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Optical Fibre Communication
Systems
Lecture 2: Nature of Light and Light
Propagation
Professor Z Ghassemlooy
Northumbria Communications Laboratory
School of Informatics, Engineering and
Technology
The University of Northumbria
U.K.
http://soe.unn.ac.uk/ocr
Prof. Z Ghassemlooy
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Contents







Wave Nature of Light
Particle Nature of Light
Electromagnetic Wave
Reflection, Refraction, and Total Internal Reflection
Ray Properties in Fibre
Types of Fibre
Fibre Characteristics
 Attenuation
 Dispersion
 Bandwidth Distance Product
 Summary
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Wave Nature of Light
• Newton believed in the particle theory of light. He explained the
straight-line casting of sharp shadows of objects placed in a light
beam. but he could not explain the textures of shadows
• Wave
theory:
Explains
the
interference where the light intensity
can be enhanced in some places and
diminished in other places behind a
screen with a slit or several slits. The
wave theory is also able to account for
the fact that the edges of a shadow are
not quite sharp.
This theory describes: Propagation,
reflection, refraction and attenuation
Prof. Z Ghassemlooy
G Ekspong, Stockholm University,
Sweden, 1999.
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Wave Nature of Light - contd.
1864 James Clerk Maxwell
His mathematical theory of electromagnetism led to the view that
light is of electromagnetic nature, propagating as a wave from the
source to the receiver.
1880s Heinrich Hertz
Discovered experimentally the existence of electromagnetic waves at
radio-frequencies.
Wave theory does not describe the absorption of light by a
photosensitive materials
1900-20 Max Planck, Neils Bohr and Albert Einstein
Invoked the idea of light being emitted in tiny pulses of energy
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Particle Nature of Light
Light behaviour can be explained in terms of the amount of energy
imparted in an interaction with some other medium. In this case, a
beam of light is composed of a stream of small lumps or QUANTA of
energy, known as PHOTONS. Each photon carries with it a precisely
defined amount of energy defined as:
Wp = h*f
Joules (J)
where; h = Plank's constant = 6.626 x 10-34 J.s, f = Frequency Hz
The convenient unit of energy is electron volt (eV), which is the kinetic energy
acquired by an electron when accelerated to 1 eV = 1.6 x 10-19 J.
• Even although a photon can be thought of as a particle of energy it still has a
fundamental wavelength, which is equivalent to that of the propagating wave as
described by the wave model.
• This model of light is useful when the light source contains only a few photons.
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Electromagnetic Spectrum
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Electromagnetic Radiation
• Carries energy through space (includes visible light, dental x-rays,
radio waves, heat radiation from a fireplace)
• The wave is composed of a combination of mutually perpendicular
electric and magnetic fields the direction of propagation of the wave
is at right angles to both field directions, this is known as an
ELECTROMAGNETIC WAVE
EM wave move through a vacuum at 3.0 x 108 m/s ("speed of light")
E  E (r , )e j ( t z )
H  H (r , )e j ( t z )
Speed of light
in a vacuum
Prof. Z Ghassemlooy
c  f 
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The Wave Equation
Solutions to Maxwell’s equations:
phase fronts


Plane wave:
k
Ee
 jk r
Spherical wave:
e  jkR
E
R
2
k  n  k0
k   0   r    0 0   r  k0

  0 / n
n  r
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One Dimensional EM Wave
• For most purposes, a travelling light wave can be presented as a
one-dimensional, scalar wave provided it has a direction of
propagation.
• Such a wave is usually described in terms of the electric field E.
Wavelength 
A plane wave propagating
in the direction of z is:
Eo
z
Phase
E ( z, t )  Eo sin( t  z )
2 

The propagation constant (or wave number)  
 vp
Phase velocity v p  c / n
n = Propagation medium refractive index
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Polarization
Light is a transverse, electromagnetic wave, where the transverse nature of it
can be demonstrated through polarization.
Unpolarized light source: The electric field is vibrating in many directions; all
perpendicular to the direction of propagation.
Polarized light source: The vibration of the electric field is mostly in one
direction. Any direction is possible as long as it's perpendicular to the
propagation.
Horizontal
Vertical
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Diognal
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Group Velocity
• A pure single frequency EM wave propagate through a wave guide
at a
Phase velocity v p  c / n
• However, non-monochromatic waves travelling
together will have a velocity known as Group Velocity: v g  c / ng
dn
ng  n  
d
1.49
Ref. index
Where the fibre
group index is:
ng
1.46
n
1.44
500
Prof. Z Ghassemlooy
 (nm)1700 1900
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Reflection and Refraction of Light
Medium 1
1
1
2
n1
Boundary
1
n2
Incident
ray
2
1
1 1
n1
Reflected
ray
Medium 2
n1 < n2
2
Refracted
n2 ray
n1 > n2
Using the Snell's law at the boundary we have:
n1 sin 1 = n2 sin 2
or
n1 cos 1 = n2 cos 2
1 = The angle of incident
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Total Internal Reflection
• As 1 increases (or 1
decreases) then there is no reflection
c
n1
• Beyond the critical angle, light ray
becomes totally internally reflected
When 1 = 90o (or c = 0o)
Thus the critical angle
n2
1
• The incident angle
1 =  c = Critical Angle
n1 sin 1 = n2
n1 > n2
n1 > n2
1<c
n2
1
1>
1  n2

c  sin  
 n1 
Prof. Z Ghassemlooy
c
n1
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Ray Propagation in Fibre - Bound
Rays
 > c,  > max
5
c
3
2
a
1

4
Core n1
Air (no =1)
Cladding n2
From Snell’s Law: n0 sin  = n1 sin (90 - )
 = max when  = c
Thus, n0 sin max = n1 sin c
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Ray Propagation in Fibre - contd.
n0 sin max = n1 (1 - sin2 c)0.5
Or
Since
1  n2

c  sin  
 n1 
  n 2 
n0 sin  max  n1 1   2  
  n1  
Then

n12

2 0.5
 n2
0.5


n12

2 0.5
 n2
 Numerical Aperture ( NA)
NA determines the light
gathering
capabilities of the fibre
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Ray Propagation in Fibre - contd.
Therefore
n0 sin max = NA
Fibre acceptance angle
Note n1  n2  
n
Thus
 NA 

 max  sin 1 
 n0 
Relative refractive index difference
NA  n1 (2) 0.5
Prof. Z Ghassemlooy
0.14< NA < 1
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Modes in Fibre
A fiber can support:
– many modes (multi-mode fibre).
– a single mode (single mode fiber).
The number of modes (V) supported in a fiber is
determined by the indices, operating wavelength and the
diameter of the core, given as.
2
V  2 a nc2  ncl
2a
V
NA
or


 V<2.405 corresponds to a single mode fiber.
 By reducing the radius of the fiber, V goes down, and it becomes
impossible to reach a point when only a single mode can be
supported.
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Basic Fibre Properties
Cylindrical
Dielectric
Core Cladding
Buffer coating
Waveguide
Low loss
Usually fused silica
Core refractive index > cladding refractive index
Operation is based on total internal reflection
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Types of Fibre
There are two main fibre types:
(1) Step index:
• Multi-mode
• Single mode
(2) Graded index multi-mode
Total number of guided modes M for multi-mode fibres:
Multi-mode SI
M  0.5V 2
Multi-mode GI M  0.25V 2
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Step-index Multi-mode Fibre
Input
pulse 120-400m
50-200 m
Output pulse
n1 =1.48-1.5
n2 = 1.46
dn=0.04,100 ns/km
Advantages:
• Allows the use of non-coherent optical light source, e.g. LED's
• Facilitates connecting together similar fibres
• Imposes lower tolerance requirements on fibre connectors.
• Cost effective
Disadvantages:
• Suffer from dispersion (i.e. low bandwidth (a few MHz)
• High power loss
Prof. Z Ghassemlooy
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Graded-index Multi-mode Fibre
50-100 m
Input
pulse 120-140m
n2 n1
dn = 0.04,1ns/km
Output
pulse
Advantages:
• Allows the use of non-coherent optical light source, e.g. LED's
• Facilitates connecting together similar fibres
• Imposes lower tolerance requirements on fibre connectors.
• Reduced dispersion compared with STMMF
Disadvantages:
• Lower bandwidth compared with STSMF
• High power loss compared with the STSMF
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Step-index Single-mode Fibre
Input
pulse 100-120m
8-12 m
Output pulse
n1 =1.48-1.5
n2 = 1.46
dn = 0.005, 5ps/km
Advantages:
• Only one mode is allowed due to diffraction/interference effects.
• Allows the use high power laser source
• Facilitates fusion splicing similar fibres
• Low dispersion, therefore high bandwidth (a few GHz).
• Low loss (0.1 dB/km)
Disadvantages:
• Cost
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Single Mode Fiber - Power Distribution
Optical power
Guided
Evanescent
Intensity profile of the fundamental mode
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Fibre Characteristics
• The most important characteristics that limit the
transmission capabilities are:
• Attenuation (loss)
• Dispersion (pulse spreading)
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Attenuation - Standard Fibre
SM-fiber, InGaAsP DFB-laser,
~ 1990 Optical amplifiers
InGaAsP FP-laser or LED
Attenuation (dB/km)
10
MM-fibre, GaAslaser or LED
80nm
180 nm
5
2.0
Fourth Generation,
1996, 1.55 m
WDM-systems
1.0
0.5
1300
nm
0.2
0.1
600
800
1200
1000
1400
Wavelength (nm)
1550
nm
1600
1800
c
14 Hz |
14 Hz |
Bandwidth f 


=
1.142
x
10
+
2.2475
10
1300
nm
1550 nm
2

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Attenuation (Loss ) - contd.
Fibre
Pi

L
The output power
Po
Po (L)= Pi (0).e- pL
Fibre attenuation coefficient
(p =  scattering +  absorption +  bending)
1  Po 
 p  ln  
L  Pi 
 Po 
1
Or in dB/km, fibre attenuation   log    4.343 p (km 1 )
L  Pi 
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Fibre Attenuation - contd.
• In a typical system, the total loss could bas 20-30 dB, before it
needs amplification.
So, at 0.2 dB/km, this corresponds to a distance of 100-150 km.
Attenuation along the fibre link can be
measured using Optical Time Domain
Reflectometer
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Fibre Dispersion
• Data carried in an optical fibre consists of pulses of light energy
consists of a large number of frequencies travelling at a given rate.
• There is a limit to the highest data rate (frequency) that can be
sent down a fibre and be expected to emerge intact at the output.
• This is because of a phenomenon known as Dispersion (pulse
spreading), which limits the "Bandwidth” of the fibre.
T

si(t)
Many modes
L
so(t)
Output
pulse
Cause of Dispersion:
• Chromatic (Intramodal) Dispersion
• Modal (Intermodal) Dispersion
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Chromatic Dispersion
• It is a result of group velocity being a function of wavelength.
In any given mode different spectral components of a pulse traveling
through the fibre at different speed.
• It depends on the light
source spectral characteristics.
Laser
LED
(many modes)
 = 1-2 nm
 = R.M.S Spectral
width
 = 40 nm
wavelength
• May occur in all fibre, but is the dominant in single mode fibre
• Main causes:
• Material dispersion - different wavelengths => different speeds
• Waveguide dispersion: different wavelengths => different angles
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Material Dispersion
Refractive index of silica is frequency dependent. Thus different
frequency (wavelength) components travel at different speed
RMS pulse broadening
 d 2n
 m at L
c d2
Where material dispersion
175
coefficient:
100
d n
Dm at 
c d2
ns / km
2nd window
2
ps / nm.km
Dmat 0
Note: Negative sign, indicates that low
wavelength components arrives before
higher wavelength components.
Prof. Z Ghassemlooy
-100
0.8
1.0 1.2

1.4 1.6 1.7
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Waveguide Dispersion
• This results from variation of the group velocity with wavelength for
a particular mode. Depends on the size of the fibre.
• This can usually be ignored in multimode fibres, since it is very
small compared with material dispersion.
• However it is significant in monomode fibres.
175
Waveguide dispersion
100
Dmat 0
-100
0.8
Total dispersion
Material dispersion
1.0 1.2

1.4 1.6 1.7
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Modal (Intermodal) Dispersion
• Lower order modes travel travelling almost parallel to the centre
line of the fibre cover the shortest distance, thus reaching the end of
fibre sooner.
• The higher order modes (more zig-zag rays) take a longer route
as they pass along the fibre and so reach the end of the fibre later.
• Mainly in multimode fibres
2


Cladding n2
Core n1
c
1
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Modal Dispersion - SIMMF
The time taken for ray 1 to propagate a length
of fibre L gives the minimum delay time:
Ln1
t min 
c
The time taken for the ray to propagate a length
of fibre L gives the maximum delay time:
L cos 
tmax 
c n1
Since
sin  c 
n2
 cos
n1
The delay difference Ts  tmax tmin
(n n )
Since relative refractive index
 1 2
difference
n
1
Thus
Ln12
Ts 

cn2
Prof. Z Ghassemlooy
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Modal Dispersion - SIMMF
For  1,

(n1n2 )
n2
and
NA  n1 (2) 0.5
L( NA) 2
Ts 
2cn1
For a rectangular input pulse, the RMS pulse broadening due to
modal dispersion at the output of the fibre is:
Ln1 L( NA) 2
 modal 

3.5c
7n1C
Total dispersion = chromatic dispersion + modal dispersion
T [chrom2 modal2 ]1 / 2
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Modal Dispersion - GIMMF
 The delay difference
Ln12
Ts 
2c
 the RMS pulse broadening
Ln12
 m odalGI 
34.6C
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Dispersion - Consequences
I- Frequency Limitation (Bandwidth)
T
1 0 1
0 0
1
L = L1
1 0 1
0 0
1
B
L
• Maximum frequency limitation of
signal, which can be sent along a fibre
• Intersymbol interference (ISI), which
is unacceptable in digital systems which
depend on the precise sequence of pulses.
L = L2 > L1
1 0 1
0 0
1
Intersymbol interference
II- Distance: A given length of fibre, has a maximum frequency
(bandwidth) which can be sent along it. To increase the bandwidth for
the same type of fibre one needs to decrease the length of the fibre.
Prof. Z Ghassemlooy
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Bandwidth Limitations
• Maximum channel bandwidth B:
• For non-return-to-zero (NRZ) data format: B = BT /2
• For return-to-zero (RZ) data format:
B = BT
Where the maximum bit rate BT = 1/T, and T = bit duration.
• For zero pulse overlap at the output of the fibre BT <= 1/2
where  is the pulse width.
For MMSF: BT (max) = 1/2Ts
• For a Gaussian shape pulse:BT  0.2/rms
where rms is the RMS pulse width.
For MMSF: BT (max) =0.2/ modal
or
BT (max) =0.2/ T
Total dispersion
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Bandwidth Distance Product (BDP)
The BDP is the bandwidth of a kilometer of fibre and is a constant
for any particular type of fibre.
Bopt * L = BT * L
(MHzkm)
For example, A multimode fibre has a BDP of 20 MHz.km, then:- 1 km of the fibre would have a bandwidth of 20 MHz
- 2 km of the fibre would have a bandwidth of 10 MHz
Typical B.D.P. for different types of fibres are:
•
•
•
Multimode 6 - 25 MHz.km
Single Mode 500 - 1500 MHz.km
Graded Index 100 - 1000 MHZ.km
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Bandwidth Distance Product
Bit rate B (Gbps)
100
Source spectral width < 1 nm
10
1
Source spectral width = 1 nm
0.1
1
10
100
1000
10,000
Distance L (km)
Dmat = 17 ps/km.nm
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Controlling Dispersion
For single mode fibre:
• Wavelength 1300:
- Dispersion is very small
- Loss is high compared to 1550 nm wavelength
• Wavelength 1550:
- Dispersion is high compared with 1300 nm
- Loss is low
Limitation due to dispersion can be removed by moveing
zero-diepersion point from 1300 nm to 1550 nm. How?
By controlling the waveguide dispersion.
Fibre with this property are called Dispersion-Shifted Fibres
Prof. Z Ghassemlooy
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Controlling Dispersion
20
Dispersion
shifted
10
0
Dispersion
flattened
Standard
-10
-20
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Wavelength ( m)
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Summary
• Nature of light : Particle and wave
• Light is part of EM spectrum
• Phase and group velocities
• Reflection, refraction and total internal reflection etc.
• Types of fibre
• Attenuation and dispersion
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