The attached narrated power point presentation attempts to explain the working principle of lasers as sources for optical communications. The material will be useful for KTU final year B Tech students who prepare for the subject EC 405, Optical Communications.

1. 1
Optical Sources
Principles of Lasers
MEC

2. 2
Contents
• Introduction.
• Stimulated Emission.
• Einstein Relations.
• Population Inversion
• Lasing Action.
• Energy Band Diagrams.
• Laser Efficiency.

3. 3
LASER
• LASER amplifies light – Light Amplification
by Stimulated Emission of Radiation.
• Seldom used as amplifiers - difficult to
achieve high gain and to avoid oscillation
from energy feedback.
• An optical oscillator - monochromatic,
highly coherent output.
• Formation of electromagnetic standing
wave within a cavity (optical resonator).

4. 4
Stimulated Emission

5. 5
Stimulated Emission
• Incident wave stimulates atom to emit light
energy - liberated energy adds to the wave
constructively, provides amplification.
• Light for stimulation and stimulated photon
in phase, has same polarization.
• Photon produced by stimulated emission
of identical energy to the one which
caused it, light associated with them of the
same frequency.

6. 6
Stimulated Emission
• Photon with energy hf will not necessarily
stimulate another photon with energy hf.
• Photons may be stimulated over a small
range of energies around hf - emission has
finite frequency or wavelength spread
(linewidth).
• Atom has several sublevels of equal energy
within an energy level which is then said to
be degenerate. Degeneracy parameters g1
and g2 indicate number of sublevels within
energy levels E1 and E2.
• System not degenerate, g1 = g2 = 1.

7. 7
Einstein Relations
• Rates of absorption, spontaneous and
stimulated emission – mathematical
relation.
• Atomic system in thermal equilibrium - rate
of upward transitions = rate of downward
transitions.
• Population of two energy levels described
by Boltzmann statistics.

8. 8
Boltzmann Statistics
• If N1, N2 - density of atoms in energy levels E1
and E2, g1, g2 - degeneracies of the levels, K -
Boltzmann’s constant T - absolute temperature,
then
• Upward transition/absorption rate proportional to
N1 & spectral density ρf of the radiation energy
at transition frequency f.
B12 – Einstein Coefficient of
Absorption

9. 9
Einstein Relations
• Atoms in higher/excited energy state can
undergo electron transitions from level 2 to level
1 spontaneously/stimulated by radiation field.
• Spontaneous lifetime (τ21) - average time an
electron exists in excited state before transition.
• Spontaneous emission rate = N2 x 1/τ2 = N2A21,
N2 – density of atoms with energy E2, A21 -
Einstein coefficient of spontaneous emission.
• Stimulated emission rate = N2ρf B21, B21 -
Einstein coefficient of stimulated emission, ρf -
spectral density.

10. 10
Einstein Relations
• Total transition rate from level 2 to level 1
• Thermal equilibrium, upward & downward
transition rates must be equal R12 = R21.

11. 11
Einstein Relations
• Substitute N1/N2,
• Atomic system in thermal equilibrium
produces radiation density identical to
black body radiation.
• Radiation spectral density for black body
radiating within frequency range f to f + df
given by Planck’s Relation.

12. 12
Einstein Relations
• Planck’s Relation
• Hence, Einstein’s Relation

13. 13
Einstein Relations
• When g1 = g2, probabilities of absorption and
stimulated emission are equal.
• For systems in thermal equilibrium spontaneous
emission is dominant.
• For coherent emission and amplification of light
beam, stimulated emission rate to be increased.
• Radiation density & population density of upper
level N2 to be increased versus population
density of the lower level N1 (Inversion).

14. 14
Population Inversion

15. 15
Population Inversion
• Thermal equilibrium - lower energy level
E1 of atomic system contains more atoms
than the upper energy level E2, N1 >N2.
• To achieve optical amplification create a
nonequilibrium distribution of atoms, N2 >
N1.
• Excite atoms into upper energy level E2
using external energy source - ‘pumping’.

16. 16
Population Inversion
• Pumping - apply intense radiation (from optical
flash tube/high-frequency radio field).
• Atoms excited into higher energy state through
stimulated absorption.
• Two-level system does not lend itself to suitable
population inversion.
• Equally degenerate (or not degenerate) levels
B12 = B21, probabilities of absorption and
stimulated emission equal, equal populations in
two levels.

17. 17
Population Inversion
• Population inversion obtained in systems
with three or four energy levels.
• Central metastable state - atoms spend
unusually long time.
• Stimulated emission/lasing occurs from
metastable state.

18. 18
Lasing

19. 19
Three Level - Lasing
• Initially, atomic distribution follow Boltzmann’s
law.
• With pumping some electrons excited from the
ground state into higher level E2.
• E2 is a normal level, electrons rapidly decay by
nonradiative processes to E1 or E0.
• Empty states will always be provided in E2.
• Metastable level E1 exhibits longer lifetime than
E2, allows large number of atoms to accumulate
at E1.

20. 20
Three Level - Lasing
• Over a period the density of atoms in N1
increases above the ground state N0 -
population inversion.
• Stimulated emission and hence lasing can
occur, radiative electron transitions between E1
and E0.
• Drawback - requires very high pump powers,
terminal state of laser transition is the ground
state - more than half of ground state atoms to
be pumped into metastable state for population
inversion.

21. 21
Four Level - Lasing
• Lower pumping
requirements.
• Pumping excites atoms from
ground state into E3 and
decay rapidly to metastable
level E2.
• Populations of E3 and E1
unchanged.
• Small increase in number of
atoms in E2 creates
population inversion.
• Lasing occurs between E2
and E1.

22. 22
Optical feedback and laser
oscillation
• Photon collides with an atom, in excited energy
state causes stimulated emission of a second
photon, both these photons release two more -
avalanche multiplication.
• Electromagnetic waves associated with these
photons are in phase, amplified coherent
emission obtained.
• Contain photons within laser medium, maintain
conditions for coherence for lasing.

23. 23
Lasing
• Placing or forming mirrors
(plane or curved) at either
end of the amplifying
medium.
• Optical cavity provides
positive feedback of photons
by reflection at the mirrors at
either end of the cavity.
• Fabry–Pérot resonator - after
multiple passes net gain can
be large, one mirror made
partially transmitting, useful
radiation escape from the
cavity.
n- refractive index, q- integer

24. 24
Lasing
• Stable output at saturation when optical gain is
matched by losses in the amplifying medium.
• Absorption & scattering in amplifying medium,
absorption, scattering and diffraction at mirrors and
non-useful transmission through mirrors lead to
losses.
• Oscillations occur in laser cavity over a small range
of frequencies where cavity gain is sufficient to
overcome losses.
• Device not perfectly monochromatic source, emits
over a narrow spectral band.
• Laser oscillation also in a direction transverse to the
axis.

25. 25
Frequency Variations
• Frequency variations due to thermal motion of
atoms within the amplifying medium (Doppler
broadening) and atomic collisions.
• Doppler broadening - inhomogeneous
broadening, individual groups of atoms have
different apparent resonance frequencies.
• Atomic collisions - homogeneous broadening,
every atom has the same resonant frequency
and spectral spread.

26. 26
Gain curve
• Discrete emission frequencies
• Different frequencies of
oscillation within laser cavity
depends on integer values of q,
each constitutes a resonance or
mode.
• Modes separated by frequency
interval
Broadened Laser
Transition
Discrete
Emission
Frequencies

27. 27
Threshold for Oscillation
• Minimum/threshold gain within amplifying
medium to be be attained so that laser
oscillations are initiated and sustained.
• Threshold gain determined by considering
the change in energy of a light beam.
• High threshold gain per unit length needed
to balance losses from the cavity.
• Increase in beam intensity resulting from
stimulated emission is exponential.

28. 28
Threshold for Oscillation
• If L - amplifying medium length completely
filling the region between two mirrors,
r1 and r2 – mirror reflectivities, α - single
loss coefficient per unit length/cm, then
threshold gain per unit length
• Second term on the right - transmission
loss through mirrors.

29. 29
Carrier Population Inversion
• Electrons injected into
the material fill lower
energy states in the
conduction band up to
the injection energy or
quasi-Fermi level for
electrons.
• Conserving charge
neutrality - equal density
of holes created in the
top of valence band by
absence of electrons.
Filled electron states for intrinsic direct
bandgap semiconductor

30. 30
Population Inversion
• Incident photons with energy Eg < separation
energy of quasi-Fermi levels Eq = EFc − EFv
cannot be absorbed, necessary conduction band
states are occupied.
• These photons can induce downward electron
transition from filled conduction band states into
empty valence band states.
• Basic condition for stimulated emission :
EFc − EFv > hf > Eg

31. 31
Population Inversion
• Population inversion at p–n junction by
heavy doping (degenerative doping) of
both p- and n-type material.
• Heavy p-type doping with acceptor
impurities lowers Fermi level or boundary
between filled and empty states into
valence band.
• Degenerative n-type doping cause Fermi
level to enter conduction band of the
material.

32. 32
Energy Band of Degenerate p–n
Junction
• At thermal equilibrium,
Fermi energy has the
same value throughout
the material.
• Forward bias of bandgap
voltage applied - at high
injection carrier density,
there exists an active
region near depletion
layer - contains
simultaneously
degenerate populations
of electrons and holes.

33. 33
Population Inversion
• Condition for stimulated emission satisfied
for frequency Eg/h < f < (EFc − EFv)/h.
• Any radiation of this frequency confined to
the active region will be amplified.
• Degenerative doping distinguishes a p–n
junction, provides stimulated emission.
• High impurity concentration semiconductor
causes differences in energy bands
against an intrinsic semiconductor.

34. 34
Lasing
• At high donor-level concentrations in gallium
arsenide, donor impurity levels form a band that
merges with conduction band - energy states
called ‘bandtail’ states extend into forbidden
energy gap.
• Laser transition may take place from one of
these states, lasing transitions may occur at
energies less than bandgap energy Eg (Peak
Energy < Bandgap Energy).
• Transitions may terminate on acceptor states
which because of their high concentration also
extend as a band into the energy gap.

35. 35
Fabry Perot Cavity
• Optical feedback through optical cavity.
• Each end of the junction polished or
cleaved.
• Polished end faces of the junction diode to
act as mirrors.
• Sides roughened to prevent unwanted
light emission and wasted population
inversion.

36. 36
Efficiency
• Differential external quantum efficiency -
ratio of increase in photon output rate for
given increase in number of injected
electrons.
• Pe - optical power emitted, I - current, e -
charge on an electron, hf - photon energy,
Eg - bandgap energy

37. 37
Efficiency
• Internal quantum efficiency of a
semiconductor laser
• Total efficiency (external quantum
efficiency)

38. 38
Thank You