Basic Laser Principles

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.
the basic operating principles of the laser were put forth
by charles townes and arthur schalow from the bell telephone
laboratories in 1958, and the first actual laser, based on a pink
ruby crystal, was demonstrated in 1960 by theodor maiman at
hughes research laboratories. since that time, literally thousands
of lasers have been invented (including the edible “jello” laser), but
only a much smaller number have found practical applications in
scientific, industrial, commercial, and military applications. the
helium neon laser (the first continuous-wave laser), the semiconductor
diode laser, and air-cooled ion lasers have found broad oem
application. in recent years the use of diode-pumped solid-state
(dpss) lasers in oem applications has been growing rapidly.
the term “laser” is an acronym for (l)ight (a)mplification by
(s)timulated (e)mission of (r)adiation. to understand the laser, one
needs to understand the meaning of these terms. the term “light”
is generally accepted to be electromagnetic radiation ranging from
1 nm to 1000 mm in wavelength. the visible spectrum (what we see)
ranges from approximately 400 to 700 nm. the wavelength range
from 700 nm to 10 mm is considered the near infrared (nir), and
anything beyond that is the far infrared (fir). conversely, 200 to
400 nm is called ultraviolet (uv) below 200 nm is the deep ultraviolet
(duv).
to understand stimulated emission, we start with the bohr atom.
the bohr atom
in 1915, neils bohr proposed a model of the atom that explained
a wide variety of phenomena that were puzzling scientists in the
late 19th century. this simple model became the basis for the field
of quantum mechanics and, although not fully accurate by today’s
understanding, still is useful for demonstrating laser principles.
in bohr’s model, shown in figure 36.1, electrons orbit the nucleus
of an atom. unlike earlier “planetary” models, the bohr atom has
a limited number of fixed orbits that are available to the electrons.
under the right circumstances an electron can go from its ground
state (lowest-energy orbit) to a higher (excited) state, or it can decay
from a higher state to a lower state, but it cannot remain between
these states. the allowed energy states are called “quantum”
states and are referred to by the principal “quantum numbers” 1,
2, 3, etc. the quantum states are represented by an energy-level
diagram.
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introduction to laser technology
for an electron to jump to a higher quantum state, the atom
must receive energy from the outside world. this can happen through
a variety of mechanisms such as inelastic or semielastic collisions
with other atoms and absorption of energy in the form of electromagnetic
radiation (e.g., light). likewise, when an electron dropings
from a higher state to a lower state, the atom must give off energy,
either as kinetic activity (nonradiative transitions) or as electromagnetic
radiation (radiative transitions). for the remainder of
this discussion we will consider only radiative transitions.
photons and energy
in the 1600s and 1700s, early in the modern study of light, there
was a great controversy about light’s nature. some thought that
light was made up of particles, while others thought that it was
made up of waves. both concepts explained some of the behavior
of light, but not all. it was finally determined that light is made up
of particles called “photons” which exhibit both particle-like and
wave-like properties. each photon has an intrinsic energy determined
by the equation
where n is the frequency of the light and h is planck’s constant.
since, for a wave, the frequency and wavelength are related by the
equation
where l is the wavelength of the light and c is the speed of light in
a vacuum, equation 36.1 can be rewritten as
+
-
e1 e2 e3
15
10
5
0
energy (ev)
n = 1
n = 2
n = 3
ground state
1st excited state
ionized continuum
figure 36.1 the bohr atom and a simple energy-level
diagram
ln = c (36.2)
e
hc =
l
. (36.3)
e = hn (36.1)
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it is evident from this equation that the longer the wavelength
of the light, the lower the energy of the photon consequently, ultraviolet
light is much more “energetic” than infrared light.
returning to the bohr atom: for an atom to absorb light
(i.e., for the light energy to cause an electron to move from a lower
energy state en to a higher energy state em), the energy of a single
photon must equal, almost exactly, the energy difference between
the two states. too much energy or too little energy and the photon
will not be absorbed. consequently, the wavelength of that
photon must be
likewise, when an electron decays to a lower energy level in a
radiative transition, the photon of light given off by the atom must
also have an energy equal to the energy difference between the two
states.
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.
+
-
e1 e2 +
-
e1 e2
+
-
e1 e2 +
-
e1 e2
+
-
e1 e2 +
-
e1 e2
absorption
spontaneous emission
stimulated emission
figure 36.2 spontaneous and stimulated emission
l
d
d
=
= ?
hc
e
e e e
where
m n.
(36.4)
stimulated emission zone
stimulated emission zone
excited decayed via
spontaneous emission
decayed via
stimulated emission
time
figure 36.3 amplification by stimulated emission
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e1
e4
e3
e2
level populations
quantum energy levels
} population
inversion
laser
action
ground
energy level
pumping process
figure 36.4 a four-level laser pumping system
lasing medium
high
reflector
partial
reflector
resonator support structure
excitation
mechanism
figure 36.5 schematic diagram of a basic laser
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.
the resonator
although with a population inversion we have the ability to
amplify a signal via stimulated emission, the overall single-pass
gain is quite small, and most of the excited atoms in the population
emit spontaneously and do not contribute to the overall output. to
turn this system into a laser, we need a positive feedback mechanism
that will cause the majority of the atoms in the population to contribute
to the coherent output. this is the resonator, a system of
mirrors that reflects undesirable (off-axis) photons out of the system
and reflects the desirable (on-axis) photons back into the excited
population where they can continue to be amplified.
dn ? n ? n = ( ? e?hv kt )n
1 2 1
1 / . (36.6)
now consider the laser system shown in figure 36.5. the lasing
medium is pumped continuously to create a population inversion
at the lasing wavelength. as the excited atoms start to decay, they
emit photons spontaneously in all directions. some of the photons
travel along the axis of the lasing medium, but most of the photons
are directed out the sides. the photons traveling along the axis
n
n
e e
kt
2
1
2 1 = ?
? ?? ?
?? ?
exp (36.5)
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have an opportunity to stimulate atoms they encounter to emit
photons, but the ones radiating out the sides do not. furthermore,
the photons traveling parallel to the axis will be reflected back into
the lasing medium and given the opportunity to stimulate more
excited atoms. as the on-axis photons are reflected back and forth
interacting with more and more atoms, spontaneous emission
decreases, stimulated emission along the axis predominates, and
we have a laser.
practical optical coatings
in the design of a real-world laser, the optical resonator
is often the most critical component, and,
particularly for low-gain lasers, the most critical components
of the resonator are the mirrors themselves.
the difference between a perfect mirror coating
(the optimum transmission and reflection with no
scatter or absorption losses) and a real-world coating,
capable of being produced in volume, can mean a
50-percent (or greater) droping in output power from
the theoretical maximum. consider the 543-nm
green helium neon laser line. it was first observed in
the laboratory in 1970, but, owing to its extremely
low gain, the mirror fabrication and coating technology
of the day was incapable of producing a sufficiently
loss-free mirror that was also durable. not
until the late 1990s had the mirror coating technology
improved sufficiently that these lasers could be
offered commercially in large volumes.
the critical factors for a mirror, other than transmission
and reflection, are scatter, absorption, stress, surface
figure, and damage resistance. coatings with
low damage thresholds can degrade over time and
cause output power to droping significantly. coatings
with too much mechanical stress not only can cause
significant power loss, but can also induce stress birefringence,
which can result in altered polarization
and phase relationships. the optical designer must
take great care when selecting the materials for the
coating layers and the substrate to ensure that the
mechanical, optical, and environmental characteristics
are suitable for the application.
the equipment used for both substrate polishing and
optical coating is a critical factor in the end result.
coating scatter is a major contributor to power loss.
scatter arises primarily from imperfections and inclusions
in the coating, but also from minute imperfections
in the substrate. over the last few years, the
availability of “super-polished” mirror substrates has
led to significant gains in laser performance. likewise,
ion-beam sputtering and next-generation
ion-assisted ion deposition has increased the packing
density of laser coatings, thereby reducing absorption,
increasing damage thresholds, and enabling the
use of