optics lasers
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Optics LasersTRANSCRIPT
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,
theres 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?
Itll depend on the laser mediums 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!
Its 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
(contd)
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 negativealways!
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, w: / w
satIw
The saturation intensity plays a key role in laser theory.
Both and depend on the
molecule, the
frequency, and
the various
states involved.
w ~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