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Optical amplifiers and their applicationsRef: Optical Fiber Communications by: G. Keiser; 3rd edition
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Optical Amplifiers
Two main classes of optical amplifiers include:
Semiconductor Optical Amplifiers (SOA) and
Doped Fiber Amplifiers (DFA)
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Basic operation of optical amplifiers
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Semiconductor Optical Amplifiers
There are two types of SOAs:
--- Fabry- Perot amplifiers (FPA)When the light enters FPA it gets amplified as it reflects back and forth between the mirrors until emitted at a higher intensity.It is sensitive to temperature and input optical frequency.
---Non-resonant traveling-wave amplifiers (TWA)It is the same as FPA except that the end facets are either antireflection coated or cleaved at an angle so that internal reflection does not take place and the input signal gets amplified only once during a single pass through the device. They widely used because they have a large optical bandwidth, and low polarization sensitivity.
Ref: Optical Fiber Communications by: G. Keiser; 3rd edition
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External Pumping
External pumping injection creates population inversion similar to LASERs.The rate equations can be defined as:
rstp
tntRtRttn
τ)()()()(
−−=∂
∂
qdtJtRp)()( =
is the external pumping rate, J(t) is the current density, d is the active layer thickness, and τr is the combined time constant coming from spontaneous-carrier recombination mechanism.Rst(t) is the stimulated emission and it is equal to:
phgphthgst NgvNnnavtR ≡−Γ= )()(
Non-resonant traveling-wave amplifiers (TWA)
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External Pumping (Cont…)
))(( wdhvvP
Ng
sph =
where vg is the group velocity of the incident light, Г, optical confinement factor, a is the gain constant, nth is threshold carrier density, Nph is the photon density and g is the overall gain per unit of length.
where Ps is the power of optical signal, w and d are width and the thickness of active area respectively.
Under steady state condition, variation of n vs time is zero, therefore:
rstp
nRRτ
+=
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External Pumping (cont…)
Substituting for Rp and Rst and solving for g yields:
satphphrphg
r
th
NNg
aNv
nqdJ
g;
0
/1)/(1 +=
Γ+
−=
ττ
rgsatph av
NτΓ
=1
; ⎟⎟⎠
⎞⎜⎜⎝
⎛−Γ=
r
thr
nqdJag
ττ0
where and
where go is the zero or small-signal gain per unit of length (in the absence of the signal input)
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Amplifier Gain
Amplifier gain or signal gain G is defined as:
ins
outs
PP
G,
,=
( )[ ]LzgLgG m expexp_
≡⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −Γ= αOr as we saw in the case of laser:
where, gm , α, and L are the material gain coefficient, the effective absorption coefficient of the material and amplifier length respectively. g(z) is the overall gain per unit of length.
g(z) can written as:
satamp
s
PzP
gzg
,
0
)(1
)(+
=go, Ps(z), and Pamp,sat are the unsaturated medium gain per unit of length in the absence of signal input, internal signal power at z, and amplifier saturation power.
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Amplifier Gain
The increase in the light power in incremental length of dz can be expressed as:
dzzPzgdP s )()(=
dPPzP
dzgsatamps⎟⎟⎠
⎞⎜⎜⎝
⎛+=
,0
1)(
1
∫∫ ⎟⎟⎠
⎞⎜⎜⎝
⎛+=
outPs
inPs satamps
L
dPPzP
dzg,
, ,00
1)(
1
⎟⎠⎞
⎜⎝⎛+=
GG
PP
Gins
satamp 0
,
, ln1
Which can show:
now
and finally one can see that:
where Go = exp (goL) is the single-pass gain in the absence of light.
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Amplifier gain versus power
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Erbium-Doped Fiber Optic AmplifiersErbium energy-level diagram and
amplification mechanism
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EDFA configurations
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EDFA Power-Conversion Efficiency (PCE) and Gain
The input and output power of an EDFA can be expressed:
inps
pinsouts PPP ,,, λ
λ+≤
1,
,
,
,, ≤≤≈−
=s
p
inp
outs
inp
insouts
PP
PPP
PCEλλ
ins
inp
s
p
ins
outs
PP
PP
G,
,
,
, 1λλ
+≤=
The Power Conversion Efficiency (PCE) is defined as (always less than unity)
We can also write the amplifier gain as:
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Optical AmplifiersEDFA Power-Conversion Efficiency (PCE) and Gain
1
,
, −≤
G
PP
inps
p
insλλ
In order to achieve a specific maximum gain G, the input signal power can NOT exceed a value given by
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EDFA Power-Conversion Efficiency (PCE) and Gain
( )LG eρσexpmax =
where ρ is the rare-earth element concentration and σe is the signal-emission cross section.Therefore the maximum gain or power will be defined as:
( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
+≤ins
inp
s
pe P
PLG
,
,1,expminλλ
ρσ
( )⎭⎬⎫
⎩⎨⎧
+≤ inps
pinseinsouts PPLPP ,,,, ,expmin
λλ
ρσ
Optical Amplifiers
The maximum gain in a 3 level laser medium of length L can also be given as follow (in addition to pump power, the gain depends on the filter length)
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Gain versus EDFA length
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Absorption and Emission Cross-Sections in EDFA
• The effect of absorption and emission efficiencies in external pumping in EDFA are realized by defining new parameters called Absorption Cross-Section, σaa and Emssion Cross-Section, σe respectively.
• σaa determines the pumping rate. If the pumping power is Pp and Er ground state population is N0, the pumping rate is WpN0 where,
• σe determines the medium gain, g= σeN2. N2 is metastable (inversion layer) population>N1
• Stimulated emission rate, Rs is: Where Ps-in is the incident light power.
• Therefore the pumping gain will be:L is the length of the pump.
AhP
W pap ν
σ=
AhNPgNVR inse
phgs νσ 2−==
LNN
inp
outpp
aeePP
G )( 02 σσ −
−
− ≅=
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Components for Optical Communications
• Passive ComponentsCouplers, AttenuatorsEqualizers,IsolatorsWDM• Active ComponentsModulators,Diodes,Switches,Routers
Materials for self-studies
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Some applications of Light polarization
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Optical Diode
Rutile Half wave plate
Faraday Rotator
Rutile Half Wave Plate Faraday Rotator Calcite, Rutile
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Transmission windows
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WDM
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Optical Interference
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Fiber Bragg grating
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Fiber Bragg grating fabricationPhase Mask: Direct Imprinting
0th order(Suppressed)
Diffractionm = -1
Diffractionm = +1
Phase MaskΛPM
Ge doped Fiber
248 nm Laser
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Reflection grating
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Typical WDM Network
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Simple demultiplexer function
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Extended add/drop multiplexer
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Tunable optical filter
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