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Re: A list of textbook miscon: spatial coherence




Hope you have time to READ this huge message, to say nothing of
responding. ;) I'm starting to stay up way too late recently.

On Fri, 13 Feb 1998, Bob Sciamanda wrote:

Hi Bill!
Perhaps there is our problem : temporal coherence cannot be ignored, it is
paramount! The radiation of the atoms from an ordinary "monochromatic"
source consists of truncated sine waves of finite length. The Fourier
transform of a truncated sine wave is a sinc function in frequency space,
with a non-zero line width which is inversely proportional to the duration
of the truncated sine segment in time.

I see the problem. I am stripping away most real-world phenomena and
discussing an "ideal" laser, an "undergraduate's mental laser." It is a
thought-experiment laser with characteristics chosen to emphasize one
particular phenomenon: the origin of the light's spatial coherence.
(transverse coherence, not "temporal" longitudinal coherence.)

I agree that stimulated emission and phase-locking is paramount. To
simplify my laser, I assume that all atoms emit very long wavetrains. I
assume that the wavetrains are so long that any phenomena associated with
finite wavetrain lengths and broadened line widths can be ignored. If the
sinc function obscures my view of the fundamental concepts, and if its
removal doesn't totally distort the picture, then I throw it away for now.
Linewidth is a temporal-coherence issue, and so I ignore it.

In these ordinary sources, spontaneous emission dominates and there is no
correlation among the start and stop phases of the truncated sine wave
emissions of the various atoms.

Yep. But also there is no special geometrical relationship between the
sphere waves emitted by the various atoms. If there were, then the
collection of atoms would be like a "phase-array antenna" and could send
out a parallel beam. Without a special phase relationship, the atoms'
light is like the light from incandescing gas or from an illuminated
diffuse reflector.

It is my understanding that the laser
process is dominated by stimulated emission, in which an incident wave is
"cloned" by synchronizing an already excited molecule to emit before its
time, and in phase with the incident (stimulating) wave.

Yes, but this ignores the coherent emission which goes on all the time in
any transparent medium. If atoms did not absorb photons and then emit
them coherently, then that medium would scatter light. I'm imagining the
stimulated emission process to fundamentally be an "enhanced transparancy"
phenomena. Yes, its not that simple. But start simple for k-12 level
then add other stuff later.

An example to help clarify things: imagine sunlight propagating through
glass. The atoms absorb and emit photons coherently, therefor the
propagating wave travels without scattering. Now replace the glass with
pumped laser crystal. Atoms still absorb and radiate photons coherently,
but every so often an atom will absorb one photon but radiate two. The
waves are still preserved as the would be with glass. The laser crystal
still acts "transparent", but the waves' amplitude grows as they
propagate. I imagine that objects viewed through a pumped laser crystal
will appear undistorted, but will be brighter. The laser crystal is like
a negative absorber, the opposite of sunglasses, it's "glass with gain".
It can be partially explained without QED just as lenses, prisms, and
tinted sunglasses can be partially explained without QED.

Spontaneous
emission is random in time (phase), there is no reference to which it might
be synchronized. The distinction is really a QED matter; I speak of the
effects in Maxwellian terms.

Other considerations which may be at issue:
In order for stimulated emission to dominate, one needs a population
inversion.

Yes. In my simplified model, I ignore all the finer points and simply
say "when the medium is pumped, it goes from 99% transmission to 101%
transmission per unit length." I don't want to get too reductionist and
miss the forest for the trees.

The mirrors provide the positive feedback which turns an
amplifier into an oscillator. The spatial wavefront pattern at right angles
to the propagation direction (spatial coherence) is a function of the
"waveguide modes" imposed by the mirror shapes.

Yes.

I think I'm visualizing things in a way that is non-traditional in laser
explanations, and this is causing miscommunication. Unless I can
understand lasers from ten different viewpoints, I don't really understand
them. I look for lots of alternate explanatory tacks. So...

What happens at onset of "lasing?" Imagine that you are 0.1mm tall and
looking into a pumped ruby crystal.

When the population inversion first occurs, the medium flouresces without
spatial coherence. Many atoms emit spontaneously, and these
un-phaselocked spherical wavefronts are amplified by stimulated emissions
from other atoms. Think in terms of amplification of waves, rather than
in
terms of increase in populations of coherent photons. You are 0.1mm tall.
To your eyes, the whole laser crystal glows bright red like an
incandescing filament. This collection of incoherent waves begins
reflecting in the cavity. The laser begins emitting "bright flourescence"
rather than laser light. It sends out a semi-monochromatic "white noise"
which to your eyes would appear to radiate from an extended source. But
then the light becomes progressively more and more spatially coherent.
Why? The initial "seed" was spatially incoherent light coming from the
entire volume of pumped laser crystal. Why did it end up spatially
coherent? Waveguide modes!

As you note, the stimulated emission needs an incident wave to "clone" in
order for acceptable laser light to be produced. But the indicent wave is
initially incoherent light from an extended source.

Why is my weird viewpoint important? Because I think it explains the
origin of the laser's ability to generate spatially coherent light. It
points to the fact that stimulated emission amplifies, but without
creating spatial coherence. Dump an initial blob of extended-source
flourescence into the resonator, and after a few million reflections the
spatial incoherence has vanished. This was accomplished by the resonator,
not by the stimulated emission.

Getting far away from a source will improve its use in a Young double slit
experiment (because you are asking only a tiny fraction of its immense
wavefront to be spatially coherent), but it will not improve its use in a
Michaelson interferometer - a measure of temporal coherence - related to the
duration of the separate (and randomly connected) wave trains [coherence
measured along the direction of propagation]. These phase discontinuities
do not "wash out" just by removing the source to a large distance away,
which is what I read you as saying.

Nope, for simplicity I had discarded the phase discontinuities right at
the start. I understand what you say. I was trying to communicate the same
thing as your first point: that getting far away from a source will
improve its coherence length measured transverse to propagation direction.
But I was making an additional point: feeding a light source into one end
of a very long transparent rod will cause it to become spatially coherent.
Only the light which propagates down the axis of the rod will make it to
the far end. (Or should I say that only certain waveguide modes are
supported when the rod is long.) If we optically fold our rod by using a
short rod with mirrored ends, the same thing occurs. The mirror-ended rod
is like an infinitely long rod with slightly absorbing sides. It acts to
"massage" any trapped light into having high spatial coherence.



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