OPTICAL COMMUNICATIONSOPTICAL …metrology.hut.fi/courses/S-108.3110/2009/Introduction_Light... ·...
Transcript of OPTICAL COMMUNICATIONSOPTICAL …metrology.hut.fi/courses/S-108.3110/2009/Introduction_Light... ·...
OPTICAL COMMUNICATIONSOPTICAL COMMUNICATIONSS 108 3110S-108.3110
1
Course Programg5 lectures on Fridays
First lecture Friday 06.11 in Room H-402 13:15-16:30 (15 minutes break in-between)
ExercisesDemo exercises during lecturesgHomework Exercises must be returned beforehand (will count in final grade)
Seminar presentationSeminar presentation27.11, 13:15-16:30 in Room H-402Topic to be agreed beforehand
2 labworks2 labworksPreliminary exercises (will count in final grade)
Exam 17.1215.01
5 op
2
p
Course Schedule
1. Introduction and Optical Fibers (6.11)
2. Nonlinear Effects in Optical Fibers (13.11)
3. Fiber-Optic Components (20.11)
4 Transmitters and Receivers (4 12)4. Transmitters and Receivers (4.12)
5. Fiber-Optic Measurements & Review (11.12)
3
Lecturers
In case of problems, questions...p , q
Course lecturersG. Genty (3 lectures) [email protected]. Manoocheri (2 lectures) [email protected]
4
Optical Fiber Concept
Optical fibers are light pipesOptical fibers are light pipes
Communications signals can be transmitted over these hair thin strands oftransmitted over these hair thin strands of glass or plastic
Concept is a century old
But only used commercially for the lastBut only used commercially for the last ~25 years when technology had matured
5
Why Optical Fiber Systems?
Optical fibers have more capacity than other
y p y
Optical fibers have more capacity than other means (a single fiber can carry more information than a giant copper cable!)
PricePrice
Speed
Di tDistance
Weight/size
Immune from interference
Electrical isolation
Security
6
Optical Fiber ApplicationsOptical fibers are used in many areas
> 90% of all long distance telephony
50% f ll l l t l h> 50% of all local telephony
Most CATV (cable television) networksMost CATV (cable television) networks
Most LAN (local area network) backbones
Many video surveillance links
Military
7
Optical Fiber Technology
An optical fiber consists of two different types of solid glass
Core Cladding Mechanical protection layerMechanical protection layer
1970: first fiber with attenuation (loss) <20 dB/km 1979: attenuation reduced to 0.2 dB/km commercial systems!
8
Optical Fiber CommunicationOptical fiber systems transmit modulated infrared light
FiberFiber
Transmitter ReceiverComponentsp
Information can be transmitted oververy long distances due to the low attenuation of optical fibers
9
Frequencies in Communications
10 k100 km
wire pairs Submarine cable
frequency
30 kHz3 kHz
1 km10 km wire pairs
TelephoneTelegraph
3 MH300 kHz30 kHz
10 m100 m
coaxialcable
TVRadio
300 MH30 Mhz3 MHz
10 cm1 m
waveguide Satellite 3 GHz300 MHz
1 cmwaveguide
Telephone
Radar 30 GHz
1 µm opticalfiber
TelephoneDataVideowavelength
300 THz
10
Frequencies in Communications
Optical Fiber: > Gb/sData rate
Optical Fiber: > Gb/sMicro-wave ~10 Mb/sShort-wave radio ~100 kb/sL di 4 Kb/Long-wave radio ~4 Kb/s
Increase of communication capacity and ratesrequires higher carrier frequencies
Optical Fiber Communication!
11
Optical FiberOptical fibers are cylindrical dielectric waveguides
Di l t i t i l hi h d t d t l t i it b t t i l t i fi ld
Cladding diameter
Cladding (pure silica)Core diameter
n2
Dielectric: material which does not conduct electricity but can sustain an electric field
Cladding diameter125 µm Core silica doped with Ge, Al…
Core diameterfrom 9 to 62.5 µm n1
Typical values of refractive indicesCladding: n2 = 1.460 (silica: SiO2)Core: n1 =1.461 (dopants increase ref. index compared to cladding)
A useful parameter: fractional refractive index difference δ = (n1-n2) /n1<<1
12
Fiber Manufacturing
Optical fiber manufacturing is performed in 3 steps
Preform (soot) fabricationdeposition of core and cladding materials onto a rod using vapors of SiCCL anddeposition of core and cladding materials onto a rod using vapors of SiCCL4 andGeCCL4 mixed in a flame burned
C lid ti f th fConsolidation of the preformpreform is placed in a high temperature furnace to remove the water vapor and obtaina solid and dense rod
Drawing in a towersolid preform is placed in a drawing tower and drawn into a p p gthin continuous strand of glass fiber
13
Fiber Manufacturing
Step 1 Steps 2&3
14
Light Propagation in Optical FibersGuiding principle: Total Internal Reflection
Critical angleNumerical aperture
ModesModes
Optical Fiber typesM lti d fibMultimode fibers Single mode fibers
Attenuation
DispersionpInter-modal Intra-modal
15
Total Internal Reflection
Light is partially reflected and refracted at the interface of two media with different refractive indices:
Reflected ray with angle identical to angle of incidenceRefracted ray with angle given by Snell’s law
Snell’s law:n1 sin θ1 = n2 sin θ2
Refracted ray with angle given by Snell s law
A l θ & θ d fi d
n1θ1
n1 > n2θ1
Angles θ1 & θ2 defined with respect to normal!!
n2θ21 2
Refracted ray with angle: sin θ = n / n sin θRefracted ray with angle: sin θ2 = n1/ n2 sin θ1Solution only if n1/ n2 sin θ1≤1
16
Total Internal Reflection
Snell’s law:sin θ = sin θ
sin θc = n2 / n1If θ >θc No ray is refracted!
θ1
n1 sin θ1 = n2 sin θ2
θ
is refracted!
θ1
n2n1
θ1
θ2n2n1
θcn1 > n2 n2
θ1
2
n2n1 θ1 θn2
For angle θ such that θ >θC , light is fully reflected at the core-cladding interface: optical fiber principle!
17
Numerical Aperture
For angle θ such that θ <θ max, light propagates inside the fiberFor angle θ such that θ >θ light does not propagate inside the fiber
n2
For angle θ such that θ >θmax, light does not propagate inside the fiber
Example: n1 = 1.47n2 = 1.46NA = 0.17
n1 θcθmax
1 with 2sin1
211
22
21max <<
−=≈−==
nnnnnnNA δδθ
Numerical aperture NA describes the acceptance angle θmax for light to be guided
18
Theory of Light Propagation in Optical Fiber
Geometrical optics can’t describe rigorously light propagation in fibers
Must be handled by electromagnetic theory (wave propagation)
Starting point: Maxwell’s equations
(1)
∂∂∂
−=×∇
DTBE
densityflux Magnetic : 0 += MHB µ
(3)
(2)
=⋅∇∂∂
+=×∇
DTDJH
fρd itChdensity Current :
density flux Electric :
00
0
=+=
JPED εwith
(4) 0=⋅∇ Bf densityCharge: 0=fρ
19
Theory of Light Propagation in Optical Fiber
( ) ( ) ( )( ) ( ) ( ) onPolarizatiLinear:(1) dttEtttP
trPtrPtrP NLL ,,,
∫∞+
+=
χ(1): linear( ) ( ) ( )( ) onPolarizati Nonlinear :
onPolarizatiLinear:(1)
TrP
dttrEtttrP
NL
L
,
,, 1110 ∫ ∞−−= χε χ( ): linear
susceptibility
We consider only linear propagation: PNL(r,T) negligible
20
Theory of Light Propagation in Optical Fiber
22 ( , )1 ( , )( ) LP r tE r tE r t µ ∂∂∇×∇× + = 02 2 2( , )
We now introduce the Fourier transform: ( , ) i t
-
E r tc t t
E r E(r,t)e dtω
µ
ω+∞
∞
∇×∇× + = −∂ ∂
= ∫%
( )2
( , ) ( , )k
kk
E r t i E rt
ω ω∂⇔
∂%
2(1) 2
0 02And we get: ( , ) ( , ) ( ) ( , )
which can be re
E r E r E rcωω ω µ ε χ ω ω ω∇×∇× − = +% % %
written as2
2 (1)0 02( , ) 1 ( ) ( , ) 0E r c E r
cωω µ ε χ ω ω⎡ ⎤∇×∇× − + =⎣ ⎦
% %
2
2i.e. ( , ) ( ) ( , ) 0E r E rcωω ε ω ω∇×∇× − =% %
21
Theory of Propagation in Optical Fiber
[ ]12α ⎤⎡ c [ ]
[ ])(and
)(211 with
2)(
)1(
)1(
ωχωα
ωχω
αωε
ℑ
ℜ+=⎥⎦⎤
⎢⎣⎡ += ncin n: refractive index
α: absorption[ ])(
)(and )( ωχ
ωα ℑ=
cn
( )( )0),(~),(~
),(~),(~),(~),(~ 22
=⋅∇∝⋅∇
−∇=∇−⋅∇∇=×∇×∇
ωω
ωωωω
rDrE
rErErErE
( ))()(
2ω Equation! Helmoltz : 0),(~),(~ 222 =+∇ ωωω rE
cnrE
22
Theory of Light Propagation in Optical Fiber
Each components of E(x,y,z,t)=U(x,y,z)ejωt must satisfy the Helmoltz equation
⎪⎩
⎪⎨
⎧
=>=≤=
=+∇λπ /2
0
0
2
12
022
karnnarnn
UknU for for
with Note: λ=ω /c
Assumption: the cladding radius is infiniteIn cylindrical coodinates the Helmoltz equation becomes
⎩ 0
⎪⎩
⎪⎨
⎧
=>=≤=
=+∂∂
+∂∂
+∂∂
+∂∂
00
2
12
02
2
2
2
2
22
2
/2011
λπϕ
karnnarnn
UknzUU
rrU
rrU for
for with
⎩ 00 /2 λπk
x ErE
φ
yz
Ez
Eφ
r
23
Theory of Light Propagation in Optical Fiber
U = U(r,φ,z)= U(r)U(φ) U(z)Consider waves travelling in the z direction U( ) jβzConsider waves travelling in the z-direction U(z) =e-jβz
U(φ) must be 2 periodic U(φ) =e-j lφ , l=0,±1,±2…integer
⎧ ≤
±±== −− ...2,1,0)(),,( ϕ βϕ leerFzrU zjjl
f:gets one Eq. Helmoltz the into Plugging
with
⎪⎩
⎪⎨
⎧
=>=≤=
=⎟⎟⎠
⎞⎜⎜⎝
⎛−−++ 2
1
2
222
02
2
2
/201
λπβ
karnnarnn
Frlkn
drdF
rdrFd for
for with
⎩ = 00 /2 λπk
refraction ofindex effectivean definecan One neff β = k0 neff is the ti
,such that 12 nnnnc effeff <<=ωβ
propagation constant
24
Theory of Propagation in Optical Fiber
A light wave is guided only if 0102 knkn ≤≤ βg g y
We introduce
0102 β
( )( )222
2201
2
kn
kn
−=
−=
βγ
βκ
real:0, :Note 22
γκγκ ≥
( )( ) constant! :22
022
21
20
2202
NAknnk
kn
=−=+
=
γκ
βγ real:, γκ
ldFFd ⎞⎛
:get then We
1 22
ldFFd
arFrl
drdF
rdrFd
⎞⎛
≤=⎟⎟⎠
⎞⎜⎜⎝
⎛−++ for
1
01
22
2
22
2
2
κ
arFrl
drdF
rdrFd
>=⎟⎟⎠
⎞⎜⎜⎝
⎛+−+ for 01
22
2 γ
25
Theory of Propagation in Optical Fiber
( )lJ
arJrF ll
orderithkind1off nctionBessel:
for )(:form theofareequationstheofsolutions The
st
≤= ρκ
( )lK
arKrFlJ
ll
l
orderwithkind1offunctionBesselModified:
for )(order with kind1offunction Bessel :
st
st
>= ργ
lKl order with kind1offunction BesselModified :
with
( )( )2
0222
2201
2
kn
kn
−=
−=
βγ
βκ
( ) constant! :220
22
21
20
22 NAknnk =−=+ γκ
26
Examples
l=0 l=3
K0(γr)J0(κr)K0(γr) K3(γr)J3(κr)K3(γr)r
a aar
⎨⎧ ≤
∝arrJ
rF for )(
)( 0 κ⎨⎧ ≤
∝arrJ
rF for )(
)( 3 κ
⎩⎨ < arrK
rFfor)(
)(0 γ ⎩
⎨ < arrKrF
for)()(
3 γ
27
Characteristic Equation
Boundary conditions at the core-cladding interface give a condition on the propagation constant β (characteristics equation)
β:equationsticscharacterithe
solvingby found becan constant n propagatio The
βkn
lK
KJ
Jnn
KK
JJ lm
l
l
l
l
l
l
l
l⎥⎦⎤
⎢⎣⎡
Γ+
Κ=⎥
⎦
⎤⎢⎣
⎡ΓΓ
Γ+
ΚΚΚ
×⎥⎦
⎤⎢⎣
⎡ΓΓ
Γ+
ΚΚΚ 11
)()(
)()(
)()(
)()(
q2
2220
22
22''
22
21
''
γκ aa =Γ=Κ and with
For each l value there are m solutions for βEach value βlm corresponds to a particualr fiber mode
28
Number of Modes Supported by an Optical Fiberpp y pSolution of the characteristics equation U(r,φ,z)=F(r)e-jlϕe-jβlmz iscalled a mode, each mode corresponds to a particularp pelectromagnetic field pattern of radiation
The modes are labeled LPlThe modes are labeled LPlm
Number of modes M supported by an optical fiber is related to the V parameter defined asV parameter defined as
22
210
2 nnaNAakV −==λπ
M is an increasing function of V !
λ
If V <2.405, M=1 and only the mode LP01 propagates: the fiber is said Single-Mode
29
Number of Modes Supported by an Optical FiberNumber of modes well approximated by: ( )
22 2 2 2
1 22/ 2, where aM V V n nπ
λ⎛ ⎞≈ ≈ −⎜ ⎟⎝ ⎠
1.0LP01
0.8 LP11
Example:2a =50 µmn1 =1.46 V=17.6core
21020.6
31 12 4122 32
2
nnnneff −
1 δ=0.005 M=155λ=1.3 µm
220.4 3261
51 1303 23
420.2 71045281
21 nn −
528133
0 2 4 6 8 10 12V
If V <2.405, M=1 and only the mode LP01 propagates: Single-Mode fiber!
30cladding
Examples of Modes in an Optical Fiberλ =0.6328 µm a =8.335 µm n1 =1.462420 δ =0.034
31
Examples of Modes in an Optical Fiberλ =0.6328 µm a =8.335 µm n1 =1.462420 δ =0.034
32
Cut-Off Wavelength
The propagation constant of a given mode depends on the wavelength [β (λ)]wavelength [β (λ)]
The cut-off condition of a mode is defined as β2(λ)-k02 n2
2= β2(λ)-β ( ) 0 2 β ( )4π2 n2
2/λ2=0
Th i t l th λ b hi h l th f d t lThere exists a wavelength λc above which only the fundamental mode LP01 can propagate
λλ
δδπλ 11
4052
84.12405.22405.2 ananV C ==⇔<
Example:2a =9.2 µmn1 =1.4690
δλ
δλ
π 11
54.02405.2
nna cc ==ly equivalent or
1 δ=0.0034λc~1.2 µm
33
Single-Mode Guidance
In a single-mode fiber, for wavelengths λ >λc~1.26 µm l th LP d tonly the LP01 mode can propagate
34
Mode Field Diameter
The fundamental mode of a single-mode fiber is well approximated by a Gaussian function
2⎞
⎜⎛ ρ
fb i diidf hiidAsize mode the andconstant a is where
)(
0
0
wCCeF w=
⎟⎠
⎞⎜⎜⎝
⎛−
ρ
ρ
4221for 879.2619.165.0
fromobtainedissizemodefor theion approximatgoodA
62/30 .V.VV
aw <<⎟⎠⎞
⎜⎝⎛ ++=
42for )ln(0 .V
Vaw >=
35Fiber Optics Communication Technology-Mynbaev & Scheiner
Types of Optical Fibers
Step index single modeStep-index single-mode
Cladding diameter125 µm
Core diameterfrom 8 to 10 µm n1
n2
Refractive index profile
n
δ 0 001n1p
δ = 0.001n2
r
36
Types of Optical Fibers
Step index multimodeStep-index multimode
Cladding diameterfrom 125 to 400 µm
Core diameterfrom 50 to 200 µm n1
n2
Refractive index profile
n
δ 0 01n1p
δ = 0.01n2
r
37
Types of Optical Fibers
G d d i d lti dGraded-index multimode
Cladding diameterfrom 125 to 140 µm
Core diameterfrom 50 to 100 µm n1
n2
Refractive index profile
nn1p
n2r
38
AttenuationSignal attenuation in optical fibers results form 3 phenomena:
AbsorptionScatteringBending
Loss coefficient: αα= −ePP L
inOut
αα
3434
343.4)10ln(
10log10 10 −=−=⎟⎟⎠
⎞⎜⎜⎝
⎛
dB/kfitidlli
LLPP
in
Out
α depends on the wavelength
ααα 343.4=dB:dB/kmofunitsinexpressedusually is
For a single-mode fiber, αdB = 0.2 dB/km @ 1550 nm
39
Scattering and AbsorptionShort wavelength: Rayleigh scattering
induced by inhomogeneity of the 41 t i d 2 d 3 dinduced by inhomogeneity of the
refractive index and proportional to 1/λ4
1st window 2nd 3rd820 nm 1.3 µm 1.55 µm2
IR absorption1 0
AbsorptionInfrared band
1.00.8 Rayleigh
Water peaksscattering
0.4α ∝1/λ4
UV absorptionInfrared bandUltraviolet band 0.2
UV absorption
0.1 0 8 1 0 1 2 1 4 1 6 1 83 Transmission windows
820 nm
0.8 1.0 1.2 1.4 1.6 1.8Wavelength (µm)
1300 nm1550 nm
40
Macrobending Losses
Macrodending losses are caused by the bending of fiberMacrodending losses are caused by the bending of fiber
Bending of fiber affects the condition θ < θCBending of fiber affects the condition θ < θC
For single-mode fiber, bending losses are importantfor curvature radii < 1 cmfor curvature radii < 1 cm
41
Microbending Losses
Mi d di l d b th it f fibMicrodending losses are caused by the rugosity of fiber
Micro-deformation along the fiber axis results in scattering and power loss
42
Attenuation: Single-mode vs. Multimode Fiber
4
Fundamental mode2
MMF1
Higher order mode0.4 SMF
0.2
Wavelength (µm)
0.10.8 1.0 1.2 1.4 1.6 1.8
Light in higher-order modes travels longer optical paths
Multimode fiber attenuates more than single-mode fiber
43
Dispersion
What is dispersion?P f l t lli th h fib i di d i tiPower of a pulse travelling though a fiber is dispersed in timeDifferent spectral components of signal travel at different speedsResults from different phenomena
Consequences of dispersion: pulses spread in time
3 T f di i
t t
3 Types of dispersion: Inter-modal dispersion (in multimode fibers)Intra-modal dispersion (in multimode and single-mode fibers)p ( g )Polarization mode dispersion (in single-mode fibers)
44
Dispersion in Multimode Fibers (inter-modal)
Input pulseOutput pulse
Input pulseOutput pulse
t t
In a multimode fiber, different modes travel at different speed temporal spreading (inter-modal dispersion)
Inter-modal dispersion limits the transmission capacity
The maximum temporal spreading tolerated is half a bit periodThe maximum temporal spreading tolerated is half a bit period
The limit is usually expressed in terms of bit rate-distance product
45
Dispersion in Multimode Fibers (Inter-modal)Fastest ray guided along the core center
TT∆T −=
Slowest ray is incident at the critical angle
vLand T
vLwith T
TT∆T
SLOW
SLOWSLOW
FAST
FASTFAST
FASTSLOW
==
=n2n1 θc Slow ray Fast ray
LLncvv
FAST
SLOWFAST1
=
==θ
Lnn
θL
θπL
θLL
CSLOW
FAST
2
1
sin2
coscos==
⎟⎠⎞
⎜⎝⎛ −
==Lsin
2 ⎠⎝
δcL
nn
nn
cL
nnL
cnnL
cn∆T
2
212
2
21
2
211
11 =⎥⎦
⎤⎢⎣⎡ −=−=
46
Dispersion in Multimode Fibers
1bB −tbitIf 1
21B
T
sbB
<∆
⋅= −
have must We
ratebitIf
2
21
21
2
Bnn
cL
B
< i.e. δExample: n1 = 1.5 and δ = 0.01 → B L< 10 Mb·s-1×
21
2
2ncnBL <× or
δ
Capacity of multimode step index index fibers B×L≈20 Mb/s×kmCapacity of multimode-step index index fibers B×L≈20 Mb/s×km
47
Dispersion in graded-index Multimode Fibers
Input pulseOutput pulse
Input pulseOutput pulse
t t
Fast mode travels a longer physical path Temporal spreadingis smallSlow mode travels a shorter physical path is small
Capacity of multimode graded index fibers B×L≈2 Gb/s×kmCapacity of multimode-graded index fibers B×L≈2 Gb/s×km
48
Intra-modal Dispersion
In a medium of index n, a signal pulse travels at the groupl it d fi dvelocity νg defined as: 12
2
−
⎟⎟⎠
⎞⎜⎜⎝
⎛−==
λβ
πλ
βω
dd
cddvg
Intra-modal dispersion results from 2 phenomenaMaterial dispersion (also called chromatic dispersion)Waveguide dispersiong p
Different spectral components of signal travel at different speeds
The dispersion parameter D characterizes the temporal pulse broadening ∆T per unit length per unit of spectral bandwidth ∆λ: ∆T = D × ∆λ × L
⎞⎛kmps/nm of units in modalIntra ×−=⎟
⎟⎠
⎞⎜⎜⎝
⎛=− 2
22
21
λβ
πλ
λ dd
cvddD
g
49
Material Dispersion
Refractive index n depends on the frequency/wavelength of light
Speed of light in material is therefore dependent on frequency/wavelength q y g
Input pulse, λ1
t
Input pulse, λ2 t
t
50
Material Dispersion
Refractive index of silica as a function of wavelength is given by the Sellmeier Equation
23
22
21)( λλλλ AAA
nm 68.4043 0.6961663, with ==
−+
−+
−+=
11
223
322
2
222
1
11)(
λλλ
λλλ
λλλ
λλ
A
AAAn
nm 9896.161 0.8974794, nm 116.2414 0.4079426,
====
33
22
λλ
AA
51
Material Dispersion
βλ cdv12
=⎞
⎜⎜⎛
−=−
λ1 λ2λλλπ ddnndc
vg /2 −⎠⎜⎜⎝
λ
∆λ
∆TInput pulse, λ1
∆T
L
t
Input pulse, λ2
t
L
t21 dLd ⎞
⎜⎛
2
21λ
λλλ
λλd
ndcL
vddLDL∆T
g
∆−=⎟⎠
⎞⎜⎜⎝
⎛∆=∆=
52
Material Dispersion)
2λ dnm/k
m)
0-200
km)ps/nm :(units Material ×−= 2
2
λλ
dnd
cD
ial(p
s/n -400
-600-800
DM
ater
i 800-1000
0 4 0 6 0 8 1 0 1 2 1 4 1 6 1 8
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Wavelength (µm)
53
Waveguide Dispersion
The size w0 of a mode depends on the ratio a/λ : ⎠⎞
⎜⎝⎛ ++= 62/30
879.2619.165.0VV
aw0 pλ1 λ2>λ1
⎠⎝ 62/30 VV
Consequence: the relative fraction of power in the core and claddingConsequence: the relative fraction of power in the core and cladding varies
This implies that the group-velocity νg also depends on a/λ
⎞⎛size mode the is whereWaveguide 02
022
1 w wd
dncvd
dDg
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟
⎟⎠
⎞⎜⎜⎝
⎛=
λλπ
λλ
54
Total Dispersion
WaveguideMaterialmodalIntra DDD +=−
DIntra-modal<0: normal dispersion regionD >0 l di i iDIntra-modal>0: anomalous dispersion region
Waveguide dispersion shifts the wavelength of zero-dispersion to 1.32 µm
55
Tuning Dispersion
Dispersion can be changed by changing the refractive indexChange in index profile affects the waveguide dispersionTotal dispersion is changed
20
Single-mode Fiber
n2
n1
n2
n1
10
0Single-mode Fiber Dispersion shifted Fiber
Single mode fiber: D=0 @ 1310 nm
0
-10 1 3 1 4 1 5
Dispersion shifted FiberSingle-mode fiber: D=0 @ 1310 nmDispersion shifted Fiber: D=0 @ 1550 nm
10 1.3 1.4 1.5Wavelength (µm)
56
Dispersion Related Parameters
ωβ = nc eff
s/km of units indelay group :
ββ
βωβ
⎞⎛⎞⎛
== 1
21
1
dddd
dd
vg
/kmsofunitsinparameterdispersionvelocitygroup: 2
modalIntra
β
λπβ
λω
ωβ
λβ
λ⎟⎠⎞
⎜⎝⎛−===⎟
⎟⎠
⎞⎜⎜⎝
⎛=− 22
11 21 cdd
dd
dd
vddD
g
/kmsofunitsinparameterdispersionvelocity group:2β
57
Polarization Mode Dispersion
Optical fibers are not perfectly circularp p y
x
y
In general a mode has 2 polarizations (degenerescence): x and y
x x
In general, a mode has 2 polarizations (degenerescence): x and y
Causes broadening of signal pulse g g p
LDLT ≈∆11 LD
vvLT
gygxonPolarizati≈−=∆
58
Effects of Dispersion: Pulse SpreadingTotal pulse spreading is determined as the geometric sum of
pulse spreading resulting from intra-modal and inter-modal dispersionpulse spreading resulting from intra-modal and inter-modal dispersion
222 TTTT ∆+∆+∆=∆onPolarizatimodal-IntraIntermodal
( ) ( )
( ) ( )22
22 LDLDT ×∆×+×=∆ −− modalIntramodalInter :Fiber Multimode
λ
( ) ( )22 LDLDT ×+×∆×=∆ − onPolarizatimodalIntra:FiberMode-Single λ
Examples: Consider a LED operating @ .85 µm∆λ =50 nm after L=1 km, ∆T=5.6 nsλ 50 a te , 5.6 sDInter-modal =2.5 ns/kmDIntra-modal =100 ps/nm×km
Consider a DFB laser operating @ 1 5 µmConsider a DFB laser operating @ 1.5 µm∆λ =.2 nm after L=100 km, ∆T=0.34 ns!
DIntra-modal =17 ps/nm×kmDPolarization=0.5 ps/ √km
59
Effects of Dispersion: Capacity Limitation
Capacity limitation: maximum broadening<half a bit period
<∆T 1
Capacity limitation: maximum broadening half a bit period
λ∆≈∆
<∆
−modalIntra
effects)onpolarizatig(neglectin Fiber, Mode-Single For LDT
BT
2
λ∆<⇒
−modalIntra
e ec s)opo a ag( eg ec
DLB
21
Example: Consider a DFB laser operating @ 1.55 µm∆λ =0 2 nm LB<150 Gb/s ×km∆λ 0.2 nm LB<150 Gb/s ×kmD =17 ps/nm×km If L=100 km, BMax=1.5 Gb/s
60
Advantage of Single-Mode Fibers
No intermodal dispersionp
Lower attenuation
No interferences between multiple modes
Easier Input/output couplingEasier Input/output coupling
Single-mode fibers are used in long transmission systems
61
Summary
Attractive characteristics of optical fibers:p
Low transmission loss
Enormous bandwidth
Immune to electromagnetic noise
Low cost
Light weight and small dimensions
Strong, flexible materialg,
62
SummaryImportant parameters:
NA: numerical aperture (angle of acceptance)p ( g p )V: normalized frequency parameter (number of modes)λc: cut-off wavelength (single-mode guidance)D: dispersion (pulse broadening)
Multimode fiberUsed in local area networks (LANs) / metropolitan area networks (MAN )(MANs) Capacity limited by inter-modal dispersion: typically 20 Mb/s x km for step index and 2 Gb/s x km for graded index
Single-mode fiberUsed for short/long distancesCapacity limited by dispersion: typically 150 Gb/s x kmCapacity limited by dispersion: typically 150 Gb/s x km
63