1. Lasers* Prof. Rick Trebino, Georgia Tech
Stimulated Emission
Gain
Inversion
The Laser
Four-level System
Threshold
Some lasers
Laser Transition
Pump Transition
Fast decay
* Light Amplification by Stimulated Emission of Radiation

2. 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.

3. Laser medium with gain, G
The Laser
A laser is a medium that stores energy, surrounded by two mirrors.
A partially reflecting output mirror lets some light out.
R = 100%
R < 100% I0 I1 I2 I3
Laser medium with gain, G
A laser will lase if the beam increases in intensity during a round trip:
that is, if
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 > Loss This called achieving Threshold.

4. Calculating the gain: Einstein A and B coefficients2 1
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.

5. Laser gain I(0) z L I(L) Neglecting spontaneous emission:
Laser medium
I(0) z L
I(L)
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 < N1, and there is loss (absorption).
But if N2 > N1, there’s gain, and we define the gain, G:
If N2 > N1:
If N2 < N1 :

6. Inversion Inversion N2 > N1
In order to achieve G > 1, stimulated emission must exceed absorption:
B N2 I > 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.
Energy
Inversion
Molecules
“Negative temperature”
N2 > N1

7. Achieving inversion: Pumping the laser medium
Now let I be the intensity of (flash lamp) light used to pump energy into the laser medium:
R = 100%
R < 100% I0 I1 I2 I3
Laser medium I
Will this intensity be sufficient to achieve inversion, N2 > N1?
It’ll depend on the laser medium’s energy level system.

8. Rate equations for a two-level system2 1 N2 N1
Laser
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

9. Why inversion is impossible in a two-level system2 1 N2 N1
Laser
In steady-state:
where:
Isat is the saturation intensity.
DN is always positive, no matter how high I is!
It’s impossible to achieve an inversion in a two-level system!

10. Rate equations for a three-level system
Fast decay
Laser Transition
Pump Transition 1 2 3
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

11. Why inversion is possible in a three-level system
Fast decay
Laser Transition
Pump Transition 1 2 3
In steady-state:
Now if I > Isat, DN is negative!

12. Rate equations for a four-level system
Laser Transition
Pump Transition
Fast decay 1 2 3
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:

13. Why inversion is easy in a four-level system (cont’d)
Laser Transition
Pump Transition
Fast decay 1 2 3
Why inversion is easy in a four-level system (cont’d)
Now, DN is negative—always!

14. What about the saturation intensity?
Laser Transition
Pump Transition
Fast decay 1 2 3
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, ħw: s / ħw
ħw ~10-19 J for visible/near IR light
Both s and t depend on the molecule, the frequency, and the various states involved.
t ~ to 10-8 s for most molecules to 10-3 s for laser molecules
s ~ to cm2 for molecules (on resonance)
1 to 1013 W/cm2
The saturation intensity plays a key role in laser theory.

15. Two-, three-, and four-level systems
It took laser physicists a while to realize that four-level systems are best.
Two-level system
Three-level system
Four-level system
Laser Transition
Pump Transition
Fast decay
Laser Transition
Pump Transition
Fast decay
Pump Transition
Laser Transition
Fast decay
At best, you get equal populations. No lasing.
If you hit it hard, you get lasing.
Lasing is easy!

16. Achieving Laser Threshold
An inversion isn’t 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 < 100%
The laser will lase if the beam increases in intensity during a round trip, that is, if:
Gain > Loss
This called achieving Threshold. It means: I3 > I0. Here, it means:

17. Types of Lasers
Solid-state lasers have lasing material distributed in a solid matrix (such as ruby or neodymium:yttrium-aluminum garnet "YAG"). Flash lamps are the most common power source. The Nd:YAG laser emits infrared light at 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.
Slide provided by Optics I student Kham Ho, 2004

18. 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.

19. 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.

20. Carbon Dioxide Laser
The CO2 laser operates analogously. N2 is pumped, transferring the energy to CO2.
Vibrational energy level diagram depicting the 10.6 micron infrared transition in the carbon dioxide molecule. (The nitrogen vibrational levels shown on the right are used to enhance lasing in laboratory lasers)
Image from

21. CO2 laser in the Martian atmosphere
Detuning from line center (MHz)
The small red circle centered on Chryse Planitia represents the region over which the laser emissions were detected. Solar radiation is responsible for pumping a population inversion in the carbon dioxide of the tenuous upper levels of the atmosphere of Mars (Mumma et al., 1981) and Venus (Deming et al., 1983). Population inversions have also been found in comets (Mumma, 1993). On mars, the solar pump intensity is strongest near the solar point, and falls off gradually towards the terminator. There is some locus where the inversion vanishes, but it is difficult to say exactly where that is. The R(8) transition at microns in the infrared is produced from one vibrational quanta of asymmetric stretching to one quantum of symmetric stretching with a change of one quantum of rotational energy from J=8 to J=7. (mars image courtesy : Philip James, University of Toledo; Steven Lee, University of Colorado; and NASA Hubble Space Telescope)
Due to the low densities of the lasing species in the mesosphere and thermosphere of Mars the gain is very low, about 10 percent, comparable to single-pass gains in some earth based CO2 lasers. The low gain is partly compensated by the extremely large volumes of active lasing medium. Over the very long distances scales, the exponential properties of amplified spontaneous emission produce a significant spectral signature at the lasing frequency. The laser amplification has been confirmed by several groups (Gordiets et al., Stepanova et al. and Dickinson et al.)
Spectra of martian CO2 emission line as a function of frequency difference from line center (in MHz). Blue profile is the total emergent intensity in the absence of laser emission. Red profile is gaussian fit to laser emission line. Radiation is from a 1.7 arc second beam (half-power width) centered on Chryse Planitia (long +41 lat +23). (Mumma et al., 1981)
Image from
The atmosphere is thin and the sun is dim, but the gain per molecule is high, and the pathlength is long.

22. The Helium Cadmium Laser
The population inversion scheme in HeCd is similar to that in HeNe’s 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.
Text from

23. The Argon Ion Laser Argon ion laser lines:
Wavelength Relative Power Absolute Power
454.6 nm W
457.9 nm W
465.8 nm W
472.7 nm W
476.5 nm W
488.0 nm W
496.5 nm W
501.7 nm W
514.5 nm W
528.7 nm W
Population inversion is achieved in a two step process. First of all, the electrons in the tube collide
with argon atoms and ionize them according to the scheme:
Ar (ground state) + lots of energetic electrons
Þ Ar+ (ground state) + (lots + 1) less energetic electrons .
The Ar+ ground state has a long lifetime and some of the Ar+ ions are able to collide with more
electrons before recombining with slow electrons. This puts them into the excited states according to:
Ar+ (ground state) + high energy electrons Þ Ar+ (excited state) + lower energy electrons .
Since there are six 4p levels as compared to only two 4s levels, the statistics of the collisional process
leaves three times as many electrons in the 4p level than in the 4s level. Hence we have population
inversion. Moreover, cascade transitions from higher excited states also facilitates the population
inversion mechanism. The lifetime of the 4p level is 10 ns, which compares to the 1 ns lifetime of the
4s level. Hence we satisfy tupper > tlower and lasing is possible.
Table from
Energy level diagram from
The Argon ion laser also has some laser lines in the UV.
But it’s very inefficient.

24. The Krypton Ion Laser Krypton ion laser lines: Wavelength Power
406.7 nm .9 W
413.1 nm 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

25. Dye lasers
Duarte and Piper, Appl. Opt. 23,
Dye lasers are an ideal four-level system, and a given dye will lase over a range of ~100 nm.

26. A dye’s energy levels
The lower laser level can be almost any level in the S0 manifold.
S1: 1st excited
electronic state manifold
Pump Transition
Laser Transitions
S0: Ground
electronic state manifold
Dyes are so ideal that it’s often difficult to stop them from lasing in all directions!

27. Dyes cover the visible, near-IR, and near-UV ranges.

28. Titanium: Sapphire (Ti:Sapphire)
Absorption and emission spectra of Ti:Sapphire
Upper level lifetime:
3.2 msec
oxygen
aluminum
Al2O3 lattice
Slide used with permission from Dan Mittleman
Ti:Sapphire lases from ~700 nm to ~1000 nm.

29. Diode Lasers

30. Some everyday applications of diode lasers
Slide provided by Optics I student Kham Ho, 2004
A CD burner
Laser Printer