Dear Joachim,

Thanks for the links. Several of these discuss the proposed use of Bessel beams for tractors beams, but only in theory, not in practice. The ANU photophoretic work uses a different mechanism, and appears to push, not to pull. The acoustic tweezer is a trap, based on a standing wave. What I'm looking for is an experimental demonstration of the theoretical papers' proposal of a traveling wave that pulls material back up to its source using optical recoil forces.

A recent paper in Nature Photonics also shows optical pulling forces in a theoretical way. Look here: doi:10.1038/nphoton.2011.153

Maybe this helps.

search arXiv for Novitsky and you will find several papers.

All these papers discuss the theory. None seem to include experimental verification. I'm looking for experimental realizations of these predictions.

Here is some early experimental work I did with Bessel beams. We did a lot more than published. Optical trapping was observed, but NOT tractor beam.

Thanks very much for this pointer. My group has experimentally demonstrated optical tractor beams based on a somewhat different principle, and I'm searching for experimental verification of the seemingly simpler recoil principle. The link is ...

http://physics.nyu.edu/grierlab/publications.html#solenoid5c

I have recently been working on optical space transform by using acoustic metamaterials. Basically the device in the paper i sent is packed with acoustic meta materials and then powered up. Of course it is filled with a transmission medium like glycerine. Then using an optical beam probe and collecting the light at a spectrometer I can mesure the line broadening. The pressures are well over 100 MPa. And the device creates analog black holes. I haven't published on this yet. It's still ongoing work.

Hi David --- it is rare that I submit and answer to RG, mainly because I don't know -- this is no exception albeit I have an admin task I should be doing and replying to this is more fun!

If I am honest I have never been very surprised over Bessel Beams tractors. Standard optical tweezers, in which you lead the world, also exert forces on the particle directed back towards the source. If seems to me that the important parameter is the Numerical Aperture of the the optical system (Gaussian beam) and for a Bessel beam the equivalent number is the cone angle. Depending upon the scattering force (Fresnel reflection from the particle surface) there is a lower limit to this NA, of order 0.5. I think that this tells us straight away that for a Bessel beam to exert a reverse force on the particle its cone angle needs to be similar. For a Bessel beam I think this suggests that the range over which the reverse force can be exerted cannot exceed roughly the aperture of the optical element which creates the beam.

However, I guess the question remains how might this range compare to a Gaussian beam?

When comparing a Bessel to a Gaussian I note two things. Firstly if one takes the Rayleigh range of the Gaussian beam as a metric then we see that the depth over which the Bessel beam nicely propagates is multiplied by a factor roughly equal to the number of concentric rings in the beam. Secondly that the power contained in the central spot of the Bessel is, compared to the equivalent Gaussian, reduced by the same factor. Taken all together, this suggests to me that the range over which one can observe a pull force (greater than the scattering force) is primarily related to the aperture of the beam forming element and the power of the beam - albeit over this range, the Bessel beam will have a more uniform performance, which I accept may be important. There may also be factors of two or so to play with but I doubt any massive scaling advantage.

If I were looking to make a tractor in this way I would start with a very high power laser and create a very high cone angle Bessel (ie k_r approx = k_z) containing as many rings as possible, and ensuring that the central maximum contains >10s mW. I suspect then one could indeed obtain "fracturing" over a range comparable to the aperture of the beam forming optic.

I doubt I'm saying anything here that you did not know -- but if you think I have missed something then I'd be very keen to hear.

BTW I liked very much your comment in PRL last year :)

Kind regards

Miles

Dear Miles,

Thanks for writing. I think you're absolutely right about the range of a Bessel-beam tractor: the cone angle would have to be so steep that the range would be comparable to the micrometer-scale range of an optical tweezer. This might explain why there aren't any experimental demonstrations of Marston's principle with unembellished Bessel beams. At the time I posed this question, I was concerned that there might have been such a report, and that I simply had missed it.

All the best,

David