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Transcript
Absorption and emission processes
E2
2
a absorption
a
b
c
b spontaneous emission
c stimulated emission
E1
1
Absorption
Molecule absorbs a quantum of radiation
(a photon) and is excited from 1 to 2.
M + h  M*
(state 1)
(state 2)
Spontaneous emission
M* (in state 2) spontaneously emits a
photon of radiation.
M *  M + h
Stimulated emission
A quantum of radiation is required to
stimulate M* to go from 2 to 1.
M * + h  M + 2h
LASER SPECTROSCOPY
Lecture 1 - Basics of laser systems
• Absorption and Emission processes.
• Conditions for laser action.
• Properties of laser radiation.
• Real Laser Systems.
Recommended reading - not buying!
• High Resolution Spectroscopy/Modern Spectroscopy by J.M.Hollas.
• An Introduction to Lasers and their Applications by O’Shea, Callen and
Rhodes.
• Laser Electronics by Verdeyen.
Rates of absorption and emission processes
• Rates are determined by the Einstein coefficients for each process
dN 1
 N1B12  ( )
dt
dN 2
 N 2 B21  ( )
dt
dN 2
 N 2 A21
dt
Absorption
Stimulated emission
Spontaneous emission
() is the energy density of
the incident radiation and
N1 and N2 are the
populations of states 1 and 2
respectively.
Under thermal conditions the population of two states 1 and 2, is determined
by the Boltzman distribution.
N2
  E 
 exp

N1
 kT 
Where E is the energy difference between the two states, T is the
temperature and k is Boltzmans constant.
Stimulated and spontaneous emission
Spontaneous emission
• Photons emitted in all directions and on a random time scale.
• The emitted photons are INCOHERENT
Stimulated emission
• Emitted and stimulating photons have the same :
• Frequency
• Direction
• Phase
• The emitted and incident photons are COHERENT
First condition for laser action
If N1 > N2
• If most molecules in state 1, then incoming radiation is mainly absorbed.
• Incident radiation is attenuated (reduced).
If N2 > N1
• If most molecules are in state 2, absorption of incoming radiation is hindered.
• The result is stimulated emission.
• Incident radiation is amplified.
Thus for laser action require a population inversion, N2 > N1
How to obtain a population inversion
Consider the Boltzman equation.
N2
  E 
 exp

N1
 kT 
When kT is large, the ratio of N2/N11, equal numbers of molecules in
state 1 and state 2.
When kT is small the ratio of N2/N1  0 and all molecules are in state 1.
Cannot obtain a population inversion using thermal methods in a 2 level system.
• Multi-level systems must be employed.
• Molecules need to be pumped into a higher energy state.
Various methods : electrical discharge, flashlamp excitation.
• Continuous pumping gives a Continuous Wave (CW) Laser.
• Pulsed pumping gives a Pulsed Laser (PL) output.
Population Inversion
Example of a 3 level system
E3
Rapid decay
E2
LASING
E1
• 13 transition is pumped.
• Rapid decay from 3 2.
• State 2 is metastable, excited molecules can remain in state 2 for an
extended time period, population of state 2 builds up.
• Decay from state 3 means absorption from 1 3 is favoured, creating
population inversion between 2 and 1.
• Laser action is possible between states 2 and 1.
Population Inversion
Example of a 4 level system
E4
Rapid decay
E3
LASING
E2
Rapid decay
E1
• 14 transition is pumped.
• Rapid decay from 4 3.
• A population inversion is produced between states 3 and 2.
• Laser action is therefore possible between 3 2.
• Molecules decay rapidly from 2 1, replenishing population of 1.
Laser Gain
The amount of amplification of the incident beam in a single pass is small,
a fraction of a percent/centimetre of travel.
To increase the path length through the sample could use either:
• A very long laser/gain medium.
• Mirrors to reflect the beam back into the sample.
mirror
gain medium
mirror
• The gain medium is the substance which can support the population
inversion, can be solid, liquid or gas.
• The combination of the gain medium and the mirrors is called the laser
cavity or the optical resonator.
Basics of a complete laser system
• The gain medium is pumped by some method.
• Some of the atoms/molecules are excited.
• Spontaneous emission occurs, in all directions.
• Emission along long axis of cavity is reflected back through the gain
medium.
• The spontaneously emitted photons stimulate further emission from
the medium.
• A large radiation density quickly builds up.
LASING
mirror
gain medium
mirror
mirror
gain medium
mirror
• One of the mirrors is usually partially transmitting to allow some of the
laser radiation to escape.
Summary of requirements for laser action
EXCITER
energy
GAIN MEDIUM
LASER OUTPUT
OPTICAL RESONATOR
The three components required for laser action are:
• A gain medium which can support a population inversion.
• An external exciter to create the population inversion in the gain medium.
• An optical resonator or cavity to create a high radiation density.
The various types of lasers differ in the types of gain medium, external
exciter and size and type of cavity employed.
Ruby Laser
• Invented in the 60’s, was the first proper laser.
• The gain medium is a crystal of Ruby, which is an aluminium oxide
crystal with some of the aluminium atoms replaced with chromium.
• The excitation of the ruby crystal is obtained by a flashlamp spiralled
around the crystal.
• Mirrors at each end of the crystal form the cavity.
Ruby Laser
• The lasing constituents of the Ruby crystal are the Cr3+ ions, present in
low concentration.
• The laser action follows that of a 3 level system.
4T
1
Energy
2T
2
rapid decay
4T
2
2E
LASING
4A
2
• Pump either the 4T1 or 4T2 states,
use 510-600nm or 360-450nm
radiation respectively.
• Each decays to the metastable 2E
state.
• Laser action occurs from 2E to
4A with a frequency of 694 nm.
2,
Gain Media
• Can be a solid, liquid or gas.
Name
Gain Medium
Lasing Wavelength
Uses
Nd:YAG
Neodinium ions in a
1064nm, can be
Pump source for dye
yitrium aluminium
frequency doubled to
lasers, spectroscopy,
garnet crystal.
532nm, 355nm etc.
desorption.
Chromium ions in
694 nm (red)
Medical applications,
Ruby
aluminium oxide
eg. Tattoo repoval.
crystal.
Helium Neon
Helium Neon gas
632 nm
mixture
Carbon
CO2, N2, He and CO
dioxide
mixture
Usually low power,
Laser Pointers
10.6 m
Very high power,
desorption, laser
cutting, laser etching.
Dye Lasers
Organic dyes, e.g.
Range of
Spectroscopic
Rhodamines and
200nm1000nm
applications mainly.
Coumarins
Properties of laser output
Output is intense and coherent.
The linewidth (spread of frequencies) of the laser beam is determined by
several factors:
• Doppler broadening (gases, liquids).
• Collisional broadening (gases, liquids, also solid state,due to crystal
•interactions).
• Natural linewidth of the lasing transition (uncertainty principle).
• Number of modes active in the cavity.
The linewidth of most lasers is still of the order of a wavenumber or less,
sufficient for most spectroscopic applications.
To achieve very narrow line widths (for rotational spectroscopy) optical
components can be inserted into the cavity to narrow the number of modes
which are active, or to favour a single mode.
The Optical resonator
• The size and quality of the cavity are crucial for successful laser action.
• To support lasing the length of the cavity (L) must be and integral (n)
number of half wavelengths (/2).
 
L  n 
2
(This is the condition for constructive interference.)
• For each cavity, many modes can satisfy this resonance condition.
• Laser output is, therefore, composed of a spread of frequencies.
The Optical resonator
The Quality or Q-factor of a laser cavity is essentially a measures the
ability of a laser cavity to store energy.
The Q factor can be related to the energy stored in the cavity Ec, and the
amount lost, Et, by the following equation.
Q
2Ect
Et
Every laser cavity must have some loses due to the partially reflective
nature of the cavity mirrors.
Q-switching is a method of producing short pulses of very high energy in
pulsed laser systems.
Q-switching is often achieved by having shutters or a saturatable absorber in
the cavity.
Tunablity of wavelength.
Most lasers emit a single, or several discrete frequencies of radiation.
However, for many spectroscopic applications wavelength tunability is
necessary.
Solution is to use a dye laser pumped by a fixed frequency laser.
The gain medium is an organic dye, which has a broad emission and
absorption profile.
LASING
• Population inversion occurs
between v`=0 in S1 and v``=n in S0.
• Emission frequency selected by a
diffraction grating.
• Used to stimulate further emission
from amplifier dye cells.