Two types of optical amplifiers - ttu.ee 10.pdf · Fiber Optical Communication Lecture 10, Slide 4...
Transcript of Two types of optical amplifiers - ttu.ee 10.pdf · Fiber Optical Communication Lecture 10, Slide 4...
Fiber Optical Communication Lecture 10, Slide 1
Lecture 10
• Two types of optical amplifiers:
– Erbium-doped fiber amplifier (EDFA)
– Raman amplifiers
• Have replaced semiconductor optical amplifiers in the course
Fiber Optical Communication Lecture 10, 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 10, 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 10, Slide 4
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 10, Slide 5
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 10, Slide 6
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 10, Slide 7
Bidirectional pumping scheme (7.1.3)• In bidirectional pumping, the gain is
– αp is the loss at the pump wavelength
– g1 and g2 are constants proportional to the launched pump power
• Assuming equal pump powers and that initial and final signal power = 1
• Assuming backward pumping (g1 = 0)
• Figure shows backwards and bidirectional Raman amplification
– EDFA case shown for comparison
– Raman evens out power fluctuations
)](exp[)exp()( 21 zLgzgzg App
z
L
LLzLzp
Ap
ApAp
A
)2/sinh(2
)2/sinh()2/(sinh[exp)(
z
L
zLzp
Ap
p
A
1)exp(
1)exp(exp)(
Fiber Optical Communication Lecture 10, Slide 8
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 10, Slide 9
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 10, Slide 10
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 10, Slide 11
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 10, Slide 12
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 10, Slide 13
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 10, Slide 14
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 10, Slide 15
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 10, Slide 16
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 10, Slide 17
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 10, Slide 18
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 10, Slide 19
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 10, Slide 20
Raman amplifiers (7.3)
• Raman amplifiers are based on stimulated Raman scattering
• The pump and the signal co-propagate
– Power is transferred during transmission
– The pump wavelength is shorter than the signal wavelength
– The excess energy is given to the medium (the fiber)
• A molecular vibration (optical phonon) is created
• The pump and signal can propagate in different directions
Fiber Optical Communication Lecture 10, Slide 21
Raman gain and bandwidth (7.3.1)• The Raman gain spectrum is a property of amorphous glass
• The Raman gain coefficient is proportional to the pump intensity Ip
– ap is the cross-sectional area of the pump beam, depends on fiber type
• DCF has a small core diameter and a large gR/ap
• Figure shows gR/ap and normalized gains
• Gain peaks at 13.2 THz
– Shift between absorbed and emitted photons is called Stokes shift
• Similar gain spectra for all fibers
– The FWHM of the gain peak is nearly 6 THz
• Requires rather high powers
– Example (see the book): G > 20 dB requires > 5 W in a 1-km-long fiber
)()(
)()(),( zPa
gzIgzg p
p
RpR
Fiber Optical Communication Lecture 10, Slide 22
Raman induced signal gain (7.3.2)• Consider a CW signal and a CW pump
– Frequency ratio occurs since pumpphotons have higher power
• If the pump is undepleted (affected only by loss), we have
• The amplifier gain is given by
– Obtained as (output power with Raman)/(output power without Raman)
• Figure shows:
– Amplifier gain increases exponentially...
– ...until gain saturation occurs
pspRspppp
sppRsss
PPagPdzdP
PPagPdzdP
)/)(/(/
)/(/
])0()/exp[()0()( eff LLPagPLP sppRss ppLL /)]exp(1[eff
La
PgL
L
L
a
PggLgG
pp
Rp
p
RA
0eff000 }1{),exp(
Fiber Optical Communication Lecture 10, Slide 23
Raman induced signal gain• The pump supplies the signal with power
– When the transferred energy is significant, the pump is depleted
– The gain is decreased, referred to as gain saturation
• The saturated amplified gain can be found numerically...
– Like in figure on previous slide
• ...or analytically, assuming αs = αp, as
• Figure shows gain-saturation characteristics
– Gain is reduced by 3 dB when GAr0 ≈ 1
– In a system, Raman amplifiers typicallyoperate in the unsaturated regime
)0(
)0(,
)exp()1(0)1(
0
0
0
p
s
s
p
r
A
ss
P
Pr
Gr
LrG
Fiber Optical Communication Lecture 10, Slide 24
Multiple-pump Raman amplification (7.3.3)• A WDM system with many channels require broadband amplifiers
– 100 channels may require uniform gain over 70–80 nm (10 THz)
• Broadband amplification can be achieved with
– Hybrid EDFA/Raman amplification
– Raman amplification using multiple pump lasers
• Multiple-pump Raman amplification
– Will set up a superposition of gain spectra
• Is more broadband since it is flatter
– Requires careful selection of the pump wavelengths
• Will determine the gain ripples
– Requires consideration of pump–pump interactions
• The pump waves are affected by the Raman interaction
• In general, this is studied numerically
– A large coupled system of differential equations must be solved