Here we report how ultrafast pulsed illumination at low average power results in a stable three- dimensional (3D) optical trap holding latex nanoparticles which is otherwise not possible with continuous wave lasers at the same power level. The gigantic peak power of a femtosecond pulse exerts a huge instantaneous gradient force that has been predicted theoretically earlier and implemented for microsecond pulses in a different context by others. In addition, the resulting two-photon fluorescence allows direct observation of trapping events by providing intrinsic 3D resolution.
© 2009 Optical Society of America
Optical waveguides have illuminating applications in numerous experiments that spatially deliver electromagnetic waves at optical wavelengths. One such example is the optical tweezer or single beam gradient optical trap that makes use of a tightly focused laser beam having a transverse Gaussian intensity profile to trap particles of various sizes ranging from a few micrometers to a few nanometers. Over the past few decades laser tweezers have grown from a mere trapping instrument to a powerful tool to measure and control tiny forces that dictate many fundamental physical, chemical, and biological processes. Detailed discussions on various aspects of optical trapping can be found in numerous reviews [1, 2, 3] and texts [4, 5]. The major advantage of laser tweezers over mechanical transducers, e.g., scanning force microscopy (SFM), cantilevers, or microneedles, is the accessible low force range (from to ) that they offer, which renders them more suitable for biological applications .
Recently, there have been several reports to trap and manipulate individual metallic and dielectric nanoparticles by laser tweezers instead of traditional methods such as atomic force microscopy (AFM). These are of utmost importance in manipulating and patterning nanoparticles to achieve different needs, e.g., spectroscopy of trapped particles based on localized surface plasmon (LSP)  and Raman measurement , nanolithography , trapping and manipulating carbon nanotubes , and gold nanoparticles . Even viruses and bacteria, ranging in size from a few tens to a few hundred nanometers, have been trapped optically . All these experiments suffered from their own drawbacks. The experiments made use of cw near-infrared (NIR) lasers to trap particles with diameters (d) nearly an order of magnitude smaller than the laser wavelength (); therefore the trapping forces are largely governed by Rayleigh scattering where the particle is regarded as a point dipole. For Rayleigh particles in the limit of ( being the wavenumber), the gradient force (F) on the dipolar particle equals 10] or tobacco-mosaic viruses (TMVs)  has been found to be . It is interesting to note here that, although the volume of these particles satisfy the Rayleigh criterion, the actual dimensions do not; e.g., in one experiment  the cylindrical TMV had a length of , which is close to the trapping wavelength () used. A spherical particle is an automatic choice to avoid this issue. However, earlier efforts  revealed that higher power levels are required to stably trap latex nanoparticles; the exertable force was found to be smaller for latex nanoparticles than for gold nanoparticles, making the former a poor choice for nanoscale applications. Another problem is direct observation of trapped nanoparticles under traditional white light illumination (bright-field microscopy) methods for observing trapping of Mie particles (). Alternative choices of using other far-field observation methods such as differential inter ference contrast (DIC) or fluorescence  microscopic techniques suffer from the fact that the maximum resolution is bound by the diffraction limit that is much more than the particle diameter. In addition, the presence of scattering or luminescent background obscures the image, which can be taken care of by confocal detection for fluorescence-based methods. Also, observation by scattering of auxiliary laser light  acts as perturbation to the trapping laser field.
We have shown how ultrafast pulses lead to stable trapping of latex nanoparticles three dimensionally in space at power levels where cw lasers cannot lead to a stable trap. In addition, background-free two-photon fluorescence from the trapped particles provides a unique way of observing them, which is much better than the scattering-based methods.
The experimental setup sketched in Fig. 1 is a thoroughly modified version of our previous arrangement as described elsewhere . We used NIR (centered at ) mode-locked pulsed excitation (at pulse repetition rate) of a Ti:sapphire laser (Mira900-F pumped by Verdi5, Coherent Incorporated) that can also operate in a cw mode. Two-photon fluorescence was induced when the laser was operated in the pulsed mode. The expanded laser beam, shown as a solid (red) line, was passed through a telescopic arrangement along with two steering mirrors and sent to the microscope objective (UPLSAPO 1.4 NA 100XO, Olympus Incorporated) of a completely homemade benchtop inverted microscope. A dichroic mirror, placed just before the objective lens, has reflectance at ; at the same wavelength the objective transmits yielding of the light at the sample. This was confirmed by measuring the laser power with a powermeter (FieldMate, Coherent) as well as a silicon amplified photodiode (PDA100A-EC, Thorlabs). The two-photon-induced fluorescence, shown as a dashed-dot (green) line, as well as the backscattered light, shown as a dashed (red) line, was collected by a photomultiplier tube (PMT) using appropriate bandpass filters. The PMT signal was collected by an automotive oscilloscope or picoscope (Pico Technology) triggered by a rotating-disk optical chopper (with a 30 slot wheel) run by a tunable frequency driver (MC1000A, Thorlabs) and operating at . Thus, our robust setup is capable of measuring the two-photon fluorescence as well as the backscattered light to observe trapping of tiny nanoparticles in real time; it can also acquire video microscopy by bright-field illumination (not shown) and dark-field fluorescence generation. We trapped fluorophore (having single-photon absorption maxima at and an emission maximum at ) coated polystyrene 100 nm diameter latex beads (F8800, Molecular Probes). A dilute and slightly alkaline (pH of ~8) solution of the sample was well sonicated and was used immediately for the trapping experiments to avoid aggregation. The pulsed excitation simultaneously traps as well as generates backscattered (under both pulsed and cw modes) as well as fluorescence signals (only under a pulsed mode). Since in this case the wavelength of trapping light is nearly eight times larger than the particle diameter, the particle dimensions are in the Rayleigh regime.
3. Results and Discussion
The laser was first set to operate in a pulsed mode. At the time-averaged laser power at the sample tweezing is evident by occurrence of random spikes [see Fig. 2a] indicative of biased diffusion of particles into the trapping zone  with seldom seen trapping that lasted a few seconds [see Fig. 2b]. The height of the signal directly corresponds to the number of particles being trapped simultaneously. A more stable trap was observed when the average power was elevated to as shown in Figs. 3a, 3b depicting fluorescence and a backscattered signal, respectively. Figure 3a clearly shows trapping of a single particle followed by another one; the relative strength of fluorescence has nearly a 1:2 ratio (after background subtraction), which confirms the number of trapped particles (the spikes with larger heights are due to aggregates rapidly diffusing across the focal volume). However, when the laser was switched to the cw mode, the tweezing action had much higher power (), and a stable trap with subsequent particle aggregation was observed at an even higher power () as shown in Fig. 4. Thus, these results clearly indicate the crucial role of ultrashort pulses in trapping tiny particles as explained below.
Multiphoton fluorescence has been previously combined with optical trapping using cw excitation [18, 19]. The main advantage of nonlinear fluorescence generation is that, since it is confined only within the tiny focal volume [20, 21], any persistent fluorescence signal corresponds only to the trapped particles that can be observed despite the presence of many other out-of-focus particles within the cone of illumination. Also, the effect of two-photon absorption on force calibration is negligible; since the probability of two-photon absorption is very low, we can completely neglect recoil force that is due to absorption of photons arriving in one direction with omnidirectional emission . This is one advantage over using auxiliary lasers for observation by scattering as the secondary laser light perturbs the trapping force field.
The use of cw lasers for multiphoton absorption has been surpassed by mode-locked subpicosecond pulsed lasers to circumvent the low absorption cross sections of common fluorophores. Owing to its fleeting temporal existence, a femtosecond laser pulse has enormous peak power compared with its time averaged power; the typical ratio between them being :1. The high photon flux increases the trap stiffness (or force constant) to such an extent that a stable trap is observed at the same average power level of cw lasers that cannot trap nanoparticles. Wang and Zhao  derived an analytical expression for instantaneous longitudinal and transverse (gradient) radiation force components for pulsed excitation acting on Rayleigh particles; each pulse exerts a ponderomotive force on the particle, and the steepness of the associated potential well overcomes the Brownian fluctuations leading to a stable trap. The calculations have shown that the necessary condition for trapping is given by the Boltzmann factor, , with where is the Boltzman constant; T is the absolute temperature; is the vacuum permittivity; and are the refractive indices of the particle and surroundings, respectively, with ; r is the radius of the trapped particle; U is the pulse energy; c is the speed of light in vacuum; is the beam radius at the focus (taken to be ); and τ is the pulse width. At and , and are 1.57845 and 1.32896, respectively (www.refractive index.info). For average power, U is nearly 0.3 nJ, yielding the Boltzmann factor to be , indicating that radiation force can overcome thermal motions. Our finding is also supported by the previously reported use of short pulses ( duration) capable of overcoming adhesive interaction between a glass surface and the particles attached to the glass due to large peak gradient force () .
For a Mie particle Brownian motion is sluggish and a shallow potential well (offered by a cw or time- averaged pulsed laser) is good enough to trap it. In contrast, a rapidly moving Rayleigh particle cannot be trapped with a shallow force field, but it can be efficiently trapped when the well depth is steep, provided the particle does not diffuse away within the time period of the periodic force field (discussed in detail in the following section). In other words, to realize the effects of instantaneous forces, we must design an experiment that can sense the difference between cw versus pulsed excitation, and trapping Rayleigh particles is one such experiment as the random Brownian motion of a tiny Rayleigh particle is sensitive to the instantaneous force field. This is precisely the reason why the stiffness of an ultrashort laser trap has been reported to be equal to that with cw excitation with the same average power . Even earlier theoretical calculations  failed to differentiate between cw and pulsed excitation due to sampling of the pulses. As we discussed above, the Wang and Zhao theory  managed to distinctively provide evidence of stable trapping with femtosecond laser pulses, which is distinctly evident in our experiments. However, experimental measurement of the instantaneous force by a femtosecond pulse is not possible by any of the present-day techniques for measuring trap stiffness; for example, the time scales associated with the viscous drag method are so slow compared with the pulse rate that the instantaneous force averages out. Therefore, further research needs to be pursued with regard to the precise measurement of instantaneous trap stiffness.
The pulse repetition rate is a crucial factor for stably trapping Rayleigh particles. Within (inverse of ) the time lag between two consecutive pulses and the already trapped particle does not leave the trapping region. Considering Brownian motion of the particle, let us assume that the particle moves in a straight line in a single step during the blanking time of the laser such that, during that time interval, it covers the maximum path distance. For a Brownian particle, the distance covered after a single step is given by22]. Now the size of the particle dictates whether it will leave a trap within the time period when no light is present to hold it. Thus for a fixed focal dimension there is an optimal trade-off between the particle diameter and the pulse repetition rate for the particle being trapped over time. The high repetition-rate (HRR) lasers seem to be a good choice for this reason. The additional advantage of using pulsed lasers is that it causes minimal heating compared with cw excitation  owing to possible heat diffusion during the interpulse time lag. Also, since the two-photon-induced heating is largely mediated by solvent , the low absorption coefficient of water at the NIR wavelength used  makes it suitable for biological applications.
In summary, we have shown how to exploit the huge pulse power of ultrafast pulsed lasers with a high repetition rate to hold tiny Rayleigh particles that were thought to be untrappable at low optical power levels. In addition, the method offers clear observation of trapping events owing to the nonlinear fluorescence generation. However, much work is still needed to calibrate the instantaneous stiffness that is due to a single pulse. Trapping and manipulating particles of much smaller size by use of this technique are currently being pursued in our laboratory.
A. K. De and D. Roy thank the Council of Scientific and Industrial Research (CSIR), India, for graduate fellowships. We also thank the Department of Science and Technology (DST), India, and the Wellcome Trust Foundation, UK, for funding. The help from Saptaparna Das, Shaon Chakrabarty, and Anirban Roy is gratefully acknowledged.
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