
How To Turn A Laser Into A Tractor Beam - Anon84
http://www.technologyreview.com/blog/arxiv/26448/?ref=rss
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rflrob
How does this not violate the conservation of momentum (and/or energy)? It
seems like the outgoing photon must have some increased momentum (proportional
to h/lambda), which also means it will have increased energy (~ h * c/lambda),
which it must have gotten from the tractored particle. The induced multipoles
ought to be a higher energy than the ground state, though, so where did the
extra energy come from?

~~~
ars
You could conserve momentum by having the photons continue after interacting,
but at a higher energy level (i.e. heavier). But I can't figure out how to do
that and also conserve energy.

One possibility is that you end with the object at a standstill, so while you
need to move it, you don't actually need any extra momentum or energy to do
so. If there was some way to borrow it maybe? Sideways motion perhaps?

~~~
rflrob
> Sideways motion perhaps?

Now that I have some time to read the paper, on the second page there's this
sentence: "The Fourier decomposition of a PIB consists of plane wave
components whose k-vectors form a cone that make an angle Theta_0 with the
z-axis." The way it must get momentum is having the outgoing light be more
collimated than the incoming light.

My _new_ question is, How is this different from an Optical Trap? I'm
imagining the point of the cone at the particle, but that may not actually be
the case, and my skimming of the article is not enough to make sense of figure
3.

~~~
gjm11
Not only is the point of the cone not at the particle; it's not even _in the
same space_ as the particle! The cone is in the Fourier transform of the beam.

A standard optical trap, applied to very small objects, works like this: the
electric field causes polarization in the thing being trapped, turning it into
a little dipole; it then exerts a force on the induced charges, basically
pulling on each end of the dipole; that force is bigger in regions of greater
field intensity; the net effect is a small force pulling the object towards
where the field is bigger. (In an electromagnetic wave there is also a
magnetic field, which also acts on the objects, but the effects of those
average out to zero over each cycle of the wave.)

Now, really the effect of an electric field on a particle is more complicated
than just turning it into a dipole. There will be higher-order stuff as well.
The authors of this paper claim that if you look at the quadrupole term and
consider interactions between the different terms (warning: I am not at all
sure I understand this bit, and they've left the details to a supplementary
section that appears not to be included in the paper on the arXiv), then with
a suitably shaped beam and the right sort of particle you can get a backward
pull against the direction of propagation of the wave. (So, yes, the light
will have to emerge travelling more-directly-forward than it went in, so to
speak. Which is ... counterintuitive.)

So it's different from an optical trap in that it relies on higher-order
effects, and a more sophisticated beam shape, and it can only work on very
small objects (the higher-order stuff gets averaged away for bigger ones; so I
don't think you could use this technique for things like biological
specimens). But it uses much the same underlying physics.

[EDITED to add: their trick also doesn't work for the very _smallest_ objects,
substantially below one wavelength. It works only in the "Mie regime", meaning
with particles whose size is comparable to the wavelength.]

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iwwr
What does this mean: "the photons must simultaneously excite several
multipoles within the particle, which scatter the beam" ?

~~~
jessriedel
When trying to find out how an object is going to interact with the
electromagnetic field, it's generally useful to decompose the charge
distributed on the object into "multipole modes". It turns out that any
arbitrary distribution of charges can be expressed as a sum of such
multipoles, and the interaction of each multipole with the E&M field can be
solved even though the object itself may be too complicated. Usually, only the
first few multipoles are important, which allows efficient computation of the
objects behavior by summing up the contribution of the first few multipoles.

The first multipole ("monopole") is just the net charge of the object. The
second multipole ("dipole") is the degree to which the object has positive
charge distributed toward one side and negative charge toward another.

A single isolated point charge is a perfect monopole, with zero higher-order
multipole components. An object composed of two opposite charges of equal
magnitude, separated by a distance, is a perfect dipole, with zero monopole
and higher-order multipole components. And so on.

Apparently, the point is that objects which are electromagnetically simple
(such as a single point charge) cannot be pulled by a tractor beam. Instead,
the object must be complicated such that it has several large multipole
components which interact in the right ways to produce a net pull.

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jessriedel
Typo in article: There is, of course, still a potential gradient. As the
abstract notes, the important thing is that there is no _equilibrium point_ ,
i.e. no place where the gradient is zero. The object can be pulled all the way
back to the source.

~~~
gjm11
No, it's not a typo.

Standard "optical tweezers" pull things towards regions of higher intensity
(it's the _intensity_ gradient, not the _potential_ gradient, that's relevant
here), so you can't pull anything past where the intensity is maximal. But the
technique described in the paper works even with no intensity gradient along
the direction of beam propagation. (I think that if there were one, the
gradient force would swamp their new force, but I'm not sure.)

~~~
jessriedel
Whoops, looks like I was confused about the terminology. Thanks.

In case anyone else reads this: according to the wikipedia article, the term
"intensity" in "intensity gradient"--in this context--is just the strength of
electric (and magnetic) field associated with the laser. The electric field,
in turn, is the gradient of the electric potential [1]. Point charges will
follow the _potential_ gradient, but neutral dieletric objects (which I think
is what optical tweezers are usually used on, and which usually can be modeled
as dipoles) will follow the _intensity_ gradient.

Simple dipoles can be pulled with optical tweezers, but limits on laser power
mean that the distance between intensity extrema (and so the maximum distance
things can be pulled) is relatively short. The hypothetical tractor beam only
works on objects more electrically complicated than dipoles, but doesn't rely
on following an intensity gradient and can pull all the way back to the
source.

[1] This may not be quite applicable here because of the ambiguities in
defining a potential for non-static electric fields like those of lasers.

