 (a) Potential energy U pot /kB T (T = 25◦C) and gradient force (black arrows) for a 300-nm YAG:Ce3+ particle. (b) Intensity (colormap in W/m2 ) and scattering force (arrows). The particle is equidistant from both fiber extremities, which are separated each other by a distance of 0.5μm. c). Plots are given in the transverse plane (xy) centered between the two fibers. The white arrow indicates the polarization of the guided mode.
writes < Ftotal >=
V
d 3 r(∇i · < Ti j (r) >) =
S
(< Ti j (r) > ·n)dA
(5)
with the (ij) element of the Maxwell tensor Ti j = Di E j + Bi H j − are the electric displaceδi j (1/2)(Di Ei + Bi Hi ) (D, E, B, and H ment, electric field, magnetic density flux, and magnetic field, respectively). This force is calculated as the time-averaged flux of MST through a closed surface surrounding the finite particle 31–33 . Here S is a sphere 10 nm away from the particle surface. The electric field intensity is represented in Fig.9. It is strongly perturbed by the 300-nm particle so that the dipolar approximation does not hold. As shown in Fig.10.a and Fig.10.b, the total force follows a restoring force behavior < Ftotal >= −κr. Therefore, we again define a trap stiffness constant according to a linear fit on the total force. We achieve an axial stiffness constant of 4019 pN·μm−1 ·W−1 and transverse stiffness constants of 274 / 321 pN·μm−1 ·W−1 , along and perpendicular to the field polarization, respectively. The transverse stiffness constant are similar to those determined from the dipolar approximation. The axial stiffness constant obtained within the dipolar approximation is strongly overestimated by a factor of 2.6. However, the dipolar approximation qualitatively explains the restoring force as an addition of the harmonic gradient force and the scattering force that also pushes the particle towards the trap center thanks to the symmetric configuration. These results are summarized in table 1 as well as for a 60-nm particle. Numerical simulations show that
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
bg 0 the particle and the term i 6πε α0 is the radiative reaction correc0 tion that describes finite size effects.
Page 7 of 9
Nanoscale View Article Online
Fig. 8 Potential energy U pot /kB T (T = 25◦C) as a function of the particle position. (a) Transverse cross-section along (blue dots) and perpendicular to (green dots) the electric field polarization direction. (b) Axial cross-section. Dots and solid lines correspond to the calculated potential energy and harmonic fit, respectively.
the dipolar approximation is reasonable for particle sizes below 200 nm.
Fig. 10 (a) Total EM force obtained by MST as a function of the particle position. (a) Transverse cross-section along (blue dots) and perpendicular to (green dots) the electric field polarization direction. (b) axial cross-section. Dots and solid lines correspond to the calculated total force and its linear fit, respectively.
d part [nm]
orientation
300
trans. / ⊥ axial trans. / ⊥ axial
60
κ [pN·μm−1 ·W−1 ] Dipolar MST 317 / 281 274 / 321 10336 4019 3.5 / 3.2 4.5 / 3.4 110 120
Table 1 Comparison between both transverse and axial stiffness constants obtained by the dipolar approximation and the MST calculation for d = 500 nm. and ⊥ stand for the transverse direction parallel and perpendicular to the electric field, respectively.
Fig. 9 Electric field norm (colormap in V/m) for a 300-nm YAG:Ce3+ particle.
We also compare the optical force calculated using the exact MST formalism to the above dipolar approximation. Along the axial direction, the total force is F 145 pN near each tip apex that is about three times below the dipolar estimation. In the transverse plane, F 21 pN and F 24 pN at 80 nm from the center, in direction parallel and perpendicular to the electric field polarization and is always attractive. Therefore, the MST is needed to explain the stable optical trapping of 300-nm particles. Finally, as the tips separate each other, several lobes of field interference appear between them (see Fig.3.b), each of them rendering a potential energy well. From our discussion about the dipolar approximation and MST formalism, we expect theoretically multiple stable trapping positions in the axial direction. The
distance between two wells is λ /2nw ≈ 300 nm, that is below the stable positions measured experimentally (Fig. 4.b). The discrepancy is probably due to the convolution with the particle size in the experiment. The 300-nm YAG:Ce3+ particles therefore feel several potential wells so that, even though it is difficult to estimate an axial stiffness constant in this case, the potential energy still present an harmonic-like behavior in the transverse plane located in the center between the two tips 34 . Due to numerical difficulties, we were not able to determine the optical force from exact MST calculations for dsep = 2.5 μm. However, since we have shown that the dipolar approximation leads to quantitative values for the stiffness constant in the transverse plane, we compare in table 2 the calculated (within the dipolar approximation) and measured stiffness constant and achieve a good agreement for the separation distance of about 3μm. Last, by taking into account the Brownian motion we estimate 1–9 | 7
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Nanoscale
Page 8 of 9 View Article Online
d part [nm]
Orientation
300 60
trans / ⊥ trans / ⊥
κ [pN·μm−1 ·W−1 ] Dipolar Exp. (d = 2.5 μm) (d = 3 μm) 74 / 64 35 1.6 / 1.5 2
Table 2 Comparison between calculated (within dipolar approximation) and measured transverse stiffness constants. and ⊥ stand for the transverse direction parallel and perpendicular to the electric field, respectively.
a lower particle size limit for efficient trapping. Assuming a minimal depth of potential energy of about 10 kB T (T = 298 K) 35 , the minimum particle size for this trap is about 25 nm.
4
Conclusions
In conclusion, 300-nm and 60-nm luminescent cerium-doped YAG particles are stably optically trapped in the far field. Their residual Brownian motion is used to study the optical tweezers properties. The trapping potential is harmonic in the transverse direction. In the axial direction, the interference pattern of the counter-propagative waves is revealed by the observation of several metastable traps. Normalized transverse stiffness values of 35 and 2 pN·μm−1 ·W−1 for 300-nm and 60-nm YAG:Ce3+ particles are measured, respectively with 3 μm tip-to-tip distance, in qualitative agreement with numerical simulations. Finally, we estimate that this optical tweezer should efficiently traps particles down to 25 nm size. This point will be of great interest in various applications, e.g. tag tracking within biological cells. In the near future, we will combine the long time photostability of the luminescent nanoparticles and the far-field unperturbed trapping to investigate the optical properties of isolated luminescent nanoparticles at the single particle level. Moreover, we have shown that several stable positions exist between the two tips, with a separation distance that can be controlled by the wavelength of the optical trap. This can be used to control the distance between two or more nanoparticles and investigate e.g. the energy transfer in between.
Acknowledgements Funding for this project was provided by the French National Research Agency in the framework of the FiPlaNT project (ANR-12BS10-002).
References 1 A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm and S. Chu, Opt. Lett., 1986, 11, 288–290. 2 S. Lee, B. Joo, P. J. Jeon, S. Im and K. Oh, Biomed. Opt. Express, 2015, 6, 4417–4432. 3 S. K. Mondal, S. S. Pal and P. Kapur, Opt. Express, 2012, 20, 16180–16185. 4 S. Sarkar Pal, S. K. Mondal, D. Kumbhakar, R. Kumar, A. Akula, R. Ghosh and R. Bhatnagar, Appl. Phys. Lett., 2014, 104, 031105. 5 S. K. Mohanty, K. S. Mohanty and M. W. Berns, J. Biomed. Opt., 2008, 13, 054049. 8|
1–9
6 Z. Liu, C. Guo, J. Yang and L. Yuan, Opt. Express, 2006, 14, 12510–12516. 7 W. Zhu, T. Shi, Z. Tang, B. Gong, G. Liao and J. Tully, Opt. Express, 2013, 21, 6919–6927. 8 X. Xu, C. Cheng, H. Xin, H. Lei and B. Li, Sci. Rep., 2014, 4, 3989. 9 S. Valkai, L. Oroszi and P. Ormos, Appl. Opt., 2009, 48, 2880– 2883. 10 R. S. R. Ribero, O. Soppera, J. Viegas, A. Guerreiro and P. A. S. Jorge, Proc. of SPIE, 2015, 9379, 93790N. 11 Z. Liu, L. Wang, P. Liang, Y. Zhang, J. Yang and L. Yuan, Opt. Lett., 2013, 38, 2617–2620. 12 E. R. Lyons and G. J. Sonek, Appl. Phys. Lett., 1995, 66, 1584– 1586. 13 J. Huang, X. Liu, Y. Zhang and B. Li, Photon. Res., 2015, 3, 308–312. 14 R. M. Gelfand, S. Wheaton and R. Gordon, Opt. Lett., 2014, 39, 6415–6417. 15 A. El Eter, N. M. Hameed, F. I. Baida, R. Salut, C. Filiatre, D. Nedeljkovic, E. Atie, S. Bole and T. Grosjean, Opt. Express, 2014, 22, 10072–10080. 16 J. Berthelot, S. S. Acimovic, M. L. Juan, M. P. Kreuzer, J. Renger and R. Quidant, Nat. Nanotechnol., 2014, 9, 295– 299. 17 J.-B. Decombe, S. Huant and J. Fick, Opt. Express, 2013, 21, 30521–30531. 18 J. B. Decombe, S. K. Mondal, D. Kumbhakar, S. S. Pal and J. Fick, IEEE J. Sel. Top. Quant. Elec., 2015, 21, 4500106. 19 R. Kasuya, T. Isobe and H. Kuma, J. Alloys Compd., 2006, 408-12, 820–823. 20 A. Revaux, G. Dantelle, N. George, R. Seshadri, T. Gacoin and J.-P. Boilot, Nanoscale, 2011, 3, 2015–2022. 21 Y. Tanaka, A. Sanada and K. Sasaki, Sci. Rep., 2012, 2, 764. 22 K. Berg-Sørensen and H. Flyvberg, Rev. Sci. Instrum., 2004, 75, 594–612. 23 www.comsol.com. 24 C. Pin, B. Cluzel, C. Renaut, E. Picard, D. Peyrade, E. Hadji and F. de Fornel, ACS Phot., 2015, 2, 1410–1415. 25 A. A. Al Balushi, A. Kotnala, S. Wheaton, R. M. Gelfand, Y. Rajashekara and R. Gordon, Analyst, 2015, 140, 4760–4778. 26 A. Grigorenko, N. Roberts, M. Dickinson and Y. Zhang, Nat. Photon., 2008, 2, 365. 27 Y. Tanaka, S. Kaneda and K. Sasaki, Nano Letters, 2013, 13, 2146–2150. 28 A. Kontnala and R. Gordon, Nano Lett., 2014, 14, 853–586. 29 S. Albaladejo, M. I. Marqués, M. Laroche and J. J. Sáenz, Phys. Rev. Lett., 2009, 102, 113602. 30 M. Nieto-Vesperinas, P. C. Chaumet and A. Rahmani, Phil. Trans. R. Soc. A, 2004, 362, 719–737. 31 F. J. Valdivia-Valero and M. Nieto-Vesperinas, Opt. Express, 2012, 20, 13368–13389. 32 F. Valdivia-Valero and M. Nieto-Vesperinas, Opt. Commun., 2013, 294, 351 – 360.
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Page 9 of 9
Nanoscale View Article Online
DOI: 10.1039/C5NR07727C
9164, 916430. 35 L. Novotny and B. Hecht, Principles of nano-optics, Cambridge University Press, New York, 1st edn, 2006.
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
33 J. M. Auñón, F. J. Valdivia-Valero and M. Nieto-Vesperinas, J. Opt. Soc. Am. A, 2014, 31, 206–216. 34 J.-B. Decombe, G. Dantelle, T. Gacoin, F. J. Valdivia-Valero, G. Colas des Francs, S. Huant and J. Fick, Proc. of SPIE, 2014,
1–9 | 9
Nanoscale Accepted Manuscript
This article can be cited before page numbers have been issued, to do this please use: J. Decombe, F. Valdivia-Valero, G. Dantelle, G. Leménager, T. Gacoin, G. Colas des Francs, S. Huant and J. Fick, Nanoscale, 2016, DOI: 10.1039/C5NR07727C.
This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains.
www.rsc.org/nanoscale
Page 1 of 9
Nanoscale View Article Online
Luminescent nanoparticle trapping with far-field optical fiber-tip tweezers Jean-Baptiste Decombe,a† Francisco J. Valdivia-Valero,b Géraldine Dantelle,a Godefroy Leménager,c Thierry Gacoin,c Gérard Colas des Francs,b Serge Huant,a and a Jochen Fick ∗
We report stable and reproducible trapping of luminescent dielectric YAG:Ce3+ nanoparticles with sizes down to 60 nm using far-field dual fiber tip optical tweezers. The particles are synthesized by a specific glycothermal route followed by an original protected annealing step, resulting in significantly enhanced photostability. The tweezers properties are analyzed by studying the trapped particles residual Brownian motion using video or reflected signal records. The trapping potential is harmonic in the transverse direction to the fiber axis, but reveals interference fringes in the axial direction. Large trapping stiffnesses of 35 and 2 pN·μm−1 ·W−1 are measured for a fiber tip-to-tip distance of 3 μm and 300-nm and 60-nm particles, respectively. The forces acting on nanoparticles are discussed within the dipolar approximation (gradient and scattering force contributions) or exact calculations using the Maxwell Stress Tensor formalism. Prospects for trapping even smaller particles are discussed.
1
Introduction
Trapping and manipulation of micro- and nanoparticles were introduced in 1986 by A. Ashkin 1 . This noninvasive instrument has developed many interesting applications, e.g. in biology where it is used for cell manipulation with high precision and free of any mechanical contact. Besides the historical approach of strong focused laser beam tweezers, a great variety of optical fiber-based tweezers was developed. Optical fiber tweezers are very flexible and easy to use as they do not use bulky high N.A. microscope objectives and require little alignment. Moreover, controlled nano-structuring of the optical fiber allows to transform the fiber guided modes into advanced beam types such as non-diffracting and self-healing quasi-Bessel beams 2 , 3D bottle beams 3 or optical vortices 4 . In most cases the nano-structuring relies on relatively fast and competitive techniques such as wet chemical etching 3–8 or photopolymerization 9,10 . Optical tweezing with single fiber and dual fiber geometries
a
Univ. Grenoble Alpes, Inst NEEL, 38000 Grenoble, France CNRS, Inst NEEL, 38000 Grenoble, France. b Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRSUniversité Bourgogne Franche-Comté, 21078 Dijon, France. c Physique de la Matière Condensée, CNRS UMR 7643, Ecole Polytechnique, 91128 Palaiseau, France. † Present address: Louisiana State University, Baton Rouge, USA. ∗ Fax: +33 476 887988; Tel: +33 456 387148; E-mail: jochen.fi[email protected]
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 focus point at a certain distance to the tip end 5,11 . In the dual fiber approach, with two equally illuminated fiber tips facing each other, the radiation pressure vanishes at equilibrium 12 . Efficient trapping can thus be obtained at relatively low light intensities. Moreover, asymmetric radiation pressure distributions can be engineered to control the particle position or the orientation of non spherical particles such as nano-wires 8 or biological cells 13 . In addition, trapping one nanoparticle far from the probe opens the door to the investigation of its optical properties at the single particle level in absence of perturbation by the surroundings. In a different approach, cleaved optical fibers or fiber tips can be used as a support to metallic nano-structures for plasmonic trapping 14–16 . These sorts of optical near-field tweezers are well adapted for dielectric nanoparticle or single molecule trapping. Their excitation efficiency and flexibility were significantly enhanced by using a fibered approach. Their main drawback, however, is in the need for cost and time intensive clean room nanostructuring technology. A further problem is that the trapped particle is most likely in contact with the metallic structure, what can strongly modify its optical properties. In this context, we have demonstrated stable and reproducible trapping of 1 μm dielectric particles using dual fiber tip tweezers with Gaussian 17 and quasi-Bessel beams 18 . In the present pa1–9 | 1
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Nanoscale
Page 2 of 9 View Article Online
DOI: 10.1039/C5NR07727C
2 2.1
ally detectable during hours whereas single raw particles become undetectable after few minutes due to photobleaching, in agreement with previous observations of nanoparticle powder 20 .
Methods Nanoparticle elaboration
YAG:Ce3+ particles with high luminescence quantum yield, excellent photostability and well-defined size distribution are elaborated using a glycothermal synthesis in combination with an original protected annealing procedure 19,20 . Yttrium acetate hydrate (7.425 mmol, 1.976 g), cerium acetate hydrate (0.15 mmol, 47.6 mg for a 2 at.% doping) and aluminium isopropoxide (12.5 mmol, 2.55 g) are mixed together with 53 mL of butanediol and poured into a 75-mL autoclave (Parr, Series 4740 High Pressure Vessel). The autoclave is heated at 300◦ C for 3 hours and then cooled down to room temperature. The obtained mixture is washed three times in ethanol by successive centrifugations (11000 rpm for 10 minutes). The resulting yellowish solution is a suspension of YAG:Ce nanoparticles in ethanol. Size selection is performed using short and fast centrifugation steps. A short centrifugation (1 min at 11 000 rpm) allows retrieving the smallest particles. A Dynamic Light Scattering (DLS) measurement gives an average size for the particles in suspension of 60 ± 40 nm (Fig.1.a.) The biggest particles can be retrieved by performing several centrifugations (11000 rpm, 1 min) and considering only the particles at the bottom. After 3 centrifugations, the particles at the bottom are redispersed into ethanol. Their averaged size is 300 ± 100 nm, determined by DLS and confirmed by SEM observations. In order to improve the optical properties of the as-made YAG:Ce nanoparticles, the obtained colloidal solutions (containing either the 60-nm or 300-nm nanoparticles) are mixed with a silica sol according to the procedure reported in 20 . After drying, the composite is grounded and then heated at 1000◦ C for 12 hours. A second annealing is performed (600◦ C for 12 hours under a Ar/H2 reductive atmosphere) to maintain the cerium ions into a +III oxidation degree. The last step of this process is to remove the silica matrix by a HF dissolution, consisting in adding a 2.5 vol.% HF solution to the composite and stirring the mixture for 3 hours. The obtained annealed nanoparticles are redispersed in water. Their size (60 nm or 300 nm) is preserved thanks to this protected annealing process. Particle absorption and emission spectra before and after the protected annealing are presented in Fig.1.b. Two excitation peaks are observed at 340 and 450 nm, associated with the Ce3+ 4f ⇒ 5d(2 B1g ) and 4f ⇒ 5d(2 A1g ) transitions, respectively. An intense and wide emission peak is obtained in the visible range due to 5d ⇒ 4f transitions. The main absorption peak is narrower for annealed particles because of the enhanced uniformity of the Ce3+ environment. The most important point is, however, their exceptional photostability. Annealed particles are individu2|
1–9
Fig. 1 (a) Statistical size distribution of the synthesized 60-nm YAG:Ce3+ particles. Inset : TEM image of the corresponding particles. (b) Absorption and emission spectra of the YAG colloidal solution before and after the protected annealing. Inset : Ce3+ energy diagram.
2.2
Optical tweezers set-up and characterization methods
The core of the used optical tweezers is made of two optical fiber tips facing each other (Fig. 2). Each tip is mounted on a set of x − y − z piezoelectric translation stages, allowing for easy fiber alignment with sub-micrometer precision 17 . The fiber tips are elaborated by chemical wet etching from standard single mode optical fibers. Their full tip angle is about 15◦ with apex sizes in the order of 60 nm. The emitted beam is of Gaussian shape with an 8◦ emission angle in water and a minimal beam waist of 900 nm. The trapping laser intensity is directly measured at each fiber tip in air and corrected for emission in water. The relative light intensities of the 808 nm trapping laser in the two fiber tips is controlled by an half-have plate and a polarized beam splitter. In each arm, a 90/10 beam splitter allows to record the light intensity which is back-reflected from the fiber tip. This back-reflection consists of the sum of the reflections from the fiber tip and the trapped particle together with the transmitted light
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
per we show that our far-field approach allows to trap dielectric nanoparticles as small as 60 nm without any need for metallic plasmonic structures. This is a large step forward compared to previous works which mainly deal with trapping of micrometersize objects. Furthermore, our approach offers the prospect for trapping even smaller particles, which is of interest for cell biology or sensor applications.
Page 3 of 9
Nanoscale View Article Online
DOI: 10.1039/C5NR07727C
2.3 Modelisation of the fibered optical tweezer We have performed 3D numerical simulations using a finite element method (FEM) 23 . The model is described in Fig. 3.a. It consists of two tapered silica fibers (optical index 1.45) with an input diameter Din = 1 μm, and a tapered full angle 2α = 15◦ . The radius of curvature of the output is fixed to 50 nm. The whole system is immersed in water and the input port of the fiber is excited with the linearly polarized fiber mode HE11 (effective index Ne f f = 1.3888 at λ = 808 nm). The input power is fixed to Pin = 1 W. In order to avoid parasitic reflexions at the borders of the window, we are using perfectly matched layers (PML). The mode propagation within the fibers is clearly visible in Fig.3.b. The interference pattern (interfringe of λ /2nw = 304 nm) originates from the two counter-propagating waves exiting from the elongated fibers. Fig. 2 Scheme of the optical nano-tweezers set-up.
from the second opposite fiber tip. Particle trapping is visualized by a homemade microscope using an x50 large working distance objective. A CMOS camera allows video recording at rates of up to 300 fps. The Ceriumdoped nanoparticles are excited through the microscope using a second laser emitting at 457 nm and a dichroic mirror. Different particle tracking algorithms were developed to obtain particle position records from the trapping videos. The particle positions in axial and transverse directions with respect to the fiber axis are distinguished. Two complementary methods are used to study the trapping properties: Boltzmann statistics 21 and power spectrum analysis 22 . The first method is based on the fact that the probability density P(x) of finding the particle in the potential well U(x) at a certain position x can be described using Boltzmann statistics. In the case of an harmonic trapping potential U(x) = κ/2 · x2 , the stiffness can be directly obtained by fitting P to the Gaussian function P(x) = exp(−κx2 /2kB T ), with κ the trap stiffness, kB the Boltzmann constant, and T the temperature. Generally, Boltzmann statistics works for any type of trapping potential. The definition of the trap stiffness κ becomes, however, irrelevant for a non-harmonic potential. In the second method, the oscillation power spectrum of the residual Brownian motion of the trapped particle is approximated by the Lorentzian function : P( fk ) =
kB T 2π 2 γ0 ( fc2 + fk2 )
(1)
with fc = κ/2πγ0 the corner frequency, γ0 = 6πηa the Stokes friction coefficient, η the dynamic viscosity of the host media, and a the particle radius. In practice, the trap stiffness is obtained by numerical fitting (in the log/log space) of the entire experimental spectra to Eq. 1. This method only works for harmonic potentials.
Fig. 3 (a) Calculation scheme for the silica nano-tips facing each other, immersed in water (dielectric constant εbg = n2bg = 1.77), and separated by dsep . The geometrical parameters are indicated on the figure. (b) Map of the electric field norm (in V/m) in the axial direction for a 300-nm particle between the tips separated by dsep = 2.5 μm. Each fiber is excited with Pin = 1 W HE11 fiber mode.
3
Results and discussion
3.1 Nanoparticle trapping 3.1.1 300-nm particles Stable and reproducible trapping of 300-nm YAG:Ce3+ is realized for light intensities (at the end of the fiber tips) down to 4 mW and for tip-to-tip distances up to 8 μm. The trapping properties are systematically studied by varying the injected light intensities 1–9 | 3
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
Moreover, the Stokes coefficient has to be known. The main advantage consists of its applicability to the video position records and to the back-reflected signal.
Nanoscale
Page 4 of 9 View Article Online
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
and the fiber tip-to-tip distances for trapping of one single particle. The shape and strength of the trapping potential is different in the axial and transverse directions. In the transverse direction, the position distribution statistics clearly indicates a harmonic potential (Fig. 4.a). The trap stiffness linearly increases with light intensities for all fiber tip-to-tip distances. This feature confirms the fact that particle trapping is only due to optical forces. Any influence from the fiber tips can be neglected. Furthermore, one can define a normalized trapping constant. For example a high value of κ˜ tr. = 35 pN·μm−1 ·W−1 was measured for a tip-to-tip distance of 3 μm. The reference power is taken at the end of a single fiber 17 .
Fig. 4 (a) Transverse position distribution of a 300 nm YAG:Ce3+ trapped particle for several fiber tip-to-tip distances. Inset: Fluorescence microscopy image of a trapped 300-nm particle (b) Axial position distribution for orthogonal (blue) and parallel (red) polarizations. Bold line are best Gaussian fits; In b), the thin red line is a guide to the eye for peak position visualization.
For the axial direction, the position distribution statistic is more complex (Fig. 4.b). Depending on the relative polarization of the two counter-propagating light beams, we observe some substructures. The distribution is fitted to series of equidistant Gaussian peaks with 350 nm spacing. This distance is of the order of half the trapping laser wavelength in water (304 nm). The subpeaks progressively disappear when annihilating the interference fringes by turning the relative polarization of one of the input beams. Additionally, this modification has no influence on the 4|
1–9
transverse trapping properties. This feature can only be observed for the 300-nm particles, i.e. particles of similar size than the interference fringe spacing. Larger micro-particles "feel" more than one (typically two or three) fringe at a time, resulting in averaging of the effect. As will be shown below, the Brownian motion of smaller (60 nm) particles is too large to resolve this substructure. The fiber tip-to-tip distance dependency of the trapping properties are studied in the 2 to 6 μm range and for a light intensity of 47 mW. The relative polarization is chosen to cancel the interference fringes. The trap stiffness is calculated applying Boltzmann statistics (Fig. 4) and power spectra method. In the later case video observation records and back-reflection signals (Fig 5.a) are used.
Fig. 5 Power spectra from the back-reflection (a) and normalized trapping stiffness along transverse direction (b) of a 300 nm YAG:Ce3+ as a function of fiber tip-to-tip distances. Inset : Stiffness along axial direction.
As expected, the trap stiffness deduced from all three methods is increasing with decreasing distance (Fig. 5.b). The experimental error was estimated to 15% from different sets of identical measurements (not shown here.) The values from Boltzmann statistics and back-reflection signals are in very good agreement. Values from the power spectra analysis of the video records are, however, diverging at short tip-to-tip distances. This difference can be explained by the camera readout frequency limitation. In
Nanoscale Accepted Manuscript
DOI: 10.1039/C5NR07727C
Page 5 of 9
Nanoscale View Article Online
order to clearly observe the weak photoluminescence of 300-nm particles, the camera integration time was fixed at 10 ms, thus limiting the resulting power spectra cutoff frequency to 50 Hz. On the other hand, the corner frequency of the trapped particle ( fc = κ/2πγ0 ) is about 90 (20) Hz for 2 (6) μm tip-to-tip distances. Consequently, the numerical fitting to Eq. 1 becomes inaccurate for small tip-to-tip distances. The higher readout frequency (≈ 5 kHz) of the back-reflection makes this method a better choice. Its main drawback consists, however, in the difficulty to distinguish the contributions from the particle position oscillations in transverse and axial directions (Fig. 5.a). In the case of 1 μm particles, we observe two distinct corner frequencies (not shown here) corresponding to the transverse and axial cases, respectively. For the present 300-nm particles, the power spectra are dominated by the contribution of the transverse oscillation. The inflection of the axial trapping contribution at low frequencies cannot be resolved. 3.1.2 60-nm particles In order to evaluate the limits of our far-field tweezers approach we are trapping 60-nm particles. Stable trapping is observed for tip-to-tip distances between 2 and 6 μm. In the case of these very small particles, trapping is, however, only possible for high light power of 46 mW. This remains, however, a remarkable result as stable and reproducible nanoparticle trapping using a far-field approach with micrometer-size beams is not straightforward. For the small particles the possibility to calculate the trap stiffness by the power spectra analysis of the back-reflection signals is of paramount interest. In fact, the low luminescence level of the 60-nm YAG:Ce3+ requires to increase the camera integration time, thus limiting its frequency to 20 fps. The estimated corner frequencies are in the 10 to 30 Hz range. Thus, the actual video frequency is too low for precise particle position tracking. Consequently, Boltzmann statistics and power spectra analysis of the recorded videos are not feasible anymore. The power spectra of the back signal (recorded at 5 kHz) show clearly the expected Lorentzian shape (Fig. 6.a, log-log scale). Such as in the case of the 300-nm particles, the power spectra are, however, dominated by the transverse trapping properties. Thus only the transverse stiffness constant can be measured. A value of κ˜ tr. = 2 pN·μm−1 ·W−1 is calculated for a tip-to-tip distance of 3 μm. This value is about 20 times smaller compared to the 300-nm particles. Trapping stiffness comparison with different tweezers approaches is not straightforward. Only few work is reported for the intermediate particle size of 60 to 300 nm. Beam-focusing and plasmonic tweezers are mainly dealing with micrometer or small nanometer particles, respectively. Moreover the comparison is complicated as some approaches does not allow straightforward trap stiffness intensity normalization or are measuring directly the optical forces. In this context the trap stiffness of 2.3 and 0.1 pN/μm (transverse / axial directions) measured with 300 nm particles are comparable with 2.5 and 8.3 pN/μm measured for 500 nm polystyrene particles trapped by a silicon nanocavity 24 . Considering a recently published comparison of plasmonic
Fig. 6 Power spectra from the back-reflection (a) and deduced normalized trap stiffness (b) of a 60-nm YAG particle as a function of fiber tip-to-tip distances. Inset : Fluorescence microscopy image of a trapped 60-nm YAG particle.
tweezers 25 , comparable values of 13 pN·μm−1 ·W−1 were measured for trapping 200 nm particles with a nano pillar approach 26 . Higher values have, however, been measured plasmonic nano block pairs (4000 pN·μm−1 ·W−1 ; 100 nm particles 27 ) or double nano-holes (100 pN·μm−1 ·W−1 ; 10 nm particles 28 ). However, compared to plasmonic tweezers, our approach does not require any clean-room elaboration techniques and one has also to take into account that our tweezers approach is contactless. 3.2 Theoretical discussion In order to understand the physical origin of the optical trap, we first discuss the case of a fiber tip-to-tip distance of 0.5 μm in the framework of the dipolar approximation. This configuration leads to one spot between the two tips which is associated to a single stable trapping position. The dipolar response of the dielectric nanoparticle (radius a, dielectric constant ε p ) is described by the effective polarisability: αe f f =
α0
n k3
bg 0 1 − i 6πε α0 0
(2)
1–9 | 5
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Nanoscale
Page 6 of 9 View Article Online
DOI: 10.1039/C5NR07727C ε −ε
where α0 = 4πε0 ε p ε pp+2εbgbg a3 is the quasi-static polarisability of n k3
In the dipolar approximation, the optical force can be separated in two contributions 29 : a conservative gradient force Fgrad that derives from a potential energy U pot and a scattering optical force Fscat along the beam propagation direction. These two (time-averaged) forces express: < Fgrad >
=
−∇U pot
(3)
< Fscat >
=
σnbg < S > cnbg
(4)
where U pot = −(1/4)ℜ{αrad }|E|2 is the potential energy of the dipolar particle in the presence of the electric field scattered at the tip end, σnbg = (nbg k0 /εbg ε0 )ℑ{αrad } the particle scattering cross } the time-averaged Poyntsection, and < S >= (1/2)ℜ{E ∧ H c ing vector. cnbg = nbg is the speed of light in the background medium. Finally, the resulting optical force acting on the particle < Ftotal >=< Fgrad > + < Fscat > can be attractive or repulsive depending on the ratio between the (attractive) gradient force and the (repulsive) scattering force associated to the EM field near the fiber extremity. Due to the symmetry of the configuration, the scattering force pushes the particle towards the center between the two tips and cancels at the center. The gradient force, estimated to about 22 fold higher than the scattering force, also traps the particle in the middle between the two tips. The potential energy and optical forces acting on a 300 nm YAG:Ce3+ (n = 1.82) are represented on Figs.7.a-b in the transversal plane equidistant from both tips. The gradient force also traps the particle in the center of the transverse plane whereas the scattering force is zero at the center and along the electric field polarization but is repulsive moving away from the trap center perpendicularly to the field polarization (Fig.7.b). We estimate the transverse stiffness constant associated to the gradient force. A harmonic fit to the potential energy leads to stiffness constants of 317 and 281 pN·μm−1 ·W−1 in the direction along and perpendicular to the electric field polarization, respectively (Fig.8.a). We also observe a harmonic behavior in the axial direction (stiffness ≈ 104 pN·μm−1 ·W−1 ) (Fig.8.b). Overall, the maximum magnitude of the total force in the axial direction is reached near each tip apex F 496 pN. In the transverse plane, the total force is F 25 pN (attractive) and 8 pN (repulsive) at 80 nm away from the center in direction parallel and perpendicular to the electric field polarization, respectively. As a consequence, the centered position is a stable equilibrium except for displacements perpendicular to the field polarization due to the scattering force. The particle size (300 nm) overcomes, however, the dipolar approximation so that exact calculation of the optical forces necessitates to use the Maxwell Stress Tensor (MST) formalism 30 . Practically, the optical force cannot be separated in a gradient and scattering contributions as in the dipolar approximation but 6|
1–9
Fig. 7 (a) Potential energy U pot /kB T (T = 25◦C) and gradient force (black arrows) for a 300-nm YAG:Ce3+ particle. (b) Intensity (colormap in W/m2 ) and scattering force (arrows). The particle is equidistant from both fiber extremities, which are separated each other by a distance of 0.5μm. c). Plots are given in the transverse plane (xy) centered between the two fibers. The white arrow indicates the polarization of the guided mode.
writes < Ftotal >=
V
d 3 r(∇i · < Ti j (r) >) =
S
(< Ti j (r) > ·n)dA
(5)
with the (ij) element of the Maxwell tensor Ti j = Di E j + Bi H j − are the electric displaceδi j (1/2)(Di Ei + Bi Hi ) (D, E, B, and H ment, electric field, magnetic density flux, and magnetic field, respectively). This force is calculated as the time-averaged flux of MST through a closed surface surrounding the finite particle 31–33 . Here S is a sphere 10 nm away from the particle surface. The electric field intensity is represented in Fig.9. It is strongly perturbed by the 300-nm particle so that the dipolar approximation does not hold. As shown in Fig.10.a and Fig.10.b, the total force follows a restoring force behavior < Ftotal >= −κr. Therefore, we again define a trap stiffness constant according to a linear fit on the total force. We achieve an axial stiffness constant of 4019 pN·μm−1 ·W−1 and transverse stiffness constants of 274 / 321 pN·μm−1 ·W−1 , along and perpendicular to the field polarization, respectively. The transverse stiffness constant are similar to those determined from the dipolar approximation. The axial stiffness constant obtained within the dipolar approximation is strongly overestimated by a factor of 2.6. However, the dipolar approximation qualitatively explains the restoring force as an addition of the harmonic gradient force and the scattering force that also pushes the particle towards the trap center thanks to the symmetric configuration. These results are summarized in table 1 as well as for a 60-nm particle. Numerical simulations show that
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
bg 0 the particle and the term i 6πε α0 is the radiative reaction correc0 tion that describes finite size effects.
Page 7 of 9
Nanoscale View Article Online
Fig. 8 Potential energy U pot /kB T (T = 25◦C) as a function of the particle position. (a) Transverse cross-section along (blue dots) and perpendicular to (green dots) the electric field polarization direction. (b) Axial cross-section. Dots and solid lines correspond to the calculated potential energy and harmonic fit, respectively.
the dipolar approximation is reasonable for particle sizes below 200 nm.
Fig. 10 (a) Total EM force obtained by MST as a function of the particle position. (a) Transverse cross-section along (blue dots) and perpendicular to (green dots) the electric field polarization direction. (b) axial cross-section. Dots and solid lines correspond to the calculated total force and its linear fit, respectively.
d part [nm]
orientation
300
trans. / ⊥ axial trans. / ⊥ axial
60
κ [pN·μm−1 ·W−1 ] Dipolar MST 317 / 281 274 / 321 10336 4019 3.5 / 3.2 4.5 / 3.4 110 120
Table 1 Comparison between both transverse and axial stiffness constants obtained by the dipolar approximation and the MST calculation for d = 500 nm. and ⊥ stand for the transverse direction parallel and perpendicular to the electric field, respectively.
Fig. 9 Electric field norm (colormap in V/m) for a 300-nm YAG:Ce3+ particle.
We also compare the optical force calculated using the exact MST formalism to the above dipolar approximation. Along the axial direction, the total force is F 145 pN near each tip apex that is about three times below the dipolar estimation. In the transverse plane, F 21 pN and F 24 pN at 80 nm from the center, in direction parallel and perpendicular to the electric field polarization and is always attractive. Therefore, the MST is needed to explain the stable optical trapping of 300-nm particles. Finally, as the tips separate each other, several lobes of field interference appear between them (see Fig.3.b), each of them rendering a potential energy well. From our discussion about the dipolar approximation and MST formalism, we expect theoretically multiple stable trapping positions in the axial direction. The
distance between two wells is λ /2nw ≈ 300 nm, that is below the stable positions measured experimentally (Fig. 4.b). The discrepancy is probably due to the convolution with the particle size in the experiment. The 300-nm YAG:Ce3+ particles therefore feel several potential wells so that, even though it is difficult to estimate an axial stiffness constant in this case, the potential energy still present an harmonic-like behavior in the transverse plane located in the center between the two tips 34 . Due to numerical difficulties, we were not able to determine the optical force from exact MST calculations for dsep = 2.5 μm. However, since we have shown that the dipolar approximation leads to quantitative values for the stiffness constant in the transverse plane, we compare in table 2 the calculated (within the dipolar approximation) and measured stiffness constant and achieve a good agreement for the separation distance of about 3μm. Last, by taking into account the Brownian motion we estimate 1–9 | 7
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Nanoscale
Page 8 of 9 View Article Online
d part [nm]
Orientation
300 60
trans / ⊥ trans / ⊥
κ [pN·μm−1 ·W−1 ] Dipolar Exp. (d = 2.5 μm) (d = 3 μm) 74 / 64 35 1.6 / 1.5 2
Table 2 Comparison between calculated (within dipolar approximation) and measured transverse stiffness constants. and ⊥ stand for the transverse direction parallel and perpendicular to the electric field, respectively.
a lower particle size limit for efficient trapping. Assuming a minimal depth of potential energy of about 10 kB T (T = 298 K) 35 , the minimum particle size for this trap is about 25 nm.
4
Conclusions
In conclusion, 300-nm and 60-nm luminescent cerium-doped YAG particles are stably optically trapped in the far field. Their residual Brownian motion is used to study the optical tweezers properties. The trapping potential is harmonic in the transverse direction. In the axial direction, the interference pattern of the counter-propagative waves is revealed by the observation of several metastable traps. Normalized transverse stiffness values of 35 and 2 pN·μm−1 ·W−1 for 300-nm and 60-nm YAG:Ce3+ particles are measured, respectively with 3 μm tip-to-tip distance, in qualitative agreement with numerical simulations. Finally, we estimate that this optical tweezer should efficiently traps particles down to 25 nm size. This point will be of great interest in various applications, e.g. tag tracking within biological cells. In the near future, we will combine the long time photostability of the luminescent nanoparticles and the far-field unperturbed trapping to investigate the optical properties of isolated luminescent nanoparticles at the single particle level. Moreover, we have shown that several stable positions exist between the two tips, with a separation distance that can be controlled by the wavelength of the optical trap. This can be used to control the distance between two or more nanoparticles and investigate e.g. the energy transfer in between.
Acknowledgements Funding for this project was provided by the French National Research Agency in the framework of the FiPlaNT project (ANR-12BS10-002).
References 1 A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm and S. Chu, Opt. Lett., 1986, 11, 288–290. 2 S. Lee, B. Joo, P. J. Jeon, S. Im and K. Oh, Biomed. Opt. Express, 2015, 6, 4417–4432. 3 S. K. Mondal, S. S. Pal and P. Kapur, Opt. Express, 2012, 20, 16180–16185. 4 S. Sarkar Pal, S. K. Mondal, D. Kumbhakar, R. Kumar, A. Akula, R. Ghosh and R. Bhatnagar, Appl. Phys. Lett., 2014, 104, 031105. 5 S. K. Mohanty, K. S. Mohanty and M. W. Berns, J. Biomed. Opt., 2008, 13, 054049. 8|
1–9
6 Z. Liu, C. Guo, J. Yang and L. Yuan, Opt. Express, 2006, 14, 12510–12516. 7 W. Zhu, T. Shi, Z. Tang, B. Gong, G. Liao and J. Tully, Opt. Express, 2013, 21, 6919–6927. 8 X. Xu, C. Cheng, H. Xin, H. Lei and B. Li, Sci. Rep., 2014, 4, 3989. 9 S. Valkai, L. Oroszi and P. Ormos, Appl. Opt., 2009, 48, 2880– 2883. 10 R. S. R. Ribero, O. Soppera, J. Viegas, A. Guerreiro and P. A. S. Jorge, Proc. of SPIE, 2015, 9379, 93790N. 11 Z. Liu, L. Wang, P. Liang, Y. Zhang, J. Yang and L. Yuan, Opt. Lett., 2013, 38, 2617–2620. 12 E. R. Lyons and G. J. Sonek, Appl. Phys. Lett., 1995, 66, 1584– 1586. 13 J. Huang, X. Liu, Y. Zhang and B. Li, Photon. Res., 2015, 3, 308–312. 14 R. M. Gelfand, S. Wheaton and R. Gordon, Opt. Lett., 2014, 39, 6415–6417. 15 A. El Eter, N. M. Hameed, F. I. Baida, R. Salut, C. Filiatre, D. Nedeljkovic, E. Atie, S. Bole and T. Grosjean, Opt. Express, 2014, 22, 10072–10080. 16 J. Berthelot, S. S. Acimovic, M. L. Juan, M. P. Kreuzer, J. Renger and R. Quidant, Nat. Nanotechnol., 2014, 9, 295– 299. 17 J.-B. Decombe, S. Huant and J. Fick, Opt. Express, 2013, 21, 30521–30531. 18 J. B. Decombe, S. K. Mondal, D. Kumbhakar, S. S. Pal and J. Fick, IEEE J. Sel. Top. Quant. Elec., 2015, 21, 4500106. 19 R. Kasuya, T. Isobe and H. Kuma, J. Alloys Compd., 2006, 408-12, 820–823. 20 A. Revaux, G. Dantelle, N. George, R. Seshadri, T. Gacoin and J.-P. Boilot, Nanoscale, 2011, 3, 2015–2022. 21 Y. Tanaka, A. Sanada and K. Sasaki, Sci. Rep., 2012, 2, 764. 22 K. Berg-Sørensen and H. Flyvberg, Rev. Sci. Instrum., 2004, 75, 594–612. 23 www.comsol.com. 24 C. Pin, B. Cluzel, C. Renaut, E. Picard, D. Peyrade, E. Hadji and F. de Fornel, ACS Phot., 2015, 2, 1410–1415. 25 A. A. Al Balushi, A. Kotnala, S. Wheaton, R. M. Gelfand, Y. Rajashekara and R. Gordon, Analyst, 2015, 140, 4760–4778. 26 A. Grigorenko, N. Roberts, M. Dickinson and Y. Zhang, Nat. Photon., 2008, 2, 365. 27 Y. Tanaka, S. Kaneda and K. Sasaki, Nano Letters, 2013, 13, 2146–2150. 28 A. Kontnala and R. Gordon, Nano Lett., 2014, 14, 853–586. 29 S. Albaladejo, M. I. Marqués, M. Laroche and J. J. Sáenz, Phys. Rev. Lett., 2009, 102, 113602. 30 M. Nieto-Vesperinas, P. C. Chaumet and A. Rahmani, Phil. Trans. R. Soc. A, 2004, 362, 719–737. 31 F. J. Valdivia-Valero and M. Nieto-Vesperinas, Opt. Express, 2012, 20, 13368–13389. 32 F. Valdivia-Valero and M. Nieto-Vesperinas, Opt. Commun., 2013, 294, 351 – 360.
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
DOI: 10.1039/C5NR07727C
Page 9 of 9
Nanoscale View Article Online
DOI: 10.1039/C5NR07727C
9164, 916430. 35 L. Novotny and B. Hecht, Principles of nano-optics, Cambridge University Press, New York, 1st edn, 2006.
Nanoscale Accepted Manuscript
Published on 05 February 2016. Downloaded by University of California - San Diego on 09/02/2016 06:29:06.
33 J. M. Auñón, F. J. Valdivia-Valero and M. Nieto-Vesperinas, J. Opt. Soc. Am. A, 2014, 31, 206–216. 34 J.-B. Decombe, G. Dantelle, T. Gacoin, F. J. Valdivia-Valero, G. Colas des Francs, S. Huant and J. Fick, Proc. of SPIE, 2014,
1–9 | 9
