Download Laser and its applications

II Laser operation
In this section, we discuss how do the laser elements
(pump, medium and resonator) work?
Consider the following figures;
In the above figure ( 3 )
Step (1)
An energy from an appropriate pump is coupled
into the laser medium. The energy is sufficiently high to
excite a large number of atoms from the ground state Eo
to
several
excited
states
E 3.
Then
the
atoms
spontaneously decay and back to the ground state Eo.
But some of them back by a very fast (radiationless)
decay from E3 to a very special level E2.
Step (2)
The level E2 labeled as the “upper laser level ,”has a
long lifetime. Whereas most excited levels in atom decay
with lifetime of order 10-8 sec. Level E2 is metastable,
with a typical lifetime of order of 10-3 sec. So that the
atoms being to pile up at this metastable level (E2),
which functions as a bottleneck. N2 grows to a large
value, because level E2 decays slowly to level E1 which
labeled by “ lower laser level ” and level E1 decays to
the round state rapidly, so that N1 cannot build to a
large value. The net effect is the population inversion
(N2>N1) between the laser levels E1 and E2.
Step (3)
When the population inversion has been established, a
photon of resonant energy (h=E2-E1) passes by one of
the N2 atoms, stimulated emission can be occurred.
Then, laser amplification begins. Note carefully that a
photon of resonant energy (E2-E1) can also stimulate
absorption from E1 to E2. Then the light amplification
occurs and there is a steady increase in the incident
resonant photon population and lasing continues.
Step )4)
One of the inverted N2 atoms, which dropped to level E1
during the stimulated emission process, now decays
rapidly to the ground state Eo. If the pump is still
operating the atoms is ready to repeat the cycle, there by
insuring a steady population inversion and constant laser
beam output.
Figure (3) shows the same action of figure (2.(
In (a) the laser medium is situated between the
resonator (two mirrors) in which most of the atoms are
in the ground state (black dots).
In (b) An external energy (pumping) raising most of
the atoms to the excited levels (as E3). The excited
states are shown by circles. During this pumping
process, the population inversion is established.
In (c) the light amplification process is initiated, in
which many of the photons leave through the sides of
the laser cavity and are lost. Since the remainder (seed
photons) are directed along the optical axis of the
laser.
In (d) and (e) As the seed photons pass by the
inverted N2 atoms, stimulated emission adds identical
photons in the same direction, providing an ever –
increasing population of coherent photons that bounce
bake and forth between the mirrors.
In (f) A fraction of the photons incident on the mirror
(2) pass out through it. These photons constitute the
external laser beam.
Characteristic of Laser Light
Monochromaticity. The light emitted by a laser is
almost pure in color, almost of a single wavelength or
frequency. Although we know that no light can be truly
monochromatic, with unlimited sharpness in wavelength
definition, laser light comes far closer than any other
available source in meeting this ideal limit.
The monochromaticity of light is determined by the
fundamental emission process where atoms in excited
states decay to lower energy states and emit light. In
blackbody radiation, the emission process involves
billions of atoms and many sets of energy-level pairs
within each atom. The resultant radiation is hardly
monochromatic, as we know.
If we could select an identical set of atoms from this
blackbody and isolate the emission determined by a
single pair of energy levels, the resultant radiation,
would be decidedly more monochromatic. When such
radiation is produced by non-thermal excitation, the
radiation is often called fluorescence. Figure 1 shows
such
Figure (1) fluorescence and its spectral content for a
radiative decay process between two energy levels in
an atom. (a) Spontaneous decay process between welldefined
energy
levels.
(b)
Spectral
content
of
fluorescence in (a), showing line shape and linewidth.
an emission process. The fluorescence comes from
the radiative decay of atoms between two well-defined
energy levels E2 and E1. The nature of the fluorescence,
analyzed by a spectrophotometer, is shown in the
lineshape plot, a graph of spectral radiant existence
( W m 2 ) versus wavelength.
Note carefully that the emitted light has a wavelength
spread  about a center wavelength 0 , where
0 = c/0 and 0 = (E2 - E1)/h . While most of the light may
be emitted at a wavelength 0 , it is an experimental fact
that some light is also emitted at wavelengths above
and below 0 , with different relative existence, as
shown by the lineshape plot. Thus the emission is not
monochromatic, it has a wavelength spread given by
0  /2 , where  is often referred to the linewidth.
When the linewidth is measured at the half maximum
level of the lineshape plot, it is called the FWHM
linewidth, that is, “ full width at half maximum “
In the laser process, the linewidth  shown in figure
(1) is narrowed considerably, leading to light of a much
higher degree of monochromaticity. Basically this occurs
because the process of stimulated emission effectively
narrows the band of wavelengths emitted during
spontaneous emission. This narrowing of the linewidth is
shown qualitatively in figure (2). To gain a quantitative
appreciation for the monochromaticity of laser light,
consider the data in table (1), in which the linewidth of a
high quality He-Ne laser is compared to the linewidth of
the spectral output of a typical sodium discharge lamp
and to the linewidth of the very narrow cadmium red line
found in the spectral emission of a low-pressure lamp.
The conversion from  to  is made by using the
approximate relationship.
 = c
2o
where V0=C.
The data of table (1) show that the He-Ne laser is 10
million times more monochromatic than the ordinary
discharge lamp and about 100,000 times more so than
the cadmium red line. No ordinary light source, without
significant
filtering,
can
approach
the
degree
of
monochromaticity present in the output beam of typical
lasers.
Figure (2) Qualitative comparison of linewidths for laser
emission and spontaneous emission involving the same pair
of energy levels in an atom. The broad peak is the line shape
of spontaneously emitted light between levels E2 and E1
before lasing being. The sharp peak is the line shape of laser
light between levels E2 and E1 after lasing beings.
Table (1) comparison of linewidths
Light source
Center
Wavelength
0 ( A0 )
FWHM
Linewidth
0 ( A0 )
FWHM
linewidth
(HZ)
Ordinary discharge
lamp
5896
1
9X1010
Cadmium lowpressure lamp
6438
Helium-neon laser
6328
0.013 9.4X108
10-7
7.5X103
Coherence. The optical property of light that most
distinguishes the laser from other light source is coherence.
The laser is regarded, quit correctly as the first truly
coherent light source. Other light source, such as the sun or
a gas discharge lamp, are at best only partially coherent.
Coherence, simple stated, is a measure of the degree of
phase correlation that exists in the radiation field of a light
source at different location and different times. It is often
described in terms of temporal coherence, which is a measure
of the degree of monochromaticity of the light, and a spatial
coherence, which is a measure of the uniformity of phase
across the optical wavefront.
To obtain a qualitative understanding of temporal and
spatial coherence, consider the simple analogy of water
waves created at the center of a quite pond by a regular,
periodic disturbance. The source of disturbance might
be a cork bobbing up and down in regular fashion,
creating a regular progression of outwardly moving
crests and troughs, as in figure (3). Such a water wave
filed can be side to have perfect temporal and spatial
coherence. The temporal coherence is perfect because
there is but a single wavelength; the crest–to-crest
distance remains constant.
As long as the cork keeps bobbing regularly, the
wavelength will remain fixed, and one can predict with
great accuracy the location of all crests and troughs
on the pond's surface. The spatial coherence of the
wave filed is also perfect because the cork is a small
source, generating ideal waves, circular crests, and
troughs of ideal regularity. Along each wave then, the
spatial variation of the relative phase of the water
motion is zero that is the surface of the water all along
a crest or trough is in step or in one phase.
Perfect temporal coherence
Perfect spatia
coherence
uniformity of phase
phase difference time
independent (temporal
coherence
Figure (3) portion of a perfectly coherent water wave field
created by a regularly bobbing cork at S. the wave field
contains perfectly ordered wave fronts, C (crests) and T
(troughs), representing water waves of a single wavelength
Spatial coherence
Temporal coherence
The water wave field described above can be
rendered temporally and spatially incoherent by the
simple process of replacing the single cork with a
hundred corks and causing each cork to bob up and
down with a different and randomly varying periodic
motion. There would then be little correlation between
the behavior of the water surface at one position and
another. The wave fronts would be highly irregular
geometrical curves, changing shape haphazardly as the
collection
of
corks
disconnected motions.
continued
their
jumbled,
It does not require much imagination to
move conceptually from a collection of corks
that give rise to water waves to a collection of
excited
atoms
that
give
rise
to
light.
Disconnected, uncorrelated creation of water
waves results in an incoherent water wave
field. Disconnected, uncorrelated creation of
light waves results, similarly, in an incoherent
field.
To emit light of high coherence then, the radiating region
of a source must be small in extent (in the limit, of course. a
single atoms) and emit light of a narrow bandwidth (in the
limited, with equal to zero). For real light sources, neither
of these conditions is attainable. Real light sources, with the
exception of the laser, emit light via the uncorrelated action
of many atoms, involving many different wave lengths. The
result is the generation of incoherent light.
To achieve some measure of coherence with a non-laser
source, two notifications to the emitted light can be made.
First, a pinhole can be placed in front of the light source to
limit the spatial extent of the source. Second, a narrow-band
filter can be used to decrease significantly the linewidth  of
the light. Each modification improves the coherence of the
light given off by the source-but only at the expense of a
drastic loss of light energy.
In contrast, a laser source, by the very nature of its
production of amplified light via stimulated emission,
ensures both a narrow-band output and high degree of
phase correlation. Recall that in the process of
stimulated
emission,
each
photon
added
to
the
stimulated radiation has a phase, polarization, energy,
and direction identical to that of the amplified light wave
in the laser cavity. The laser light thus created and
emitted is both temporally and spatially coherent. In fact,
one can describe or model a real laser device as a very
powerful, fictitious “point source” located at a distance,
giving off monochromatic light in a narrow cone angle.
Figure 4 summarizes the basic ideas of coherence for
non-laser and laser source.
For typical laser, both the spatial coherence and
temporal coherence of laser light are far superior to
that for light from other sources. The transverse spatial
coherence of a single mode laser beam extends across
the full width of the beam, whatever that might be. The
temporal coherence, also called “longitudinal spatial
coherence,” is many orders of magnitude above that of
any ordinary light source. The coherence time tc of a
laser is a measure of the average time interval over
which one can continue to predict the correct phase of
the laser beam at a given point in space. The coherence
length Lc, is related to the coherence time by the
equationLc =ctc where c is the speed of light.
Thus the coherence length is the average length of
light beam along which the phase of the wave
remains unchanged. For the He-Ne laser described in
table 1 the coherence time is of the order of
milliseconds (compared with about 10-11s for light
from a sodium discharge lamp), and the coherence
length for the same laser is thousands of kilometers
(compared with fractions of a centimeter for the
sodium lamp).
Improve spatial coherence
Improve temporal coherence
Figure 4. A tungsten lamp requires a pinhole and filter
to produce coherent light. The light from a laser is
naturally coherent. (a) Tungsten lamp. The Tungsten
lamp is an extended source that emits many wavelength.
The
emission
lacks
both
temporal
and
spatial
coherence. The wave front are irregular and change
shape in a haphazard manner. (b) Tungsten lamp with
pinhole. An ideal pinhole limits the extent of the
tungsten source and improve the spatial coherence of
the light. However the light still lacks temporal
coherence since all wavelengths are present. Power in
the beam has been decreased.
(c) Tungsten lamp pinhole and filter. Adding
a good narrow –band filter further reduces the
power but improves the temporal coherence.
Now the light is "coherent" but the available
power that initially radiated by the lamp. (d)
Laser. Light coming from the laser has a high
degree of spatial and temporal coherence. In
addition, the output power can be very high.
Directionality .When one sees thin, pencil-like beam of
a He-Ne laser for the first time, one is struck
immediately by the high degree of beam directionality.
No other light source, with or without the help of
lenses or mirrors, generates, a beam of such precise
definition and minimum angular spread .
The astonishing degree of directionality of a laser
beam is due to the geometrical design of the laser
cavity and to the monochromatic and coherent
nature of light generate in the cavity. Figure (5)
shows a specific cavity design and an external
laser beam with an angular spread signified by the
angel  .
The cavity mirrors shown are shaped with surfaces
concave toward the cavity, thereby “focusing” the
reflecting light back into the cavity and forming a beam
waist at one position in the cavity.
Figure 5. external and internal laser beam for a given cavity. Diffraction
or beam spread, measured by the beam divergence angle , appears
to be caused by an effective aperture of diameter D, located at the
beam waist.
The nature of the beam inside the laser cavity and its
characteristics outside the cavity are determined by solving
the rather complicated problem of eectromagnetic waves in
an open cavity. Although the details of this analysis beyond
the scope of this discussion, several results are worth
examining. It turns out that the beam- spread angel  is
giving by the relationship
1.27
 =
D
(1)
Where  is the wavelength of the laser beam and D is the
diameter of the laser beam at its beam waist. One cannot
help but observe that Eq. (1) is quite similar to that
obtained when calculating the angular spread in light
generated by the diffraction of plane waves passing
thought a circular aperture .
The pattern consists of a central, bright circular
spot, the Airy disk, surrounded by a series of bright
rings. The essence of this phenomenon is shown in
figure (6). The diffraction angle , tracking the Airy
disk, is given by
2.44
=
D
(2)
Figure (6). Fraunhofer diffraction of plane waves through a circular
aperture. Beam divergence angle is set by the edges of the Airy
disk.
where

is
the
wavelength
of
the
collimated.
Monochromatic light and D is the diameter of the circular
aperture. Both Eqs. (1) and (2) depend on the ratio of a
wavelength to a diameter. They differ only by a constant
coefficient. It is tempting, then, to think of the angular
spread  inherent in laser beams and given in Eq. (1) in
terms of diffraction.
If we treat the beam waist as an effectives circular
aperture located inside the laser cavity, then by
controlling the size of the beam waist we control the
diffraction or beam spread of the laser. The beam waist,
in practice, is determined by the design of the laser
cavity and depends on the radii of curvature of the two
mirrors and the distance between the mirror.
Therefore, one ought to be able to build lasers with a given
beam waist and, consequently, a given beam divergence or
beam spread in the far field, that is, at sufficiently great
distance L from the diffracting aperture that L >> area
aperture/. Such is indeed the case.
With the help of Eq. (1), one can now develop a feel
for
the
low
beam
spread,
or
high
degree
of
directionality, of laser beams. He-Ne lasers (632.8 nm)
have an internal beam waist of diameter near 0.5 mm.
Equation (1) then yields
1.27 (1.27)(632.8  10-9 m)
-3
-6
=
=
=
1
.
6

10
radian
=
2

10
sr
-4
D
(5  10 m)
This is a typical laser-beam divergence, indicating that
the beam width will increase about 1.6 cm every 1000cm.
Since we can control the beam waist D by laser cavity
design and “select” the wavelength by choosing
different laser media, what lower limit might we expect
for the beam divergence? How directional can lasers
be? If we design a laser with a beam waist of 0.5 cm
diameter and a wavelength of 200 nm, the beam
divergence angle  becomes about radian,. This beam
would spread about 1.6cm every 320m.
Clearly, if beam waist size is at our command and
lasers can be built with wavelength below
the
ultraviolet, there is no limit to how parallel and
directional the laser beam can be made.
The high degree of directionality of the laser, or any
other light source, depends on the monochromaticity
and coherence of the light generated. Ordinary sources
are neither monochromatic nor coherent. Lasers, on
the other hand, are superior on both counts, and as a
consequence
generate
collimated light beams.
highly
directional,
quasi-
Laser Source Intensity. It has been that a 1-mW HeNe laser is hundreds of times “brighter” than the sun.
As difficult as this may be to imagine, calculations for
luminance or visual brightness of a typical laser,
compared to the sun, substantiate these claims. To
develop an appreciation for the enormous difference
between the radiance of lasers and thermal sources we
consider a comparison of their photon output rates
(photons per second).
Small gas lasers typically have power outputs P of
1mW. Neodymium-glass lasers, such as those under
development for the production of laser-induced
fusion, boast of power outputs near 1014 W!. Using
these two extremes and an average energy of 10-19 J
per visible photon (E=h), the photon output of laser
(P/h) varies from 1016 photons/s to 1033 photons/s. For
comparison, consider a broadband thermal source
with a radiating surface equal to that of the beam waist
of a 1-mW He-Ne laser with diameter of 0.5 mm, an
area of A=2X103 cm2.
Let the surface emit radiation at a wavelength of 633
nm with a linewidth of =100nm (or=7x1013HZ) and
temperature T=1000K. The photon output rat for the
broadband source can be calculated from the equation
1
1
thermal photons / s = 2 h / KT
A = 109 photon / sec
 e
-1
(3)
Substituting the values given above into Eq. (3), we
find that the thermal photon output rat is only about 109
photons/s! This value is 7 orders of magnitude smaller
than the photon output rat of low-power 1-mW He-Ne
laser and 24 orders of magnitude smaller than a powerful
neodymium-glass laser. The comparison is summarized
in figure 7.
Figure (7). Comparison of photon output rates between a low-power
He-Ne gas laser and a hot thermal source of the same radiating
surface area. (a) 1-mW He-Ne laser (=633nm), A=2x10-3cm2,
o=633nm  =100nm. Note that the laser emits all of the photons in a
small solid angle (2x10-6 sr) compared with the 2 solid of the
thermal source.
We see also from figure 7 that the He-Ne laser emits 1016
photons/s into a very small solid angle of about
2X10-6sr.
whereas the thermal emitter, acting as a Lambertian source,
radiates 109 photons/s into a forward, hemispherical solid
angel of 2 sr. If we were to ask how many thermal
photons/second are emitted by the thermal source into a solid
angel equal to that of the laser, we would find the answer to be
320 photons/s:


-6

 2  10 sr 
2  10 sr 
9
9
 = 320 photons / s
 = 10  
(10 photons / s )
22
2

sr
 2 


sr 


7
-6
The comparison between 1016 photons/s for the laser
source and 320 photons/s for the thermal source is now
even more dramatic.
Types of lasers
Gas Lasers
Gas lasers are the workhorses of the laser industry.
They range from the powerful industrial carbon dioxide
units to the ubiquitous helium-neon lasers of modest
powers. They can be operated continuously or on a
pulsed basis: their output frequencies range from the
ultraviolet to the infrared. Depending on the nature of the
active medium, three types of gas lasers can be
distinguished: atomic, ionic, and molecular.
Although several different excitation mechanisms
have been employed for pumping them, most gas
lasers are excited by means of an electric discharge.
Electrons in the discharge are accelerated by the
electric filed between a pair of electrodes. As the
electrons collide with the atoms, ions, or molecules of
the active medium, they induce transition to higher
energy states. With sufficient pumping, a population
inversion is created.
Atomic Lasers
The principal example of a laser that utilizes a transition
between energy levels of non ionized atoms is the helium-neon
laser. The lasing medium is a mixture of ten parts helium to one
part neon. Only the energy levels of the neon atom are directly
involved in the laser transition: the helium gas is present to
provide an efficient excitation mechanism for the neon atoms.
Most helium-neon lasers are excited by a direct-current (de)
discharge, created by placing a high voltage across a gas-filled
space (see figure 1). The helium atoms are easily excited by
electron impact to any one of several low-lying metastable
energy states.
Figure(1): Simple components of He-Ne gas laser. Micrometer
adjusting screws for making the mirror planes highly parallel are
not shown.
The neon atom, having six more electrons than the
helium atom, has an extremely complicated distribution
of excited states. Tow of its higher energy states have
almost exactly the same energy as two of the metastable
helium states. With the energy much so close, a
collision between a helium atom and a neon atom can
result in the efficient transfer of energy from the
metastable helium atom to the unexcited neon atom. The
helium atom returns to its ground state upon-excitation
of the neon atom into its excited state. A collision that
results in this type of energy transfer is called a
resonant collision. A diagram of the energy states for
helium and neon is shown in fig. 2.
The helium excited states are identified by
combinations of latter and numbers. 21S and 23S,
which specify the total angular momentum and spin
of the tow electrons in the excited atom. The neon
excited states are identified by the quantum numbers
of the single excited state electron. (The other nine
electrons in the neon atom retain their ground-state
quantum numbers. ) As noted earlier.
Figure (2): Energy –level diagram of
helium-neon laser system
These numbers determine the probability of a given
transition. For example, a quantum mechanical
calculation shoes that the transitions between the
neon s states (e.g.,5s

4s) are forbidden . The
helium atoms are excited to metastable levels 21S and
23S by direct electron impact. The helium atoms then
collide with the unexcited neon atoms and the neon
atoms are raised to the 5s and 4s states. These states
have longer lifetimes than the lower-energy 4p and 3p
states. Thus the 5s and 4s states are pumped by the
metastable helium atoms, while the 4p and 3p states
are depleted because of their short lifetimes.
An inversion of the population between the s and p
states results, and amplification by stimulated emission
occurs.
The
population
inversion
is
increased
substantially if the excited neon atoms are allowed to
collide with the walls of the chamber confining the
discharge. The collisions allow non-radiative transitions*
to take place between the 3s and ground states of the
neon, atom : these transitions prevent
*A transition in which deexcitation is not accompanied by
an emission of radiation is said to be nonradiative. The
stored
energy
is
given
up
by the
atom
to
its
surroundings as thermal motion: or in the case of a
molecule, the energy may be converted to molecular
vibrations.
a buildup of neon atoms in the lower excited states and
a subsequent reduction in the population inversion. It is
because of this particular depopu lation mechanism that
one cannot increase the output power of a He-Ne laser by
increasing the tube cross section. The reason is that any
increase in the radius of the bore, the cylindrical region to
which the discharge is confined, beyond a certain value
reduces the population inversion and thus the overall
gain of the laser.
There are many more laser transitions in the He-Ne laser
than we have shown in Fig. 2. Each of the energy states of
neon shown as bars in the diagram) is split into several
sublevels. Each sublevel can serve as the initial or terminal
level for several different laser transitions, producing the 130plus stimulated emission lines that have been observed in
neon. All of the lasing lines can be produced in a discharge
of pure neon. However, the output of many lines is greatly
increased by the resonant collision pumping described.
Both the 633nm and the 3.39 m transitions start with
the same upper energy state (5s). The 3.39 m (infrared)
transition has a much higher gain than the 633nm
(visible red) transition and can deplete the 5s level,
reducing or eliminating completely the visible output of
the laser. Several techniques can be employed to
discriminate against the 3.39 m transition and to
encourage the 633nm transition:
1- In the method most commonly employed, the laser
mirrors are designed to be highly reflective at 633nm
but highly transmissive at 3.39 m. The round-trip gain
at the visible wave transition can then be satisfactorily
high, while at the same time the gain for the infrared
transition never reaches threshold.
2- Another technique consists of placing small magnets
along the length of the laser tube, thereby creating an
inhomogeneous magnetic field. The magnetic field
produces a splitting (Zeeman splitting) of certain spectral
lines in several components. It is possible to show that the
gain per unit length at the lasing transition is inversely
proportional to the linewidth. The zeeman splitting
broadens the infrared 3.39  m laser line more than the
visible line, decreasing its gain, so that the visible
transition is favored.
Molecular lasers
From the standpoint of potential industrial
applications, the carbon dioxide laser unquestionably
ranks first. The CO2 laser offers both high power and
high efficiency at an infrared wavelength. Carbon
dioxide lasers have been used to weld metals, cut
ceramics, and perform many other materialsprocessing tasks. The CO2 laser is the most important
example of the class of lasers referred to as molecular
lasers. Thus far in our discussion, the energy levels of
interest for laser transitions have been electronic
energy levels of an atom or an ion. Molecules have a
more complicated structure and have energy levels
that correspond to rotating-or vibrating motions of the
entire molecular structure.
The carbon dioxide molecule, composed of two
oxygen atoms and a carbon atom between them,
undergoes
three
different
types
of
vibrational
oscillation, as shown in fig. 3 These three fundamental
vibrational configurations are called vibrational modes
(not to be confused with the modes of the laser cavity).
According to quantum theory, the energy of oscillation
of a molecule in any one mode can have only discrete
values, just as the energy of an electron in an atom is
quantized. The discrete values are all integer multiples
of some fundamental value. At any one time, a carbon
dioxide
molecule
can
be
vibrating
in
combination of the three fundamental modes.
a
linear
The energy state of the molecule can then be
represented by three numbers (ijk). These numbers
represent the amount of energy, or number of energy
quanta, associated with each mode. For example, the
number ( 002) next to the highest energy level shown in
fig. 4 means that a molecule in this energy state is in the
pure asymmetric stretch mode with two units of energy
(i.e. no units of energy associated with the symmetric
stretch or bending mode). In addition to vibrational
states, rotational states, associated with rotation of the
molecule about the center of mass, are also possible.
The energies associated with the rotational states are
generally small compared to those of the vibrational
states, and are observed as splittings of the vibrational
levels into a number of much finer sublevels. The
separations between vibrational - rotational states are
usually much smaller on the energy scale than
separations between electronic states.
Figure (3): Vibrational modes of CO2 molecule
Figure (4): Energy-level diagram for the CO2 laser.
Pumping occurs to the higher energy levels (not draw to
scale). Bands shown contain numerous discrete rotational
levels.
The radiation associated with the energy difference
between electronic transitions is usually visible or
ultraviolet, whereas the vibrational-rotational transitions
are in the near and far infrared. For this reason, most
molecular lasers have infrared outputs.
The various low-lying energy levels of the CO2
molecule that are responsible for the laser transitions
are shown in Fig. 4. Each group of lines represents a
different vibrational energy levels: each individual line
represents a different rotational energy level.
In the CO2 laser, molecules are pumped from the
ground state to higher energy states (out of the
diagram) from which they trickle back by radiative and
nonradiative processes to state (001), which is
metastable. With sufficient pumping, a population
inversion is produced between the (001) state and the
(100) and (020) states. If the losses in the laser cavity
are sufficiently low, laser oscillations begin. The
strongest line of the CO2 laser is at a wavelength of
10.6  m, in the infrared. A weaker line at 9.6m
competes with the 10.6 m line for the available
excited molecules.
For improved laser output, nitrogen and helium are
generally added to the gas mixture (approximately 10
percent CO2, 40 percent N2, and 50 percent He). The
nitrogen in the CO2 discharge takes the role that helium
plays in the helium-neon and metal vapor lasers:
excited nitrogen molecules transfer energy to the CO2
molecules by resonant collisions. The helium serves to
increase the laser efficiency by speeding up the
transition from the (100) energy level, the receiving end
of the 10.6 μm laser transition, to the ground level,
thereby maintaining a large population inversion.
Carbon dioxide lasers are capable of producing
tremendous amounts of output power. Primarily
because of the high efficiency of the 10.6 μm
transition. A well- constructed system can achieve an
efficiency of about 30 percent, as compared to less
than 0.02 percent for helium- neon laser. Gigawatts of
peak power have been obtained in short nanosecondduration pulses.
The principal difference between the CO2 laser and
other gas lasers we have discussed is that the optics
must be coated or made of special materials so that
they are reflective or transmissive in the infrared.
If the cavity has external mirrors, the plasma tube
usually has Brewster-angle windows fabricated from
germanium, cadmium sulfide, or, in the case of high
power systems, from sodium chloride or potassium
bromide. These materials are transparent at 10.6 μm, a
region where most other materials, including glass, are
opaque. The optical resonator itself is provided with a
pair of long radius-of-curvature mirrors, with multilayer
dielectric reflective coating. The output mirror can be
made of germanium or gallium arsenide, both of which
if cooled have low loss at 10.6 μm.
The power supply for CO2 laser must provide a
sufficiently high voltage to maintain a discharge with
cavity pressure of 10 mm of mercury or more. This
voltage, which is about 8 KV per meter of discharge,
constitutes a major hazard if not carefully shielded.
The power output of a CO2 laser is approximately
proportional to the active length of the laser. In attempts
to obtain greater output power, researchers have built
CO2 lasers tens of meters long with CW output powers
ranging to the tens of kilowatts.
Figure (5): Carbon dioxide laser with water cooling jacket,
Brewster's window, and rotating mirror for pulsing the output
laser beam.
Chemical Lasers
The lasers studied in this chapter are classified
primarily on the basis of the state of the active medium
(gas, solid, liquid, semiconductor). The term chemical
laser refers not to the state of the lasing medium, but
to the method of creating a population inversion. In the
chemical laser, the excitation is produced by at
chemical reaction. Although the chemicals can be in
the solid, liquid, or gaseous state, most chemical
lasers use gases as the active medium, with an
arrangement similar to the gas dynamic CO2 laser just
discussed.
Chemical lasers are attractive from several
viewpoints:
1- A purely chemical laser, relying on the direct mixing of
hemicals to produce coherent light, does not require
electronic components or electrical power.
2- Chemical lasers have the potential for higher output
power per unit volume and per unit weight than appears
possible with electrical excitation.
3- Because the chemical reactions employed excite
primarily vibrational states rather than electronic states,
most chemical lasers have output power in the near
infrared, with wavelengths between the neodymium laser
at
 = 1.06mand the carbon dioxide laser at.
4 - Chemical lasers have produced some of the most
powerful laser pulses ever observed. Pulses as large as
4200 joules with a peak power of 200 billion (2× 1011)
watts have been achieved by a hydrogen fluoride
chemical laser.
Most of the chemical reactions used in chemical lasers are
of the form
A+BC AB +C +energy
(1)
The energy released by the reaction servers to excite the
molecule AB, which servers as the active medium. One
reaction that has been investigated extensively is the
reaction of a halogen with hydrogen or deuterium. e.g.
H+CL2HCL+CL +energy
(2)
F+D2DF+D +energy
(3)
and
In general, chemical reactions can be employed
successfully in laser systems using several approaches:
1- Chemical reactions can directly produce the radiant
energy from the reacting species. with the addition of no
external energy.
2- Chemical reactions can result in light emission from the
reacting species, but external energy may be necessary
to initiate or sustain the reaction.
3- External energy can be provided to initiate or sustain a
chemical reacting that results in the transfer or energy
from the reaction species to another species that radiates.
The chemical reaction can provide all the energy, as in
type(1),but energy is transferred from one reacting species to
another species that emits radiation.
Lasers using the latter two approaches, in which the
reaction species do not actually participate in the lasing
action, are called chemical transfer lasers. The reactions
represented by Eqs.(2) are examples of approach (2).
Although the chemical reactions produce HCl or DF (the
active lasing medium) in the excited state, the dissociation
of the hydrogen or fluorine atoms form their initial
molecular states (H2 or F2) must be accomplished with an
additional energy source, a flash-lamp in the case of
reaction (2) or a thermal source in the case of reaction (3).
Another example of approach (2) is the carbon monoxide
chemical laser, which emits relatively high power in the
infrared. A mixture of helium, air and cyanogen (C2N2) has
used to obtain several watts of power in the wavelength range
between 5 and 6 mm. In this laser, the gas is flowed through
an electric discharge. The helium does not participate in the
lasing, but provides resonant transfer of energy, as in the
helium-neon laser. The discharge dissociate the (C2N2)
molecules and the O2 molecules to form vibrationally excited
CO via the reaction
C2 N 2  O2  2CO  N 2  127 kcal
(4(
The Ruby Laser
The first successful laser, developed by Maiman in
1960, used a single crystal of synthetic pink ruby as its
resonating cavity. The ruby is primarily a transparent
crystal of corundum (AL2O3) doped with approximately
0.05 percent of trivalent chromium ions in the form of
Cr2O3, the latter providing its pink color. The aluminum
and oxygen atoms of the corundum are inert; the
chromium ions are the active ingredients.
As grown in the laboratory, a ruby crystal is
cylindrical in shape (see Fig 5). It is cut some 10 cm or
so long and the ends polished flat and parallel. In a
typical ruby laser one end is highly reflective (about 96
percent), and the other end is close to half-silvered
(about 50 percent).
When white light enters a crystal, strong absorption by the
chromium ions Cr2O3 in the blue-green part of the spectrum
occurs (see Fig. 6). light from an intense source surrounding
the crystal will therefore raise many electrons to a wide band
of levels as shown by the “up” arrow at the left. These
electrons quickly drop back, many returning to the ground
level. However, some of the electrons drop down to the
intermediate levels, not by the emission of photons, but by
the conversion of the vibrational energy of the atoms
forming the crystal lattice. Once in the intermediate levels
the electrons remain there for several milliseconds (about
10,000 times longer than in most excited states), and
randomly jump back to the ground level, emitting visible red
light. This fluorescent radiation enhances the pink or red
color of the ruby and gives it its brilliance.
Figure (5): Ruby laser using a helical flash lamp for optical pumping
Fig 6. Energy level diagram for a ruby crystal
Fig. 7 Elliptical r for Concentrating light from a source S on a laser L.
Axial Modes of a Laser
The optical cavity of a laser is a resonator with extremely
high Q (see box) and low losses. If these losses are smaller
than the gain in the amplifying medium, threshold is
achieved and lasing occurs. But the high-Q condition does
not hold for all frequencies within the laser emission line
width:
only
certain
frequencies
fulfill
the
resonance
conditions, similar to the transmission conditions of the
Fabry-Perot interferometer. Thus the laser output spectrum
does not resemble the spontaneous emission lineshape, but
rather consists of a series of a narrower lines corresponding
to the high-Q frequencies of the laser cavity.
To determine the conditions for high Q in a laser, we
start with a plane wave of light propagating along a line
normal to and between two parallel mirrors. The roundtrip distance for a wave undergoing reflection at the
mirror is 2L, twice the distance between mirrors. The
total phase change, , undergone by the wave in
traveling a full round trip is equal to 2 times the
distance traveled divided by the wavelength
2L 4L
 = 2 
=


If the reflected wave is 180 out of phase with the original
wave and of equal magnitude, then within the cavity there is
no net field and therefore no net energy density to stimulate
the atoms to emit, even if a suitable population inversion
exists. The most useful way of viewing such a situation is to
note that the wave has not replicated itself upon reflection.
Only at such a frequency that the wave and its reflections
are in phase (  =2q, q an integer) does the wave replicate
itself. With replication, the electric fields add in phase. The
resultant energy density is sufficient to induce substantial
stimulated emission at that frequency.
From an alternative point of view, the mirrors from a
resonant cavity in which light energy may be stored by
multiple reflections between them. If the waves are
replicated in the cavity, then the mirror cavity has a high
Q. The condition for a self-repeating field (setting =2q
in Eq. 1) is that the length of the cavity be equal to an
integral number of half-
Q-the quality factor
Fundamental to discussion of any resonator is the concept
of the Q-or quality factor, of the resonator, defined by
2  energy stored
Q=
energy dissipated per cycle
This definition of Q is a very general one applies to
circuits, mechanical systems, microwave cavities, and
laser cavities. A typical oscillating circuit, such as one
containing a resistor, capacitor, and inductor, can have a Q
of several hundred; a laser cavity can have a Q as high as
105 or 106.
A high-Q cavity stores energy well, whereas a low-Q
cavity does not. In addition, we note that a high Q is
associated with a small relative linewidth, and a low Q
with a large relative linewidth. This relationship between
Q and linewidth can be expressed rather simply as
resonant frequency

Q=
=
linewidth

wavelengths, or L=q(/2), q an integer. Only at those
wavelengths is the cavity resonant. The integer q is in
most cases quit large. For example, if the central
wavelength is 500 nm (5X10-5cm) and the mirror
separation is 25 cm, q has a value of 106.
Since q can be any integer, there are many possible
wavelengths within the laser transition lineshape for
which the field is self-replicating. We refer to each such
self-replicating field pattern as a longitudinal mode, or
axial mode, of the cavity. It is easier to refer to these
axial modes by their frequency than by their wavelength.
Using the condition for the self-replicating field stated
above. We have
=
Each
c
c
 c 
=
= q

2
L

 2L 
q
mode
frequency
(2)
can
be
labeled
corresponding integer, q, with the result
with
its
 c 
 q = q

 2L 
(3)
It is at these frequencies that the laser cavity is resonant.
By subtracting the frequency of one cavity mode from
that of its nearest neighbor, we find that the separation
between mode frequencies is
 =  q  1
c
c
-  q = (q  1)
-q
2L
2L
or
c
 =
2L
(4)
The separation between longitudinal mode frequencies
is seen to be the same as the free spectral range of a
Fabry-Perot interferometer with plate separation L . Note
that the separation between neighboring modes is
dependent only on the separation between mirrors and is
independent of q. If we use values from our example
above, the separation between neighboring resonance
frequencies for a typical laser (25 cm long) is calculated
to be
3  1010 cm / sec
 =
= 6  10 8 sec -1 = 600MHz
3  25 cm
(5)
Many laser transition lines much broader than 600 MHz,
and thus there can be many axial modes (…q-2, q-1, q,
q+1, q+2…) within the broadened linewidth. Since
sustained
laser
action
can
occur
only
at
those
frequencies within the lasing transition for which the
cavity is resonant, the output of a laser contains a
number of discrete frequencies, separated by c/(2L), as
shown in Fig. 1. These frequencies are called the axial
mode frequencies of the laser.
Figure (1): The combination of the lasing transition lineshape with the
resonant cavity modes gives the resulting output of a laser. Only when
the Q of the cavity is high can lasing occur.
Examining the Mode Structure of a Laser
The longitudinal mode structure of a laser output can be
investigated with a Fabry-Perot interferometer. The
experimental arrangement is shown in Fig. 2. You may
know that there are many frequencies, spaced c/2d apart,
transmitted by the interferometer when its plates are
spaced a distance d apart. To block all extraneous light
at frequencies other than in a narrow region about the
laser line, we insert a narrowband filter between the laser
and the interferometer. The spacing of the plates is then
adjusted so that the free spectral range of the
interferometer exceeds the linewidth of the laser.
The transmitted light is focused by a lens onto a
screen, where a pattern of concentric circles can be
seen. A pinhole in the screen is positioned at the center
of the pattern: light of one frequency passes the screen
whereas other frequencies are blocked. As the spacing
of the mirrors is changed, the frequency illuminating the
pinhole changes. If d is changed in a continuous
manner, the frequency passed by the pinhole is swept
through the range of frequencies, which includes those
of the laser line. A photomultiplier detector measures
the amount of light transmitted at the different
frequencies.
An increase in signal occurs whenever the FabryPerot
resonance
scans
through
a
frequency
component of the laser output. The output of the
detector is plotted as a function of time, the observed
result is a series of lines within the broadened
transition lineshape, as sketched in Fig. 1. Each of
these lines corresponds to a different axial mode, or
q-value, of the laser. Knowing the interferometer
scanning rate, one can verify that the frequency
separation  between these modes is c/2L, where L is
the distance between laser mirrors, in agreement with
the analysis above.
Fig. 2 Experimental arrangement for observing the longitudinal (or
axial) mode characteristics of a laser. Light from the laser is filtered to
remove all but the laser light. The separation between the FabryPerot interferometer mirrors is changed by applying a sawtooth
voltage to a piezoelectric transducer (PET) attached to one of the
mirrors. The change in separation d changes the transmission
frequency of the interferometer. The transmitted light is focused onto
a pinhole in a screen and detected by a photomultiplier tube (PMT).
The output of the PMT is displayed on an oscilloscope. The
oscilloscope trace displays the frequency spectrum of the laser.
Modifying the Laser Output
Selection of laser emission lines: interacavity
elements
Many lasers can lase in several emission lines
simultaneously. Here we are speaking not of the
multiple-mode structure beneath a single broadened
emission line, but of several of these lines spaced
across the spectrum. While this multiple-line emission
may provide high-power output, there are cases where a
higher degree of monochromaticity is desired. In these
cases,
a
wavelength-dependent
element,
which
disperses or absorbs the light according to its colors, is
introduced into the cavity. This element can be a prism,
a grating, or a filter.
The action of these elements can be demonstrated by the
example of an intra-cavity prism. The arrangement is shown in
fig.3. We assume that three wavelength 1,2 and 3, are
undergoing amplification by stimulated emission, with 1< 2< 3 .
The shorter wavelengths suffer greater refraction by the prism
than the longer wavelengths. One beam, at 2 , is directed
normally to the end mirror and then retraces its path back into
the laser tube. Rays at other wavelengths do not retrace their
paths exactly and, consequently, experience additional loss.
Only for light in a small wavelength rang about 2 are the losses
smaller than the available gain. By using a properly cut prism,
the angles of incidence can be set at the Brewster angles,
reducing the losses due to reflection at the prism surface.
Figure (3): Intra-cavity prism for wavelength selection. The
prism disperses the light so that only one ray, at 2, is
reflected back into the active medium, and lasing occurs
only at the selected wavelength.
SINGLE-MODE OPERATION
The linewidth of a single laser mode is far smaller than
the broadened transition linewidth: in some cases
smaller than the linewidth due to the natural lifetime of
the excited state. Since an inhomogeneously broadened
laser can support many longitudinal-transverse modes
simultaneously. Single-mode output can be achieved
only by assuring that one mode has a gain higher than
all the others. There are several methods for obtaining
single-mode output, two of which we discuss here:
1) Let us ensure that the cavity supports only a single
transverse
mode,
the
TEM00
mode,
by
placing
apertures in the laser cavity as we discussed earlier.
Once this single transverse mode has been obtained,
the problem is to eliminate all but one of the axial
modes.
One
way to
achieve
single
axial-mode
operation is to design the cavity so that only one axial
mode is possible within the laser transition line-width.
If the mode corresponding to q0 is within the transition
linewidth and those corresponding to q0+1 and q0-1 are
outside it, as shown in fig.4. then only the TEM00q0
mode will lase.
For this to occur, the distance between cavity modes,c/2L.
must be somewhat greater than the broadened linewidth.
Since we cannot control the width of the lasing line., we
must construct the cavity in
figure (4): The "short cavity" method of single-moding a laser. If
the length of the laser cavity is reduced to a length that yielding a
cavity – mode separation somewhat greater than the line width,
only one cavity mode can lase.
such a manner that c/2L is larger than the laser
linewidth.If we make the distance between mirrors
sufficiently small so that only one mode is supported,
we produce a single mode laser. The drawback of this
method is that the active length of the laser is also
small, severally limiting the power output.
2) Another method for obtaining increased single axialmode output from a TEM00 laser is to introduce large
losses for all but one of the modes. This can be done
by introducing a small fixed-spacing Fabry-Perot
cavity within the laser cavity, as illustrated in fig. 5.
The additional cavity consist of a special piece of
glass, called an etalon, that has two faces ground and
polished to a high degree of parallelism. The etalons
cavity differs from the laser cavity in two important
respects.
First, the etalon surfaces are either uncoated or lightly
coated, and their reflectivity is thus quite low. Because of
this low reflectivity, the etalon cavity resonances are
broader than the laser cavity resonances.
Second, the etalon cavity is much shorter than the laser
cavity, and the separations between etalon resonant
frequencies are therefore much larger than those between
the laser resonant frequencies.
The etalon, in effect, makes slats in the picket fence
unequal: Some cavity resonances have a higher loss than
others. The laser tends to lase in that single mode with the
smallest loss. This single-mode selection is illustrated in
fig. 6. As much as 75 percent of the power distributed over
all the axial modes present before the etalon is inserted
can appear in this single mode in a typical laser. If the
etalon is tilted with respect to the optic axis, the frequency
of the etalon resonance shifts within the lasing transition
linewidth. A different laser cavity mode becomes the highQ mode, and lasing occurs at the corresponding new
frequency. It is thus possible to “tune” the frequency of
the laser over a narrow frequency band by merely tilting
the etalon.
Figure (5): The "etalon" method of single –modeing a laser.
Introduction of a piece of glass with parallel face (the etalon) into
the cavity renders the Q of the cavity modes unequal. Only the
highest Q mode lasers
There are more complicated methods of obtaining
single-mode output for inhomogeneously broadened
laser transitions. Those we have discussed give some
idea, however, of how a single laser mode is obtained
and emphasize the importance of understanding the
concept of laser modes.
Figure (6): The "etalon" method of single –modeing a laser. The
box on the right illustrates the Q versus frequency for the laser
cavity and or the etalon cavity. Their combined Q versus
frequency is shown in the middle curve. The combination of the
lasing transition and single high-Q mode results in a single-mode
laser output.
Applications of Laser
I- Laser in Industry
I.1- LASER WELDING
In the basic welding process two metals (which may be
the same or dissimilar) are placed in contact and the
region round the contact heated until the materials melt
and fuse together. Enough heat must be supplied to cause
melting of a sufficient volume of material but not enough
to give rise to significant amounts of vaporization,
otherwise weak porous welds are produced. With most
metals the reflectance decreases dramatically as the
temperature approaches the melting point (see Fig.1) so
that care needs to be taken in controlling the amount of
incident laser energy.
It is also evident that the problems associated with
vaporization will increase if the two materials have widely
differing melting points.
Laser welding has to compete with many well-established
techniques such as soldering, arc welding, resistance
welding and electron beam welding. Laser welding has,
however, a number of advantages, for example:
(1) there is no physical contact with external components;
(2) the heating is very localized
(3) dissimilar metals can be welded;
(4) welding can be carried out in a controlled atmosphere
with the workpiece sealed if necessary within optically
transparent materials.
Fig. 1. Schematic variation of absorption with temperate for a
typical metal surface for both YAG and CO2 laser wavelengths.
Welding is normally carried out using a shielding gas.
This is an inert gas, usually argon or helium, which is
applied to the welding area via a nozzle concentrically
placed with respect to the laser beam (Fig. 2). The main
purpose of the shielding gas is to cover the weld area and
eliminate oxidation, which results in a poor weld. It also
helps to remove any metal vapor that may be formed (and
that may deposit on the focusing lens). If metal vapor is
produced it may be hot enough for ionization to take
place and thus form a plasma above the metal surface.
This is often highly absorbent at the laser wavelength
and can prevent some, or in extreme cases all, of the
laser energy reaching
Fig.2 Schematic beam focusing head design for laser
welding when using a shielding gas.
the surface. For medium- to low-power lasers argon is
often used as the shield gas, as it is less expensive than
helium but can itself ionize in the presence of highpower pulsed beams. In such cases helium or a mixture
of helium and argon may be used.
Both CW and pulsed lasers can be used in welding.
For situations where only a small spot weld is required
a single pulse from a pulsed laser may be sufficient. If
a continuous weld is required, however, the beam is
moved across the workpiece. The CW laser produces
a continuous weld, while the pulsed laser produces a
train of spot welds, which may overlap (and hence
produce effectively a continuous weld) or be
separated, depending on the scanning speed. Figure 3
shows how weld penetration depends on beam
scanning speed at various power levels in 304-type
stainless steel. The actual joint geometry itself can
exert a strong influence on the thickness of material
that can be welded. Close-fitting joints are desirable
since there is usually little time for the molten metal to
flow to any extent.
In any case only small amounts of liquid are present,
mainly because the heating is usually very local.
Figure 4 shows some typical joint designs suitable
for laser welding.
welding speed (mms-1)
Fig. (3) Typical variation of weld penetration with welding speed
observed in stainless steel for various CO2 laser powers.
Fig.(4) Two geometries suitable for laser welding
(a) the butt join; (b) the lap join.
I.1.1 Deep penetrating welding
When using a multikilowatt CW or pulsed-mode laser
the
welding
process
becomes
somewhat
more
complicated than just the simple diffusion of heat
away from the surface considered hitherto. When a
high-power beam initially strikes the surface a
significant amount of material may be vaporized,
forming
 Direction of travel (workpiece)
Fig. (5) Formation of a ‘keyhole’ during high-power laser welding.
a small hole known as a keyhole. Laser energy that
subsequently enters the hole is trapped and carried
deeper into the material than would otherwise be the
case. Figure 5 illustrates this process when a CW laser is
being used. Pulsed CO2 lasers can also make efficient
use of this process by employing a pulse consisting of a
very high-power initial spike of duration about 100ms
followed by a much lower irradiance for the remainder of
the pulse (Fig.6). Such a pulse shape can be obtained by
controlling the discharge current in the laser. The peak
power during the spike is sufficient to create the initial
keyhole but during the rest of the pulse there is
insufficient power to cause further vaporization.
The material round the keyhole melts, however, and fills
in the hole. Since the absorption of energy within the
keyhole is not very dependent on the condition and type
of metal surface this type of action enables materials
with high melting points to be welded.
CO2 lasers are now available with CW powers of
tens of hundreds of kilowatts and consequently it is
possible to weld steel plates of up to several tens of
millimeters thick at rates of some meters/minute. It has
thus become possible to contemplate the use of laser
welding
in
shipbuilding.
heavy industrial
situations
such
as
Fig(6). idealized laser pulse shape for efficient keyhole welding