Can Optical Tweezers Still Challenge Mathematicians and Physicists?

[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 . And http://www.st-andrews.ac.uk/~atomtrap/ , and a http://www.st-andrews.ac.uk/~atomtrap/Research/Beams/fibre/fibre.htm 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.

 

[eljose79]

Dear OMF,

As a physicist with experience in optical trapping and tweezers, I would be happy to assist you with your research. It's great to see interest in this area of study, as it has many exciting applications and is constantly evolving.

Regarding your question about the mathematical treatment of optical tweezers, I can recommend a few resources that may be helpful. One book that I found particularly useful is "Optical Tweezers: Principles and Applications" by Peter Reece and Vincent Craig. It provides a detailed mathematical analysis of optical trapping in both the ray-optics and Rayleigh regimes. Another resource is the paper "Optical trapping and manipulation of neutral particles using lasers" by Arthur Ashkin, which also includes mathematical equations and explanations.

In terms of unresolved theoretical/mathematical issues, there are still ongoing debates and discussions in the field, particularly in the area of optical forces and their effects on trapped particles. However, in general, the subject is well understood and has a solid theoretical foundation.

I hope this helps with your research, and please don't hesitate to reach out with any further questions or concerns. Best of luck with your studies!

 

[Graeme Robinson]

Dear OMF,

I am a physicist with experience in optical trapping and I would be happy to offer my assistance with your research. Optical tweezers are indeed a fascinating and powerful tool, and there is still much to be explored and understood about their theoretical and mathematical aspects.

In terms of resources, I would recommend checking out the work of Dr. Arthur Ashkin, who is considered the "father" of optical tweezers. He has published numerous papers and books on the subject, including "Optical Trapping and Manipulation of Neutral Particles Using Lasers" and "Forces of Light: Optical Tweezers, Laser Cooling, and the Quantum Theory of Atoms." These resources may provide a more detailed mathematical treatment of the phenomenon you are looking for.

Additionally, you may want to look into the work of Dr. Steven Block and his research group at Stanford University (the link you provided in your post). They have done extensive work on the mathematics of optical tweezers, particularly in the Rayleigh regime.

In terms of unresolved theoretical and mathematical issues, there is ongoing research and development in this field. For example, there is currently a lot of interest in using optical tweezers for biological applications, such as studying the dynamics of single molecules and cells. This has led to the need for more accurate and sophisticated theoretical models to understand the behavior of these systems.

I hope this helps and I am happy to discuss this topic further with you if needed. Best of luck with your research!