# Optical Tweezers Help Wanted:

1. Nov 17, 2004

### ObsessiveMathsFreak

Help Wanted:
Lone maths freak seeks aid from physicists for research into optical trapping/optical tweezers

Ok just for the benefit of those who may not be aware,
Optical tweezers or optical traps are a relatively recent experimental technique
in which focused lasers are used to trap neutral particles in three dimensions.

Put a little more simply(and imprecisely), optical tweezers are like the tractor beam in
star trek for very tiny particles and even atoms. Transparent particles are drawn to the
center of the laser beam, as are atoms, and with the right focus on the lens, particle can also be lifted upwards by the beam.

A simple google on optical trapping will bring up a host of links to optical tweezers resources. They're used for crazy experiments, like measuring the tension in the cell walls of bacteria, or with molecular motors. Here a good http://www.stanford.edu/group/blocklab/Optical%20Tweezers%20Introduction.htm [Broken]. And http://www.st-andrews.ac.uk/~atomtrap/ [Broken], and a http://www.st-andrews.ac.uk/~atomtrap/Research/Beams/fibre/fibre.htm [Broken] of pong with micron sized particles!
They're understood in two regimes. Firstly, where the size of the particle $$r$$ is much greater that the wavelength of the laser $$\lambda$$
$$r >> \lambda$$ (ray-optics/Mie regime)
And secondly, where the size of the particle(usually an atom or molecule), is much less that the wavelength of the light
$$r << \lambda$$ (Rayleigh regime)
When $$r \sim \lambda$$ things start to go wrong, and the models don't work very well.

My problem?
I'm looking around for resources on the mathematics of optical tweezers. Strictly speaking, some kind of detailed mathematical treatement of the phenomeon. I've found a number of links to the ray optics rescources, but hardly any on the Rayleigh regime. Any links would be very handy.

I'm also very ignorent of the current state of optical tweezer theory in general. Are there still unresolved theoretical/mathematical issues with optical tweezers, or is the subject a closed book in this regard.
I'm not ignorent of the myriad of applications of optical tweezers/traps however. I seem to find two or three new experiments involving them everyday, they are obviously a very powerful and useful(and in fact relatively cheap) tool.

All help is welcome. Thanks in advance. OMF.

P.S. Hope everyone enjoys the links.

Last edited by a moderator: May 1, 2017