1. Signal Degradation
in
Optical Fiber
(Attenuation & Dispersion)

2. Linear effects are the effects do not dependent on the power.
Attenuation and dispersion are the power independent effects.
Nonlinear effects are power dependent effects.

3.  In this Chapter we are going to see,
1. What are the loss or signal attenuation mechanisms in a
fiber? (How Far?)
2. Why and to what degree do optical signals get distorted as
they propagate along a fiber? (How Fast?)
 Signal attenuation (also known as fiber loss or signal loss) is
one of the most important properties of an optical fiber, because it
largely determines the maximum unamplified or repeater less
separation between a transmitter and a receiver.
 The distortion mechanisms in a fiber cause optical signal pulses
to broaden as they travel along a fiber.
 The signal distortion mechanisms thus limit the information-
carrying capacity of a fiber.

4. :: NONLINEAR SCATTERING ::
DWDM
 Interaction of light waves with phonons in the silica medium.
 Energy gets transferred from lower λ to higher wavelength λ.

5. :: SELF & CROSS PHASE MODULATION ::
DWDM
 Phase angle depends on light intensity.
 Φ= γ Pin Leff for SPM.
 Φ1= γ (Pin1+ Pin2+ Pin3) Leff for CPM/XPM.

6. :: FOUR WAVE MIXING ::
DWDM
 FWM gives rise to new frequencies.
 These signals appear as crosstalk to existing signals.
 Effect is higher when ∆λ is less.
 FWM increases as CWDM – WDM – DWDM

7. Attenuation

8. :: ATTENUATION ::
DWDM
Effect of Attenuation and Noise
 Reduces the signal power during transmission.
 Limits the Link Length.
 i.e. How FAR ?

9. Attenuation (fiber loss):
 Power loss along a fiber:
Z=0 Z= l
 p l
P(0) mW P(l )  P(0)e mw
 p z
P( z )  P(0)e [3-1]
 The parameter  p is called fiber attenuation coefficient in a units
of for example [1/km] or [nepers /km]. A more common unit is
[dB/km] that is defined by:
10  P(0) 
 [dB/km]  log    4.343 p [1 / km] [3-2]
l  P(l ) 

10. Fiber loss in dB/km:
z=0 Z=l
P(0)[dBm]
P(l )[dBm]  P(0)[dBm]  [dB/km]  l[km] [3-3]
 Where [dBm] or dB milli watt is 10 log (P [mW]).

11. Attenuation Units:
 As light travels along a fiber, its power decreases exponentially with
distance.
 P(O) is the optical power in a fiber at the origin (at z = 0),then the
power P(z) at distance z further down the fiber is,
 αp is the fiber attenuation coefficient given in units of, km-1.
 Other units for αp can also be designated by nepers .
 For simplicity in calculating optical signal attenuation in a fiber, the
attenuation coefficient is expressed in dB/km.
 This parameter is generally referred to as the fiber loss
or fiber attenuation.

12. Basic attenuation mechanisms in a fiber:
 Absorption (Intrinsic & Extrinsic)
 Scattering ( Linear & Non linear)
 Bending losses (Micro bending & Macro bending)
 Attenuation is wavelength dependent hence proper
selection of operating wavelength is required.

13. (1) Absorption: (Material Absorption)
 Material absorption is a loss mechanism related to the
material composition and fiber fabrication process.
 This results in the dissipation of some of the transmitted
optical power as heat in the waveguide.
 Absorption is classified into two basic categories:
Intrinsic and extrinsic.
Intrinsic Absorption:
 It is caused due to the interaction of free electrons
within the fiber material and the light wavelength.
 This wavelength spectrum interacts differently with
the atoms of the fiber material.

14. Extrinsic Absorption:
 It is mainly due to the impurities injected into the
optical fiber mix during the fabrication process.
 The metal ions are the most undesirable impurity in an
optical fiber mix because the presence of metal ions
influence and alter the transmission properties of the fiber.
 This results the loss of optical power.

15. (2) SCATTERING LOSS:
 Scattering loss is the loss associated with the
interaction of the light with density fluctuations in
the fiber.
 Small (compared to wavelength) variation in material
density, chemical composition, and structural
inhomogeneity scatter light in other directions and absorb
energy from guided optical wave.

16. Linear scattering:
 Here the amount of optical power transferred from a
wave is proportional to the power in the wave. There is
no frequency change in the scattered wave.
 Rayleigh scattering
 Mie Scattering
Rayleigh scattering:
 It results from the interaction of the light with the
inhomogeneties in the medium that are one-tenth of the
wavelength of the light. Rayleigh scattering in a fiber can
be expressed as :
 It means that a system operating at longer wavelengths
have lower intrinsic loss.

17. Mie Scattering:
 If the defects in optical fibers are larger than λ/10 the
scattering mechanism is known as 'Mie scattering'.
 These large defect sites are developed by the
inhomogeneities in the fiber and are associated with in
complete mixing of waveguide dopants or defects formed
in the fabrication process.
 These defects physically scatter the light out of the fiber
core.
 Mie scattering is rarely seen in commercially
available silica-based fibers due to the high level of
manufacturing expertise.

18. Non-linear scattering:
 High electric fields within the fiber leads to the non-linear
scattering mechanism.
 It causes the scattering of significant power in the forward,
backward or sideways depending upon the nature of the
interaction.
 This scattering is accomplished by a frequency shift of
the scattered light.
Raman scattering: (forward light scattering or SRS)
 It is caused by molecular vibrations of phonons in the
glass matrix.
 This scattering is dependent on the temperature of
the material.

19. Brillouin scattering: (backward light scattering or SBS ).
 It is induced by acoustic waves as opposed to
thermal phonons.
 Brillouin scattering is a backscatter phenomenon.
 The importance of SRS and SBS is that they can be the
limiting factor in high-power system designs.
 Raman scattering loss is unaffected by spectral source
width but requires at least an order of magnitude more
power for onset.
 Brillouin scattering loss can be decreased by using a light
source with a broad spectral width. A broad spectral
width reduces the light-material interaction.

20. Absorption & scattering losses in fibers:

21. Typical spectral absorption
&
scattering attenuations for a single mode-fiber

22. (3) RADIATIVE LOSS (BENDING LOSS):
 Radiative losses occur whenever an optical fiber
undergoes a bend of finite radius of curvature.
 Fibers can be subjected to two types of bends :
macroscopic bend and the microscopic bend.
Macro bending losses :
 It occur due to the bends of radii larger than the
fiber diameter.
 These losses are also called 'large-curvature radiation
losses'.

24.  For slight bends, the excess loss is extremely small. As the
radius of curvature decreases, the loss increases
exponentially until a certain critical radius occurs. At this
point the macro bend losses are significant.
 These losses become extremely large when the bend
crosses the critical/threshold point.
 The macro bend losses occur when optical fibers are
packed for transportation to the field of installation
during installation process.

25. Micro bend losses:
 These losses are associated with small perturbations of the fiber,
induced by the factors like uneven coating application or cabling
induced stresses.
 The results of the perturbations is to cause the coupling of propagating
modes in the fiber by changing the optical path length. This de
stabilisation of the modal distribution causes the lower-order modes to
couple to the higher-order modes which are lossy in nature.

26. Dispersion

27. 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 any electromagnetic signal
propagating in a physical medium is degraded
because the various wave characteristics (i.e.,
frequencies) of the signal have different
propagation velocities within the physical
medium.

28. Signal Distortion in Fiber:
 The optical signal that propagates through
an optical fiber suffers from distortion (i.e.
change in shape). This effect of pulse
broadening in fiber is known as Dispersion.
 Different frequency components travel at different
velocities in fiber, arriving at different times at the
receiver.
 Broadening of Pulse.

29. Information Capacity determination:

30. •A measure of information capacity of an optical fiber for digital transmission
is usually specified by the bandwidth distance product BW  L in
GHz.km.
•For multi-mode step index fiber this 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.

31.  Types of Dispersion:
 (A) Intermodal dispersion
 (B) Intramodal Dispersion:
◦ (i) Material Dispersion
◦ (ii) Waveguide Dispersion
(C) Polarization Mode Dispersion (PMD)
 This distortion effects are due to
intramodal dispersion and intermodal
delay effects, which can be explained by
the group velocities of the guided modes.
 'Group velocity' is the speed at which the
energy in a particular mode travels along
the fiber.

32. Inter-modal (or) Modal dispersion (or) Group delay:
 Pulse broadening due to intermodal dispersion results
from the propagation delay differences between the
modes within a mu1timode fiber.
 The pulse in different modes travel along the channel
with different group velocities.
 The pulse width at the output depends on the
transmission times of the slowest and the fastest modes.
 This dispersion creates the fundamental difference in
the overall dispersion for the different fiber types.
 Hence SI multimode fibers exhibit a large amount of
intermodal dispersion giving the greatest pulse
broadening.

33. Inter-modal (or) Modal dispersion (or) Group delay:
 The intermodal dispersion in multimode fibers can be
minimized by adopting optimum refractive index profile
provided by the near parabolic profile of most GI fibers.
 So, the overall pulse broadening in multimode GI fibers
is less than that of the SI fibers.
 Thus GI fibers used with a multimode source gives a
tremendous bandwidth advantage over multimode SI
fibers.
 To eliminate the Intermodal Dispersion SMF is the best
solution.

34. Group Velocity
• Wave Velocities:
• 1- Plane wave velocity: For a plane wave propagating along z-axis in an
unbounded homogeneous region of refractive index n1 , which is
represented by exp( jωt  jk1 z ) , the velocity of constant phase plane is:
 c
v  [3-4]
k1 n1
• 2- Modal wave phase velocity: For a modal wave propagating along z-axis
represented byexp( jωt  jz ) , the velocity of constant phase plane is:
ω
vp 

[3-5]
3- For transmission system operation, the most important & useful type of
velocity is the group velocity, V g . This is the actual velocity which the
signal information & energy is traveling down the fiber. It is always less
than the speed of light in the medium. The observable delay experiences by
the optical signal waveform & energy, when traveling a length of l along
the fiber is commonly referred to as group delay.

35. Group Velocity & Group Delay
• The group velocity is given by:
dω
Vg  [3-6]
d
• The group delay is given by:
l d
g   l [3-7]
Vg dω
• It is important to note that all above quantities depend both on frequency
& the propagation mode.
• In order to see the effect of these parameters on group velocity and delay,
the following analysis would be helpful.

36. Input/Output signals in Fiber Transmission
System
• The optical signal (complex) waveform at the input of fiber of length l is
f(t). The propagation constant of a particular modal wave carrying the
signal is  (ω). Let us find the output signal waveform g(t).
 is the optical signal bandwidth.
Z=l
z-=0
 c  
~
f (t ) 

 f ( )e jt d [3-8]
c 
 c  
~
g (t ) 

 f ( )e jt  j ( ) l d [3-9]
c 

37. If    c
d 1 d 2
 ( )   ( c )  (   c )  (   c ) 2  ...
d
[3-10]
  c 2 d 2   c
 c   / 2  c   / 2 d
jt  j [  ( c )  (  c )] l
~ ~ d
g (t )   f ( )e jt  j ( )l d   f ( )e d
  c
 c   / 2  c   / 2
 c   / 2 d
j ( t  l )
~ d
 e  j ( c )l  f ( )e d
  c
 c   / 2
 j ( c ) l d
e f (t  l )  e  j ( c )l f (t   g )
d
[3-11]
  c
d l
g  l  [3-14]
d   c Vg

38. How to characterize dispersion?
• Group delay per unit length can be defined as:
g d 1 d 2 d
  
2c d
[3-15]
L dω c dk
• If the spectral width of the optical source is not too wide, then the delay
d g
difference per unit wavelength along the propagation path is approximately
For spectral components which are  apart, symmetrical around center d
wavelength, the total delay difference  over a distance L is:
d g L  d 2 d  
2
      2
  
2 
d 2c  d d 
d d  L   d 2 
      L 
d d V   d 2  [3-16]
 g   

39. d 2
• 2  is called GVD parameter, and shows how much a light pulse
d 2
broadens as it travels along an optical fiber. The more common parameter
is called Dispersion, and can be defined as the delay difference per unit
length per unit wavelength as follows:
1 d g d  1


   2c  2
D 
d  V g 
[3-17]
L d   2
• In the case of optical pulse, if the spectral width of the optical source is
characterized by its rms value of the Gaussian pulse   , the pulse
spreading over the length of L,  g can be well approximated by:
d g
g     DL  [3-18]
d
• D has a typical unit of [ps/(nm.km)].

40. Intramodal dispersion:
 It is pulse spreading that occurs within a single mode
of light source. It is due to the group velocity which is a
function of the wavelength.
 As the intramodal dispersion is dependent on the
wavelength, its effect on signal distortion increases
with the spectral width of the optical source. It is
normally characterized by the RMS spectral width.
 The LEDs have an RMS spectral width of about 5% of
the central wavelength, whereas the LASER diodes
have much narrower spectral widths of 1 to 2 nm.
 The main causes of intramodal dispersion are :
Material & Waveguide dispersion.

41. Material or Chromatic Dispersion:
 In SMF due to the diffraction property, there is spread of narrow pulses in
the constant refractive index core material is called intramodal dispersion.
 This dispersion arises due to the variation of the
refractive index of the core material as a function of
optical wavelength.
 This causes a wavelength dependence of the group
velocity of any given mode; that is, pulse spreading
occurs even when different optical wavelengths follow
the same optical path.

42. Material Dispersion
Input Cla dding
v g ( 1 )
Core Output
Emitter v g ( 2 )
Very short
light puls e
Intensity Intensity Intensity
Spectrum, ² 
Spread, ² 
 t t
1 o 2 0 
All excitation sources are inherently non-monochromatic and emit within a
spectrum, ², of wavelengt hs. W aves in t he guide wit h different free space
wavelengths travel at different group velocities due t o the wavelength dependenc
of n1. T he waves arrive at t he end of the fiber at different t imes and hence result
a broadened output pulse.
© 1999 S.O. K asap,Optoelectronics rentice H all)
(P

43. Material Dispersion
• The refractive index of the material varies as a function of wavelength, n( )
• Material-induced dispersion for a plane wave propagation in homogeneous
medium of refractive index n:
d 2 d 2 d  2 
 mat L  L  L n( ) 
dω 2c d 2c d  
 
L dn 
  n  [3-19]
c d 
• The pulse spread due to material dispersion is therefore:
d mat L  d 2 n
g     2  L  Dmat ( )
d d
[3-20]
c
Dmat ( )
is material dispersion

44. Waveguide Dispersion:
 Waveguide dispersion occurs since the propagation of light in the core and cladding
layers differ.
 Considering the ray theory approach, it is equivalent to the angle between the ray
and the fiber axis vary with wavelength.
 This leads to variation in the transmission time of the rays and hence the dispersion.
 If β is the propagation constant for a SM fiber, then
the fiber exhibits the waveguide dispersion if
 In multimode fibers, the majority of modes propagate
far from the cut-off.
 They are almost free of waveguide dispersion and is
negligible when compared to the material dispersion.

46. Polarization Mode dispersion
Intensity
t
Output light puls e
z 
n1 y // y Core Ex
 = P ulse spread
Ex Ey
n1 x // x Ey
t
E
Input light pulse
Suppose that the core refractive index has different values along two orthogonal
directions corresponding to electric field oscillation direction (polarizations). We can
take x and y axes along these directions. An input light will travel along the fiber with Ex
and Ey polarizations having different group velocities and hence arrive at the output at
different times
© 1999 S.O. K asap,Optoelectronics rentice H all)
(P

47. Modal Dispersion
• Dispersion means the difference in arrival time of the light
rays at the output end of an optical fiber.
• Modal dispersion is caused by the difference in rays path
(with equal wave length) due to variation in light incidence
angles at the input end. It occurs only in multimode fibers
• Material dispersion is related to the variation of light
velocity in a given fiber material due to the difference in
propagated light wave.
Number of modes
 2
( Diameter of core  NA  )
Number of mod es  
2 47

48. A
Input pulse
Output pulse
LMax
t
Critical
LMin
angle
For instance, if n1 = 1.5 and  = 0.01, then the numerical aperture is
0.212 and the critical angle  r,cr, is about 12.5 degrees.
48

49. • i = 0 and path length=L (fiber length).
• The longest path occurs for  i = i, CR and can be estimated as:
L
LMAX 
sin   CR 

L 1L L 1  n2
T   
sin   CR   1  1

  n1   1
 sin   CR
  
 c  sin   CR 
  n1
L  n1  L n1 2
T   n1  
 n 1  c  n 

c  2  2
1
TB  ; B is the bit rate in bits per second
B n2 c
BL  2 
1 n1 
T  TB ; T  ; therefore B  T  1
B
For  = 0.002 in a small-step index optical fiber:
Mb
B  L  150  km 49
s

50. B Mbps
150
1
1 150 L km
50

51. Bandwidth of a Multimode Optical Fiber
• To estimate the bandwidth of an optical fiber, we can convert from a
bit transfer rate to a bandwidth. In one signal period, two bits can be
transferred, so the maximum signal frequency is simply one-half the
bit transfer rate.
B c  n2 c  n2
f MAX  ; f MAX  W 
2 2  n1    L
2
2  n1    L
2
• Light frequencies used in fiber optic systems use a carrier frequency between 1014 and 1015 Hz 5
(10 to
6
10 GHz). The theoretical bandwidth of a fiber optic system is about 10% of the carrier frequency, or up to
10,000-100,000 GHz!
51