Lasers

1
Lasers
Prof. Rick Trebino, Georgia Tech www.physics.gatec
h.edu/frog/lectures

• Stimulated Emission
• Gain
• Inversion
• The Laser
• Four-level System
• Threshold
• Some lasers

Light Amplification by Stimulated Emission of
Radiation
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Stimulated emission leads to a chain reaction and
laser emission.
If a medium has many excited molecules, one
photon can become many.
Excited medium
This is the essence of the laser. The factor by
which an input beam is amplified by a medium is
called the gain and is represented by G.
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The Laser
A laser is a medium that stores energy,
surrounded by two mirrors. A partially reflecting
output mirror lets some light out.
Usually, additional losses in intensity occur,
such as absorption, scat-tering, and reflections.
In general, the laser will lase if, in a round
trip Gain gt Loss
This called achieving Threshold.
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Calculating the gainEinstein A and B
coefficients

• In 1916, Einstein considered the various
  transition rates between molecular states (say, 1
  and 2) involving light of irradiance, I
• Absorption rate B N1 I
• Spontaneous emission rate A N2
• Stimulated emission rate B N2 I

where Ni is the number density of molecules in
the ith state, and I is the irradiance.
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Laser gain

• Neglecting spontaneous emission

Stimulated emission minus absorption
Proportionality constant is the absorption/gain
cross-section, s
The solution is
There can be exponential gain or loss in
irradiance. Normally, N2 lt N1, and there is
loss (absorption). But if N2 gt N1, theres
gain, and we define the gain, G
If N2 gt N1
If N2 lt N1
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Inversion

• In order to achieve G gt 1, stimulated emission
  must exceed absorption
• B N2 I gt B N1 I
• Or, equivalently,
• This condition is called inversion.
• It does not occur naturally. It is
• inherently a non-equilibrium state.
• In order to achieve inversion, we must hit the
  laser medium very hard in some way and choose our
  medium correctly.

N2 gt N1
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Achieving inversion Pumping the laser medium
Now let I be the intensity of (flash lamp) light
used to pump energy into the laser medium
Will this intensity be sufficient to achieve
inversion, N2 gt N1? Itll depend on the laser
mediums energy level system.
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Rate equations for a two-level system
Pump
Rate equations for the densities of the two
states
Stimulated emission
Spontaneous emission
Absorption
If the total number of molecules is N
Pump intensity
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Why inversion is impossible in a two-level system
In steady-state
where
Isat is the saturation intensity.
DN is always positive, no matter how high I is!
Its impossible to achieve an inversion in a
two-level system!
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Rate equations for a three-level system
Assume we pump to a state 3 that rapidly decays
to level 2. No pump stimulated emission!
Spontaneous emission
The total number of molecules is N
Level 3 decays fast and so is zero.
Absorption
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Why inversion is possible in a three-level system
In steady-state
Now if I gt Isat, DN is negative!
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Rate equations for a four-level system
Now assume the lower laser level 1 also rapidly
decays to a ground level 0.So ! And
As before
The total number of molecules is N
Because
At steady state
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Why inversion is easy in a four-level system
(contd)
Now, DN is negativealways!
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What about the saturation intensity?
A is the excited-state relaxation rate 1/t
B is the absorption cross-section, s, divided by
the energy per photon, hw s / hw
hw 10-19 J for visible/near IR light
Both s and t depend on the molecule, the
frequency, and the various states involved.
t 10-12 to 10-8 s for most molecules
10-9 to 10-3 s for laser molecules
s 10-20 to 10-16 cm2 for molecules (on
resonance)
1 to 1013 W/cm2
The saturation intensity plays a key role in
laser theory.
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Two-, three-, and four-level systems
It took laser physicists a while to realize that
four-level systems are best.
Four-level system
Three-level system
Two-level system
Fast decay
Fast decay
Laser Transition
Pump Transition
Fast decay
At best, you get equal populations. No lasing.
If you hit it hard, you get lasing.
Lasing is easy!
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Achieving Laser Threshold
An inversion isnt enough. The laser output and
additional losses in intensity due to absorption,
scattering, and reflections, occur.

I0
I1
Laser medium
I3
I2
Gain, G exp(gL), and Absorption, A exp(-aL)
R 100
R lt 100
The laser will lase if the beam increases in
intensity during a round trip, that is, if
This called achieving Threshold. It means I3 gt
I0. Here, it means
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Types of Lasers

• Solid-state lasers have lasing material
  distributed in a solid matrix (such as ruby or
  neodymiumyttrium-aluminum garnet "YAG"). Flash
  lamps are the most common power source. The
  NdYAG laser emits infrared light at 1.064 nm.
• Semiconductor lasers, sometimes called diode
  lasers, are pn junctions. Current is the pump
  source. Applications laser printers or CD
  players.
• Dye lasers use complex organic dyes, such as
  rhodamine 6G, in liquid solution or suspension as
  lasing media. They are tunable over a broad range
  of wavelengths.
• Gas lasers are pumped by current. Helium-Neon
  lases in the visible and IR. Argon lases in the
  visible and UV. CO2 lasers emit light in the
  far-infrared (10.6 mm), and are used for cutting
  hard materials.
• Excimer lasers (from the terms excited and
  dimers) use reactive gases, such as chlorine and
  fluorine, mixed with inert gases such as argon,
  krypton, or xenon. When electrically stimulated,
  a pseudo molecule (dimer) is produced. Excimers
  lase in the UV.

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The Ruby Laser
Invented in 1960 by Ted Maiman at Hughes Research
Labs, it was the first laser. Ruby is a
three-level system, so you have to hit it hard.
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The Helium-Neon Laser
Energetic electrons in a glow discharge collide
with and excite He atoms, which then collide with
and transfer the excitation to Ne atoms, an ideal
4-level system.
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Carbon Dioxide Laser
The CO2 laser operates analogously. N2 is
pumped, transferring the energy to CO2.
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CO2 laser in the Martian atmosphere
The atmosphere is thin and the sun is dim, but
the gain per molecule is high, and the pathlength
is long.
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The Helium Cadmium Laser
The population inversion scheme in HeCd is
similar to that in HeNes except that the active
medium is Cd ions. The laser transitions occur
in the blue and the ultraviolet at 442 nm, 354 nm
and 325 nm. The UV lines are useful for
applications that require short wavelength
lasers, such as high precision printing on
photosensitive materials. Examples include
lithography of electronic circuitry and
making master copies of compact disks.
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The Argon Ion Laser
Argon ion laser lines Wavelength Relative
Power Absolute Power 454.6 nm .03 .8 W
457.9 nm .06 1.5 W 465.8 nm .03 .8 W
472.7 nm .05 1.3 W 476.5 nm .12 3.0 W
488.0 nm .32 8.0 W 496.5 nm .12 3.0 W
501.7 nm .07 1.8 W 514.5 nm .40 10.0 W
528.7 nm .07 1.8 W
The Argon ion laser also has some laser lines in
the UV. But its very inefficient.
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The Krypton Ion Laser
Krypton ion laser lines Wavelength Power
406.7 nm .9 W 413.1 nm 1.8 W 415.4 nm .28
W 468.0 nm .5 W 476.2 nm .4 W 482.5 nm .4
W 520.8 nm .7 W 530.9 nm 1.5 W 568.2 nm 1.1
W 647.1 nm 3.5 W 676.4 nm 1.2 W
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Dye lasers
Dye lasers are an ideal four-level system, and a
given dye will lase over a range of 100 nm.
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A dyes energy levels

• The lower laser level can be almost any level in
  the S0 manifold.

S1 1st excited electronic state manifold
Laser Transitions
Pump Transition
S0 Ground electronic state manifold
Dyes are so ideal that its often difficult to
stop them from lasing in all directions!
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Dyes cover the visible, near-IR, and near-UV
ranges.
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Titanium Sapphire (TiSapphire)
TiSapphire lases from 700 nm to 1000 nm.
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Diode Lasers
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Some everyday applications of diode lasers
A CD burner
Laser Printer
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A laser in space
Triply ionized carbon at 1548.2 Å
Hubble Space Telescope image of unstable star Eta
Carinae, The double lobed structure is the
expanding stellar atmosphere. This bipolar
structure is similar to that of other laser
stars.
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Laser Safety Classifications
Class I - These lasers are not hazardous. Class
IA - A special designation that applies only to
lasers that are "not intended for viewing," such
as a supermarket laser scanner. The upper power
limit of Class IA is 4 mW. Class II - Low-power
visible lasers that emit above Class I levels but
at a radiant power not above 1 mW. The concept is
that the human aversion reaction to bright light
will protect a person. Class IIIA -
Intermediate-power lasers (cw 1-5 mW), which are
hazardous only for intrabeam viewing. Most
pen-like pointing lasers are in this class.
Class IIIB - Moderate-power lasers ( tens of
mW). Class IV - High-power lasers (cw 500 mW,
pulsed 10 J/cm2 or the diffuse reflection
limit), which are hazardous to view under any
condition (directly or diffusely scattered), and
are a potential fire hazard and a skin hazard.
Significant controls are required of Class IV
laser facilities.