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