Lasers* Laser
Transition
Pump
Transition
Fast decay
Fast decay
* Light Amplification by Stimulated Emission of Radiation
The Ruby Laser
1960
1965
THE LARGEST LASER IN THE WORLD
National Ignition Facility
192 beams,
4 MJ per pulse
"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).
SINGLE ATOM LASER
NANOLASERS
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
The first room temperature UV nanowire lasers
P. Yang, UC Berkeley 2001
Courtesy A. Siegman
Charles Townes (and Mrs Townes) - 2006
Interaction of light with excited media
Excited media? Matter which has energy in excited energy levels
Process of excitations
Eg
Eexcited
Excitation
Absorption
De-excitation
Emission
Assumptions - quantized energy levels - electronic, vibrational rotational
Limitations – Optical processes only
Energy levels
Emission and Absorption – Basic ideas
Restrict ourselves to two level system
E1
E
2
E2 – E1 = hn = hc/l
E1
E
2
E1
E
2
E1
E
2
Three basic processes
ground state
rest state
excited state
temporary state
Absorption Spontaneous
Emission Stimulated
Emission
N2
N1
Number of atoms (or molecules) / unit volume
N = number density N = N1 + N2
N1,2 = population of levels 1 & 2
Spontaneous emission
Probability that the process occurs can be defined by
Rate of decay of the upper state population E1
E
2
N 2
N1
22 AN
dt
dN
sp
rate of spontaneous decay (units = 1/ time) Einstein A Coefficient
Asp
1 = spontaneous emission lifetime ( radiative lifetime)
Note: Rate of spontaneous decay defined for a specific transition
Absorption and Stimulated Emission
We can write the rate of change of population
2212 NW
dt
dN
st
E1
E
2
Stimulated
Emission
N2
N1
E1
E2
Absorption
N2
N1
However, now the rate of stimulated emission
is dependent on the intensity of the EM wave
FW 2121
stimulated emission
cross-section (units = area)
Photon flux
(number of photons/ unit area/unit time)
Similarly for Absorption
1121 NW
dt
dN
ab
FW 1212
absorption cross-section
Stimulated emission leads to a chain
reaction and laser emission.
Excited medium
If a medium has many excited molecules, one photon can become
many.
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.
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.
The Laser
A laser is a medium that stores energy, surrounded by two mirrors.
A partially reflecting output mirror lets some light out.
A laser will lase if the beam increases in intensity during a round trip:
that is, if 3 0I I
R = 100% R < 100%
I0 I1
I2 I3 Laser medium
with gain, G
Calculating the gain:
Einstein 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
2
1
Laser gain
Neglecting spontaneous emission:
2 1
2 1
dI dIc BN I - BN I
dt dz
B N - N I
2 1( ) (0)expI z I N N z
2 1expG N N L
[Stimulated emission minus absorption]
Proportionality constant is the
absorption/gain cross-section,
2 1g N N
1 2N N
If N2 > N1:
If N2 < N1 :
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:
The solution is:
Laser medium
I(0)
z L 0
I(L)
Inversion
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.
N2 > N1
En
erg
y
Inversion
Molecules
“Negative
temperature”
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.
Rate equations for a
two-level system
Rate equations for the densities of the two states:
21 2 2( )
dNBI N N AN
dt
12 1 2( )
dNBI N N AN
dt
22 2d N
BI N ANdt
Absorption Stimulated emission Spontaneous
emission
1 2N N N
1 2N N N
If the total number
of molecules is N:
2 1 2 1 22 ( ) ( )N N N N N
N N
2d N
BI N AN A Ndt
2
1
N2
N1
Laser Pump
Pump intensity
Why inversion is impossible
in a two-level system
0 2BI N AN A N
1 / sat
NN
I I
/ 2satI A B
In steady-state:
( 2 )A BI N AN
where:
N is always positive, no matter how high I is!
It’s impossible to achieve an inversion in a two-level system!
2d N
BI N AN A Ndt
/( 2 )N AN A BI
/(1 2 / )N N BI A
Isat is the saturation intensity.
2
1
N2
N1
Laser
Rate equations for a
three-level system
Assume we pump to a state 3 that
rapidly decays to level 2.
21 2
dNBIN AN
dt
11 2
dNBIN AN
dt
1 22 2d N
BIN ANdt
Absorption
Spontaneous
emission
1 2N N N
1 2N N N
The total number
of molecules is N:
22N N N
d NBIN BI N AN A N
dt
Fast decay
Laser
Transition
Pump
Transition
1
2
3
Level 3
decays
fast and
so is zero.
12N N N
Why inversion is possible
in a three-level system
1 /
1 /
sat
sat
I IN N
I I
/satI A B
In steady-state:
( ) ( )A BI N A BI N
where:
Now if I > Isat, N is negative!
( ) /( )N N A BI A BI
Isat is the saturation intensity.
d NBIN BI N AN A N
dt
0 BIN BI N AN A N
Fast decay
Laser
Transition
Pump
Transition
1
2
3
Rate equations for a
four-level system
Now assume the lower laser level 1
also rapidly decays to a ground level 0.
20 2
dNBIN AN
dt
1 0,N
22 2( )
dNBI N N AN
dt
2N N
Laser
Transition
Pump
Transition
Fast decay
Fast decay
1
2
3
0 As before:
Because 0 2N N N
The total number
of molecules is N :
0 2N N N
d NBIN BI N A N
dt
At steady state: 0 BIN BI N A N
Why inversion is easy
in a four-level system
(cont’d)
0 BIN BI N A N
/
1 /
sat
sat
I IN N
I I
/satI A Bwhere:
Isat is the saturation intensity.
Now, N is negative—always!
Laser
Transition
Pump
Transition
Fast decay
Fast decay
1
2
3
0
( / ) /(1 / )N BIN A BI A
/( )N BIN A BI
( )A BI N BIN
What about the
saturation intensity?
A is the excited-state relaxation rate: 1/
/satI A B
Laser
Transition
Pump
Transition
Fast decay
Fast decay
1
2
3
0
B is the absorption cross-section, , divided by
the energy per photon, ħw: / ħw
satIw
The saturation intensity plays a key role in laser theory.
Both and
depend on the
molecule, the
frequency, and
the various
states involved.
ħw ~10-19 J for visible/near IR light
~10-12 to 10-8 s for molecules
~10-20 to 10-16 cm2 for molecules (on
resonance)
105 to 1013 W/cm2
Two-, three-, and four-level systems
Two-level
system
Laser
Transition
Pump
Transition
At best, you get
equal populations.
No lasing.
It took laser physicists a while to realize that four-level systems are
best.
Four-level
system
Lasing is easy!
Laser
Transition
Pump
Transition
Fast decay
Fast decay
Three-level
system
If you hit it hard,
you get lasing.
Laser
Transition Pump
Transition
Fast decay
pumping
R2 R1 l gain/m = g
Round trip Gain (Loss) = egl R1 egl R2 = R1 R2 e
2gl
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...
GAIN IN AN OPTICAL RESONATOR
Achieving Laser Threshold
An inversion isn’t enough. The laser output and additional losses in
intensity due to absorption, scattering, and reflections, occur.
The laser will lase if the beam increases
in intensity during a round trip, that is, if:
3 0 0exp( ) exp( ) exp( ) exp( )I I gL L R gL L I
R = 100% R < 100%
I0 I1
I2 I3 Gain, G = exp(gL), and
Absorption, A = exp(-L)
Gain > Loss
Laser medium
2( ) ln(1/ )g L R
This called achieving Threshold (minimum pump power of a laser
required for laser emission). It means: I3 > I0. Here, it means:
21RRR where
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
319101 cmN
220102 cm1011.0 cm
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108018.5
108018.51016036.12
101
106036.1102
032072.0/
032072.0011.0021072.0021072.0
21072.081.0
1ln52
1ln2
19
18
2
18
2
19
2
19
12
18
2012
orN
N
NN
NNN
gNN
gg
g
RLg
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 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.
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.
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.
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. http://en.wikipedia.org/wiki/Helium-neon_laser
Carbon Dioxide Laser
The CO2 laser operates analogously. N2 is pumped, transferring
the energy to CO2.
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.
The Argon
Ion Laser
Argon 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 Krypton Ion Laser
Krypton 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
Dye lasers
Dye lasers are an ideal four-level system, and a given dye will lase
over a range of ~100 nm.
A dye’s energy levels
The lower laser level can be almost any level in the S0 manifold.
S0: Ground
electronic state
manifold
S1: 1st excited
electronic state
manifold
Laser Transitions
Dyes are so ideal that it’s often difficult to stop them from lasing in all
directions!
Pump Transition
Dyes cover the visible, near-IR, and
near-UV ranges.
Titanium: Sapphire (Ti:Sapphire)
oxygen
aluminum Al2O3 lattice
Absorption and emission
spectra of Ti:Sapphire
Upper level lifetime:
3.2 msec
Ti:Sapphire lases from
~700 nm to ~1000 nm.
Diode Lasers
Some everyday applications of diode
lasers
A CD burner Laser Printer
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.