What about
optical tweezers?

Principle of operation

The fundamental principle behind the operation of optical tweezers is the fact, that light carries momentum, which is proportional to the propagation vector of the electromagnetic field. When a light ray passes though a dielectric material suspended in a fluid media of lower refractive index (for example a polystyrene sphere suspended in water) the optical path is bent by refraction in the material which corresponds to a transfer of momentum from the light to the refracting particle. The force exerted by the light or "radiation pressure" as it is sometime called is actually capable of pushing small particles around.

In a practical optical tweezer, we wish to trap and hold particles in all three spatial dimensions, rather than using the light to push them about. This requires that we simultaneously trap the particles both laterally (x-y plane) and axially (z direction). This can be accomplished if the laser beam striking the sphere has a sufficiently steep intensity gradient in all three directions as was first realised by Ashkin.^1,2 A Gaussian beam profile focussed through a high numerical aperture microscope objective provides the required intensity profile for such a trap. The way in which the force components act to trap and hold the particle is shown in the figure. In this figure, the effects resulting in axial and lateral trapping have been separated for clarity.

A schematic diagram for the Axial and Lateral trapping of a bead in a Gaussian laser beam brought to a focus by a high numerical aperture objective. Axial trapping arises through the compensation of the scattering force (which pushes the bead in the direction of beam propagation) by the gradient force (which acts towards the focal spot). Lateral trapping arises form a gradient force acting towards the higher intensity region of the Gaussian beam profile (see Ashkin^2,3).

When placed in an intense laser beam with a Gaussian beam profile, a dielectric particle will experience a net lateral force acting towards the high intensity region of the beam as shown in the figure. The intensity gradient in the x-y plane causes the sphere to be pushed towards the centre of the beam and because of the Gaussian beam symmetry, the sphere is thus effectively trapped in the x-y direction. There is also a scattering force component, acting to push the bead in the direction of laser beam propagation. For complete 3-D trapping, this effect of this scattering force must be counteracted. If the objective lens has a sufficiently high numerical aperture, (NA) then there will also be a steep intensity gradient in the z-direction. This gradient has the effect, of introducing a force directed towards the focal point of the lens opposing the scattering force arising from the radiation pressure in the z-direction.

This somewhat simplified description of the nature of radiation pressure, based on ray optics can be directly applied in an optical tweezer set-up. An expanded Gaussian laser beam directed though a microscope objective can therefore trap a particle in all three dimensions, the position of the particle being controlled by adjusting the focal point and angle of the input beam.

References

1. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
2. A. Ashkin, J. M. Dziedic, J. E. Bjorkholm and S. Chu, Opt. Lett. 11, 288 (1986).
3. A. Ashkin, J. M. Dziedic and T. Yamane, Nature 330, 769 (1987).

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