A single optical fiber probe has been used to trap a solid 2 µm diameter glass bead in 3-D in water. Optical confinement in 2-D was produced by the annular light distribution emerging from a selectively chemically etched, tapered, hollow tipped metalized fiber probe. Confinement of the bead in 3-D was achieved by balancing an electrostatic force of attraction towards the tip and the optical scattering force pushing the particle away from the tip.
©2003 Optical Society of America
Considerable progress  has been made using highly focussed laser beams to optically trap and manipulate micrometer-sized particles since the technique was first invented by Ashkin in 1970 . Applications now range from atom cooling  to measurements of femtonewton force microscopy of single extended DNA molecules .
Laser tweezer applications in turbid biological media present significant challenges since it is difficult to achieve a tightly focussed laser beam necessary for optical trapping. The problem is most severe in thick samples where spherical aberration of the focussing beam further weakens the optical trapping forces . This problem can be solved using optical fibers to carry the light to the object which you wish to trap. In 1993 Constable used two opposing fiber probes to achieve stable 3-dimensional light trapping of small dielectric spheres . In the following years a number of papers have described the use of multiple fibers to trap particles in 3-D [7–9]. More recently a single fiber-optic probe was used to trap and manipulate a microsphere on a surface (i.e., 2-D) .
Over the last decade researchers have demonstrated increased three dimensional trapping efficiency of low dielectric constant,reflective and absorbing, micron sized particles using annular shaped (doughnut) focussed Gaussian-Laguerre laser beams [11–15]. Recent theoretical papers suggest that there may be an advantage to using radially polarized annular shaped light beams in tapered Near-Field Scanning Optical Microscopy (NSOM) probes to (1) increase the electric field enhancement at the metallic tip for spectroscopy and nanopatterning applications  or (2) use radially polarized light to produce a sub-diffraction limited (e.g. λ/5) spot size at the exit of the probe which doesn’t increase in size too quickly in the direction of light propagation and therefore may be useful as a “virtual tip” in NSOM experiments . In this paper we demonstrate that an annular light distribution created by a partially metalized hollow-tipped tapered fiber probe can trap and manipulate a 2µm diameter solid glass bead in water. The force produced by the light pressure on the particle in the direction of light propagation can be balanced by an electrostatic return force towards the highly tapered tip to produce particle trapping in 3-D. To the best of our knowledge this is the first report of trapping a dielectric particle in 3-D using a single fiber probe.
The experimental layout is shown in Fig. 1. The optical source was a polarized Lightwave Electronics Inc. cw laser operating at a wavelength of 1.32 µm. The laser beam first passed through a half-wave plate to permit rotation of the polarization. The beam then passed through a polarizing cube beamsplitter and was coupled into the core of an approximately 1m long single-mode fiber using a x16 magnification, NA=0.32 microscope objective. A laser power of ≈10mW was typically coupled into the fiber. The output end of the fiber was placed inside a few mm thick droplet of water parallel to the plane of a glass slide. An overhead long working distance microscope objective (NA=0.5) together with a Panasonic video camera were used to image the fiber tip region. Some of the light traveling down the fiber core was retroreflected from the metalized probe tip and returned through the lens to be directed by the beamsplitter to a Newport model 1830-C powermeter for detection. The back-reflected signal at the detector, which consisted of a small depolarized component due to the polarization scrambling nature of the fiber, was optimized to ensure that the laser light was efficiently coupled into the small 4µm diameter core and directed all the way to the fiber tip. The combination of the half-wave plate and the polarizing beamsplitter acted as a variable attenuator to permit continuous variation of the laser power delivered into the fiber probe.
The probes were made from a high GeO2 doped,high NA (0.3), single-mode (at λ=1.55µm) fiber obtained from Fibercore Inc.. The fiber was first etched in 6:1 buffered oxide etchant (BOE), hydrofluoric acid (HF) and water solution with a volume ratio of NH4F:HF:H2O=1.5:1:1 for 95 minutes (T≈23°C) to reduce the 125µm fiber diameter down to approximately 50 µm. The 6:1 BOE contained 6 volumes of ammonium fluoride NH4F and 1 volume of HF. The probe was then etched for 50 minutes in a 10:1 BOE room temperature solution. The final fiber diameter was ≈20 µm. It has been shown that selective etching of highly GeO2 doped single-mode fibers can produce a conical structure at the end of the fiber whose base corresponds to the core of the fiber [18,19]. This occurs because the doped core region etches slower than the undoped cladding. However there are a number of telecom fibers, which as a result of the manufacturing process,have a narrow, low index of refraction center inside the high index core. Etching of these fibers in BOE produces a hollow region in the center of the conical structure . A typical etched hollow core fiber is shown in Fig. 2. The height of the conical structure is ≈3µm,while the depth of the hole is ≈1µm. The thickness of the annular rim is ≈750 nm and the hole diameter is ≈1µm.
When light is coupled into the tapered region of the uncoated probe tip shown in Fig. 2 the air inside the hole and surrounding the tip acts as a low index of refraction cladding to effectively confine the light into the annular silica region. Figure 3 shows NSOM beam scans of the light distribution emanating from a non-metalized selectively etched Fibercore Inc. fiber in air as a function of the distance from the probe tip. The laser source was an unpolarized He-Ne laser (at λ=633nm). The NSOM experiment was performed using the apparatus described in Ref. . The light collection resolution was 140 nm as determined by the diameter of the probe aperture. In Fig. 3(a) one can observe a very well defined 1.9 µm wide annular light distribution very close to the exit surface of the probe. However as one moves away from the surface the light distribution starts to fill the interior of the annulus such that by ≈1µm from the surface a substantial central component has developed leading ultimately to an approximately Gaussian shaped light distribution 2 µm beyond the surface. It is interesting that the full width at half maximum of the central component remains quite narrow (400 nm) even a micron beyond the probe tip. When such a probe is immersed in water the higher index of refraction of water compared to air acts to diminish the annular guiding action. We therefore totally metalized the probes with aluminum (thickness ≈100 nm) then used focussed ion -beam technology (FIB)  to nanoslice off the metal on the end face of the probe to expose the annular silica region surrounding a metallic coated hole. NSOM beam scans confirmed the annular light distribution exiting such a metalized probe although it was not possible to accurately measure the distribution due to multiple light reflections and interference effects which ocurred between the two closely spaced partially metalized probe surfaces.
In another version of probe construction, which didn’t utilize pre-etching to reduce the probe diameter, the probes were entirely coated with a thin layer of gold then the probe tips were pressed against a glass surface in a controlled fashion to push the malleable metal off the top surface of the probe to reveal the silica glass but still leaving the gold inside the hole to create an annular silica region . The transmission of the probe and the far-field diffraction pattern were monitored to determine when to stop the process.
The nominal 2 µm diameter solid glass microspheres were purchased from Structure Probe Inc.. The spheres were made of borosilicate glass (ρ=2.5 g/cm3) and have an index of refraction of 1.56 at λ=589 nm. This glass is transparent at the λ=1.3 µm laser wavelength. A number of glass beads were first attached to a fiber, which was inserted into the water. The trapping fiber probe tip was used to pluck off one of the spheres attaching it to the side of the conical tip. The tip was then shaken to permit the bead to fall close to the front of the probe tip. The cw laser was then quickly unblocked to allow ≈2mW of light exiting the annular region to trap the glass bead.
The results of the fiber-particle trapping experiment are shown in the video in Fig. 4. The 2 µm glass sphere was trapped in 3-D approximately 1µm away from the end face of the fiber probe. Blockage of the laser beam caused the bead to slowly move back to the probe tip and also fall slightly to the back side of the probe under the influence of gravity. When the laser beam was reinstated the bead popped out to sit again at the 1µm separation. This sequence was highly repeatable. A striking feature of the trapping was the ability to rapidly translate the fiber in 3-D at tens of microns per second while keeping the particle locked in position relative to the probe tip with sub-micron accuracy. Translation of the fiber probe in the vertical direction i.e. into and out of focus is not shown in the video clip but was demonstrated separately. If the bead was allowed to fall a few microns in front of the probe tip, rather than close to the tip, light pressure pushed it off to the right typically at a speed of ≈20 µm/s. Nearly identical trapping performance was obtained with the gold coated probe tip.
Confinement of the 2µm diameter glass bead by an annular light distribution was anticipated based upon optical tweezer experiments using highly focussed annular beams [11–15]. The minimum trapping force to overcome the net force of gravity and particle buoyancy is estimated to be ≈5×10-14 N. In principle we can get a better idea of the confinement force using Stoke’s equation to estimate the drag force on the microsphere required to dislodge the particle as it is translated through the water .
In Eq. (1) FD is the drag force on the sphere, η is the viscosity of the surrounding medium (for water at 20°C η=1.0×10-2 P), “a” is the radius of the sphere and “v” is the maximum observable speed that the sphere was translated. Unfortunately it was not possible to move our translational stages fast enough to observe the removal of the sphere. Therefore we can only put a lower limit on the confinement force using a value of 20µm/s for the maximum observable translational speed. The value for the lower limit on FD is ≈4×10-13 N an order of magnitude higher than the force required to balance the resultant force of gravity and buoyancy on the sphere. The large radial confining force accounts in part for the remarkable stability of the observed particle trapping.
The 1.9 µm diameter annular light distribution intercepts the nearly matched diameter of the microsphere providing a scattering force, which pushes the particle away from the fiber tip when the laser is on. The filling in of the annular region beyond ≈1µm from the tip to form more of a Gaussian shaped beam results in a loss of radial confinement and the development of a larger scattering force, which continues to push the particle away from the tip. An estimate for the scattering force is 6×10-12 N for a transmitted power level of ≈2mW exiting the probe tip . However in the case of our fiber probe the absence of tight focusing (i.e., no lensing effects) of the beam away from the tip rules out the possibility that a gradient force can counteract the scattering force . Therefore the observation of particle confinement along the axis of the fiber probe was unexpected and occurred when attention was paid to creating a good electrical conducting path from the metalized probe tip back ≈1cm to a position where the fiber probe could be electrically grounded. This necessitated making sure that the last portion of the probe, which included a number of millimeters of the acrylate jacketed portion of the fiber, was sufficiently well metalized. This observation suggests that the restoring force to balance the scattering force might be electrostatic in nature.
It is well known that glass microspheres can acquire a negative surface charge in water, primarily through the dissociation of terminal silanol groups . The surface charge density on a glass sphere is estimated to be somewhere around 700 e/µm2 . A calculation of the induced charge distribution on the metalized tip region and the resultant Coulomb force of attraction is complicated due to the 3-dimensional geometry of the probe tip and the presence of the metallic coated hole which is electrically isolated by the annular silica region from the outside electrically grounded metal coating. In addition localized surface charging of laser irradiated sharp metalized tips (the so-called lightening rod effect) is known to occur and has even been suggested as a means of trapping sub-micron dielectric particles . All we can say at this point without a serious theoretical analysis is that it appears quite feasible to achieve Coulomb forces at the pN level required to balance the scattering forces.
There is an alternative explanation for the observed particle confinement, which must be considered. It is well known from research on NSOM fiber probes that significant heating of the highly tapered metalized tips occurs at mW power levels . It is possible that thermally driven vortices in the water caused by the hot tip somehow provide a trapping force on the glass microsphere. In Ref. the authors claim that very small, difficult to observe, vortices apparently explain a puzzling experimental observation that two negatively charged microbeads floating in water attracted each other when they were near a glass surface . In our experiments we failed to observe any particle trapping when the probe tip was completely metalized implying that the light distribution emerging from the tip rather than just a hot tip was required. Since the glass bead was transparent at the laser wavelength (λ=1.32µm) and water absorption was insignificant over the 1µm distance it is unlikely that the transmitted light could have produced any thermal vortices. However it is possible that a thermal gradient was produced across the metal-dielectric annular region due to the different thermal properties of the platinum coating and the silica fiber. Such a gradient might initiate vortices contributing to particle trapping normal to the light propagation direction. If we assume that such vortices also acted on the particle forcing it back towards the tip then blockage of the laser beam should have, due to the fast thermal response of the small tip, rapidly eliminated any thermal vortices. In this case the particle should have just drifted downward under the force of gravity. This is contrary to what we observed experimentally which was that the particle always went back to the probe tip. This seems to rule out thermal vortices participating in the restoring force driving the particle back to the probe, however further research is required using fine powders and a high magnification microscope to try to visualize any vortices.
At slightly higher laser powers than the 10mW coupled into the fiber we generated a microbubble centered on the conical tip. Stable microbubble generation will be the topic of a future paper. The laser power threshold for bubble formation increased as the quality of the water improved (e.g., use of distilled water instead of tap water) presumably due to a lower air and nucleation center content. This resulted in a larger laser power operating window for the observation of particle trapping.
Optical confinement of a particle in 2-D using a single fiber probe results from the novel hollow tip fiber design, which is used to define an annular light distribution. The trapping should be insensitive to the laser wavelength used provided the silica is optically transparent at the chosen laser wavelength. Therefore it should be possible to select alternative lasers which might, for example, produce less damage in biological samples. In future we plan to investigate the nature of the electrostatic restoring force and whether it is possible to enhance 3-D trapping by applying a small voltage to the probe. We will also be investigating to what extent is it important to have a good match between the size of the annulus and the particle size. It should be possible to fabricate annular diameters ranging from 500 nm to ≈5µms using selective chemical etching of commercially available GeO2 doped fibers. Smaller annulli in the 50 nm range can be fabricated using focussed ion-beam hole drilling technology . Probes based on such small apertures will of course have to contend with the particle’s Brownian motion during trapping which appeared to be insignificant for micron sized particles.
Potential applications of the fiber based particle trapping described in this paper will likely take advantage of being able to trap particles in highly turbid media since it is only necessary to preserve the tight annular light distribution over a distance of a few microns. The hollow tipped fiber probes may also be of interest as a technique for effectively picking up and transporting a small microbead which might contain a sensor or a drug or might be used as a small light source . It might also be possible to use two opposing fiber probes with at least one probe having an annular light distribution which can be used as an “eraser” laser beam in a two color, beyond the diffraction limit, super-resolution microscope [31, 32] for use in turbid media.
In this paper we have used a novel hollow-tipped fiber probe design, which produces an annular light beam to efficiently trap a 2 µm diameter glass microsphere in water in three dimensions with sub-micron accuracy. It is believed that trapping in the direction of light propagation was possible due to an electrostatic force produced by surface charging effects, which balanced the scattering force on the glass microsphere.
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