1. Oct 20, 2005

### pallidin

Greetings,
I have a question. Why does light spread?
That is, if I have a laser beam transmitted over distance, the light "cone" seems to get larger. Is this a function of laser optics or poor design? Or is there something about light which tends to "push away" from nearby photons in the stream?

2. Oct 20, 2005

### Staff: Mentor

I see two factors contributing to laser beam spread:
(1) The mirrors being not exactly parallel
(2) Diffraction​
I doubt photon-photon interaction would be a factor.

I think we have a couple of members who are laser/optics experts. Perhaps they'll give you a more authoritative answer.

3. Oct 20, 2005

### Claude Bile

Laser beams spread due to diffraction. The degree to which the beam is diffracted depends on a couple of things.

- The size of the aperture that the beam is being emitted from.
- The number of transverse modes present within the cavity.

Diffraction is a fundamental property of light that cannot be eliminated completely. It can be reduced by filtering out higher-order transverse modes (which reduces the output power of the laser), but beyond that, you are at the mercy of Maxwell's equations!

Claude.

Last edited: Oct 20, 2005
4. Oct 20, 2005

### Staff: Mentor

Thanks, Claude. (And, yes, you were the expert I was hoping would answer. )

5. Oct 20, 2005

### Claude Bile

Not a problem!

6. Oct 20, 2005

### pervect

Staff Emeritus
I'm not a laser expert, but the root cause of laser beam spread is diffraction. Diffraction is a general property of electromagnetic waves.

Usually, the "Gaussian Beam" approximation can be used if you want to calculate the spread of a laser beam. See for instance:

http://www.rp-photonics.com/gaussian_beams.html

This formula is good only near the axis of the beam (this is known as the paraxial approximation). The formula is not exact, but gives a reasonable approximation to the expected spread when the angle is not too far away from the axis. The detailed derivation of the formula is rather involved, but it can be derived from Maxwell's equation with a LOT of work.

http://www.hep.princeton.edu/~mcdonald/examples/oblate_wave.pdf

for instance, derives the Gaussian beam approximation from Maxwell's equations (which describe how electromagnetic waves propagate) using "oblate spherical coordinates". I haven't gone through this derivation myself in any detail - one look at it was enough to know that I wasn't THAT interested in Gaussian beams :-).

The Gaussian beam approximation also ignores some higher order effects due to the apertures that any real laser beam must pass through. I don't have any real detailed references for this effect, but one website that gives some formulas where the beam is aperature limited with a circular cross section is:

(it's oriented towards interstellar communications applications).

Maxwell's equations are, of course, the fundamental equations that describe how light and other electromagnetic radiation propagates in the classical limit as a wave.

7. Oct 21, 2005

### heaven eye

well I am not an expert in physics but I think its because the laser waves have same frecuency or "little difference in frequency" which makes them move in one line (but the proof that laser have little difference in frequencies that when you sent laser on far wall you will see that the area of laser on wall is more than the hole on the laser-machine "usually laser pen" but laser diffractive is much less than light diffractive .

I think thats why laser looks straight more than light

regards
heaven eye

8. Oct 21, 2005

### Staff: Mentor

The reason why laser light is "straighter" (less divergent) than an ordinary beam of light is that it is highly collimated: The light must pass back and forth many times between nearly parallel mirrors; "off axis" beams do not last long. (The laser beam does spread, as explained by Claude and pervect, due to unavoidable diffraction effects.)

9. Oct 21, 2005

### pervect

Staff Emeritus
As an alternative to using Maxwell's equations, Huygen's principle is often used to explain diffraction in a quantitative fashion. Huygen's principle gives the correct solution for the wave equation in 3 dimensions, so the two approaches are entirely equivalent.

Single slit diffraction is the sort that's usually taught, but the idea can be extended to square or round holes as well without too much work.

http://en.wikipedia.org/wiki/Huygen's_principle

10. Oct 21, 2005

### androz

I would like to add something to this discussion.

There are beam that are not affected by diffraction too much. Those beam
shapes are called non-diffracted beams. A good example is Bessel like beams.
Bessel beams can be generated with axicon (conical lens). With this special
lens, you can focus a beam on several millimeters, that could be an interesting
thing for many applications.

Diffraction is like an operator that act on the fields of the light beam. If you
are able to find an invariant to this operator, you could find mathematically
beams that do not diffract, then that your beam does not spread. It supposes
of course that all the optics around is perfect, and that your beam travels in
vaccum to avoid diffusion issues or other stuffs.

11. Oct 21, 2005

### pallidin

Great explanations! Thanks to everyone for taking the time to explain this to me. If anyone else has more to add, please feel free.

12. Oct 22, 2005

### pervect

Staff Emeritus
Would you happen to know of any publically accessible papers or URL's about Bessel-like beams? I see a few hits from google, but so far they all ask for  when I try to view the paper :-(.

13. Oct 22, 2005

### androz

Well......
I've only read articles in scientific publications like the ones of the Optical Society of America or whatever. But I don't know anything that is free.
If you are not so far from a university, perhaps I could search for some references and give them to you. I'm not sure I am allowed to forward you
any digital version of such papers :uhh:, so I won't take the risk.
I look for the references and I'll post them here.

14. Oct 22, 2005

### pallidin

15. Oct 23, 2005

### androz

So the first man who have proposed the discussed term "nondiffracting beam"
is named J. Durnin, and the first time was in 1986-1987.
Another man has published a lot in this area : Z. Bouchal
Here are some links to the subject. The first one is quite the same as the one
given by pallidin. The second is the most interesting, written by Bouchal. You
can find many references, it is a long article, exhautive I hope. It gives you a
large overview on the subject.

http://optica.mty.itesm.mx/pmog/projects/nondiffracting.html

http://arxiv.org/abs/physics/0309109

PS : Finally, I would like to promote my own university ... I know a
professor who works on Bessel beams, and axicon in particular. His name is
M. PichÃ©, and he wrote on nondiffracting beams :
One-dimensional description of cylindrically symmetric laser beams: application to Bessel-type nondiffracting beams,
JOSA A, Vol. 22 Issue 7 Page 1274 (July 2005)

16. Oct 24, 2005

### pervect

Staff Emeritus
Thanks for the references!! Bessel beams look like they are a lot simpler mathematically than the Gaussian beams I was trying to deal with, though it appears the Gaussian beams are easier to actually create.

17. Oct 24, 2005

### androz

Hi,
You're welcome.
I doubt that Bessel beams are simpler to deal with mathematically....

In fact, gaussian beams are really useful. All you need is the beam waist and the
radius of curvature to entirely define a gaussian beam in the paraxial approximation.
And what is VERY useful, is that you can apply ray matrices theory to gaussian
beams !! so it is very simple to determine the waist of the beam every where
you want, you also know the wavefront, you can easily apply diffraction on it
as the Fourier transform of a gaussian beam is a gaussian beam etc.

Well, I hope you are convinced of the great utility of the gaussian beam, and
don't worry, if Bessel beams were simpler, there would have been used by
scientifics for the modelisation of the laser. Even in fiber optics we approximate
the real Bessel-shaped mode by a gaussian mode to simply calculate coupling
between two fibers for example.
I think I'll stay here because I would speak a lot on gaussian beams