1. Lasers* * Light Amplification by Stimulated Emission of Radiation
Laser Transition
Pump Transition
Fast decay
* Light Amplification by Stimulated Emission of Radiation

2. The Ruby Laser
1960
1965

4. THE LARGEST LASER IN THE WORLD
National Ignition Facility
192 beams,
4 MJ per pulse

5. SINGLE ATOM LASER
"Experimental realization of a one-atom laser in the regime of strong coupling," J. McKeever, A. Boca, A. D. Boozer, J. R. Buck and H. J. Kimble, Nature 425, 268 (2003).

6. NANOLASERS The first room temperature UV nanowire lasers
Zinc oxide wires on a sapphire substrate self organized nano-wire forest
Pumped by 266 nm beamed at a slight angle laser wavelength 385 nm
P. Yang, UC Berkeley 2001

7. Courtesy A. Siegman

9. Charles Townes (and Mrs Townes) - 2006

10. Interaction of light with excited media
Excited media? Matter which has energy in excited energy levels
Process of excitations
Eexcited
De-excitation
Emission
Excitation
Absorption Eg
Energy levels
Assumptions - quantized energy levels - electronic, vibrational rotational
Limitations – Optical processes only

11. Emission and Absorption – Basic ideas
excited state
temporary state
Restrict ourselves to two level system N2 E1 E2
E2 – E1 = hn = hc/l N1
ground state
rest state
Number of atoms (or molecules) / unit volume
N = number density N = N1 + N2
N1,2 = population of levels 1 & 2
Three basic processes E1 E2 E1 E2 E1 E2
Spontaneous
Emission
Stimulated
Emission
Absorption

12. Spontaneous emission N 2 E2
Probability that the process occurs can be defined by
Rate of decay of the upper state population
rate of spontaneous decay (units = 1/ time) Einstein A Coefficient
= spontaneous emission lifetime ( radiative lifetime)
Note:
Rate of spontaneous decay defined for a specific transition

13. Absorption and Stimulated Emission
We can write the rate of change of population E1 E2
Stimulated
Emission N2 N1
However, now the rate of stimulated emission
is dependent on the intensity of the EM wave
Photon flux
(number of photons/ unit area/unit time)
stimulated emission
cross-section (units = area)
Similarly for Absorption N2 E2 N1 E1
absorption cross-section
Absorption

14. 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.

16. 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.

17. 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

18. 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 :

19. Inversion Inversion N2 > N1
In order to achieve G > 1, that is, 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

20. 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.

21. 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

22. 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!

23. 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.
Spontaneous emission
The total number of molecules is N:
Level 3 decays fast and so is zero.
Absorption

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

25. 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.
As before:
The total number of molecules is N :
Because
At steady state:

26. 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)
where:
Isat is the saturation intensity.
Now, DN is negative—always!

27. 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 molecules
s ~ to cm2 for molecules (on resonance)
105 to 1013 W/cm2
The saturation intensity plays a key role in laser theory.

28. 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!

29. GAIN IN AN OPTICAL RESONATOR
pumping R2 l
gain/m = g R1
Round trip Gain (Loss) = egl R1 egl R2 = R1 R2 e2gl
Threshold R1 R2 e2gl = 1
If round trip gain is > 1, then G = R1 R2 e2gl Note this is inherently unstable….it will gain exponentially until …...
Saturation occurs…gain saturation...

30. 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 (minimum pump power of a laser required for laser emission). It means: I3 > I0. Here, it means:
where

31. Example:
Consider that both ends of ruby laser rod of 5 cm length are coated to have a reflectance of R=0.9. what is the minimum fraction of excited Cr ions achieving the threshold condition of oscillation? Assume that the concentration of Cr ions is , the induced-emission cross-section is , and the effective loss constant of the rod is

32. 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

33. Laser light properties:
Laser light has a number of very special properties:
It is usually emitted as a laser beam which can propagate over long lengths without much divergence and can be focused to very small spots.
It can have a very narrow bandwidth, while e.g. most lamps emit light with a very broad spectrum.
It may be emitted continuously, or alternatively in the form of short or ultrashort pulses, with durations from microseconds down to a few femtoseconds.

34. 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.

35. 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.

36. 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

37. 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

38. The Argon Ion Laser Argon 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

39. The Krypton Ion Laser Krypton lines Wavelength Power 406.7 nm .9 W

40. 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.

41. 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!

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

43. 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.

44. Diode Lasers

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

46. A laser in space Triply ionized carbon at 1548.2 Å
Wavelength (nm)
P Cygni emission line profile of triply ionized carbon at Å in the central star of the cat's eye planetary nebula, NGC Courtesy of the International Ultraviolet Explorer (IUE).
Huggins and Miller were the first to observe the spectra of nova T Coronae Borealis, showing blue-shifted absorption line accompanying each emission line. The nova evolved and they later observed a spectrum characteristic of nebula. These 'P-Cygni' lines are a characteristic common to all novae and stars with strong mass ejections or violent stellar winds such as Eta Carinae. The stellar 'ashes' that accumulate often take the form of a circumstellar nebula of gas and dust.
In the late 19th century, Keeler discovered the unusual emission lines of P-Cygni, a variable star which may have had a novae phase in It had several bright lines ascribed to helium, and is now classified as a very slow nova.
A quote from C.S.Beals paper on the interpretation of these stars:
Both P-Cygni and Eta Carinae have been numbered among the novae ... This similarity with novae, considered in connection with the absorption on the violet edges of emission lines and the variation in the width of P Cygni lines with wavelength, suggest that the peculiarities in the spectra of these stars is due to the ejection of of gaseous material in a manner similar to that suggested for Wolf-Rayet stars.
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.

47. 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.
Slide provided by Optics I student Kham Ho, 2004