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.