Re: Can crystalline lasers be explained by recombination?

Greetings:

References:
Richard P. Feynman, Robert B. Leighton, Matthew Sands,
The Feynman Lectures on Physics, Volume 1, Chapter 42,
Applications of Kinetic Theory, Addison-Wesley,1977

Ben G. Streetman, Solid State Electronic Devices,
Prentice-Hall, New Jersey, 1980

Laser action does not happen when holes and electrons combine in semiconductor
lasers, that is what happens in light emitting diodes (LED) and is called
spontaneous emission. A laser uses stimulated emission which is based
on quantum mechanical principles and not thermodynamic equlibrium processes.
Below the threshold current a laser diode behaves like an LED emitting a broad
bandwidth of incoherent light by spontaneous emission. Above threshold,
stimulated emission occurs emitting light at one single frequency and suppresses,
but does not totally eliminate, spontaneous emission. Absorption
and spontaneous emission are based on thermal equlibrium. Stimulated emission
requires the concept of a negative temperature to be described thermodynamically
(See Streetman).

To answer your question I will paraphrase Professor Feynman's presentation
in words leaving out the complex mathematical formulas. The bolded text is
italicized by professor Feynman in the Lectures.

Planck's original idea was that matter was quantized but not the light
absorbed or emitted by matter: material oscillators cannot take up just any
energy, but have to take it in lumps emitting from matter. From this quantum
mechanical result there was a slow development which culminated in the
quantum mechanics of 1927. During that time Einstein made an attempt to convert
Planck's viewpoint to the idea that light was really photons and could be
considered in a certain way as particles and could also be quantized.

Einstein proposed that if such a quantized atom has light of the right
frequency shining on it, it can absorb a photon of light and make a transition
to a higher energy state and that the probability that this occurs per second
depends on two energy levels of the atom, but is proportional to how intense
the light is that is shining on it. The energy required for this is not a
constant but depends on the particular pair of energy levels: some levels are
easy to excite; some levels are hard to excite.

Now what about the rate of emission from the higher energy level to the
lower energy level. Einstein proposed that this must have two parts to it.
First, even if there were no light present, there would be some chance that
an atom in an excited state would fall to a lower state, emitting a photon;
this we call spontaneous emission. But then Einstein went further,
and by classical theory and other arguments, that emission was also influenced
by the presence of light - that when the light of the right frequency is shining
on the atom, it has an increased rate of emitting a photon that is proportional
to the intensity of the light.

Thus Einstein assumed that there are three kinds of processes: an
absorption proportional to the intensity of light, an emission proportional
to the intensity of light, called induced emission or sometimes
stimulated emission, and a spontaneous emission independent of
light.

Professor Feynman then shows that Einstein discovered that the induced
emission probability and the absorption probability must be equal. Einstein
did this work in 1916 and to actually compute the spontaneous emission rates or
other transition rates , requires a knowledge of quantum electrodynamics, which
was not discovered until eleven years later.

The possibility of induced emission has, today, found interesting
application. If there is light present, it will tend to induce the transition
downward. Now we can arrange, by some nonthermal method, to have a material with
a large energy in the upper level, while the number in the lower level is
practically zero. Then light which has the frequency corresponding to the energy
difference between the levels will not be strongly absorbed, because there are
not many atoms to absorb it. On the other hand, when light is present, it will
induce emission from the upper state! So, if we had a lot of atoms in the upper
state, there would be a sort of chain reaction, in which, the moment the atoms
begin to emit, more would be caused to emit, producing more light, and the whole
lot of them would dump down together. This is what is called a laser or maser.

Various tricks can be used to obtain the atoms in the upper energy level.
There may be even higher energy levels to which the atoms can get if we shine a
strong beam of light of high frequency. From these high levels, they may trickle
down, emitting various photons, until they get stuck into the desired upper
energy level. If they tend to stay there in the state without emitting, the
state is called metastable. And then they are all dumped down
together by induced emissions. One more technical point - if we put this system
in an ordinary box, it would radiate in many directions spontaneously,
compared with the induced emissions. But we can enhance the induced effect,
and increase its efficiency by putting nearly perfect mirrors on each side
of the box, so that the light which is emitted gets many chances to induce
emissions while reflecting back and forth from mirror to mirror. In the end
we have a nice uniform, strong beam of single frequency light, today's lasers.
End of Feynman paraphrase.

(My contribution) Luminous materials provide a good example of
metastability. After a flash of ultraviolet excitation, if the luminescent
decay occurs in less than a millisecond we call the material fluorescent
and often use it for lighting or homes, offices and schools. If the decay time
is greater than a millisecond, it is from a metastable level, and we call it
photoluminescence which can be visually observed from minutes to hours
after a short period of excitation. Thus the metastable level is a funnel that
can accumulate photons and slowly release them at a rate dependent on the
atomic structure. The metastable level can also be filled so that it can not
absorb any more photons until it drains by spontaneous emission. Cathode ray
tubes (CRT) use these types of material to store light images on the screen
with an "engineered" decay time that we call persistence. In a radar
display the screen is refreshed about once every 10 seconds as the antenna
rotates around the horizon. Thus we want the CRT to hold a target on the
display for 10 seconds until the display is refreshed and perhaps the target
has moved to another location.

During the early development of high energy gas lasers for airborne
applications (bullets of light) mirrors one meter in diameter were used
to form an optical cavity and induced emission occurred so quickly that
absorption could not refill the metastable levels quickly enough. We had
to provide an external path so that the depleted atoms would flow out of
the optical cavity and be replaced with excited atoms while the depleted
atoms were once again exited by absorption. The gas flow rate
required for these multi-kilowatt lasers became so great that a small jet
engine and supersonic gas flow became part laser pumping process.

Funnels at different heights above the ground are an interesting analogy
for quantized energy levels. Filling the funnels with a pump represents absorption.
The drain rate of each funnel represents spontaneous emission. Tipping a
funnel over and rapidly spilling some of the contents represents stimulated emission.
Thus we may have several funnels higher (greater energy) than our desired upper
laser energy funnel. These funnels drain by spontaneous emission into our
upper laser funnel hopefully keeping it full. Our lower laser level could be
the ground (the ground state) and we can easily tip the upper lever and
spill the water to the ground. to generate laser light. However; if there
is an even lower energy funnel required below our lower laser level funnel.
Our lower level must drain by spontaneous emission into the lower funnel
and or to the ground state. Laser development requires
matching the rates for filling and emptying energy levels so that we can get the maximum
tipping flow (stimulated emission) between the two funnels that repersent
our laser energy. This is not a simple task and often requires other materials
with various energy levels (funnels) to participate in the process.

Best regards, Your Mad Scientist
Adrian Popa