Re: Dispersion in an optical fibre
- From: Peter Fairbrother <zenadsl6186@xxxxxxxxx>
- Date: Sat, 02 Feb 2008 20:14:11 +0000
Edward Green wrote:
On Feb 2, 11:35 am, Peter Fairbrother <zenadsl6...@xxxxxxxxx> wrote:Edward Green wrote:On Jan 31, 7:50 am, Peter Fairbrother <zenadsl6...@xxxxxxxxx> wrote:Two occurs in larger fibers, and can be considered as the waveHere are four possible reasons, put simply as requested; butI hadn't thought of that... that's in addition to any dispersion
unfortunately there are more than four types of dispersion.
First, different wavelengths travel at different speeds because the
refractive index of fibre is not constant with respect to wavelength
(the speed of light in a medium of refractive index I is c/I).
occuring in an "empty pipe".
Second, photons which enter eg a straight fibre slightly off-axis willNeat!
bounce off the sides of the fibre more often than photons of the same
wavelength which enter on-axis, and will have further to travel.
Third, larger wavelengths will have more of their waveforms travelling
partly in the outer part of the fiber, where it travels faster than
slower wavelengths.
Fourth, light waves traveling in a fibre self-reinforce, forming static
waves a bit like the sound waves in an organ pipe. The bursts of waves
travelling in different patterns tend to travel at different speeds.
I think your two and four are different ways of expressing the same
thing: phase velocity definitely has to do with reinforcement, which,
as I said by Huygen's principle, can also be described as resulting
from disturbance propagatin everywhere with free space velocity, but
bouncing off the walls.
travelling in a zigzag path, four occurs mostly in thinner fibers and
can be considered as the wave travelling in a straight path but having
nodes and antinodes which differ for each photon.
Four is about modes, and can to a large extent be eliminated by using
monomode fiber, two isn't.
Two is dependant on the spacial spread of the beam, and four isn't,
although I agree they are similar.
I take it by "spatial" you mean "angular".
Indeed.
I'm not sure about your three. Are you thinking of something likeIt's a frequency-dependant phenomenon, as is one, but it's only really
skin effect in conductors. A mere buzz word for me, I'm afraid, but
one I'm not sure applies to light in pipes, as opposed to alternating
current in conductors. Please elaborate.
significant in thin fibers, unlike one which happens no matter the size
of the fiber. Think of it as the wave being too big to fit in the fiber,
so some of it travels in the outer part (where the speed of light is
faster).
You evidently know quite a bit more here than your self-effacing style
might have suggested.
It's not self effacement, it's just that I an not an optical engineer, or even a physicist, and you should not regard me as being authoritatively correct when talking about optics.
For instance while my post describing four different mechanisms of dispersion is probably reasonably correct, I don't know quite how important these mechanisms are in fiber design, as I have no experience of that.
[I'm a cryptologist/data security engineer, though I consider myself primarily to be a not-very-good mathematician - and the not-very-good bit is not self effacement either, generally speaking. I am considered to be at least quite good as a mathematician in my field :) ]
I wonder about a few things here.
When you say "photons", are you really alluding to a quantum optics,
or is this just a colorful way of saying describing classical light?
Is " having nodes and antinodes which differ for each photon"
translatable to a statement in classical EM, or does it really depend
on QED?
No, and yes.
I was and am trying to keep it simple, and not use math but describe a physical intuition about how these things work.
In free space photons do not usually interact with each other, although they can in a dispersive medium like the glass optical fibers are made from - however this is neither usual or significant here.
Each photon has many of the properties of a wave as well as those of a particle. Is a photon a particle or a wave? No, it's neither, it's a photon, and it behaves like a photon, not like a wave or a particle does.
It is however intuitively useful to think of light as being composed of particles (photons) which are waves.
So we have, intuitively, some light which travels down a fiber. It's composed of photons which are also waves. Some of these will find an easy path down the fiber because the vibrations (out of the possible vibrations they find in the fiber) are right for them, some will find it harder to get down and take longer.
This does not depend on either the frequency, phase or orientation of the vibrations, but on how they individually interact with the fiber.
I reread Harry C.'s first response, and you both mention the same
thing: "light travels faster near the edge". I take it then, that
without any special effort, manufactured fibers have an index of
refraction varying along the radius?
The manufacturers take a lot of special effort to ensure this - it's how an optical fiber works!
Also, you both mention beam spread. I surmise that if you take a
perfectly straight and uniform fiber and a perfectly coherent
monochromatic beam, that the fiber walls should be invisible to beam
propagation: as if you were taking a tube out of a monchromatic beam
pervading all space (which a perfectly monochromatic beam must), so
the fiber boundary conditions become irrelevant.
Fibers are not usually straight - this is one reason to have fibers in the first place. If you had a straight path, why would you use fiber?
(too many beers to do physics)
I think the conclusions in the rest of your post, below, may be correct at least to a certain extent, and I'd be interested in looking at them in more detail later - but I am too drunk to analyse them in detail now, and it is after all SaTurday night here, and I'm off to part-aaa-y!
No offense intended,
-- Peter
I think the conclusion may be true, even if the argument is suspect,.
for -- to harp back on Huygen's principle -- even a monochromatic wave
may be analyzed as spreading at all points; which just happens to
result in reinforcement along the crests of the original wave. We may
imagine that the same thing happens when a parallel tube (of any
shape?) is cut out of the space wave, with mirrored walls, so that the
reflections take the place of the missing spatial extent of the wave.
So, there may be two kinds of "bouncing off the walls": even a section
of a pure plane wave, which by ray optics is simply ignoring the
walls, is interacting with them under Huygen's principle, whereas
given a beam spread, the beam is bouncing off the walls even by ray
optics. The latter point is your "two".
As for "the wave being too big to fit in the fiber, so some of it
travels in the outer part (where the speed of light is faster)",
perhaps this aligns with the insight that shorter wavelengths should
be less affected by the walls, since the center of the waveguide looks
more like free space to them, coupled with the complication of a
variable index of refraction along the radius (?).
I see it's a complicated business, since the injected wave may have in
principle any spread over wavevector k, interacts with the boundaries,
and is further complicated by variable material properties inside the
fiber.
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- Re: Dispersion in an optical fibre
- From: Edward Green
- Re: Dispersion in an optical fibre
- From: Peter Fairbrother
- Re: Dispersion in an optical fibre
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