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OPTICAL COMMUNICATIONS
S-108.3110
1
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
2
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)
3
Lecturers
In case of problems, questions...
Course lecturers
G. Genty (3 lectures)
F. Manoocheri (2 lectures)
[email protected]
[email protected]
4
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
5
Why Optical Fiber Systems?
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
6
Optical Fiber Applications
Optical fibers are used in many areas
> 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
7
Optical Fiber Technology
An optical fiber consists of two different types of solid glass
Core
Cladding
Mechanical protection layer
1970: first fiber with attenuation (loss) <20 dB/km
1979: attenuation reduced to 0.2 dB/km
commercial systems!
8
Optical Fiber Communication
Optical fiber systems transmit modulated infrared light
Fiber
Transmitter
Components
Receiver
Information can be transmitted over
very long distances due to the low attenuation of optical fibers
9
Frequencies in Communications
100 km
10 km
wire pairs
1 km
100 m
10 m
1 cm
1 mm
wavelength
3 MHz
coaxial
cable
TV
Radio
30 Mhz
waveguide
Satellite
Radar
3 GHz
1m
10 cm
frequency
3 kHz
Submarine cable
30 kHz
Telephone
Telegraph
300 kHz
optical
fiber
Telephone
Data
Video
300 MHz
30 GHz
300 THz
10
Frequencies in Communications
Data rate
Optical Fiber: > Gb/s
Micro-wave ~10 Mb/s
Short-wave radio ~100 kb/s
Long-wave radio ~4 Kb/s
Increase of communication capacity and rates
requires higher carrier frequencies
Optical Fiber Communication!
11
Optical Fiber
Optical fibers are cylindrical dielectric waveguides
Dielectric: material which does not conduct electricity but can sustain an electric field
n2
Cladding diameter
125 µm
Core diameter
from 9 to 62.5 µm
n1
Cladding (pure silica)
Core silica doped with Ge, Al…
Typical values of refractive indices
Cladding: n2 = 1.460 (silica: SiO2)
Core: n1 =1.461 (dopants increase ref. index compared to cladding)
A useful parameter: fractional refractive index difference d = (n1-n2) /n1<<1
12
Fiber Manufacturing
Optical fiber manufacturing is performed in 3 steps
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
13
Fiber Manufacturing
Step 1
Steps 2&3
14
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
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 incidence
Refracted ray with angle given by Snell’s law
!
Snell’s law:
n1 sin q1 = n2 sin q2
Angles q1 & q2 defined
with respect to normal!
q1
n1 > n2
q1
q2
n1
n2
Refracted ray with angle: sin q2 = n1/ n2 sin q1
Solution only if n1/ n2 sin q1≤1
16
Total Internal Reflection
Snell’s law:
n1 sin q1 = n2 sin q2
q1
n1 > n2
q1
n1
n2
q2
n2
n1
n2
sin qc = n2 / n1
qc
If q >qc No ray
is refracted!
n1
n2n2
q
For angle q such that q >qC , light is fully reflected at
the core-cladding interface: optical fiber principle!
17
Numerical Aperture
For angle q such that q <q max, light propagates inside the fiber
For angle q such that q >qmax, light does not propagate inside the fiber
n2
n1
qmax
qc
Example: n1 = 1.47
n2 = 1.46
NA = 0.17
n1 n2
NA sin q max n n n1 2d with d
1
n1
2
1
2
2
Numerical aperture NA describes
the acceptance angle qmax 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
B
T
D
H J
T
D f
(3)
B 0
(4)
E
(1)
(2)
B m 0 H M : Magnetic f lux density
with
D 0E P
: Electric f lux density
J 0
: Current density
f 0
: Charge density
19
Theory of Light Propagation in Optical Fiber
Pr , t PL r , t PNL r , t
PL r , t 0 (1) t t1 E r , t1 dt1 : Linear Polarization
PNL r , T : Nonlinear Polarization
(1): linear
susceptibility
We consider only linear propagation: PNL(r,T) negligible
20
Theory of Light Propagation in Optical Fiber
2 PL (r , t )
1 2 E (r , t )
E (r , t ) 2
m0
c
t 2
t 2
We now introduce the Fourier transform: E (r , )
-
E(r,t)eit dt
k E (r , t )
k
i
E (r , )
k
t
And we get: E (r , )
2
c2
E (r , ) m0 0 (1) ( ) 2 E (r , )
which can be rewritten as
E (r , )
2
2
(1)
1
c
m
( ) E (r , ) 0
0 0
2
c
i.e. E (r , )
2
c
2
( ) E ( r , ) 0
21
Theory of Propagation in Optical Fiber
c
1
( ) n i wit h n 1 (1) ( )
2
2
and
(1) ( )
cn( )
2
n: refractive index
: absorption
~
~
~
~
E (r , ) E (r , ) 2 E (r , ) 2 E (r , )
~
~
E ( r , ) D( r , ) 0
2
~
2 ~
E (r , ) n 2 E (r , ) 0 : HelmoltzEquation!
c
2
22
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
n n1 for r a
2
2U n 2 k0 U 0 w ithn n2 for r a
k 2 /
0
Note: = /c
Assumption: the cladding radius is infinite
In cylindrical coodinates the Helmoltz equation becomes
n n1 for r a
U 1 U 1 U U
2
2
2 n 2 k0 U 0 w ithn n2 for r a
2
2
r
r r r
z
k 2 /
0
0
2
2
2
x
Er
φ
Ez
y
z
r
Eφ
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(z) =e-jbz
U(φ) must be 2 periodic U(φ) =e-j lφ , l=0,±1,±2…integer
U (r , , z ) F (r )e jl e jbz w ithl 0,1,2...
Plugging into the Helmoltz Eq. one gets :
d F 1 dF 2 2
l
2
F
n
k
b
0
2
2
dr
r dr
r
2
2
n n1 for r a
0 w ithn n2 for r a
k 2 /
0
0
One can define an effectiveindex of refractionneff
such thatb
c
neff , n2 neff n1
b = k0 neff is the
propagation
constant
24
Theory of Propagation in Optical Fiber
A light wave is guided only if n2k0 b n1k0
We introduce
2 n1k0 2 b 2
2 b 2 n2 k0 2
2 2 k02 n12 n22 k02 NA2 : constant!
Note: 2 , 2 0
, : real
We then get :
d 2 F 1 dF 2 l 2
2 F 0 for r a
2
dr
r dr
r
d 2 F 1 dF 2 l 2
2 F 0 for r a
2
dr
r dr
r
25
Theory of Propagation in Optical Fiber
T hesolutionsof theequationsare of theform:
Fl (r ) J l r
for a
J l : Bessel functionof 1st kind with order l
Fl (r ) K l r
for a
K l : Modified Bessel functionof 1st kind with order l
with
2 n1k0 2 b 2
2 b 2 n2 k0 2
2 2 k02 n12 n22 k02 NA2 : constant!
26
Examples
l=0
l=3
K0(r) J0(r) K0(r)
a
J 0 (r ) for r a
F (r )
K 0 (r ) for r a
K3(r)
r
J3(r)
a
K3(r)
r
a
J 3 (r ) for r a
F (r )
K 3 (r ) for r a
27
Characteristic Equation
Boundary conditions at the core-cladding interface
give a condition on the propagation constant b (characteristics equation)
T hepropagation constantb can be found by solving
thecharacteristics equation:
J l' ( )
K l' () n12 J l' ( )
K l' () l 2 b lm2
2
2 2
J l ( ) K l () n2 J l ( ) K l () n2 k0
with a and a
1
1
2 2
2
For each l value there are m solutions for b
Each value blm corresponds to a particualr fiber mode
28
Number of Modes Supported by an Optical Fiber
Solution of the characteristics equation U(r,φ,z)=F(r)e-jle-jblmz 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
V ak 0 NA
2a
n12 n22
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
29
Number of Modes Supported by an Optical Fiber
Number of modes well approximated by:
1.0
n1 n2
2
2
LP01
0.8
neff n2
2 a 2
2
M V / 2, where V
n1 n2
2
LP11
21
02
31 12 41
0.6
core
22 32
61
51 13
03
23
42 7104
0.4
0.2
0
2
4
6
8
10
Example:
2a =50 mm
n1 =1.46
d=0.005
=1.3 mm
V=17.6
M=155
8152
33
12
V
If V <2.405, M=1 and only the mode LP01 propagates: Single-Mode
fiber!
cladding
30
Examples of Modes in an Optical Fiber
=0.6328 mm
a =8.335 mm
n1 =1.462420
d =0.034
31
Examples of Modes in an Optical Fiber
=0.6328 mm
a =8.335 mm
n1 =1.462420
d =0.034
32
Cut-Off Wavelength
The propagation constant of a given mode depends on the
wavelength [b ()]
The cut-off condition of a mode is defined as b2()-k02 n22= b2()42 n22/20
There exists a wavelength c above which only the fundamental
mode LP01 can propagate
2
V 2.405 C
n1a 2d 1.84an1 d
2.405
2.405 c
or equivalently a
0.54 c
2 n1 d
n1d
Example:
2a =9.2 mm
n1 =1.4690
d=0.0034
c~1.2 mm
33
Single-Mode Guidance
In a single-mode fiber, for wavelengths >c~1.26 mm
only the LP01 mode can propagate
34
Mode Field Diameter
The fundamental mode of a single-mode fiber
is well approximated by a Gaussian function
w0
2
F ( ) Ce
where C is a constantand w0 themode size
A good approximation for themode size is obtainedfrom
1.619 2.879
w0 a 0.65 3 / 2
for1.2 V 2.4
6
V
V
a
w0
forV 2.4
ln(V )
Fiber Optics Communication Technology-Mynbaev & Scheiner
35
Types of Optical Fibers
Step-index single-mode
n2
Cladding diameter
125 µm
Core diameter
from 8 to 10 µm
n1
n
n1
Refractive index profile
n2
d 0.001
r
36
Types of Optical Fibers
Step-index multimode
n2
Cladding diameter
from 125 to 400 µm
Core diameter
from 50 to 200 µm
n1
n
n1
Refractive index profile
n2
d 0.01
r
37
Types of Optical Fibers
Graded-index multimode
n2
Cladding diameter
from 125 to 140 µm
Core diameter
from 50 to 100 µm
n1
n
n1
Refractive index profile
n2
r
38
Attenuation
Signal attenuation in optical fibers results form 3 phenomena:
Absorption
Scattering
Bending
Loss coefficient:
POut Pine L
P
10
10 log10 Out L
4.343L
P
ln(
10
)
in
is usually expressedin units of dB/km : dB 4.343
depends on the wavelength
For a single-mode fiber, dB = 0.2 dB/km @ 1550 nm
39
Scattering and Absorption
Short wavelength: Rayleigh scattering
induced by inhomogeneity of the
refractive index and proportional to
1/4
Absorption
Infrared band
Ultraviolet band
4
2
2nd
1.3 µm
3rd
1.55 µm
IR absorption
1.0
0.8
Rayleigh
scattering
1/4
Water peaks
0.4
UV absorption
0.2
0.1
3 Transmission windows
820 nm
1300 nm
1550 nm
1st window
820 nm
0.8
1.0
1.2
1.4
1.6
1.8
Wavelength (µm)
40
Macrobending Losses
Macrodending losses are caused by the bending of fiber
Bending of fiber affects the condition q < qC
For single-mode fiber, bending losses are important
for curvature radii < 1 cm
41
Microbending Losses
Microdending 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
2
Fundamental mode
Higher order mode
MMF
1
0.4
SMF
0.2
0.1
0.8
1.0
1.2
1.4
Wavelength (µm)
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?
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
t
t
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)
44
Dispersion in Multimode Fibers (inter-modal)
Input pulse
Output pulse
Input 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 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
Slowest ray is incident at the critical angle
n2
n1
ΔT TSLOW TFAST
qc
Slow ray
Fast ray
q
with TFAST
LFAST
L
and TSLOW SLOW
vFAST
vSLOW
vFAST vSLOW
c
n1
LFAST L
L
LSLOW
L
cosθ
n
n
n L n2 n1 L
ΔT 1 L 1 L 1
1
δ
c
n2c
n2 c n1 n2 c
2
2
2
L
L
n
1L
π
sin θC n2
cos
sin θ
2
46
Dispersion in Multimode Fibers
If bit rate B b s 1
We must have T
L n12
1
i.e.
d
c n2
2B
or L B
1
2B
Example: n1 = 1.5 and d = 0.01 → B × L< 10 Mb∙s-1
cn2
2n12d
Capacity of multimode-step index index fibers B×L≈20 Mb/s×km
47
Dispersion in graded-index Multimode Fibers
Input pulse
Output pulse
Input pulse
t
Fast mode travels a longer physical path
Slow mode travels a shorter physical path
t
Temporal spreading
is small
Capacity 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 group
1
velocity ng defined as:
d 2 db
vg
db
2
c
d
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
DIntramodal
d 1
d vg
2
2
d
b
in units of ps/nm km
2
2c d
49
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
50
Material Dispersion
Refractive index of silica as a function of wavelength
is given by the Sellmeier Equation
A32
A12
A2 2
n ( ) 1 2
2
2
2
2
1 2 3 2
w ith A1 0.6961663, 1 68.4043 nm
A2 0.4079426, 2 116.2414 nm
A3 0.8974794, 3 9896.161nm
51
Material Dispersion
1
1
2 db
c
v g
n dn / d
2c d
2
T
Input pulse, 1
t
t
Input pulse, 2
t
L
d 1
ΔT LD L
d vg
2
L
d
n
2
c
d
52
DMaterial (ps/nm/km)
Material Dispersion
0
-200
-400
DMaterial
-600
d 2n
(units : ps/nm km)
2
c d
-800
-1000
[email protected] mm
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Wavelength (µm)
53
Waveguide Dispersion
1.619 2.879
The size w0 of a mode depends on the ratio a/ : w0 a 0.65 V 3 / 2 V 6
1
2 > 1
Consequence: the relative fraction of power in the core and cladding
varies
This implies that the group-velocity ng also depends on a/
DWaveguide
d 1
d vg
d
w herew0 is the mode size
2 2 nc d w2
0
54
Total Dispersion
DIntramodal DMaterial DWaveguide
DIntra-modal<0: normal dispersion region
DIntra-modal>0: anomalous dispersion region
Waveguide dispersion shifts the wavelength of zero-dispersion to 1.32 mm
55
Tuning Dispersion
Dispersion can be changed by changing the refractive index
Change in index profile affects the waveguide dispersion
Total dispersion is changed
20
Single-mode Fiber
10
n2
n2
n1
n1
0
Single-mode Fiber
Dispersion shifted Fiber
Single-mode fiber: D=0 @ 1310 nm
Dispersion shifted Fiber: D=0 @ 1550 nm
Dispersion shifted Fiber
-10
1.3
1.4
1.5
Wavelength (µm)
56
Dispersion Related Parameters
b
neff
c
1 db
b1 : group delay in units of s/km
vg d
d 1
d vg
db1 db1 d
2c
DIntramodal
b2 2
d d d
b 2 : group velocity dispersionparameter in units of s2 /km
57
Polarization Mode Dispersion
Optical fibers are not perfectly circular
y
x
x
In general, a mode has 2 polarizations (degenerescence): x and y
Causes broadening of signal pulse
T L
1
1
DPolarizati on L
vgx vgy
58
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
T T 2
Intermodal
T 2
Intra-modal
Multimode Fiber : T
T 2
Polarizati on
DInter modal L 2 DIntramodal L 2
Single - Mode Fiber : T
DIntramodal L 2 DPolarizati on
Examples: Consider a LED operating @ .85 mm
=50 nm
DInter-modal =2.5 ns/km
DIntra-modal =100 ps/nm×km
Consider a DFB laser operating @ 1.5 mm
=.2 nm
DIntra-modal =17 ps/nm×km
DPolarization=0.5 ps/ √km
L
2
after L=1 km, T=5.6 ns
after L=100 km, T=0.34 ns!
59
Effects of Dispersion: Capacity Limitation
Capacity limitation: maximum broadening<half a bit period
1
2B
For Single - Mode Fiber, T LDIntramodal
T
(neglecting polarization effects)
1
LB
2 DIntramodal
Example: Consider a DFB laser operating @ 1.55 mm
=0.2 nm
D =17 ps/nm×km
LB<150 Gb/s ×km
If L=100 km, BMax=1.5 Gb/s
60
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
61
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
62
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
63