Optical Fibres and Telecommunications
Lecture 13 – Introduction to Amplifiers
Optical Fibres and Telecommunications – Optical Amplifiers
Section 4 – Optical Amplifiers
Optical Fibres and Telecommunications – Optical Amplifiers
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Introduction to amplifier section
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The need for amplifiers.
Measuring power – the dBm.
Amplifier theory.
Erbium doped fibre amplifier.
Raman amplifiers
Semiconductor optical amplifiers.
Optical Fibres and Telecommunications – Optical Amplifiers
Today
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Where are we?
Requirement for amplification.
Measuring power.
Calculating Pout for simple fibre links.
Gain characteristics.
Noise
Optical Fibres and Telecommunications – Optical Amplifiers
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Last time
• Transmitters
– Components required.
– Modulation formats.
• Receivers
– Quantizers
– Clock recovery
– Optical front end
• Repeaters
– Regenerators
– 3R regeneration
Optical Fibres and Telecommunications – Optical Amplifiers
The need for amplifiers
• Attenuation causes signal power to drop through a fibre
link.
• Launching very high powers can cause problems.
– Non-linear effects.
– Fibre damage.
– Coupling problems for high power sources.
• Need to use amplifiers to increase signal power.
• Can use a repeater – problem is conversion to electrical.
Slow, power-hungry and multiple components.
• Want optical amplifiers within the telecomms system !
Optical Fibres and Telecommunications – Optical Amplifiers
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Time out – measuring power !
Example:
Amplifier gain = 37 dB
Power in = 0.003 mW
What is the power out ?
Pout = Gain x Pin
Pout = 103.7 x 0.003 mW
Pout = 5012 x 0.003 mW
Pout = 15mW
This is a cumbersome and error prone method.
Is there a better way ?
Optical Fibres and Telecommunications – Optical Amplifiers
Logarithmic Power – the dBm
• If we could write power on a log scale, we can just add
things up and take them away !
• Only need to do conversions as and when we need to know
the power in mW.
• Big advantages when you looking at much more
complicated systems.
• PdBm=10 log10 (PmW/1mW) - Very important definition !
• PmW=10P /10 - Inverse
dBm
Optical Fibres and Telecommunications – Optical Amplifiers
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Examples
1 mW =
0 dBm
35 mW =
15.4 dBm
143 mW = 21.6 dBm
0.04 mW = -14.0 dBm – Remember the – sign !
16.2 dBm = 41.7 mW
-36 dBm = 2.5x10-4 mW = 0.25µW
Optical Fibres and Telecommunications – Optical Amplifiers
Example again
Example:
Amplifier gain = 37 dB
Power in = 0.003 mW
What is the power out ?
PdBm = -25.2 dBm
Pout
= Pin + Gamp
= -25.2 + 37
= 11.8 dBm
= 15 mW
Optical Fibres and Telecommunications – Optical Amplifiers
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More complicated example
100km Fibre
Loss =20dB
100km Fibre
Loss =20dB
2mW Launched
Amplifier
Gain = 36dB
What is Pout ?
Pin= 2mW = 3dBm
Pout = 3 – 20 + 36 –20 dBm = -1 dBm = 0.1mW
Much simpler !!!
Optical Fibres and Telecommunications – Optical Amplifiers
One for you !
140km Fibre
Loss =0.2dB/km
5mW Launched
100km Fibre
Loss =0.2dB/km
Amplifier
Gain = 22dB
Coupled power = 7dBm
First fibre loss = 140 x –0.2 = -28dB
Amplifier Gain = +22dB
Second fibre loss = 100 x –0.2 = -20dB
Pout = ???
(-21dBm)
(1dBm)
(-19dBm)
Output power = -19dBm = 0.012mW
Optical Fibres and Telecommunications – Optical Amplifiers
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Back to Amplifiers
Pump Energy (Light !!!)
Low Power
Input
Gain Medium
High Power
Output
Optical Fibres and Telecommunications – Optical Amplifiers
What’s happening in an amplifier ?
Energy
Pump excites electron to level 2
2
Non-radiative decay 2→3
3
Population inversion between 3 & 4
Incoming photon induces stimulated
emission
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1
Further stimulated emission occurs
→ Amplification !
Electrons return to ground state.
Optical Fibres and Telecommunications – Optical Amplifiers
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Gain
Output Power
Gain Characteristics
Saturation Regime
Small Signal
Regime
Input Power
Optical Fibres and Telecommunications – Optical Amplifiers
Gain Characteristics 2
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Amplification occurs by stimulated emission.
Gain is not constant with power.
Gain is saturated by high power input signal.
Too much pump power can also cause a saturation effect.
If the gain, G, is given in dB and the power is measured in
dBm:
– Pout dBm = Pin dBm + Gamplifier dB.
– Pout mW = Pin mW x Gamplifier.
• Generally MUCH easier to work in dBm / dB !
Optical Fibres and Telecommunications – Optical Amplifiers
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Gain Characteristics 3
Change of intensity, I, of an optical signal passing through a gain medium:
dI
= gmI = σ ∆NI
dz
(a)
gm = gain coefficient, σ = emission cross section, ∆N = Population inversion
Solution for a signal of initial strength I0, passing through a gain medium length l:
I = I0 e gml
What about saturation ? – Need to modify the population inversion:
∆N = ∆N0
1
1+
I
I sat
Isat is the saturation intensity that reduces the population inversion by a factor of 2.
Optical Fibres and Telecommunications – Optical Amplifiers
Gain Characteristics 4
Substituting back into (a) above:
1 dI
1
= g0
I
I dz
1+
Isat
Rearranging and integrating :
⎛ I
ln ⎜⎜ in
⎝ Iout
⎞ IExt
⎟⎟ +
= ln G 0
⎠ ISat
(b)
Iext= Extracted power = Iout-Iin , G0= Small signal gain: G 0 = e g 0 l
Optical Fibres and Telecommunications – Optical Amplifiers
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Gain Characteristics 5
Define a power gain:
Substitute (c) in (b):
G=
Iout
Iin
G = G0 e
(c)
−
IExt
ISat
So when Iext<<Isat → G=G0 Small signal regime
Iext>>Isat → G=1 Saturated gain regime
Can also define, maximum extracted power Imax:
nb. For a four level system: Isat =
Imax = Isat ln G0
hν
στ
Optical Fibres and Telecommunications – Optical Amplifiers
Noise
• A major disadvantage of amplifiers is noise.
• Amplifiers increase both the incoming signal and any
associated noise. This on its own would leave the SNR
constant.
• However amplifiers can also add noise without a
proportionate increase in signal.
• Can define the amplifier noise figure: Fn:
– Fn=(SNR)in/(SNR)out
• Fn is normally specified in dB. Typical value might be
~6dB.
• Increase of signal power normally allows us to tolerate the
slightly higher SNR.
Optical Fibres and Telecommunications – Optical Amplifiers
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Amplified Spontaneous Emission - ASE
• The major source of noise in an amplifier is Amplified
Spontaneous Emission (ASE.)
• As well as stimulated emission, spontaneous emission can
occur.
• Spontaneous photons following the same path as the signal
are amplified via stimulated emission.
• Random in phase → Noise in signal bandwidth !
• Can derive an expression for the average total ASE power:
– PASE=2µhνGamp ∆ν
– Gamp = amplifier gain, ∆ν = amplifier bandwidth.
– µ is the population inversion factor → µ=N2/(N2-N1)
Optical Fibres and Telecommunications – Optical Amplifiers
The effect of ASE
-37
-9
-47
-19
-57
-29
-67
1526nm
1576nm
-39
1526nm
1576nm
Increased Noise !
Figures from Ghatak – Introduction to Fibre Optics
Optical Fibres and Telecommunications – Optical Amplifiers
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Conclusions
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Why do we need amplifiers?
Easier ways of dealing with power.
Calculations for simple fibre links.
Gain behaviour:
– Small signal gain.
– Gain saturation.
• Noise figures
• Amplified Spontaneous Emission (ASE)
Optical Fibres and Telecommunications – Optical Amplifiers
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