The reason single-beam optical tweezers require a high numerical aperture can be understood by thinking about the force on a tiny dielectric particle. Incoming light from the trapping laser causes an oscillating electric dipole in the particle, which in turn re-radiates light. Because this scattered light goes in all directions, it has no net momentum. Consequently, some momentum is transferred to the particle, pushing it along in the direction of the light's propagation. This is referred to as the "scattering force". At the same time, the induced dipole feels a force pulling it up the gradient of the beam's intensity towards the maximum. Only at relatively high numerical aperture is this gradient force high enough to overcome scattering in the axial direction, such that the particle is held stably near the focus, rather than pushed out of the trap by the scattering force.
At the tip of one of the tapered fibres used here, the light is concentrated tightly enough that there is a significant gradient of intensity, steep enough to trap a micron-sized dielectric bead at the fibre tip. However, as soon as we move even a little way from the fibre tip, scattering dominates and the bead is pushed away. The team added a second fibre to overcome this problem, creating two counterpropagating beams such that the scattering forces cancel at a point (or two points) between the two fibres. This dual-fibre geometry, first used to hold and deform biological cells by Guck et al. in 2001, is reminiscent of the very first optical trap built by Arthur Ashkin in 1970. His trap used two low numerical aperture lenses to form the counterpropagating, diverging laser beams that held the particles.
In their paper, the authors discuss the characterisation of traps formed by two co-axial tapered optical fibres, measuring both the optical field (with a method akin to SNOM) and the effective potential of the trap (using video particle tracking). They find a good agreement with the established theory, that trap stiffness is roughly linear with laser power and that the trap becomes less stiff as the fibres are moved further apart (because the optical field is weaker in the centre, where the particles are held).
One interesting development this work anticipates is the potential to shape the fibre tips and craft sub-diffraction-limited optical fields; metallized fibres as used in SNOM tips can focus light into a spot tens of nanometres across, creating an intensity gradient much higher than that available with even a high-NA lens. This might prove very useful indeed for trapping metal nanoparticles or other highly scattering objects, and the techniques outlined here would be perfect for characterising such a system.
Lastly, fibre-based traps can work with samples that are inaccessible to the high-power microscope that is required for conventional optical traps; they can be used anywhere one can fit a mechanical probe. Today's micromanipulators can position the tip of a fibre with sub-nanometre accuracy, over a range of centimetres, combining the benefits of optical trapping with those of mechanical manipulation. Such a system would, of course, resemble rather neatly the artist's impression of optical tweezers!
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