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7/29/2019 dispersion in optical fiber
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Dispersion in Optical Fiber
Unit 1.2
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Dispersion in Optical Fibers
Dispersion: Any phenomenon in which the velocity of propagation of any
electromagnetic wave is wavelength dependent.
In communication, dispersion is used to describe any process by which anyelectromagnetic signal propagating in a physical medium is degradedbecause the various wave characteristics (i.e., frequencies) of the signalhave different propagation velocities within the physical medium.
Effects the information carrying capacity of the fiber
There are 3 dispersion types in the optical fibers, in general:
1- Inter-modal dispersion
2- Intra-modal dispersion: Material Dispersion andWaveguide Dispersion
3- Polarization-Mode Dispersion
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Dispersion & Inter Symbol Interference (ISI)
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
A measure of informationcapacity of an optical fiber for
digital transmission is usually
specified by the bandwidth
distance product
in GHz.km.
For multi-mode step index fiberthis quantity is about 20
MHz.km, for graded index fiber
is about 2.5 GHz.km & for single
mode fibers are higher than 10
GHz.km.
LBW
Dispersion limits the maximum pulse rate that can propagate in a fiber of a given length
Dispersion causes distortion in the pulse train in the fiber. Two neighboring pulses may
overlap after some distance and the receiver is no longer able to distinguish between the
two pulses.
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Intermodal DispersionDue to modal delay, each mode travels a different distance in the fiber
Appears only in multimode fiber
Due to each mode having a different group velocity
Intra modal dispersionAlso called Chromatic Dispersion or group velocity dispersion
Pulse spreading in a single mode fiber
Due to the finite spectral width of the optical source, each wavelength travels with a different
velocity
Intra modal dispersion increases with the spectral width of the source. For LED source withcentral wavelength 850 nm the spectral width is of the order of 36 nm. LASER diodes have a
much smaller spectral width (1 to 2 nm)
Main causes of intra modal dispersion
1. Material dispersion: Due to the variation of the refractive index of the core material as a
function of wavelength. Pulse spreading occurs even if each wavelength follows the same
path2. Waveguide dispersion: Due to the different refractive index of the core and cladding. Part
of the optical power propagate in the cladding and therefore travels faster the that
propagating in the core because the refractive index of the cladding is less than that of the
core. Waveguide dispersion can be ignored in a multimode fiber but its effect is significant
in single mode fiber
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Material and Waveguide Dispersion
t
Spread,
t0
Spectrum,
12o
Intensity Intensity Intensity
Cladding
CoreEmitter
Very short
light pulse
vg(2)
vg(
1)
Input
Output
All excitation sources are inherently non-monochromatic and emit within aspectrum, , of wavelengths. Waves in the guide with different free spacewavelengths travel at different group velocities due to the wavelength dependenceofn1. The waves arrive at the end of the fiber at different times and hence result in
a broadened output pulse.
1999 S.O. Kasap,Optoelectronics(Prentice Hall)
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Polarization mode dispersion
Due to difference in the refractive
index along the vertical and the
horizontal axis
The two components of the wave
(Horizontal and Vertical) will thentravel with different velocities
This result in the change in the
polarization of the wave as well as
dispersion and pulse spreading
Core
z
n1x
// x
n1y
// y
Ey
Ex
Ex
Ey
E
= Pulse spread
Input light pulse
Output light pu lse
t
t
Intensity
Suppose that the core refractive index has different values along two orthogonaldirections corresponding to electric field oscillation direction (polarizations). We cantake x andy axes along these directions. An input light will travel along the fiber with ExandEy polarizations having different group velocities and hence arrive at the output at
different times
1999 S.O. Kasap, Optoelectronics(Prentice Hall)
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Multipath Dispersion On The Basis Of Ray Model
Consider two rays one axial and the other corresponding to the angle of incidence very
nearly equal but greater to the critical angle c
mL/Cosm
Cladding
m
m
c L
Core
The axial ray travels a distance Lwithin the core of refractive index
n1 with velocity v = c/n1 in time
t1 = L/v = L n1 /c
The most oblique ray which
corresponds to = m Will cover
the same axial length (actual lengthL/Cosm ) in time
t2 = (L/Cosm ) /v
= L n1 /(c Cosm )
= L n1 /(c Sin c )= L n1 /(c (n2 /n1 ))
= Ln12 /cn2
Because Sin c = n2 /n1
The two rays are launched at the
same time but will separated by a
time interval t after travelling the
length L
t = t2 - t1 = Ln12 /cn2 - L n1 /c
t = (Ln1
/c)((n 1 - n2 )/n2 ))= (Ln1
2 /cn2)
Thus the light rays within the cone of angle within
= 0 and = m will be broadened as they
propagate down the fiber.
Pulse broadening per unit length ist/L = (n1
/ n2 )((n 1 - n2 )/c ))
This is referred to as the multipath
time dispersion
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The capacity of the fiber is defined in terms ofbit-rate distance BL. In order that
the neighboring signal pulse to be distinguishable at the reciever the pulse spread
should be < 1/B (1/B = width of the bit period
For a high performance link the requirement is t 0.1/B, however in general it is
taken as t < 1/B
The bit rate distance product is then given by
BL = (n2 /n12 )(c/ )
Example:
n1 = 1.480, n2 = 1.465 and = 0.01t = 50 ns/Km which means that the pulse broadens by 50 ns after travelling a
distance of 1 Km in the fiber.
The bit-rate distance product is BL = 20 Mb/s-Km
For a graded index fiber the bit-rate distance product can be 1Gb/s-Km
Alternately:
Let us say that the system allows a spread of 25%Bit rate is 10Mb/s, that is one pulse every 100 ns and allowable spread is 25ns
The permissible transmission length of the fiber then is 500 m
If the bit rate is increased to 100 Mb/s That is one pulse every 10 ns and allowable
spread of 2.5 ns
Then the permissible transmission length of the fiber will now be only 50 m
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Wave Velocities: Group Velocity
Plane wave velocity: For a plane wave propagating alongz-axis in an
unbounded homogeneous region of refractive index , which isrepresented by , the velocity of constant phase plane is:
Modal wave phase velocity: For a modal wave propagating alongz-axisrepresented by , the velocity of constant phase plane is:
For transmission system operation the most important & useful type of
velocity is the group velocity, . This is the actual velocity which thesignal information & energy is traveling down the fiber. It is always lessthan the speed of light in the medium. The observable delay experiences bythe optical signal waveform & energy, when traveling a length ofl alongthe fiber is commonly referred to as group delay.
1n)exp( 1zjktj
11 n
c
kv
)exp( zjtj
pv
gV
How to characterize dispersion?
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Group Velocity & Group Delay The group velocity is given by:
The group delay is given by:
It is important to note that all above quantities depend both on frequency
& the propagation mode.
d
dVg
d
dlV
l
g
g
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Group delay per unit length can be defined as:
Group delay per unit length = 1/Vg Vg =c(dk/d)=d/d, Vg is the velocity at which the energy in a pulse travels along a fiber.
If the spectral width of the optical source is not too wide, then the delay
difference per unit wavelength along the propagation path is approximately
For spectral components which are apart, symmetrical around center
wavelength, the total delay difference over a distanceL is:
d
d
cdk
d
cd
d
L
g
2
1
2
d
d g
2
2
2
22
22
d
dL
V
L
d
d
d
d
d
d
d
d
c
L
d
d
g
g
L- distance travelled
propagation constant
k=2/
= ck
d-1 = - -2 d
As the signal propagate along the fiber each spectral component
can assumed to travel independently and to undergo a time delay
or group delay per unit length g /L in the direction of propagation
In terms of the angular frequency
this is written as
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The factor is called GVD parameter (Group velocity delay), andshows how much a light pulse broadens as it travels along an optical fiber. Themore common parameter is called Dispersion, and can be defined as the delaydifference per unit length per unit wavelength as follows:
In the case of optical pulse, if the spectral width of the optical source ischaracterized by its rms value of the Gaussian pulse , the pulse spreadingover the length of L, can be well approximated by:
The factor D
Is designated as dispersion, D has a typical unit of [ps/(nm.km)]. It is a resultof material dispersion and the waveguide dispersion
D = Dmat + Dwg The material dispersion and the waveguide dispersion are intricately
related as the in both cases the basic dispersive property is the refractiveindex of the medium
2
2
2
d
d
22
211
c
Vd
d
d
d
L
Dg
g
g
d
d2
2 2
22
d
d
c
L
d
d g
g
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Material Dispersion The refractive index of the material varies as a
function of wavelength,
Material-induced dispersion for a planewave propagation in homogeneous medium of
refractive index n: here = 2n()/and k = 2 /
The pulse spread due to material dispersion
is therefore:
)(n
d
dnn
c
L
nd
dL
cd
dL
cd
dL
mat
)(2
22
22
)(2
2
mat
matg DL
d
nd
c
L
d
d
)(matD is material dispersion
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A plot of material dispersion
ps/nm-Km verses wavelength is as
shown for two different fibers puresilica fiber and fiber made of 86.5
silica and 13.5 germanium dioxide.
Material dispersion can be reduced
by1. Choosing a source of narrower
spectral width 2. Using higher operating
wavelength
It is seen that for a given fiber
the material dispersion is zero at
a particular wavelength
Material Dispersion
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In this case we assume that the refractive index is constant and is independent of
wavelength. The group delay i.e. the time required for a mode to travel along the fiber of
length L
dk
kbdnn
c
Lwg
)(22
The normalized propagation constant b can be expressed as
21
2
2
2
2
1
2
2
22//
nn
nk
nn
nkb
For n1 n2 andsmall value of
index difference = (n1 - n2 )/n1
And therefore
= n2 k(b + 1) therefore
In terms of normalized frequency parameter
Delay time due to waveguide dispersion can then be expressed as:
2)( 22/12
2
2
1 kannnkaV
dV
Vbdnn
c
Lwg
)(22
Waveguide Dispersion
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Waveguide Dispersion Delay time due to waveguide dispersion
dV
VbdnncLwg )(22
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
The first term is a constant and second term
represent the group delay arising from the
waveguide dispersion.
Plot shows the wave guide dispersion for thevarious modes of a step index fiber as a
function of V
It shows that the group delay is different for
every guided mode.
Thus these modes arrive at the fiber end at
different times depending on their groupdelay resulting in the spread of the pulse
For a multimode fiber the waveguide
dispersion is very small as compared to the
material dispersion and therefore can be
neglected
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Waveguide dispersion in single mode fibers
For single mode fibers, waveguide dispersion is in the same order of material
dispersion. The pulse spread wg over the distribution of wavelength can be
well approximated as:
Where Dwg is the waveguide dispersion
The figure shows the magnitude of the
material and waveguide dispersion for
fused silica core SM fiber with V = 2.4
The two dispersion cancel and give a
zero dispersion at 1320 nm
2
2
2 )()(dV
VbdV
c
LnDL
d
dwg
wg
wg
[3-25]
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
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Polarization Mode dispersion
The effects of fiber-birefringence on the polarization states of an optical are
another source of pulse broadening. Polarization mode dispersion (PMD)is due to slightly different velocity for each polarization mode because of
the lack of perfectly symmetric & anisotropicity of the fiber. If the group
velocities of two orthogonal polarization modes are then the
differential time delay between these two polarization over a
distanceL is
The rms value of the differential group delay can be approximated as:
gygx vv and
pol
gygx
polv
L
v
L [3-26]
LDPMDpol [3-27]
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Optimum single mode fiber & distortion/attenuation
characteristics
Fact 1) Minimum distortion at wavelength about 1300 nm for single mode
silica fiber.
Fact 2) Minimum attenuation is at 1550 nm for sinlge mode silica fiber.
Strategy: shifting the zero-dispersion to longer wavelength for minimum
attenuation and dispersion by Modifying waveguide dispersion by
changing from a simple step-index core profile to more complicated
profiles. There are four major categories to do that:1- 1300 nm optimized single mode step-fibers: matched cladding (mode
diameter 9.6 micrometer) and depressed-cladding (mode diameter about 9
micrometer)
2- Dispersion shifted fibers.
3- Dispersion-flattened fibers.4- Large-effective area (LEA) fibers (less nonlinearities for fiber optical
amplifier applications, effective cross section areas are typically greater
than 100 ).2m
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Chromatic & Total Dispersion
Chromatic dispersion includes the material & waveguide dispersions.
Total dispersion is the sum of chromatic , polarization dispersion and other
dispersion types and the total rms pulse spreading can be approximately
written as:
LD
DDD
chch
wgmatch
)(
)(
[3-28]
LDDDD
totaltotal
polchtotal
... [3-29]
Si l d fib di i
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Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Single mode fiber dispersion
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Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Single mode fiber dispersion
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Single mode Cut-off wavelength & Dispersion
Fundamental mode is with V=2.405 and
Dispersion:
For non-dispersion-shifted fibers (1270 nm 1340 nm)
For dispersion shifted fibers (1500 nm- 1600 nm)
0111 LPorHE2
2
2
1
2 nnVa
c
[3-30]
LD
DD
d
dD wgmat
)(
)()()(
[3-31]
[3-32]
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Dispersion for non-dispersion-shifted fibers
(1270 nm 1340 nm)
is relative delay minimum at the zero-dispersion wavelength , and
is the value of the dispersion slope in .
2
2
000 )(
8)(
S
0 0 0S.km)ps/(nm2
0
)( 00
d
dDSS
[3-33]
[3-34]
400 )(14
)( SD [3-35]
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Dispersion for dispersion shifted fibers (1500
nm- 1600 nm)
2
00
0 )(2
)( S
00 )()( SD
[3-36]
[3-37]
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Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Example of dispersion
Performance curve for
Set of SM-fiber
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Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Example of BW vs wavelength for various optical sources for
SM-fiber.
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MFD
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
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Bending Loss
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
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Bending effects on loss vs MFD
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
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Bend loss versus bend radius
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
07.0;1056.3
m60;m6.3
2
233
n
nn
ba
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Kerr effect
Innn 20 Kerr nonlinearity in fiber, where I is the intensity ofOptical wave.
Temporal changes in a narrow optical pulse that is subjected to Kerr nonlinearity inA dispersive medium with positive GVD.
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First-order Soliton
Temporal changes in a medium with Kerr nonlinearity and negative GVD. Since dispersion tends to broaden the pulse, Kerr
Nonlinearity tends to squeeze the pulse, resulting in a formation ofoptical soliton.
BENDING LOSS B di th fib l tt ti B di l i l ifi d di t th
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BENDING LOSS. - Bending the fiber also causes attenuation. Bending loss is classified according to the
bend radius of curvature: microbend loss or macrobend loss. Microbends are small microscopic bends of
the fiber axis that occur mainly when a fiber is cabled. Macrobends are bends having a large radius of
curvature relative to the fiber diameter. Microbend and macrobend losses are very important loss
mechanisms. Fiber loss caused by microbending can still occur even if the fiber is cabled correctly. During
installation, if fibers are bent too sharply, macrobend losses will occur.
Microbend losses are caused by small discontinuities or imperfections in the fiber. Uneven coating
applications and improper cabling procedures increase microbend loss. External forces are also a source of
microbends. An external force deforms the cabled jacket surrounding the fiber but causes only a small
bend in the fiber. Microbends change the path that propagating modes take, as shown in figure 2-23.
Microbend loss increases attenuation because low-order modes become coupled with high-order modes
that are naturally lossy.
Figure 2-23. - Microbend loss.Macrobend losses are observed when a fiber bend's radius of curvature is large compared to the fiber
diameter. These bends become a great source of loss when the radius of curvature is less than several
centimeters. Light propagating at the inner side of the bend travels a shorter distance than that on the
outer side. To maintain the phase of the light wave, the mode phase velocity must increase. When the
fiber bend is less than some critical radius, the mode phase velocity must increase to a speed greater than
the speed of light. However, it is impossible to exceed the speed of light. This condition causes some of
the light within the fiber to be converted to high-order modes. These high-order modes are then lost or
radiated out of the fiber.
Fiber sensitivity to bending losses can be reduced. If the refractive index of the core is increased, then
fiber sensitivity decreases. Sensitivity also decreases as the diameter of the overall fiber increases.
However, increases in the fiber core diameter increase fiber sensitivity. Fibers with larger core size
propagate more modes. These additional modes tend to be more lossy.
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