Download laser2-broadening

B.SC.II
PAPER-B
(OPTICS and LASERS)
Submitted by
Dr. Sarvpreet Kaur
Assistant Professor
PGGCG-11, Chandigarh
Unit-IV
Lasers and Fiber
optics
Atomic Line Widths
The widths of atomic lines are of
considerable importance in atomic
spectroscopy. Narrow lines are highly
desirable for both absorption and
emission because they reduce the
possibility of interference due to
overlapping spectra. The line width ½
of an atomic absorption or emission line
is defined as its width in wavelength
units when measured at one half the
Line broadening
Spectral lines are not infinitely narrow, but show a certain width. A large variety
of phenomena contribute to the observed linewidths. In principle we distinguish
homogeneous and inhomogeneous broadening. In the first case all molecules
that contribute to the absorption line suffer from the same broadening. In the
second case different molecules absorb at slightly different frequencies due to
small variations in their direct environment
For the homogeneous contribution to the
linewidth we have
 hom
T1=Excited state
lifetime
1
1


2T1 T2
T2=pure
dephasing time
For the inhomogeneous contribution: the
transition frequencies are taken from some
distribution: Inhomogeneous distribution function
(IDF)
Line broadening (Homogeneous and non-homogeneous)
arises from four sources:
1. The uncertainty effect (because of
uncertainties
in
the
transition
times)(homogeneous)
2. The Doppler effect (because of rapid
movement of atoms)(non-homogeneous)
3. Pressure effect due to collision between
atoms of the same kind and with foreign
atoms.(non-homogeneous)
4. Electric and magnetic field effects.
Line broadening
• Classical theory leads to the following
equation for the shape of a line (transition). It
is called the Lorentz profile
 / 4
 L ( ) 
 ( 0  ) 2  ( / 4 ) 2 
Since the Lorentz profile is normalized we
find by integrating over all frequencies

 d
0
2
res
n
e
( ) 
4me 0c
Line broadening
• The line width (full width at half maximum) of the
Lorentz profile is the damping parameter, .
• For an isolated molecule the damping parameter
can be interpreted as the inverse of the lifetime of
the excited quantum state.
• This is consistent with the Heisenberg Uncertainty
Principle
h
Et 
2
h
1
t 

2 .h 2
• If absorption line is dampened solely by the natural
lifetime of the state this is natural broadening

Pressure broadening
• For an isolated molecule the typical natural
lifetime is about 10-8 s, 5x10-4 cm-1 line width
• Collisions between molecules can shorten this
lifetime
• These collisions can be viewed as ‘billiard ball’
reactions, or as the overlapping of the potential
fields of the two molecules.
• The collision process leads to a Lorentz line
shape.
Pressure broadening
• Clearly the line width will depend on the
number of collisions per second,i.e. on the
number density of the molecules
(Pressure) and the relative speed of the
molecules (the square root of the
temperature)
nv rel
n T
 L  L ( STP)
  L ( STP)
nL v rel ( STP)
nL T0
Doppler broadening
• Second major source of line broadening
• Molecules are in motion when they absorb. This
causes a change in the frequency of the
incoming radiation as seen in the molecules
frame of reference (Doppler effect)
• Let the velocity be v, and the incoming
frequency be , then
  
'
v cos

v v cos
v
 
  (1  cos )
c
c
Doppler broadening
• In the atmosphere the molecules are moving with
velocities determined by the Maxwell Boltzmann
distribution
1/ 2
 m 

f ( v X )dv X  
 2k BT 
where v 0  2k BT / m
exp(  v 2X / v 02 )dv X
Doppler broadening
•The cross section at a frequency  is the sum of all
line of sight components

 n ( )   dv x f ( v x ) n  (1  v x / c)

1/ 2  
 m 

 
 2k BT 
2
2
v
/
v

exp(
dv
0 ) n (  v x / c )
x
 x

1/ 2
 m 
2 2
2
2


exp  c (  0 ) / v 0 v0
S

 2k BT 


Doppler broadening
•
We now define the Doppler width as
 D  v 0v0 / c
 n ( )  S  D ( ) 
S
D

exp  (  0 ) 2 /  D2

Comparison of line shapes
The Uncertainty Principle
• Classical physics
– Measurement uncertainty is due to limitations of
the measurement apparatus
– There is no limit in principle to how accurate a
measurement can be made
• Quantum Mechanics
– There is a fundamental limit to the accuracy of a
measurement determined by the Heisenberg
uncertainty principle
– If a measurement of position is made with
precision x and a simultaneous measurement of
linear momentum is made with precision p, then
the product of the two uncertainties can never be
less than h/2
xpx 
Two-level Laser System
• Unimaginable
as absorption and stimulated processes
neutralize one another.
• The material becomes transparent.
Three-level Laser System
• Initially excited to a
short-lived high-energy
state .
• Then quickly decay to
the intermediate
metastable level.
• Population inversion is
created between lower
ground state and a
higher-energy
metastable state.
Three-level Laser System
 3   2 1   2
Nd:YAG laser
  1.06  m
τ2  2.3 104 s
He-Ne laser
1  3.39  m 2  0.6328  m
3  1.15  m
τ  100ns τ1  10ns
2
Four-level Laser System
• Laser transition takes
place between the
third and second
excited states.
• Rapid depopulation of
the lower laser level.
Four-level Laser System
 3   2
Ruby laser
1  0.6943m
2  0.6928m
τ  10 s τ  3  10 s
3
7
3
2
Common Components of all Lasers
1.
Active Medium
The active medium may be solid crystals such as ruby or Nd:YAG, liquid
dyes, gases like CO2 or Helium/Neon, or semiconductors such as GaAs.
Active mediums contain atoms whose electrons may be excited to a
metastable energy level by an energy source.
2.
Excitation Mechanism
Excitation mechanisms pump energy into the active medium by one or
more of three basic methods; optical, electrical or chemical.
3.
High Reflectance Mirror
A mirror which reflects essentially 100% of the laser light.
4.
Partially Transmissive Mirror
A mirror which reflects less than 100% of the laser light and transmits the
remainder.
Mirrors form an optical resonator
22
Laser Components
Gas lasers consist of a gas filled tube placed in the laser cavity. A
voltage (the external pump source) is applied to the tube to excite the
atoms in the gas to a population inversion. The light emitted from this
type of laser is normally continuous wave (CW).
23
Laser Construction
Pump Source
• Provides energy to the laser system
• Examples: electrical discharges, flashlamps,
arc lamps and chemical reactions.
• The type of pump source used depends on
the gain medium.
→A helium-neon (HeNe) laser uses an
electrical discharge in the helium-neon
gas mixture.
→Excimer lasers use a chemical reaction.
Gain Medium
• Major determining factor of the wavelength of
operation of the laser.
• Excited by the pump source to produce a
population inversion.
• Where spontaneous and stimulated emission
of photons takes place.
• Example:
solid, liquid, gas and semiconductor.
Optical Resonator
• Two parallel mirrors placed around the
gain medium.
• Light is reflected by the mirrors back into
the medium and is amplified .
• The design and alignment of the mirrors
with respect to the medium is crucial.
• Spinning mirrors, modulators, filters and
absorbers may be added to produce a
variety of effects on the laser output.