laser fundamentals

1. Laser Fundamentals

2. Outline
 Definition
 Introduction
 Elements of Laser
 Working Principle of Laser
 Atomic Excitation
 Decay of Excited States
 Einstein Coefficients – absorption, spontaneous emission
and stimulated emission
 Lasing Conditions
 Emission Broadening
 Threshold Requirements
 Resonator Stability
 Pumping Tchniques
 Cavity Modes

3. Definition
 Laser - Light amplification by stimulated emission
of radiation
 Processes involved – Spontaneous emission,
Stimulated emission, Optical feedback
 Key elements - Gain/amplifying medium,
Resonator, Pumping mechanism
Optical feedback
Pumping process
Amplifying medium

4. Introduction
Unique Properties of Laser
 Monochromaticity: the light emitted by a laser is
almost pure in colour, almost of a single
wavelength of frequency.
 Coherence: is a measure of the degree of phase
correlation that exists in the radiation field of a
light source at different locations and different
times.
 Directionality: high degree of directionality, i.e.
minimum angular spread
 Intensity/power: Possible to produce extremely
high power – more than 1015 Watt peak power
demonstrated.

5. Introduction
Unique Properties of Laser
 Temporal coherence length, i.e the average
length of light beam along which the phase of
the wave remains unchanged.

6. Introduction
Example
What is the temporal coherence length lc of
a mercury vapor lamp emitting in the green
portion of the spectrum at a wavelength of
546.1 nm with an emission linewidth of Δν
= 6 x 108
Hz?
Given that
where ∆λ is the linewidth which the degree
of monochromaticity of the laser ligth.
c
νλ
λ
∆
=∆

7. Elements of Laser

8. Elements of Laser
Amplifying medium
 Determines the
wavelength of the laser
radiation. The amplifying
medium consists of the
laser host and laser
atoms. Laser
amplification relies on
stimulated emission, thus
the most important
requirement is its ability
to support a population
inversion between energy
levels of the laser atoms.
Must have more
population in excited
state than in lower level.

9. Elements of Laser
Pumping Mechanism
 In thermal equilibrium,
populations follow
Boltzmann distribution –
cannot produce a
population inversion
 Energy input from the
pump source which is
necessary to get inversion.
Pump excites the
population selectively to
upper laser level.
Populations depend on
relaxation rates.

10. Elements of Laser
Resonator
 Resonator is an optical
feedback that directs
photons back and forth
through the laser
medium. Amplification of
an optical signal from a
single pass through the
medium is quite small,
after multiple passes the
net gain can be large.
Consists of a pair of
aligned plane or curved
mirrors centred along the
optical axis of the laser
system.

11. Working Principle of Laser
 The amplifying medium is being pumped so as to achieve
population inversion between two energy levels in the
medium.
 A process known as spontaneous emission will then occur,
where atoms in the metastable state will drop to lower
energy level and releases energy in the form of photons.
 Seed photons due to this spontaneous emission will then
initiate a process called stimulated emission between the two
energy levels. The photons emitted will have the same
frequency and phase.
 An optical cavity that confines and directs the growing
number of resonant energy photons back and forth through
the laser medium, continually exploiting the population
inversion to create more and more stimulated emissions,
thereby creating more and more photons.
 Once the gain is higher than the loss, a certain amount of
laser light will be coupled out of the cavity through the output
coupler mirror to form the external laser beam.

12. Working Principle of Laser

13. Working Principle of Laser
Atomic Excitation
 Can be provided either thermally,
optically or electrically.
 Can transfer electrons from the valence
band to the conduction band.
 When the electrons are moved to the
conduction band, the vacant sites in the
valence band where the electrons were
allocated are referred to as holes.

14. Working Principle of Laser
Decay of excited states
 Electrons can decay from the
conduction band to the valence
band by “recombining” with holes.
 When this occurs, the electrons can
either radiate the energy or give it
up via interactions or collisions with
the material lattice.

15. Working Principle of Laser
Absorption
 The rate of upward transition or absorption is
proportional to both the density of atoms in the lower
or ground energy state and the spectral density of the
radiation energy at the transition frequency.
 Hence, the upward transition rate maybe written as,
Einstein coefficient of absorption
)(υuBN
dt
dN
lul
u
=
Einstein coefficient of absorption
spectral density of the radiation energy

16. Working Principle of Laser
Spontaneous Emission
 The atom returns to the lower energy state in an
entirely random manner.
 A natural process that occurs without any external
stimulus.
 Each photon radiated when one of the atoms decays
would have a frequency of,
( )
h
E
h
EE ullu
ul
∆
=
−
=υ
And a wavelength of
ul
ul
n
c
υ
λ =

17. Working Principle of Laser
Spontaneous Emission
 The change of the population density Nu as the population
is transferred to level l,
uul
u
NA
dt
dN
−=
•The solution to the above equation is,
Einstein coefficient for spontaneous emission
Population density

18. Working Principle of Laser
Spontaneous Emission
 For more general case, in which the population in level u
decays radiatively to several lower-lying levels, the
solution for the decay is written as,
•The lifetime of energy level u is completely determined by
the reciprocal of the sum of all possible radiative decay rate
to lower-lying levels.

19. Working Principle of Laser
Stimulated Emission
 As the density of atoms in the upper energy state
is Nu, the rate of stimulated downward transition
is proportional to both Nu and the spectral density
u(ν) of the radiation energy at the transition
frequency ν.
 Hence the rate of stimulated emission is given by
( )υuNB
dt
dN
uul
u
−=
Einstein coefficient for stimulated emission