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Fiber Optical Communication Lecture 6, Slide 1
Lecture 6
• Two types of optical amplifiers:
– Erbium-doped fiber amplifier (EDFA)
– Raman amplifiers
• Have replaced semiconductor optical amplifiers in the course
Fiber Optical Communication Lecture 6, Slide 2
Benefits and requirementsBenefits:
• Eliminates the need for optoelectronic regenerators in loss-limited systems
• Can improve the receiver sensitivity
• Can increase the transmitted power
• Can be used at all bit rates and for all modulation formats
• Can amplify many WDM channels simultaneously
Requirements:
• An ideal amplifier has
– High gain, high output power, and high efficiency
– Large gain bandwidth
– No polarization sensitivity
– Low noise
– No crosstalk between WDM channels
– Ability to amplify broadband analog and digital signals (kHz –100’s GHz)
– low coupling losses to optical fibers
Fiber Optical Communication Lecture 6, Slide 3
Amplifier applications
Four main applications:
• In-line: Compensates for transmission losses
• Power amp: Increases the transmitter output power
• Pre-amp: Enhances the sensitivity of the receiver
• (LAN amp: Compensates for coupling losses in a network)
Fiber Optical Communication Lecture 6, Slide 4
Fiber Optical Communication Lecture 6, Slide 5
• Electrical symbol rate: 32.4Gbd
• Polarization multiplexed 64QAM format
• 272 lasers at 33 GHz spacing (SE = 7.1 b/s/Hz) covering 73 nm
• Bit rate: 32.4 G x 2 x 6 x 272 = 105,8 Tb/s
• 66.7% overhead 63.5 Tb/s data rate
Fiber Optical Communication Lecture 6, Slide 6
5380 km transmission
Fiber Optical Communication Lecture 6, Slide 7
Amplifier types• Doped fiber amplifiers use excitation of ions in the host fiber
– The erbium-doped fiber amplifier (EDFA) is most common
• Optically pumped by laser light at higher energy (shorter wavelength)
• Raman and Brillouin amplifiers use nonlinear processes to transfer energy from the pump wave to the signal
– Vibrations (phonons) in the silica glass are involved in the process
• Parametric amplifiers use a nonlinear process (FWM) to transfer energy from the pump wave to the signal
• Semiconductor optical amplifiers (SOA) are electrically pumped
– Also called semiconductor laser amplifier (SLA)
– In principle, a semiconductor laser biased below threshold
Fiber Optical Communication Lecture 6, Slide 8
General concepts• Amplification can be lumped or distributed
– An EDFA is lumped
• Gain occurs in a short piece of fiber
– Raman amplifiers are often distributed
• Gain occurs within the transmission fiber itself
• An EDFA relies on stimulated emission
– A stimulated transition to a lower energy level ⇒ emission of a photon
– Energy is ”pumped” into the medium to induce population inversion
• Without population inversion, absorption will dominate
– Even in the absence of an input photon, spontaneous emission occurs
• Will add noise in optical amplifiers
• In a Raman amplifier, power is transferred from a pump wave
– Pump has shorter wavelength (1.45 μm for 1.55 μm signal)
– Pumping can be done in forward or backward direction (or both)
• Backward pumping minimizes transfer of pump intensity noise
Fiber Optical Communication Lecture 6, Slide 9
Lumped versus distributed amplification (7.1.2)• Lumped amplification
– The optical power decreases as Pout = Pin exp(–αz)
– With amplifier spacing LA, the gain is adjusted to G = exp(αLA)
• Typical spacing is 30–100 km
– The spacing must not necessarily be uniform
• Distributed amplification
– Denoting the gain by g0(z), we get
– Ideally g0(z) = α, but the pump power is not constant ⇒ gain decreases with distance from pump source
– Condition for compensation over distance LA is
– LA is then known as pump-station spacing
zpzg
dz
zdp])([ 0
A
L
LdzzgA
0
0 )(
Fiber Optical Communication Lecture 6, Slide 10
Gain in a pumped medium• We consider
– A two-level system, i.e., there are two different energy levels
– Population inversion is obtained with either optical or electrical pumping
• The gain coefficient, g [m-1], depends on the frequency ω and the intensity P of the signal being amplified
• The gain has a Lorentzian shape
– g0 is the peak gain coefficient determined by the amount of pumping
– ω0 and T2 are material parameters
• The saturation power is denoted by Psat
• When P = Psat, we have
sat
2
2
2
0
0
1 PPT
gg
021
0)( gg
Fiber Optical Communication Lecture 6, Slide 11
Unsaturated gain• When P << Psat, we can neglect the saturation term
• The FWHM bandwidth of the spectrum is
• The amplifier bandwidth is of more interest
– Use
to get the power gain
– The amplifier bandwidth is obtained from
and is found to be
)/(1)2/( 2Tgg
zPg
dz
zdP
])(exp[0 zgPzP
]exp[0in
out LgP
LP
P
PG
2ln
2ln
0
Lgga
Fiber Optical Communication Lecture 6, Slide 12
Saturated gain• Study the gain at the gain peak
• Integrating using P(0) = Pin and P(L) = Pout, we get
– G0 is the small signal gain
• The output saturation power is defined as the power when G = G0 /2
– Independent of G0 for large gain
sat
0
1 PzP
zPg
dz
zdP
sat
out1
0
in
out P
P
G
G
eGP
PG
Lg
eG 0
0
satsat0sat
0
0sat
out 7.02ln12
2lnPPGP
G
GP
Fiber Optical Communication Lecture 6, Slide 13
Erbium-doped fiber amplifiers (EDFA) (7.2)• The silica fiber acts as a host for erbium ions
– Erbium can provide gain close to 1.55 μm
– Optically pumped to an excited state to obtain gain
Fiber Optical Communication Lecture 6, Slide 14
Pumping and gain spectrum (7.2.1)• The energy levels of Er3+ ions have
energy levels suitable to amplify light in the 1550 nm region
– Gain peak is at 1530 nm
– Bandwidth is 40 nm
• The EDFA is optically pumped at 1480 nm or 980 nm
– 980 nm gives better performance
• Absorption and gain spectra are seen in the figure
– Absorption is for unpumped fiber
– Gain spectrum is shifted towardslonger wavelengths
Fiber Optical Communication Lecture 6, Slide 15
EDFA energy states• Energy levels in Erbium are
broadened into bands
– The gain spectrum is continuous
• Typical density of Erbium in the fiber is 1019 ions/cm3
– Relative concentration of ≈ 500 ppmcompared to index-raising dopants
• Erbium is a small perturbation
• Two possible pump wavelengths:
– 980 nm (4I15/2 – 4I11/2 transition), decays rapidly to 4I13/2
– 1480 nm (4I15/2 – 4I13/2 transition), pumping to edge of the first excited state
• The 4I13/2 state is called the meta-stable state, lifetime of ≈ 10 ms
• Usually sufficient to consider only the ground state and the meta-stable state
– The EDFA can be approximated as a two-level system
Fiber Optical Communication Lecture 6, Slide 16
EDFA gain spectrum• The EDFA gain spectrum depends on
– The co-dopants (usually germanium)
– The pump power
– The erbium concentration
• Figure shows typical gain spectrum at large pump power and absorption spectrum (without pumping)
• The transition cross-sections describe the medium capability of producing gain and absorption
– the EDFA cross-section is different for absorption and emission and differentfor the pump (σp
a, σpe) and the signal
(σsa, σs
e)
Fiber Optical Communication Lecture 6, Slide 17
EDFA characteristicsAdvantages
• High gain (up to 50 dB possible)
• Low noise figure (3–6 dB) (noise is discussed in next lecture)
• High saturation power (> 20 dBm)
• Small coupling loss to optical fiber
• No cavity ⇒ no gain frequency dependence due to reflections
• No polarization dependence
• Does not chirp signal
• Long excited state population lifetime ⇒ no crosstalk
Disadvantages
• Not very compact (compared to a semiconductor laser)
• Operates at a fixed wavelength
• Relies on external optical pumps (not electrically pumped)
Fiber Optical Communication Lecture 6, Slide 18
Two-level model (7.2.2)• The erbium population density is N2 in the meta-stable state and N1 in
the ground state ⇒ N1 + N2 = Nt = total erbium density
• We here assume σpa = σp, σp
e ≈ 0, σsa ≈ σs
e = σs, loss is negligible
• The rate equations describe the evolution of the densities
– The photon fluxes are
• ap,s are the cross-sectional area for the fiber modes
• Signal and pump powers evolve according to
– Γp,s are the mode confinement factors
• This gives
1
2211
2 )(T
NNNN
dt
dNsspp
dt
dN
dt
dN 21
pp
p
pha
P
ss
ss
ha
P
ppp
pPN
dz
dP1
ssss PNN
dz
dP)( 12
1
22 11
T
N
dz
dP
hadz
dP
hadt
dN s
ssp
p
ppp
Fiber Optical Communication Lecture 6, Slide 19
Two-level model• A steady-state solution is obtained by setting the time derivative to zero
• We obtain equations for the powers according to
– where αp,s = σp,sΓp,sNt are pump and signal absorption coefficients and
• Use N1 and N2 solutions in Ps and Pp eqs on last slide, integrate z = 0 to L
dz
dP
ha
T
dz
dP
ha
TN s
sss
p
ppp
11
2
''
'
21
1
ps
ssps
PP
PP
dz
dP
''
'
21
1
ps
ppsp
PP
PP
dz
dP
sat
'
p
p
pP
PP
sat
'
s
ss
P
PP
1,
,,sat
,T
haP
sp
spsp
sp
satsat
00exp
0 p
ss
sss
ppp
p
ppL
p
p
P
LPP
a
a
P
LPPe
P
LPp
2/
0
2/
0exp
0 satsat
s
pp
ppp
sss
s
ssL
s
s
P
LPP
a
a
P
LPPe
P
LPs
Fiber Optical Communication Lecture 6, Slide 20
EDFA gain modeling results• The (implicit) analytical expressions can be used to study the EDFA gain
• Pump power increase ⇒ small-signal gain increases
– Until all ions are excited, full population inversion, gives lowest noise figure
• Longer EDFA ⇒more ions to excite ⇒ (potentially) larger gain
• For fixed pump power, an optimal length exists that maximizes the gain
– shorter fiber ⇒ the pump power is not fully used
– too long fiber ⇒ part of EDFA is not sufficiently pumped
• 35 dB gain can be realized with < 10 mW pump power
Fiber Optical Communication Lecture 6, Slide 21
System aspects of EDFAsMulti-channel amplification in EDFAs:
• T1,EDFA ≈ 10 ms, the amplifier is “slow” to react on changing input power
– No problems related to gain modulation when doing WDM amplification
Accumulation of ASE:
• In cascaded EDFAs, ASE will cause two particular problems
– Increasing degradation of the SNR after each amplifier
– Eventually gain saturation caused by the ASE ⇒ less signal gain
Pulse amplification in EDFAs:
• Amplification of pulses in saturated EDFAs do not suffer from chirp or distortion due to gain dynamics
• For very short pulses (< 1 ps) however:
– Gain is reduced in the spectral wings due to the finite bandwidth
– GVD and nonlinearities will influence the pulse (EDFA length 100 m)
Fiber Optical Communication Lecture 6, Slide 22
Lecture
• Noise from optical amplifiers
– EDFA noise
– Raman noise
• Optical SNR (OSNR), noise figure, (electrical) SNR
• Amplifier and receiver noise
– ASE and shot/thermal noise
• Preamplification for SNR improvement
Fiber Optical Communication Lecture 6, Slide 23
Amplifier noise• All amplifiers add noise
– To amplify (make a larger copy), a physical device must ”observe” the signal
– Cannot be done without perturbing the signal
• Assured by the Heisenberg uncertainty principle
• Lumped and distributed amplification have different performance
• Noise comes from spontaneously emitted photons
• These have random
– direction
– polarization
– frequency (within the band)
– phase
• Some of these add to the signal
– Causes intensity and phase noise
Fiber Optical Communication Lecture 6, Slide 24
• Optical signals are often characterized by the optical SNR (OSNR)
– Easily measured with an optical spectrum analyzer (OSA)
• Makes signal monitoring in the lab easy ⇒ is very popular
• The definition of the OSNR is
– The index X and Y denote the two polarizations
• The OSNR is related to the SNR, Q, and BER
• OSNR is usually normalized to a 0.1 nm bandwidth
– Entire signal power is included, noise is measured over 0.1 nm
– Implies required OSNR (for given BER) is bit rate-dependent
Definition of the optical SNR
OSNR
ASE
signal
Ynoise,Xnoise,
Ysignal,Xsignal,
2}signalonpolarizatisingleFor{OSNR
P
P
PP
PP
Fiber Optical Communication Lecture 6, Slide 25
EDFA noise (7.2.3)• The noise is called amplified spontaneous emission (ASE)
– Is being amplified since there is gain
– Will reach the receiver (remaining optical path is amplified)
• The ASE power at the output of the EDFA
– Δν0 is the effective bandwidth of the optical filter used to suppress noise
– SASE is the (onesided) noise power spectral density (PSD)
– This is the power per polarization
• nsp is the spontaneous-emission factor also known as the population-inversion factor
– For an EDFA
oo GhnSP )1(0spASEASE
112
2
12
2sp
NN
N
NN
Nn
a
s
e
s
e
s
Fiber Optical Communication Lecture 6, Slide 26
OSNR due to EDFA noise (7.4.1)• The OSNR is reduced each time a signal is amplified
– Each EDFA add to the noise PSD due to the generation of more ASE
• After NA amplifiers in a link with span loss equal to the gain in each amplifier and with identical EDFA noise performance, we have
• In dB and dBm at 1550 nm and Δν0 = 0.1 nm, we have
Ps
EDFALA
1 2 NAPs
dBm58dB][dB][2dB][dBm][OSNR spindB GnNP A
GhnN
P
GhnN
P
PN
P
oAooAA 1.0sp
in
sp
in
ASE
in
2)1(22OSNR
Fiber Optical Communication Lecture 6, Slide 27
What is the max. transmission distance with 100 km or 50 km EDFA spacing?
– A 10 Gbit/s system with a OSNR requirement of 20 dB
– The loss is 0.25 dB/km and 2nsp = 5 dB
– The launched power into each span is 1 mW per WDM channel
– LA = 100 km ⇒ NA = 8 dB = 6.3 ⇒ 6 amps ⇒ 700 km
– LA = 50 km ⇒ NA= 20.5 dB = 112.2 ⇒ 112 amps ⇒ 5650 km
• The amplifier spacing plays a critical role for the OSNR
– Short LA: Noise accumulates slowly ⇒ high OSNR at receiver
– Long LA: Few EDFAs are needed ⇒ system cost is lower
• Shows trade-off between cost and performance
– Techniques that enable cost reduction are desirable
• This can, for example, be error correction or distributed amplification
• Hints that distributed amplification may perform better
OSNR due to EDFA noise, example
dBm58dB][dB][2dB][dBm][OSNR spindB GnNP A
Fiber Optical Communication Lecture 6, Slide 28
OSNR due to EDFA noise, amplifier spacing• We can express the number of amplifiers as
– LT is the total system length
– This gives the OSNR
• We see that
• Figure shows maximum system length = ”system reach”
– OSNR = 20 dB
– α = 0.2 dB/km
– nsp =1.6
– Δν0 = 100 GHz
G
LN T
Aln
)1(2
lnOSNR
1.00sp
in
GLhn
GP
T
G
GP
ln
1ASE
Fiber Optical Communication Lecture 6, Slide 29
Electrical signal-to-noise ratio (SNR) (7.5.1)• The Q and BER are determined by the SNR in the detected current
– Agrawal calls this ”electrical signal-to-noise ratio” to separate from OSNR
• An EDFA can improve the sensitivity of a thermally noise limited receiver
– A preamplified optical receiver
– The added optical noise can be much smaller than the thermal noise
• The generated photocurrent in the receiver is
– Ecp = ASE co-polarized with signal
– Eop = ASE orthogonal with signal
– is = Shot noise
– iT = Thermal noise
• The ASE has a broad spectrum, and can be written
– The magnitude square is a multiplication ⇒ new frequenciesare generated ⇒ “beating”
Gnsp
PinBPF
receiver
Tssd iiEEEGRI
2
op
2
cp
M
m
mms tiiSE1
2/1
ASEcp )exp()(
Fiber Optical Communication Lecture 6, Slide 30
Electrical signal-to-noise ratio (SNR)• The received electrical current is
– isig-sp = signal-ASE beat noise term
– isp-sp = ASE-ASE beat noise term
• The variance of the noise terms are
– Δν0 is bandwidth of optical bandpass filter (rejects out-of-band noise)
• The SNR is here defined as
Tssd iiiiGPRI spspspsig
fSGPR sd ASE
22
spsig 4 )2/(4 0
2
ASE
22
spsp ffSRd
fPGPRq sds )(2 ASE
2 fRTk LBT )/4(2
222
spsp
2
spsig
2
2
2
)(SNR
Ts
sdGPRI
Fiber Optical Communication Lecture 6, Slide 31
Impact of ASE on SNR (7.5.2)• Let us compare the SNR without and with amplification by an EDFA
– Amplifier and bandpass filter is inserted before the receiver
– Notice that σs are different in the two cases (σT stays the same)
– We neglect σsp-sp and the noise current contribution to shot noise to get
– We use the PSD and the ideal responsivity
– We get
• Notice: kT is ratio (thermal noise)/(shot noise) without amplification
• All quantities in the denominator (2qRdPsΔf) are kept constant!
222
spsp
2
spsig
2
amp22
2
amp no
)(SNR,
)(SNR
Ts
sd
Ts
sd GPRPR
2
2
2
ASE
2
2
amp no
amp
)(
)2(
)2()4(
)(
SNR
SNR
sd
Tsd
Tsdsd
sd
PR
fPqR
fGPqRfSGPR
GPR
GhnGGhnS 0sp0spASE }1{)1( )/( 0hqRd
2
spamp no
amp
//12
1
SNR
SNR
GkGn
k
T
T
fPqRk
sd
TT
2
2
Fiber Optical Communication Lecture 6, Slide 32
A thermal noise-limited receiver• How is the SNR changed in the thermal limit?
• First assume that thermal noise dominates before and after amplification
– There is a huge improvement in the SNR
• Signal power is increased, noise power remains constant
• However, at high G, we cannot ignore the other noise terms
• Study the realistic case that thermal noise dominates before and is negligible after amplification
– SNR improvement saturates as G is increased
– Improvement can be very large
2
22
spamp no
amp
///12
1
SNR
SNRG
Gk
k
GkGn
k
T
T
T
T
spsp
2
spamp no
amp
2/12//12
1
SNR
SNR
n
k
Gn
k
GkGn
k TT
T
T
In the thermal limit, amplification improves the SNR
Fiber Optical Communication Lecture 6, Slide 33
A shot noise-limited receiver, noise figure (7.2.3)• Now instead assume that the optical signal has high power
– Thermal noise is negligible
– The SNR is decreased by the amplification
• The noise figure is defined
• The SNR values are what you would obtain by putting an ideal receiver before and after an EDFA, respectively
– Ideal means shot noise-limited, 100% quantum efficiency
• Our study above has provided us with the (inverse) minimum value
spsp
2
spamp no
amp
2
1
/12
1
//12
1
SNR
SNR
nGnGkGn
k
T
T
EDFA amplification of a perfect signal decreases the SNR by > 2nsp (> 3dB)
out
in
)SNR(
)SNR(NF nF
22 sp nFn
Fiber Optical Communication Lecture 6, Slide 34
Noise figure• For an EDFA, the noise figure is
• In reality, N1 and N2 change along the EDFA
– Pump power and signal power are not constant
– The rate equations can be solved numerically
• Figure shows
– Noise figure and amplifier gain as a function of...
– ...pump power and amplifier length
• A long amplifier
– Can provide high gain
– Requires high pump power
sp2nFn 112
2
12
2sp
NN
N
NN
Nn
a
s
e
s
e
s
Fiber Optical Communication Lecture 6, Slide 35
Noise figure• The noise figure is increased
– If the population inversion is incomplete (somewhere in the amplifier)
– If there are coupling losses into the amplifier
• Pumping is facilitated by pumping at 980 nm
– No stimulated emission caused by pump photons (σpe ≈ 0)
• Corresponding energy level is almost empty (short-lived)
– Noise figure ≈ 3 dB is possible, 3.2 dB has been measured
• With 1480 nm pumping σpe ≠ 0
– Ground state will always be populated by some ions
• Some excited ions will be stimulated by pump photons to relax
– Noise figure is larger for this case
• Coupling into and out of an EDFA is efficient
• Typical EDFA modules have Fn = 4–6 dB
Fiber Optical Communication Lecture 6, Slide 36
SNR/OSNR relation• In general, there is no simple relation between the OSNR and the SNR
– OSNR is prop. to the optical power, SNR is prop. to the electrical power
– Electrical power is proportional to the (optical power)2
• Not true in a coherent receiver
• When signal–ASE noise is dominating we have
• For a single-polarization signal, we can use
– Es is the energy per symbol, fs is the symbol rate (in baud)
– Es/SASE is often written Es/N0 is digital communication literature
– The relation between Es/N0 and the BER depends on the type of receiver, modulation format and more
OSNR244
)(SNR 1.0
ASE
1.0
ASE
2
2
ffP
GP
fSGPR
GPR s
sd
sd
1.0ASE1.0ASE 22OSNR
sss f
S
E
S
P
Fiber Optical Communication Lecture 6, Slide 37
Receiver sensitivity and Q factor (7.6.1)• When shot noise and thermal noise are negligible:
– The statistics are not Gaussian (cannot have negative current)...
– ...but Gaussian statistics are often used anyway for simplicity
• The receiver sensitivity is then
• Assuming that Prec = Nphν0B and Δf = B/2, we get
• The number of photons per bit depends on
– The BER (via Q), the noise figure, and the receiver bandpass filter
2
spsp
2
spsig
222
spsp
2
spsig
2
1 Ts
2
spsp
22
spsp
2
0 T
2
102
0recf
QQfFhP o
2
1
2
1 02
fQQFN op
Low-noise amplification and narrow filtering is critical for high performance
Fiber Optical Communication Lecture 6, Slide 38
Receiver sensitivity of preamplified receiver• Using Fo = 2, Q = 6, Δν0 = B⇒ Np= 43 photons per bit on average
• The quantum limit is Np = 10 photons per bit on average
BER = 10-9
Np = 100 is realistic with a reasonable noise figure and filter bandwidth
Fiber Optical Communication Lecture 6, Slide 39
Relation between Q and the OSNR• When ASE noise dominates, we have
– Δνo = bandwidth of optical bandpass filter [nm]
– Δf = equivalent receiver electrical bandwidth [GHz]
• In figure, Δνo = 0.4 nm
– Reasonable value for a 10 Gbit/s system
• The necessary OSNR = 15–20 dBat a bit rate of 10 Gbit/s
111.0
OSNR4
1.0OSNR2
125
o
oo
fQ
0
2
4
6
8
10
12
14
16
13 15 17 19 21 23 25OSNR (dB) @ 0.1 nm
Q (
lin
ear)
f =5GHz10 GHz20 GHz
BER = 10-12
If we know the OSNR and the bandwidths, we can find Q and the BER