Re: LASERS

[William Beaty <billb@ESKIMO.COM>]

On Sat, 1 May 1999, Ludwik Kowalski wrote:

> It turns out that photons produced by stimulated emission travel in the
> same direction as those which trigger the decay. Furthermore, they are
> perfectly synchronized with the original photons.

I haven't yet encountered a detailed textbook explanation of the above
issues.  As a student I always wondered how the laser's atoms "know" to
send out photons in the same direction as the stimulating light.

After gaining some experience in visualizing QM phenomena, I see that if
we ignore the particle nature of light for a moment, and instead imagine
the lasing atoms to be an array of sphere-wave emitters operating in
phase-lock, then the directed emission of the laser photons can be
explained fairly easily.  (I suspect that some people see using the wave
nature of light to explain lasers as somewhat blasphemous.  Most textbooks
traditionally concentrate exclusively on the particle nature of light when
explaining laser concepts.  Yet light is not made of little flying
baseballs!)

If a single atom of the lasing medium emits a spherical EM wave, and the
"crests" of the wave are in phase with the stimulating planewave, then
this will create a 3D interference pattern, right?  And this pattern will
have a central node which has an axis parallel to the direction of the
stimulating wave.  As the planewave travels, the part of the wave that is
"downstream" from the lasing atom will be amplified because of the summing
of the two in-phase wavefronts.  No big mystery. (It helps to sit down
with a compass and some lined paper, and draw a bullseye pattern with the
circles drawn tangent to the parallel lines.  Then imagine that the
bullseye pattern is growing outwards as the parallel lines move along.)

However, the rest of the interference pattern will act to spread light in
non-parallel directions, as if the atom was scattering the incoming
planewave while amplifying it.  I found this to be confusing, but then I
remembered the "Huygens wavelet" explanation for the transparency of
glass: all of the circular wavelets tend to cancel out except in the
direction of the original wave.   In other words, *one* lasing atom will
emit light in other directions, but *millions* of lasing atoms, arranged
in a random array (or in an array with element spacing << wavelength),
should mutually cancel their off-axis emissions, leaving waves with a
single direction of emission which is parallel to the direction of the
stimulating wave.

A better way to imagine it: visualize that the incoming planewave
stimulates a large number of atoms to emit their light, then mentally
remove the planewave again.  What we have left is an example of a
phase-array emitter.  The stimulated laser atoms emit their waves with a
special constant phase relationship which generates a directed beam!  The
stimulating planewave simply acted as a "reference clock" which organized
the atoms to act as a "transmitter antenna" which emits a directional
beam.

So, this:

> It turns out that photons produced by stimulated emission travel in the
> same direction as those which trigger the decay. Furthermore, they are
> perfectly synchronized with the original photons.

...is a bit misleading, since it implies that individual photons are like
baseballs with positions and trajectories, and that atoms somehow know to
eject their photons so they travel in line with incoming photons.  From my
understanding of QM, this does not occur.  Instead, if we explain the
process of stimulated emission using waves, and then use the waves to
predict the distribution of photons, then we explain why the atoms SEEM to
send out photons with a trajectory parallel to the stimulating photons.

I realize that my explanation above is a bit too longwinded for Ludwik's
small handout.  Mostly this is my response to a little niggling issue that
caused me confusion as a student (and which in later years I never saw
discussed in any textbook.)  I suspect that I am probably not unique, and
others besides myself have wondered about this issue.

PS, if the stimulating light is seen as a WAVE rather than photons, then
we can explain why a photon can stimulate a *nearby* atom.  If light is a
space-filling wave, it jostles *all* the atoms in the laser by a small
amount, even if no photon strikes the stimulated atom.  If we keep in mind
both the hail-of-photons model of light and the space-filling-fields
model, some things become less confusing.

Or is the total quantity of confusion conserved, and we're just moving it
from laser explanations and saving it up for QM explanations?

:)


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