laser fundamentals

1. Elements of Laser

2. Working Principle of Laser

3. Working Principle of Laser
Einstein’s assumptions & implications
 Thermodynamic equilibrium at arbitrary
temperature T exists between the radiation field
and the atoms
 The spectral density u(ν) of the radiation energy
has the distribution characteristics of a blackbody
at temperature T
 The atom population densities Nl and Nu at energy
levels El and Eu, respectively, are distributed
according to the Boltzman distribution at that
temperature
 Population densities Nl and Nu are constant in time

4. Working Principle of Laser
 The radiative process and assumptions above, it follows
that the rate of change of atoms in level Eu is given by
( ) ( )υυ uBNuBNAN
dt
dN
lululuulu
u
+−−== 0
The spectral energy density can be written as
( )
1
18
/3
33
−
= kTh
ec
hn
u υ
υπ
υ
The Boltzman distribution
( ) kTh
l
ukTEE
l
u
l
u
e
g
g
e
g
g
N
N lu // υ−−−
==
…..(1)
…..(2)
…..(3)

5. Working Principle of Laser
 Solving eq.(1) in terms of u(υ) and substituting Nu/Nl from
eq. (3), we obtain
( )
( )
ul
kTh
lu
u
l
ul
ulullu
ul
BeB
g
g
A
BNNB
A
u
−





=
−
=
// υ
υ
Compare it to eq. (2), gives
3
33
8
c
hn
B
A
ul
ul υπ
= lululu BgBg =
……(5) ……(6)
……(5)

6. Working Principle of Laser
The importance of eqs. (5) and (6) cannot be underestimated.
They tell us that:
(i) The fundamental Einstein’s coefficients Aul, Bul and Blu are all
inter-related.
(ii) guBul = glBlu , i.e. stimulated emission and absorption are
inverse processes. However note that the rate dNu/dt and
dNl/dt differ depending on the population densities Nu and Nl.
If Nu > Nl it leads to an increase in u(υ), an amplification. And
if Nl > Nu it leads to a decrease in u(υ), an attenuation. For
laser to operate, it is necessary that Nu be greater than Nl – a
condition called population inversion.
(iii) Since Bul/Aul is proportional to the reciprocal of the cube of
the frequency, the higher the frequency the smaller Bul
becomes in comparison with Aul. Since Bul is related to
stimulated emission and Aul is related to spontaneous
emission, it would seem that lasers of short wavelength
radiation would be more difficult to build and operate.Two important ideas for the successful operation of a laser
emerge from a review of Einstein’s study of the interaction of
electromagnetic radiation with matter are, stimulated emission
and population inversion.

7. Lasing condition
Population inversion
 Necessary condition for amplification.
 The case of the upper level being more populated than the lower level.
 If stimulated emission rate exceeds absorption rate, net optical gain.
 The relationship for the intensity at a specific distance z into medium
at a frequency ν and width Δν can be expressed as,

8. Population inversion

9. Population inversion
 If the value of the exponent is positive, the
beam will increase in intensity and so
amplification will occur.
 If it is negative, the beam will decrease in
intensity and absorption will occur.
 The values of σul and z are always positive, thus
amplification will occur only if
 This condition is not normal under thermal
equilibrium
l
l
u
N
g
g
N =u

10. Emission Broadening

11. Emission Broadening
Homogeneous Broadening
 Due to the isotropic collisions with other atoms, which also
causes non-radiative decay
 The processes lead to a Lorentzian distribution of emitting
frequencies
 All of the atoms in level u have an equal probability of
participating in the emission at any frequency ν of that
emission shape – all atoms behave the same way

12. Emission Broadening
Homogeneous Broadening
 The process can decrease either the decay time τu of
the atoms residing in the excited level u OR affect the
linewidth – depending on collision intervals
 Dephasing collisions interrupts the phase of radiating
atoms without increasing their population decay rate

13. Emission Broadening
Inhomogeneous
 Do not affect the lifetime, but do affect the linewidth
 The processes include Amorphous Crystal broadening,
Doppler broadening and Isotope broadening
 Emission processes that lead to a Gaussian distribution of
emitting frequencies
 Specific portions of the population density Nu contribute to
different portions of the emission linewidth

14. Emission Broadening
Amorphous Crystal Broadening
 Glass materials have various small regions
oriented in slightly different directions
 Thus, each of the glass molecules can have
slightly different energy levels
 This leads to different radiating frequencies for
 different regions
 Since the emission line is composed of the sum of
all of the individual lines, this leads to a much
broader emission spectrum

15. Emission Broadening
Doppler Broadening
 Due to random movements of radiating atoms in all
directions with a range of velocities
 This causes frequency shifts depending on the
directions of the movements
 The faster the atoms move on the average, the broader
the bandwidth
 A single photon might be able to stimulate one atom to
emit because that atom happened to be Doppler shifted
to the photon’s frequency, but it might not be able to
stimulate another atom because it had a different
Doppler shift than the first
 I.e. different atoms contribute to the gain at different
frequencies within the laser bandwidth

16. Emission Broadening
Isotope Broadening
 Due to the presence of more than one isotropic
form of the species
 These different isotopes consist of atoms having
the same number of protons and electrons, but
with different numbers of neutrons
 Atoms with slightly different numbers of neutrons
within their nuclei exhibit small differences in
energy level values
 The slightly different energy level values for
different isotopes provide slightly different
frequencies for the transitions