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Laser Trapping

How to do it

There are a number of different types of laser trap which can be used to trap different types of particles. Exotic traps will be considered later. By far the most common type of laser trap is the single-beam gradient trap, also known as optical tweezers, or laser tweezers.

Laser tweezers general setup A single-beam gradient trap can be simply constructed by tightly focussing a laser beam using a high numerical aperture microscope objective. The beam will be focussed to a very small spot size, creating a strong intensity maximum at the focus, which can be used to trap high-index transparent particles. The same apparatus can also be used as a convergence trap to two-dimensionally trap absorbing particles.

Why it works

Different types of particles will experience different types of forces. These can be divided into two main forces - gradient forces, proportional to the intensity gradient, and scattering (absorption and reflection) forces proportional to the intensity. Gradient forces can be used to three-dimensionally trap particles, while scattering forces can be used for two-dimensional trapping of non-transparent particles.

Gradient forces

Gradient forces can be considered from two viewpoints - reaction forces due to refraction of rays or waves, and polarisation forces, due to induced dipole moments within the particle. The former is appropriate for large particles (compared to the wavelength), the latter for small particles.

[pic for refraction forces pic]
As a ray of light is refracted, the direction, and thus the momentum, of the ray changes. To produce a change in momentum, there must be a force acting on the ray, and there must be an equal and opposite reaction force back on the refracting material. As seen in the picture, if a spherical particle with a higher refractive index than its surroundings moves away from the beam focus, the forces act to move it back towards the focus.

If the particle is sufficiently small so the the beam cannot accurately be described in terms of rays, it is more useful to consider the particle as a polarisable particle in an electric field. This is easiest for very small particles which will not significantly affect the beam - in this case, the beam is not affected by the position of the particle, and the intensity can be assumed to be uniform throughout the particle. In the general case, the intensity inside the particle varies with both the position within the particle and the position of the particle within the beam.

[longer blurb and equations for dipole forces]

Scattering forces

[radiation pressure]

Transparent particles

Transparent particles are trapped in the beam focus if the refractive index of the particle is higher than the refractive index of the surrounding medium (high-index particles). Trapping requires the gradient force to be larger than the scattering and absorption forces which will tend to push the particle along the beam axis.

Absorbing particles

For strongly absorbing particles, the gradient force is negligible. The particles cannot be three-dimensionally trapped by a single beam. The particle can, however, be trapped two-dimensionally in a region where the beam is converging.

[pic]

[And a bit more]

Reflective particles behave in a similar way, but the particle geometry becomes more important, as the direction of the momentum transfer depends on the directions of both the incident and reflected light.

Small metallic particles

These particles are polarisable, with a polarisability of [equation], and can be trapped with gradient forces.

Atoms

Atoms can usually be treated as very small classical particles. However, the refractive index and absorptivity of atoms are strongly dependent on the frequency of the incident light. Therefore, the behaviour of the atom at any time is dependent on the velocity of the atom (due to Doppler shifts). The frequency profile (spectrum) of the trapping beam is also very important. In general, atom trapping requires a laser beam tuned to close to a transition frequency (spectral line) of the atoms in question. Atoms will experience either attractive or repulsive gradient forces, depending on the detuning between the laser and the atomic transition. Attractive forces result from [RED/BLUE]-detuned incident light, and repulsive forces from [RED/BLUE]-detuned light. The atom will also experience a scattering force due to absorption (with a force in the direction of the beam) followed by spontaneous emission (in all directions, with a zero average recoil force).

[BRIEFLY LASER COOLING AND TRAPPING - HOLLOW BLOCKED BEAMS TO DO BOTH]

[ABSENCE OF USUAL VISCOUS FORCES. VERY WEAK BEAMS MEAN DISCRETE ABSORPTION AND EMISSION NEED TO BE TAKEN INTO ACCCOUNT]

Gradient trapping

Convergence trapping

Repulsive gradient trapping

  1. Single-beam gradient trap (aka optical tweezers)
  2. Optic fibre divergence trap
  3. Single-beam convergence trap
  4. Multiple-beam convergence trap
  5. Multiple-beam attractive gradient trap
  6. Multiple-beam repulsive gradient trap
The radiation pressure forces carried by the lens, and this provides the intensity gradient needed to trap transparent particles (or polarisable particles such as small metal spheres) at the beam focus. Between the lens and the beam focus, the light is converging; this convergence can be used to trap absorbing particles two-dimensionally.

For more information on how to build your own optical tweezers, see [more to come].

Why it works