Re: Laser light

[William Beaty <billb@eskimo.com>]

On Thu, 12 Dec 1996, James Mclean wrote:

> William Beaty says:
> > Can anyone on phys-L poke holes in my reasoning?  I'm convinced that
> > stimulated emission causes brighter light, not "in phase" light, and the
> > light-amplifying properties of lasing media is not the source of the
> > coherence of laser light. 
>
> Certainly the in-phase character of the stimulated light must be one
> necessary condition to make "in phase" light.  Otherwise, new phases would
> be continually created, so the laser would never settle down to one phase.

True, but look at it like this: the in-phase stimulated emission explains
why laser media are transparent.  It's like the Huygens wavelet
description that explains why glass is transparent.  The wavelets are
re-emitted in phase.  In-phase emission guarantees that the properties of
the stimulating wave are preserved, meaning that the lasing medium is
simply transparent.  If stimulated emission had random phase, I suppose
the laser medium would behave as an amplifying diffuser.  To create pure
plane waves, the guts of the laser would have to be transparent, but the
transparent property does not explain the origin of the near-perfect plane
waves (or sphere wave if mirrors are concave.)


> If I understand correctly, you are suggesting that the spatial (ie
> transverse) coherence of laser light is due to the multiple mirror
> bounces.

Yes.  Or another way to imagine it: remove the pair of plane mirrors and
replace the laser with an *extremely* long rod of pumped laser medium.  If
spontaneous emission begins at many places near one end of the rod, the
light will initially be as spatially incoherent as light from any
flourescent material.  But as it progresses, the wave train will act less
and less three-dimensional, with less and less individual sphere waves
which cross each other.  Waves from the various sources will superpose and
become more and more like a single train of plane waves.  If the laser
material has no discontinuities, then after the wave is a few
light-seconds distant from the initally incoherent emitters, the wave
train will have become a single perfect plane wave.  All the initial
individual waves will have summed at a distance, in the same way that
light from various points on a distant star sum at the earth to a
near-perfect plane wave with immense spatial coherence length.

All this happens even if the laser medium is removed.  The in-phase
emission has no bearing.  The laser medium simply amplifies the moving
wave.  Like a transparent attenuator but with negative attenuation.  Like
sunglasses which make the world brighter rather than dimmer.

If instead of a million-KM laser rod we use a pair of parallel mirrors to
form an "infinite tunnel" with a short laser rod then again a perfect
plane wave will be formed.  The mirrors preserve the "long rod" behavior
but fold the optics into a resonable size.  If we could look into the end
of a large-diameter laser having plane parallel mirrors, we should see an
"infinite tunnel" of repeated reflections, with an intensely bright
star-like point shining from the far end of the tunnel.

So, a possible K-6 explanation of a laser: a Laser is like one of those
"disco infinity" mirrors with the infinite tunnel effect, or like standing
between parallel mirrors at a science museum.  But instead of the tunnel
appearing darker and darker as it retreats into the depths, it looks
brighter and brighter because of amplification effect, and at the infinite
depth you see an intensely bright star, and the infinite tunnel emits
perfectly plane-wave light. 

> What is your explanation for the temporal coherence?

You got me on that one.  I've been satisfied with the explanation that
perfect monochromaticity equals high temporal coherence.  If the light had
poor temporal coherence, it would mean that there is a spread of
frequencies, or that the phase of the wave train has glitches every so
often.  A flourescent solid or cool gas should have a narrow spectral line
width.  Is this enough to explain the long temporal coherence length of
laser light?  If sodium light is passed through a *very* small pinhole, is
the temporal coherence length fairly long?

I recall being told that the temporal coherence of HeNe lasers varies
periodically along the beam, with the tube length determining the period.
A 20cm tube would give high coherence between beams with 0cm, 20cm, 40cm
pathlength difference, but the coherence would be terrible between beams
with 10cm, 30cm, etc. pathlength difference.  I don't have an explanation
for this.  Does it involve interference between the "comb" of frequencies
which resonate the spacing between the mirrors.  Oh, now I see what you
mean.  The line width of the flourescing atoms might be fairly broad,
leading to poor temporal coherence, but if the mirror spacing only allows
n, n+1, n+2, etc. wavelengths to resonate, then whichever wavelength falls
near the peak of the emission spectrum might take over all the metastable
atoms, and the laser's spectral line width would be incredibly narrow. 
And temporal coherence length would be long.  Hey, I didn't understand
that before.  I know I read about it, but it didn't connect at the time. 
So, if spatial coherence comes from mirror bouncing, then temporal
coherence comes from the length between mirrors.

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