1
OPTICAL COMMUNICATIONS
S-108.3110
2
Course Program 5 lectures on Fridays
First lecture Friday 06.11 in Room H-402 13:15-16:30 (15 minutes break in-between)
Exercises Demo exercises during lectures Homework Exercises must be returned beforehand (will
count in final grade) Seminar presentation
27.11, 13:15-16:30 in Room H-402 Topic to be agreed beforehand
2 labworks Preliminary exercises (will count in final grade)
Exam 17.12 15.01
5 op
3
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)
5. Fiber-Optic Measurements & Review (11.12)
4
Lecturers
In case of problems, questions...
Course lecturers G. Genty (3 lectures) [email protected] F. Manoocheri (2 lectures)
5
Optical Fiber Concept
Optical fibers are light pipes
Communications signals can be transmitted over these hair thin strands of glass or plastic
Concept is a century old
But only used commercially for the last ~25 years when technology had matured
6
Optical fibers have more capacity than other means (a single fiber can carry more information than a giant copper cable!)
Price
Speed
Distance
Weight/size
Immune from interference
Electrical isolation
Security
Why Optical Fiber Systems?
7
Optical Fiber Applications
> 90% of all long distance telephony
> 50% of all local telephony
Most CATV (cable television) networks
Most LAN (local area network) backbones
Many video surveillance links
Military
Optical fibers are used in many areas
8
Optical Fiber Technology
Core Cladding Mechanical protection layer
An optical fiber consists of two different types of solid glass
1970: first fiber with attenuation (loss) <20 dB/km 1979: attenuation reduced to 0.2 dB/km commercial systems!
9
Optical Fiber Communication
Optical fiber systems transmit modulated infrared light
Transmitter Receiver
Fiber
Components
Information can be transmitted oververy long distances due to the low attenuation of
optical fibers
10
Frequencies in Communications
1 m
1 cm
10 cm
1 m
10 m
100 m
1 km
10 km
100 km
waveguide
coaxialcable
wire pairs
opticalfiber
TelephoneDataVideo
SatelliteRadar
TVRadio
Submarine cableTelephoneTelegraph
wavelength
frequency
300 THz
30 GHz
3 GHz
300 MHz
30 Mhz
3 MHz
300 kHz
30 kHz
3 kHz
11
Frequencies in Communications
Optical Fiber: > Gb/sMicro-wave ~10 Mb/sShort-wave radio ~100 kb/sLong-wave radio ~4 Kb/s
Data rate
Increase of communication capacity and rates
requires higher carrier frequencies
Optical Fiber Communication!
12
Optical fibers are cylindrical dielectric waveguides
Cladding diameter125 µm
Cladding (pure silica)
Core silica doped with Ge, Al… Core diameter
from 9 to 62.5 µm
Typical values of refractive indices Cladding: n2 = 1.460 (silica: SiO2)
Core: n1 =1.461 (dopants increase ref. index compared to cladding)
n1
n2
Optical Fiber
A useful parameter: fractional refractive index difference = (n1-n2) /n1<<1
Dielectric: material which does not conduct electricity but can sustain an electric field
13
Fiber Manufacturing
Preform (soot) fabrication deposition of core and cladding materials onto a rod using vapors of SiCCL4 and GeCCL4 mixed in a flame burned
Consolidation of the preform preform is placed in a high temperature furnace to remove the water vapor and obtain a solid and dense rod
Drawing in a tower solid preform is placed in a drawing tower and drawn into a thin continuous strand of glass fiber
Optical fiber manufacturing is performed in 3 steps
14
Fiber Manufacturing
Step 1 Steps 2&3
15
Light Propagation in Optical Fibers
Guiding principle: Total Internal Reflection Critical angle Numerical aperture
Modes
Optical Fiber types Multimode fibers Single mode fibers
Attenuation
Dispersion Inter-modal Intra-modal
16
Total Internal Reflection
n2
n11
2
Snell’s law:n1 sin 1 = n2 sin 2
n1 > n2
Light is partially reflected and refracted at the interface of two media with different refractive indices: Reflected ray with angle identical to angle of incidence Refracted ray with angle given by Snell’s law
1
Refracted ray with angle: sin 2 = n1/ n2 sin 1
Solution only if n1/ n2 sin 1≤1
Angles 1 & 2 defined with respect to normal!!
17
Total Internal Reflection
n2
n11
2
Snell’s law:n1 sin 1 = n2 sin 2
n2
n1c
n1 > n2
sin c = n2 / n1If >c No
ray is refracted!
For angle such that >C , light is fully reflected at the core-cladding interface:
optical fiber principle!
n2n1
n2
n2
1
18
Example: n1 = 1.47 n2 = 1.46
NA = 0.17
Numerical Aperture
n2n1 c
max
For angle such that < max, light propagates inside the fiber
For angle such that >max, light does not propagate inside the fiber
1 with 2sin1
211
22
21max
n
nnnnnNA
Numerical aperture NA describes the acceptance angle max for light to be guided
19
Geometrical optics can’t describe rigorously light propagation in fibers
Must be handled by electromagnetic theory (wave propagation)
Starting point: Maxwell’s equations
Theory of Light Propagation in Optical Fiber
(4)
(3)
(2)
(1)
0
B
DT
DJH
T
BE
f density Charge :
density Current :
density flux Electric :
densityflux Magnetic :
0
00
0
f
J
PED
MHB
with
20
Theory of Light Propagation in Optical Fiber
onPolarizati Nonlinear :
onPolarizati Linear :(1)
TrP
dttrEtttrP
trPtrPtrP
NL
L
NLL
,
,,
,,,
1110
We consider only linear propagation: PNL(r,T) negligible
(1): linear susceptibility
21
Theory of Light Propagation in Optical Fiber
22
02 2 2
2(1) 2
0 02
( , )1 ( , )( , )
We now introduce the Fourier transform: ( , )
( , )( , )
And we get: ( , ) ( , ) ( ) ( , )
which can be re
L
i t
-
kk
k
P r tE r tE r t
c t t
E r E(r,t)e dt
E r ti E r
t
E r E r E rc
22 (1)
0 02
2
2
written as
( , ) 1 ( ) ( , ) 0
i.e. ( , ) ( ) ( , ) 0
E r c E rc
E r E rc
22
Theory of Propagation in Optical Fiber
)()(
and
)(2
11 with
2)(
)1(
)1(2
cn
nc
in
0),(
~),(
~),(
~),(
~),(
~),(
~ 22
rDrE
rErErErE
Equation! Helmoltz : 0),(~
),(~
2
222 rE
cnrE
n: refractive index: absorption
23
Theory of Light Propagation in Optical Fiber
Each components of E(x,y,z,t)=U(x,y,z)ejt must satisfy the Helmoltz equation
Assumption: the cladding radius is infinite In cylindrical coodinates the Helmoltz equation becomes
/2
0
0
2
12
022
k
arnn
arnn
UknU for
for
with
00
2
12
02
2
2
2
2
22
2
/2
011
k
arnn
arnn
Uknz
UU
rr
U
rr
U for
for
with
x
yz
ErEz
Eφ
r
φ
Note: =/c
24
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(z) =e-jz
U(φ) must be 2 periodic U(φ) =e-j lφ , l=0,±1,±2…integer
00
2
1
2
222
02
2
2
/2
01
...2,1,0)(),,(
k
arnn
arnn
Fr
lkn
dr
dF
rdr
Fd
leerFzrU zjjl
for
for
with
:gets one Eq. Helmoltz the into Plugging
with
,such that
refraction ofindex effectivean definecan One
12 nnnnc
n
effeff
eff
= k0 neff is the propagation
constant
25
Theory of Propagation in Optical Fiber
A light wave is guided only if
We introduce
arFr
l
dr
dF
rdr
Fd
arFr
l
dr
dF
rdr
Fd
for
for
:get then We
01
01
2
22
2
2
2
22
2
2
0102 knkn
constant! :22
022
21
20
22
202
22
2201
2
NAknnk
kn
kn
real:,
0, :Note 22
26
Theory of Propagation in Optical Fiber
lK
arKrF
lJ
arJrF
l
ll
l
ll
order with kind 1 offunction Bessel Modified :
for )(
order with kind 1 offunction Bessel :
for )(
:form theof are equations theof solutions The
st
st
constant! :
with
220
22
21
20
22
202
22
2201
2
NAknnk
kn
kn
27
Examples
a a
K0(r)J0(r)K0(r) K3(r)J3(r)K3(r)
a
r
r
l=0 l=3
arrK
arrJrF
for
for
)(
)()(
0
0
arrK
arrJrF
for
for
)(
)()(
3
3
28
Characteristic Equation
aa
kn
l
K
K
J
J
n
n
K
K
J
J lm
l
l
l
l
l
l
l
l
and with
11
)(
)(
)(
)(
)(
)(
)(
)(
:equation sticscharacteri the
solvingby found becan constant n propagatio The
2
2220
22
22''
22
21
''
Boundary conditions at the core-cladding interface give a condition on the propagation constant (characteristics equation)
For each l value there are m solutions for Each value lm corresponds to a particualr fiber
mode
29
Number of Modes Supported by an Optical Fiber
Solution of the characteristics equation U(r,φ,z)=F(r)e-jle-jlmz is called a mode, each mode corresponds to a particular electromagnetic field pattern of radiation
The modes are labeled LPlm
Number of modes M supported by an optical fiber is related to the V parameter defined as
M is an increasing function of V !
If V <2.405, M=1 and only the mode LP01 propagates: the fiber is said Single-Mode
22
210
2nn
aNAakV
30
Number of Modes Supported by an Optical Fiber
Number of modes well approximated by:
If V <2.405, M=1 and only the mode LP01 propagates: Single-Mode fiber!
2
2 2 2 21 2
2/ 2, where
aM V V n n
cladding
Example:2a =50 mn1 =1.46 V=17.6=0.005 M=155=1.3 m
core
1.0 LP01
0.8 21
02 0.6 31 12 41
22 0.4 32 61
51 13 03 23
42 0.2 71 04 52 81
33 0 2 4 6 8 10 12
V
21
2
nn
nneff
LP11
31
Examples of Modes in an Optical Fiber
=0.6328 m a =8.335 m n1 =1.462420 =0.034
32
Examples of Modes in an Optical Fiber
=0.6328 m a =8.335 m n1 =1.462420 =0.034
33
Cut-Off Wavelength
The propagation constant of a given mode depends on the wavelength [ ()]
The cut-off condition of a mode is defined as 2()-k02
n22= 2()-42 n2
2/
There exists a wavelength c above which only the fundamental mode LP01 can propagate
11
11
54.02
405.2
84.12405.2
2405.2
nna
ananV
cc
C
ly equivalent or
Example:2a =9.2 mn1 =1.4690=0.0034c~1.2 m
34
Single-Mode Guidance
In a single-mode fiber, for wavelengths >c~1.26 m
only the LP01 mode can propagate
35
Mode Field Diameter
Fiber Optics Communication Technology-Mynbaev & Scheiner
The fundamental mode of a single-mode fiber is well approximated by a Gaussian function
42for )ln(
4221for 879.2619.1
65.0
from obtained is size mode for theion approximat goodA
size mode the andconstant a is where
)(
0
62/30
0
2
0
.VV
aw
.V.VV
aw
wC
CeF w
36
Step-index single-mode
Types of Optical Fibers
Refractive index profile
Cladding diameter125 µm
Core diameterfrom 8 to 10 µm n1
n2
n
n2
n1
r
37
Step-index multimode
Types of Optical Fibers
Refractive index profile
Cladding diameterfrom 125 to 400 µm
Core diameterfrom 50 to 200 µm n1
n2
n
n2
n1
r
38
Graded-index multimode
Types of Optical Fibers
Refractive index profile
Cladding diameterfrom 125 to 140 µm
Core diameterfrom 50 to 100 µm n1
n2
n
n2
n1
r
39
Attenuation Signal attenuation in optical fibers results form 3
phenomena: Absorption Scattering Bending
Loss coefficient:
depends on the wavelength
For a single-mode fiber, dB= 0.2 dB/km @ 1550 nm
343.4
343.4)10ln(
10log10 10
dB :dB/km of units in expressedusually is
LLP
P
ePP
in
Out
LinOut
40
Scattering and Absorption
Short wavelength: Rayleigh scattering induced by inhomogeneity of the
refractive index and proportional to 1/4
Absorption Infrared bandUltraviolet band
3 Transmission windows 820 nm 1300 nm 1550 nm
4 1st window 2nd 3rd
820 nm 1.3 µm 1.55 µm 2
IR absorption
1.0 0.8 Rayleigh
Water peaks scattering
0.4 1/4
0.2 UV absorption
0.1 0.8 1.0 1.2 1.4 1.6 1.8
Wavelength (µm)
41
Macrodending losses are caused by the bending of fiber
Bending of fiber affects the condition < C
For single-mode fiber, bending losses are important for curvature radii < 1 cm
Macrobending Losses
42
Microdending losses are caused by the rugosity of fiber
Micro-deformation along the fiber axis results in scattering and
power loss
Microbending Losses
43
Fundamental mode
Higher order mode
Attenuation: Single-mode vs. Multimode Fiber
Light in higher-order modes travels longer optical paths
Multimode fiber attenuates more than single-mode fiber
Wavelength (µm)
4
2 MMF
1
0.4 SMF
0.2
0.1 0.8 1.0 1.2 1.4 1.6 1.8
44
Dispersion
What is dispersion? Power of a pulse travelling though a fiber is dispersed in time Different spectral components of signal travel at different speeds Results from different phenomena
Consequences of dispersion: pulses spread in time
3 Types of dispersion: Inter-modal dispersion (in multimode fibers) Intra-modal dispersion (in multimode and single-mode fibers) Polarization mode dispersion (in single-mode fibers)
t t
45
Input pulse
Dispersion in Multimode Fibers (inter-modal)
t
Input pulseOutput pulse
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 period
The limit is usually expressed in terms of bit rate-distance product
46
Dispersion in Multimode Fibers (Inter-modal)
Ln
n
θ
L
θπL
θ
LL
LL
n
cvv
v
Land T
v
Lwith T
TTΔT
CSLOW
FAST
SLOWFAST
SLOW
SLOWSLOW
FAST
FASTFAST
FASTSLOW
2
1
1
sin2
coscos
δc
L
n
n
n
n
c
L
n
nL
cn
nL
c
nΔT
2
212
2
21
2
211
11
n2n1 c
L
Slow ray Fast ray
Fastest ray guided along the core center
Slowest ray is incident at the critical angle
sin
47
Dispersion in Multimode Fibers
21
2
2
21
1
2
2
1
2
1
n
cnBL
Bn
n
c
L
BT
sbB
or
i.e.
have must We
rate bit If
Example: n1 = 1.5 and = 0.01 →B L< 10 Mb∙s-1
Capacity of multimode-step index index fibers B×L≈20 Mb/s×km
×
48
Input pulse
Fast mode travels a longer physical path
Slow mode travels a shorter physical path
Dispersion in graded-index Multimode Fibers
t
Input pulseOutput pulse
t
Temporal spreading is small
Capacity of multimode-graded index fibers B×L≈2 Gb/s×km
49
Intra-modal Dispersion
In a medium of index n, a signal pulse travels at the group velocity g defined as
Intra-modal dispersion results from 2 phenomena Material dispersion (also called chromatic dispersion) Waveguide dispersion
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 : T = D × × L
kmps/nm of units in modalIntra
2
22
2
1
d
d
cvd
dD
g
12
2
d
d
cd
dvg
50
Material Dispersion
Refractive index n depends on the frequency/wavelength of light
Speed of light in material is therefore dependent on frequency/wavelength
Input pulse, 1
t
Input pulse, 2
t
t
51
Material Dispersion
nm 9896.161 0.8974794,
nm 116.2414 0.4079426,
nm 68.4043 0.6961663, with
33
22
11
223
23
222
22
221
211)(
A
A
A
AAAn
Refractive index of silica as a function of wavelength is given by the Sellmeier Equation
52
Material Dispersion
ddnn
c
d
d
cvg /2
12
L
Input pulse, 1
t
Input pulse, 2
t
1 2
2
21
d
nd
c
L
vd
dLDLΔT
g
t
T
53
Material Dispersion
km)ps/nm :(units Material 2
2
d
nd
cD
DM
ater
ial (
ps/
nm
/km
)
0
-200
-400
-600
-800
-1000
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Wavelength (µm)
54
Waveguide Dispersion
The size w0 of a mode depends on the ratio a/:
Consequence: the relative fraction of power in the core and cladding varies
This implies that the group-velocity g also depends on a/
1 2>1
size mode the is whereWaveguide 020
22
1w
wd
d
ncvd
dD
g
62/30
879.2619.165.0
VVaw
55
Total Dispersion
Waveguide dispersion shifts the wavelength of zero-dispersion to 1.32 m
WaveguideMaterialmodalIntra DDD
DIntra-modal<0: normal dispersion regionDIntra-modal>0: anomalous dispersion
region
56
Dispersion can be changed by changing the refractive index
Change in index profile affects the waveguide dispersion
Total dispersion is changed
n2
n1
Single-mode Fiber
n2
n1
Dispersion shifted Fiber
Single-mode fiber: D=0 @ 1310 nm Dispersion shifted Fiber: D=0 @ 1550 nm
20
10 Single-mode Fiber
0
-10 1.3 1.4 1.5
Wavelength (µm)
Dispersion shifted Fiber
Tuning Dispersion
57
Dispersion Related Parameters
/kms of units in parameter dispersionvelocity group:
s/km of units indelay group :
22
modalIntra
2211
1
21
1
c
d
d
d
d
d
d
vd
dD
d
d
v
nc
g
g
eff
58
Polarization Mode Dispersion
Optical fibers are not perfectly circular
In general, a mode has 2 polarizations (degenerescence): x and y
Causes broadening of signal pulse
LDvv
LTgygx
onPolarizati11
x
y
x
59
Effects of Dispersion: Pulse Spreading
Total pulse spreading is determined as the geometric sum of
pulse spreading resulting from intra-modal and inter-modal dispersion
22
22
222
LDLDT
LDLDT
TTTT
onPolarizatimodalIntra
modalIntramodalInter
onPolarizatimodal-IntraIntermodal
:Fiber Mode-Single
:Fiber Multimode
Examples: Consider a LED operating @ .85 m =50 nm after L=1 km, T=5.6 ns
DInter-modal =2.5 ns/km DIntra-modal =100 ps/nm×km
Consider a DFB laser operating @ 1.5 m =.2 nm after L=100 km, T=0.34 ns!
DIntra-modal =17 ps/nm×km DPolarization=0.5 ps/ √km
60
Effects of Dispersion: Capacity Limitation
modalIntra
modalIntra
effects) onpolarizati g(neglectin
Fiber, Mode-Single For
DLB
LDTB
T
2
1
2
1
Capacity limitation: maximum broadening<half a bit period
Example: Consider a DFB laser operating @ 1.55 m =0.2 nm LB<150 Gb/s ×km
D =17 ps/nm×km If L=100 km, BMax=1.5 Gb/s
61
Advantage of Single-Mode Fibers
No intermodal dispersion
Lower attenuation
No interferences between multiple modes
Easier Input/output coupling
Single-mode fibers are used in long transmission systems
62
Summary
Attractive characteristics of optical fibers:
Low transmission loss
Enormous bandwidth
Immune to electromagnetic noise
Low cost
Light weight and small dimensions
Strong, flexible material
63
Summary
Important parameters: NA: numerical aperture (angle of acceptance) V: normalized frequency parameter (number of modes) c: cut-off wavelength (single-mode guidance) D: dispersion (pulse broadening)
Multimode fiber Used in local area networks (LANs) / metropolitan area
networks (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 fiber Used for short/long distances Capacity limited by dispersion: typically 150 Gb/s x km