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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
NA  sin q max
Example: n1 = 1.47
n2 = 1.46
NA = 0.17
n1  n2
 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  m0 H  M : Magnetic flux density
with
D  0E  P
: Electric flux density
J 0
f  0
: Current density
: Charge density
19
Theory of Light Propagation in Optical Fiber
Pr , t   PL r , t   PNL r , t 

PL r , t    0   (1) t  t1 E r , t1 dt1 : Linear Polarizati on

PNL r , T  : Nonlinear Polarizati on
(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)eit 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  with n  1    (1) ( )
2 
2


2
and  



 (1) ( )
cn( )
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 : Helmoltz Equation!
c
2
22
Theory of Light Propagation in Optical Fiber
 Each components of E(x,y,z,t)=U(x,y,z)ejt must satisfy the Helmoltz equation
n  n1 for r  a

 2U  n 2 k0 U  0 with n  n2 for r  a
k  2 / 
 0
2
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




n
k
U

0
with
n  n2 for r  a
0
r 2 r r r 2  2 z 2
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 with l  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 with n  n2 for r  a
k  2 / 
0
 0
One can define an effective index of refraction neff
such that b 

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 n2 k0  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
The solutions of the equations are of the form :
Fl (r )  J l r 
for   a
J l : Bessel function of 1st kind with order l
Fl (r )  K l r 
for   a
K l : Modified Bessel function of 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 )  
K3 (r ) for r  a
27
Characteristic Equation
 Boundary conditions at the core-cladding interface
give a condition on the propagation constant b (characteristics equation)
The propagatio n constant b can be found by solving
the characteri stics 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-jle-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  ak0 NA 
2a

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()42 n22/20
 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 equivalent ly 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 constant and w0 the mode size
A good approximat ion for the mode size is obtained from
1.619 2.879 

w0  a 0.65  3 / 2 
for 1.2  V  2.4
6 
V
V 

a
w0 
for V  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
 POut 
10
  L
10 log 10 
 4.343L
P
ln(
10
)
 in 
 is usually expressed in 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

cos θ
n
n
n L  n2  n1 L
ΔT  1 L  1 L  1
1

δ
c
n2 c
n2 c  n1  n2 c
2
2
2
L
L
n

 1L
π
 sin θC n2
cos  θ 
sin
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
DIntramodal
d  1

d  v g
2
2


d
b

in units of ps/nm  km
2

2c 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
A32
A12
A2 2
n( )  1  2
 2
 2
2
2
1   2   3  2
with A1  0.6961663, 1  68.4043 nm
A2  0.4079426,  2  116.2414 nm
A3  0.8974794, 3  9896.161 nm
51
Material Dispersion
1
1
 2 db 
c
 
v g   
n  dn / d
 2c d 
2


T
Input pulse, 1
t
t
Input pulse, 2
t
L
d  1
ΔT  LD  L
d  v g
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/
DWav eguide
d  1

d  vg

d   
 
  where w0 is the mode size
 2 2 nc d  w2 
 0

54
Total Dispersion
DIntramodal  DMaterial  DWav eguide
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
v g d
d  1

d  v g
 db1 db1 d
 2c 

DIntramodal

 b2   2 
 d  d d
  

b 2 : group velocity dispersion parameter 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
v gx v gy
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  DIntramodal    L 2
Single - Mode Fiber : T 
DIntramodal    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  LDIntramodal 
T 
(neglectin g polarizati on effects)
1
 LB 
2 DIntramodal 
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