Laser

The term “laser” is an acronym for (L)ight (A)mplification by
(S)timulated (E)mission of (R)adiation.
Lasers are devices that produce intense beams of light which
are monochromatic, coherent, and highly collimated. The wavelength
(color) of laser light is extremely pure (monochromatic) when compared
to other sources of light, and all of the photons (energy) that
make up the laser beam have a fixed phase relationship (coherence)
with respect to one another. Light from a laser typically has very
low divergence. It can travel over great distances or can be focused
to a very small spot with a brightness which exceeds that of the
sun. Because of these properties, lasers are used in a wide variety
of applications in all walks of life.



SPONTANEOUS AND STIMULATED EMISSION






In general, when an electron is in an excited energy state, it must
eventually decay to a lower level, giving off a photon of radiation.
This event is called “spontaneous emission,” and the photon is
emitted in a random direction and a random phase. The average time
it takes for the electron to decay is called the time constant for spontaneous
emission, and is represented by t.
On the other hand, if an electron is in energy state E2, and its
decay path is to E1, but, before it has a chance to spontaneously
decay, a photon happens to pass by whose energy is approximately
E24E1, there is a probability that the passing photon will cause the
electron to decay in such a manner that a photon is emitted at
exactly the same wavelength, in exactly the same direction, and
with exactly the same phase as the passing photon. This process is
called “stimulated emission.” Absorption, spontaneous emission,
and stimulated emission are illustrated in figure 36.2.
Now consider the group of atoms shown in figure 36.3: all begin
in exactly the same excited state, and most are effectively within
the stimulation range of a passing photon. We also will assume
that t is very long, and that the probability for stimulated emission
is 100 percent. The incoming (stimulating) photon interacts with the
first atom, causing stimulated emission of a coherent photon; these
two photons then interact with the next two atoms in line, and the
result is four coherent photons, on down the line. At the end of the
process, we will have eleven coherent photons, all with identical
phases and all traveling in the same direction. In other words, the
initial photon has been “amplified” by a factor of eleven. Note that
the energy to put these atoms in excited states is provided externally
by some energy source which is usually referred to as the
“pump” source.




Of course, in any real population of atoms, the probability
for stimulated emission is quite small. Furthermore, not all of the
atoms are usually in an excited state; in fact, the opposite is true.
Boltzmann’s principle, a fundamental law of thermodynamics,
states that, when a collection of atoms is at thermal equilibrium, the
relative population of any two energy levels is given by
where N2 and N1 are the populations of the upper and lower
energy states, respectively, T is the equilibrium temperature, and k
is Boltzmann’s constant. Substituting hn for E24E1 yields
For a normal population of atoms, there will always be more
atoms in the lower energy levels than in the upper ones. Since the
probability for an individual atom to absorb a photon is the same as
the probability for an excited atom to emit a photon via stimulated
emission, the collection of real atoms will be a net absorber, not a
net emitter, and amplification will not be possible. Consequently,
to make a laser, we have to create a “population inversion.”






POPULATION INVERSION
Atomic energy states are much more complex than indicated
by the description above. There are many more energy levels, and
each one has its own time constants for decay. The four-level energy
diagram shown in figure 36.4 is representative of some real lasers.
The electron is pumped (excited) into an upper level E4 by some
mechanism (for example, a collision with another atom or absorption
of high-energy radiation). It then decays to E3, then to E2, and
finally to the ground state E1. Let us assume that the time it takes
to decay from E2 to E1 is much longer than the time it takes to
decay from E2 to E1. In a large population of such atoms, at equilibrium
and with a continuous pumping process, a population inversion
will occur between the E3 and E2 energy states, and a photon
entering the population will be amplified coherently.