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ES918/ES4C4 OpticalCommunication Systems
Background to the Assignment
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Introduction
For long distance transmission we need to
compensate for attenuation losses.
This was initially via a optoelectronic process of
optical receiver, a regeneration and equalization
system, and an optical transmitter
This is limited by the optical to electrical (OE) and
electrical to optical (EO) conversions.
Hence optical amplifiers were developed.
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Concept
The idea of an optical amplifier is the same as that of an electrical amplifier, to
increase the size of the input signal.
G
Pin
GPin
Pump
Power
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Amplifier Types
Optical amplifiers have become near essential components in optical fibre
systems. A working knowledge of them is now extremely important in optical fibrecommunications.
Several different types of optical amplifier including:
Rare earth (erbium, neodymium, praseodymium) doped fibre amplifier
(EDFA, NDFA, PDFA)
Semiconductor optical amplifier (SOA)
Non-linear fibre amplifiers: Raman fibre amplifier and Brillouin fibre amplifier
EDFAs are important for point to point long haul communications
SOAs are very noisy so have struggled to find achieve mass application
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Applications
Power Amplifier
Fibre
G
Tx
RxG
Line Amplifier
G
Preamplifier
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Basic Concepts
Most amplify light through stimulated emission Similar to a laser but without the feedback
The gain medium must be supplied energy by a pumpto create population inversion
Fibre amplifiers use optical pumps
SOAs use electrical pumps
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Energy LevelsElectrons (and holes) may occupy only a range of energy bands within materials
for quantum mechanical reasons.
Electrons normally occupy their state of lowest energy known as the ground
state.
An energy state greater than the ground state is known as an excited state.
E2
E1
Excited State
Ground State
Energy
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Photon-Electron Interactions: Spontaneous Absorption
1. Spontaneous Absorption is
when an incident photon is
absorbed in a material causing the
excitation of an electron to a higherlevel, the basis of photodiode
operation. The energy of the
photon, hf, must be the same as
E2-E1
E2
E1
Left to their own devices, all materials absorb light via this
mechanism rather than emitting any light.
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Photon-Electron Interactions: Spontaneous Emission
2. Spontaneous Emissionis when
an electron falls to a lower energy
level, the basis of LED action.
E2
E1
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Photon-Electron Interactions: Stimulated Emission
3. Stimulated Emissionis when a
photon incident upon an electron in
a high energy level causes the
electron to fall to a lower levelgenerating a second photon. This is
the basis of Light Amplification by
Stimulated Emission of Radiation
(LASER) action.
E2
E1
The photon generated has the same frequency as the incident one and thus laser light is
highly monochromatic and coherent (in phase).
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Conditions for Amplification
More electrons in higher energy levels than in lower ones (population inversion) so that
stimulated emission becomes more likely that spontaneous absorption.
We need to pump electrons into excited states by either electrical or optical means.
P
ump
E2
E1
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EDFA Energy Levels
Energy
E3
E1
E2980 nm pump
1480 nm pump 1530 nm emission
Fast non-radiative transitions
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Optical Preamplifier Configuration
Weak
Input
Signal
EDFA FilterCoupler
Pump
Laser
Isolator
Amplified
Output Signal
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EDFAAmplified Spontaneous Emission (ASE)
There will also be spontaneous emission in the amplifier. This will get amplified as
well as the signal, producing amplified spontaneous emission (ASE) noise.
The PSD of ASE noise is nearly constant (white noise) and for an amplifier with
gain G, can be written as
Note that the assignment uses photons per bit so the ASE will be in photons persecond
1spASE GhfnfS
1sp0 GnN
spontaneous-emission factor 122sp NNNn excited state
atomic
population
ground state
atomic
population
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Performance Modelling
Although the noise at the receiver is not Gaussian, we can approximate it by a
Gaussian with parameters drawn from the properties of the amplifier (see later).
The BER is then given by:
The means and variances have to be derived as on the assignment sheet.
2erfc
2
1 QPe
01
01
Q
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Moment Generating Functions
Often, the form of the noise statistics is not easy to work with.
We can make use of the moment generating function (mgf), which is defined for a
probability functionp(x)in a similar way to the Laplace transform
dxexpsM sx
There are methods based on MGFs that make the calculation of errorprobabilities much easier.
Also if we have the sum of two noise sourcesxandythe resultant pdf
is
sMsMsM YXYX But for the mgfs
ypxpyxp YX *
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Getting the Moments from mgfs - mean
As you might expect, the mgf may be used to obtain moments.
0'MxE
sMsM
dssMd ln
00
MM
Consider the log of the mgf:
10 dxxpM
0
ln
sds
sMd
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Getting the Moments from mgfs - variance
20'0''var MM 0''2 MxE
sM
sMsMsM
sM
sM
ds
d
ds
sMd2
2
2
2 ln
2
2
2
0
000
M
MMM
2
0
2
2 ln
sds
sMd
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Example: Zero mean Gaussian
Complete the square:
dxee
dxe
dxeesM
sxs
sx
sxx
22222
222
22
22
22
2
2
1
2
1
2
1
22 22222 1
sys edyeesM
22 2:Subst sxy
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Example continued
0
2ln
0
2
0
22
0
s
ss
sds
sd
ds
sMd
Zero mean Gaussian
20
2
0
lnvar
ss ds
sd
ds
sMd
ds
d
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MGF for Optical Preamplifier
sN
mGs
sN
sMmt
02
0
1exp
1
1
OOK system; includes polarisation too; we can reduce the ASE
(random, unpolarised) by keeping only one polarisation
Product of the optical filter
bandwidth and the bit time
Number of
photons in
the bit
Number of polarisations
Quantum efficiency
Simplified model
ignoring shot noise
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Assignment Guide (1)
We can use the mgf to get the mean and variance and then use these to
describe a Gaussian pdf to approximate the real one.
Assignment entails obtaining the Gaussian mean and variance then making
approximate calculations for the performance of the preamplifier as its
parameters vary.
One aim (a) is to prove:-
200,10,1
MmNGm t
22 20
2
00,1
22
0,1
MmNGNm t
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Assignment Guide (2)Hint
sN
mGs
sN
sMmt
020
1exp
1
1
sN
mGssN
Mms t
0
01
1ln2
ln
Differential of a quotientDifferential of a logarithm
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Assignment Guide (3)
Follow the instructions on the sheet to complete the
other tasks from (b)-(j)
MATLAB is suggested
Also produce a one page discussion and summary of
your conclusions
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Assignment Guide (4)
Finally:-
A one page review (excluding references) of DEVELOPMENTS inoptical amplifier MODELLING that have enhanced the modelling process
beyond that considered here (this should refer to relevant literature,
factors that are not included above and any developments in
amplifiers/communication systems themselves).
This should comprise a literature SEARCH to find examples of improved
modelling of optical preamplifiers to address questions such as:
How does the shot noise actually impact the performance?
What other effects have been left out here?What about different modulation schemes?
Ten or more references would be a good effort here.
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Assignment Guide (5)
References must be presented correctly.
Figure/equation numbers, titles, axis labels, units etc. should be
presented correctly.
Code (MATLAB preferred or otherwise) should be commented.
Any questions should be addressed to me early.