Airy beams and Bessel beams

[cyber one]

Would it be possible, in theory, for a narrow Airy beam or Bessel beam
to transverse a distance of many KM, and maintain the narrow beam the
entire distance?

The experiments I have seen, such as "Observation of Accelerating Airy
Beams" 23 November 2007 Physical Review Letters, seem to discuss only


[[Mod. note --
*Any* beam will eventually start to spread. See
http://en.wikipedia.org/wiki/Gaussian_beam
for an introduction.
-- jt]]

[p.kinsler@ic.ac.uk]

cyber one <geerj@bellsouth.net> wrote:
> Would it be possible, in theory, for a narrow Airy beam or Bessel beam
> to transverse a distance of many KM, and maintain the narrow beam the
> entire distance?

> The experiments I have seen, such as "Observation of Accelerating Airy
> Beams" 23 November 2007 Physical Review Letters, seem to discuss only


> [[Mod. note --
> *Any* beam will eventually start to spread. See
> http://en.wikipedia.org/wiki/Gaussian_beam
> for an introduction.
> -- jt]]

Exact Bessel beams don't diffract -- they're already infinitely
wide!

Approximately Bessel beams diffract to a lesser extent than
gaussian beams, but they still diffract. If you want, you can
work out how approximate your Bessel-like beam can be in order
meet your diffraction criteria at some chosen distance.


--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (PHOT) (ph) +44-20-759-47734 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[Timo Nieminen]

On Thu, 4 Dec 2008, cyber one wrote:

> Would it be possible, in theory, for a narrow Airy beam or Bessel beam
> to transverse a distance of many KM, and maintain the narrow beam the
> entire distance?

If, by "narrow" Bessel beam, you mean a Bessel beam with a narrow central
peak, then, in theory, yes, it would be possible.

Note that an ideal Bessel beam will maintain its profile indefinitely, but
isn't physically realisable, since an ideal Bessel beam has infinite
power. A truncated Bessel beam (of finite power) will need to be wide
(i.e., have many rings around the central peak) in order to maintain a
narrow central core for a long distance.

> The experiments I have seen, such as "Observation of Accelerating Airy
> Beams" 23 November 2007 Physical Review Letters, seem to discuss only
>
>
> [[Mod. note --
> *Any* beam will eventually start to spread. See
> http://en.wikipedia.org/wiki/Gaussian_beam
> for an introduction.
> -- jt]]

Any physically realisable beam will spread. Some ideal theoretical beams
such as Bessel beams won't. You could (and should) include infinite plane
waves as non-spreading ideal beams.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://espace.uq.edu.au/list/author_id/1189/

[Keith Blow]

cyber one wrote:
> Would it be possible, in theory, for a narrow Airy beam or Bessel beam
> to transverse a distance of many KM, and maintain the narrow beam the
> entire distance?
>
> The experiments I have seen, such as "Observation of Accelerating Airy
> Beams" 23 November 2007 Physical Review Letters, seem to discuss only
>
>
> [[Mod. note --
> *Any* beam will eventually start to spread. See
> http://en.wikipedia.org/wiki/Gaussian_beam
> for an introduction.
> -- jt]]
It would be better to say "Any beam of finite extent will spread".
Bessel beams have infinite extent and so do not spread. In fact they are
eigenstates of the longitudinal paraxial propagator. Such problems are
normally discussed within the context of the paraxial approximation. In
practice we only create an approximate Bessel beam which does have
finite extent and so will eventually spread.

--
Keith Blow

[cyber one]

On Dec 6, 2:07Â*am, "Jonathan Thornburg [remove -animal to reply]"
<jth...@astro.indiana-zebra.edu> wrote:
[[Mod. note -- excess quoted text snipped -- jt]]
> Among others, Keith Blow <k...@somewhere.home> expressed things clearly
> and correctly in article <ghbo69$5i...@fb07-hees.theo.physik.uni-giessen.de>,
> writing
>
> > It would be better to say "Any beam of finite extent will spread".
> > Bessel beams have infinite extent and so do not spread. In fact they are
> > eigenstates of the longitudinal paraxial propagator. Such problems are
> > normally discussed within the context of the paraxial approximation. In
> > practice we only create an approximate Bessel beam which does have
> > finite extent and so will eventually spread.
>
> --
> "Jonathan Thornburg [remove -animal to reply]" <jth...@astro.indiana-zebra.edu>
> Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
> "Washing one's hands of the conflict between the powerful and the
> powerless means to side with the powerful, not to be neutral."
> Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â*-- quote by Freire / poster by Oxfam

Thanks. For shorter beams, with one main central core, could you have,
e.g., three very-close proximity side-by-side main beams, generated by
three devices, or would the overlapping photons in the areas around
the central core of the three beams interfere with each other,
disrupting the precise interference that produces the "non-
diffracting" beams.

[Jonathan Thornburg [remove -animal to reply]]

In a moderator's note in article
<mt2.1-11092-1228438321@argon.astro.indiana.edu>, I wrote
> [[Mod. note --
> *Any* beam will eventually start to spread. See
> http://en.wikipedia.org/wiki/Gaussian_beam
> for an introduction.
> -- jt]]

As several people have pointed out, I was somewhere between unclear
and wrong. My apologies for confusing things!

Among others, Keith Blow <kb@somewhere.home> expressed things clearly
and correctly in article <ghbo69$5ii$1@fb07-hees.theo.physik.uni-giessen.de>,
writing
> It would be better to say "Any beam of finite extent will spread".
> Bessel beams have infinite extent and so do not spread. In fact they are
> eigenstates of the longitudinal paraxial propagator. Such problems are
> normally discussed within the context of the paraxial approximation. In
> practice we only create an approximate Bessel beam which does have
> finite extent and so will eventually spread.

--
"Jonathan Thornburg [remove -animal to reply]" <jthorn@astro.indiana-zebra.edu>
Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

[Timo A. Nieminen]

On Sat, 6 Dec 2008, cyber one wrote:

> On Dec 6, 2:07??am, "Jonathan Thornburg [remove -animal to reply]"
> <jth...@astro.indiana-zebra.edu> wrote:
>> Among others, Keith Blow <k...@somewhere.home> expressed things clearly
>> and correctly in article <ghbo69$5i...@fb07-hees.theo.physik.uni-giessen.de>,
>> writing
>>
>>> It would be better to say "Any beam of finite extent will spread".
>>> Bessel beams have infinite extent and so do not spread. In fact they are
>>> eigenstates of the longitudinal paraxial propagator. Such problems are
>>> normally discussed within the context of the paraxial approximation. In
>>> practice we only create an approximate Bessel beam which does have
>>> finite extent and so will eventually spread.
>
> Thanks. For shorter beams, with one main central core, could you have,
> e.g., three very-close proximity side-by-side main beams, generated by
> three devices, or would the overlapping photons in the areas around
> the central core of the three beams interfere with each other,
> disrupting the precise interference that produces the "non-
> diffracting" beams.

If the beams are mutually coherent, they'll look just as if all 3 were
from the same source. They'll interfere, and the result will depend on the
phase differences between them. If the central beam is 1/2-wave out of
phase with the two outer beams, then you'll have something very much like
an HG20 laser mode.

Note that this isn't a non-diffracting beam - the central beam will widen,
and the two outer beams will move outwards. That's along the direction the
beams lie in. Still, the central beam will spread more slowly than a
single beam of the same profile. In the other direction, all 3 will
spread.

Note that each ring of a Bessel beam has equal power (and thus the total
power is infinite) - this is why the Bessel beam is non-diffracting.

If the central beam isn't out of phase with the outer beams, the three
will merge into 1.

If the 3 beams aren't mutually coherent, then each one will spread
independently, and the beams will overlap (without (time-averaged)
interference).

You don't need to bring photons into it at all - all you need are
classical waves.

--