"I would also welcome somebody's explanations, even a semi
quantitative one. The matching of f is easy to justify on the basis of
conservation of energy. By why is polarization of "induced photons"
exactly the same as the polarization of the incoming wave? And why
do we have this perfect match of phases? It suggests that moments
of emission always correspond to an exactly well defined distance
between the incoming photon and the atom to be deexcited? I know
that the classical terminology of "exact moment and exact distance"
are not appropriate but I am using it to ask questions, not to answer
them."
Myself, I really liked William Beaty's answer: (You could say it really
resonated for me.)
"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."
William has addressed how a bunch of atoms can emit a directed beam. Let
me hazard a semiclassical explanation of how an individual atom
undergoes absorption and emission, especially stimulated emission.
(Disclaimer: I'm a chemist by training, if not by mindset, so my
language may have some terms from chemical applications of quantum
mechanics sprinkled in.)
Imagine a H atom in the 1s state. (Bad laser, but easy to visualize.)
Imagine vertically polarized light shining on it. The oscillating
electric field will polarize the electron cloud, alternately up and
down.(The magnetic field of the light has a much weaker effect, I'm
told.) As the "sloshing" gets stronger and stronger, a node develops,
and the the cloud starts to look like an asymmetric 2p orbital.
(chemists would call this an sp hybrid, with increasing amounts of p
character. s ---> sp --->sp2 ---> sp3--->p) Now the electric field acts
to even the lobes out. Finally, after much sloshing, the orbital is
fully 2p in character.
Under continued action of the light field, the process reverses, and the
the emission from 2p to 1s is stimulated, still with much sloshing.
As I recall, I originally saw this in a Scientific American article. It
was old when I saw it in 1983. Since then, I have programmed it into
MATHEMATICA. In the course of that effort, I came to answer to one of
the other natural questions involved: As I understand it, the number of
cycles it takes (amount of time) depends on the difference in frequency
between the light's frequency and the transition frequency. Poorer
frequency match means more "sloshing," and a longer time it takes to
make the hop.
The key that answers Ludwik's question (for me at least) is that the
light field causes "sloshing" that is required to be in phase with the
light, and in the same direction as the light's electric field. This is
true for all stimulated emission. From here, we can use William Beaty's
phase-array analogy to build up a laser.
My reasoning argues that the light must be polarized parallel to the
stimulating light, but does not guarantee that the light travel the same
direction. For that, maybe the best thing is William's wavelet
analysis:
". . .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. . . . "
Good luck.
--
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Dr. David W. Steyert steyert_dw@mercer.edu
Department of Chemistry (912)-752-4173
Mercer University
Macon, GA 31207
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