1. TRANSMISSION CHARACTERISTICS OF OPTICAL FIBERS
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
OFCS
TRANSMISSION CHARACTERISTICS OF OPTICAL FIBERS

2. Po=Pi 10 -αL/10 1. Attenuation
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 2
Like any communication system there are some important factors affecting performance of optical fibers as a transmission medium. The most interest are those attenuation and bandwidth
1. Attenuation
Is the ratio of the input (transmitted) optical power into the fiber to output (received) optical power from the fiber
Po=Pi 10 -αL/10
[W]
Po=Pi -αL
[dB]

3. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 3
Example
A fiber has a coupled power -8dBm and attenuation of 6 dBm/km, and a length 2 km. Calculate the output power
6dBm/km
dBm/km
Example
A fiber coupled power -8dBm and attenuation of 6 dBm/km. Find the fiber length if the output power is -30dBm.
6dBm/km

4. (1) Material absorption:
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 4
A number of mechanisms are responsible for the signal attenuation within optical fibers:
1-Material absorption 2-Scattering 3-Fiber bend losses 4-losses due coupling the source to the fibers
losses due to mismatching between the fibers (Fresnel)
losses due to splices and connectors
Losses due to deviation of geometrical and optical parameters 8-losses due to misalignments
9-Modal coupling radiation losses 10- Leaky mode losses
(1) Material absorption:
•Due to photon absorption in interaction with atoms or molecules of the material. It happens due to material composition and fabrication process impurities which causes attenuation in the transmitted optical power in the form of heat due to absorption
•It is divided into two types:
-Intrinsic
-Extrinsic
due to interaction with the main components of the glass
due to interaction with the impurities in the glass

5. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 5
100
Attenuation (db/km)
Glass Absorption in UV 10
Glass Absorption in IR 1
0.1
Intrinsic absorption
0.01 2 3 5 10
Wavelength (m)
-Intrinsic absorption occurs in the UV region and have peaks also in the IR in the 7 to 12 m region. This type of absorption is insignificant because it is out of operation band of optical fiber

6. -Transition metal ions -OH ions
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 6
-Extrinsic absorption is a major source of loss in practical fiber. There are two types are the main sources of impurity absorption :
-Transition metal ions -OH ions
•Transition metals (e.g : copper, iron, etc…) absorbs strongly in the region of interest and so must not exceed a few parts per billion to ensure losses are kept below 20dB/km
•OH absorption occurs because of excess water content and peak absorption occurs at 2.73um (resonant wavelength for absorption) .Other wavelength causes large absorptions at 1.37, 1.23 and 0.95um. Therefore for efficient propagation those wavelength must be avoided

7. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 7
(2) Scattering:
-Linear scattering due to random refractive index through the material causes some optical power transfer from one propagating mode to another, this tends to attenuation of the transmitted light as the transfer may be to a leaky or radiated mode which does not continue to propagate within the fiber core, but is radiated from the fiber
- Raleigh scattering:
Is the scattering of the photons at the random boundaries due to inhomogenities or the randomness of the refractive index fluctuations
-The glass was formed using heat, which caused a random movement of the molecules and when solidified the molecules were frozen in their random locations. This yields a random refractive index through the material

8. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 8
-This applies when a wave travel through a medium having scattering objects much smaller than the wavelength (molecular level)
-Thus, Raleigh scattering increases with the decrease in wavelength and was found to be proportional to λ-4 and can be approximated by the following expression :
L=1.7(0.85/λ)4 dB/km
- Mie scattering:
Is the scattering of the photons at the inhomogenities due to nonperfect cylindrical structure such as irregularities in the core cladding interface, core cladding refractive index difference, diameter fluctuations, strain and bubbles
-This applies when a wave travel through a medium having a wavelength
comparable to the size of inhomogenities
-It depends on the fiber material, design and manufacture
-It can be reduced by:
1-Removing imperfections due to glass manufacturing process; 2-Carefully control the fiber coating
3-Increasing the fiber guidance by increasing the relative refractive index difference

9. (3) Bend losses -Macro bend OPTICAL FIBER COMM. SYSTEM PROF. A.M.ALLAM
-Optical fibers suffer radiation losses at bends or curves. At that curvature most of the lower and higher order modes will incident at an angle less the critical, which let them out in the cladding, providing more power loss in the fiber
-Macro bend are bends that are large enough to be seen by the human eye
-Generally more at the cable level or for fibers, the bends necessary to fit fibers inside splice closures or patch panels
-Macro bending testing is done by wrapping the fiber or cable around a mandrel of a specified diameter
-The loss can be represented by a radiation attenuation coefficient which is given by :
αb=c1exp(-c2R)
where R is the radius of curvature of the fiber bend and c1, c2 are constants which are independent of R

10. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
-There is also a critical radius of curvature Rc where large bending losses can occur given by :
where λc is the cutoff wavelength of the single mode fiber
For single mode fibers the critical radius of curvature RCS can be approximately by :
-Based on these relations the criteria to reduce macro bending losses is : Designing fibers with large relative refractive index difference Operating at the possible shortest wavelength
-The losses due to bending can be determined as :
P2 / P1 = 1- ((α+2)/2α∆)[2a/R +(3λ/4πn2R)2/3]
where P1 and P2 are the power before and after bending respectively
It is possible that the cables could be run around corners better and fibers would not have as much loss when stuffed into small spaces

11. -There is no real test for micro bending
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
-Micro bend
-These are identical in effect to the macro bend but differ in size and cause Their radius is equal to, or less than, the diameter of the bare fiber which is very small indeed
-Micro bend loss refers to small scale "bends" in the fiber, often from pressure exerted on the fiber itself as when it is cabled and the other elements in the cable press on it
-i.e., these are generally a manufacturing problem. For example if the fiber gets too cold, the outer layers will shrink and get shorter. If the core/cladding shrinks at a slower rate, it is likely to kink and cause a micro bend
-There is no real test for micro bending
9/9/2014 LECTURES 11
Micro bending loss needs careful attention to the fiber coatings, if
applied in several layers) which protects the fiber from being bent

12. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 12
Example
A66.5/125GI parabolic fiber of core and cladding index and respectively operating at 1.3um . If the radius of curvature of the turn is 2cm, find the power lost in that turn
Example
Assume a multimode graded index fiber has a refractive index at the core axis of with a cladding refractive index of The critical radius of curvature which allows large bending losses to occur is 84 µm when the fiber is transmitting light of a particular wavelength. Determine the wavelength of the transmitted light
=0.82um λ

13. 6 4 2 λ [nm] The overall attenuation dB/km GI 50/125 2.7 50/125 0.7
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 13
dB/km λ
Type
Size,μm
dB/km
800 SI
62.5/125
5.0 SI
62.5/125
4.0
850
GI 3.3
62.5/125 6 4 2
The overall attenuation
GI 50/ GI
62.5/
50/
1300 GI
SM X/
λ [nm]
1550 SM
X/125
0.2
800
1000
1200
1330
1550

14. rs (4) Losses due coupling the source to the fibers
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 14
(4) Losses due coupling the source to the fibers
The power coupled to a fiber depends on many factors: the source diameter, variations of refractive index due to fabrications, variation in core diameter irregularities at interface , variation of the index profile and variation of the numerical aperture
Due to spatial distribution of the source
The power coupled to the fiber Pc is related to the power emitted from the source Ps by what is called the coupling efficiency and is defined as :
Source radiation pattern
source rs a
lost power
rs is the LED radius
Pc / Ps = (NA)2 min[1,(a /rs )2 ]= ηSI
=2n12 ∆[1-(2/(α+2))(rs /a)α]= ηGI
In SM fiber a is small, and since NA is also small, hence η is very small, so its very important to use LASER DIODE in SI and also in MM because its spread is narrow and most of the power is inside the acceptable angle of the fiber
ηlaser = 30-50%

15. (5) Fresnel reflection at fiber to fiber joint
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 15
(5) Fresnel reflection at fiber to fiber joint
When the two jointed fiber ends are smooth and perpendicular to the fiber axes, and the two fiber axes are perfectly aligned, there is a reflection causes loss or attenuation due to mismatching of the refractive index of the medium between the two jointed fibers. The fraction of the light power reflected at a single interface is:
R=[(n1-n)/(n1+n)]2
n is the refractive index of the medium between the two fibers and the transmission ratio is defined as :
ηt = Pc / Pemitted = 1-R
ηt =10log(1-R)
or in dB is
or the optical loss due to Fresnel reflection at a single interface is
Loss Fres = -10log(1-R)
This loss should be taken into consideration at both fiber interface

16. OPTICAL FIBER COMM. SYSTEM PROF. A.M.ALLAM
9/9/2014 LECTURES 16

17. Matching transformer Example
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
Example
Two identical optical fibers of core index 1.5. If the end faces of two fibers are butted together and their axes are perfectly aligned, then calculate the optical loss due Fresnel reflection when there is an air gap between the fiber end faces
Solution
R= [(1.5-1)/(1.5+1)]2
= 0.04
Loss Fres = -10log(1-R)
= 0.18 dB
Then the total losses due to Fresnel reflection at the two faces = = 0.36
Matching transformer
When two junctions( fiber and fiber , fiber and source,…) are different in index of refraction we insert a matching material between them to achieve minimum reflection as:
n  n n '
m 1 1
Example

18. (6) Losses due to splices and connectors
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 18
(6) Losses due to splices and connectors
Any communication systems have requirements for joining and terminations of the transmission medium. The number of intermediate connections or joints is dependent upon the link length between repeaters. In optical fiber the joints are:
-Fiber splices (like the soldered joints in other systems)
-Fiber demountable connectors (like plugs and sockets in other systems) These types are used to couple the light from one fiber to the adjoint one
-Fiber coupler: splits all the light ( or proportion) from the main fiber into two or more fibers. Also it combines the light from branch fibers into
the main fiber
The joint losses is critically dependent on the alignment of the two fibers

19. -different core and /or cladding diameter;
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
(7)Losses due to deviation of geometrical and optical parameters There are inherent connection problems when jointing fiber with :
-different core and /or cladding diameter;
-different NA and/or relative refractive index difference Δ;
-different refractive index profile α;
-different spot size ωo ;
-fiber faults like core ellipticity, core concentricity, …
The losses caused by these factors and Fresnel reflection loss are usually referred to what is called INTRINSIC joint losses
•The best results are achieved with compatible (same) fibers which are manufactured to the lowest tolerance, but still the problem of the quality of alignment provided by jointing mechanisms (EXTRINSIC joint loss)
9/9/2014 LECTURES 19

20. -In multimode fiber joints
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 20
•Intrinsic losses
In addition to the reflection loss the losses due to different geometry and properties of the fiber can be formulated as:
-In multimode fiber joints
Considering all the modes are equally excited in multimode (SI or GI) fibers, the loss from core
diameter mismatch can be represented as: dR
Losscd= -10log(dR/dT )2 for dR< dT otherwise =0dB dT
and the loss from refractive index profile mismatch can be represented as:
Lossα = -10log (αR(αT+2))/ (αT (αR+2))] for dR< dT otherwise =0 dB
and the loss from NA mismatch can be represented as: NA T
NAR
LossNA= -10log(NAR/NAT )2 for NAR< NAT otherwise =0 dB

21. -In single mode fiber joints
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 21
-In single mode fiber joints
The intrinsic coupling loss due to spot size mismatch can be represented as:
Losssz= -10log[4(ωoR /ωoT+ ωoT /ωoR ) -2 ] dB
where ωoR and ωoT are the spot sizes of the receiving and transmitting fibers respectively
Example
Two single mode fibers with mode field diameter of 11.2um and 8.4um are to be connected together. Assuming no extrinsic losses, determine the intrinsic loss due to the modal field diameter mismatch.
Solution
Losssz= -10log[4(4.2 / /4.2 ) -2 ]
=-10log = 0.35 dB

22. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 22
Example
When the mean optical power launched into an 8km length of fiber is 120uW, the
mean optical power at the fiber output is 3 uW. Determine:
-the overall signal attenuation or loss in dB through the fiber without connectors or splices;
-the signal attenuation per kilometer of the fiber;
-the overall signal attenuation for 10 km optical link using the same fiber with splices at 1km intervals, each giving an attenuation of 1dB;
-the numerical input/output power ratio in the previous link
Solution =

23. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 23 =

24. z (8)Misalignment losses (extrinsic loss) Longitudinal Lateral Angular
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 24
(8)Misalignment losses (extrinsic loss)
Longitudinal: the separation between the fiber
Lateral (radial, axial): offset perpendicular to the core axis
Angular : the angle between the core axes
0.1dB for z=10um
1dB for y=10um
1dB for θ=4o-5o z y
Longitudinal
Lateral
Angular θ
GI fiber
MMSI fiber

25. -In multimode fiber joints -MMSI:
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 25
-In multimode fiber joints
-MMSI:
Lateral misalignment coupling efficiency
Loss lat = -10logηlat
Lateral misalignment loss
Angular misalignment coupling efficiency
Loss ang = -10logηang
Angular misalignment loss

26. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 26
Example
SI fiber has a refractive index of 1.5 with a core diameter of 50um. The fiber is jointed with a lateral misalignment between the core axes of 5um. Determine the insertion loss at the joint due to lateral misalignment:
a-there is a small air gab at the joint; b-the gab is considered index matched
Solution a- - b-

27. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 27
Example
SI fiber has a refractive index of 1.48 with numerical aperture of 0.2. The fiber is jointed with 5o air angular misalignment of the core axes. Determine the insertion loss at the joint due to an angular misalignment
Solution =

28. -In single fiber joints
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 28
-MMGI:
Lateral misalignment coupling efficiency
ηlat = 1- Lt
where
for uniform optical power distribution for all guided modes
for uniform optical power distribution for all guided modes and leaky modes
Lt = 0.75y/a
Lateral misalignment loss
Loss lat = -10logηlat
-In single fiber joints
Considering Gaussian or near Gaussian shape of the modes propagating in single mode fibers (SI or GI) and the spot size of the two coupled fibers are the same, the total lateral and angular loss can be represented as:
ωo is the normalized spot size for single mode fiber, for the mode LP10 is different
and is given by

29. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 29
Example
SM fiber has a refractive index of 1.46 with numerical aperture of 0.1. The normalized frequency is 2.4 and the core diameter is 8um. Determine the insertion loss at the joint due lateral misalignment of 1 um and to an angular misalignment of 1o consider LP10 mode
Solution

30. light pulses as they travel along the channel
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 30
2. Bandwidth of the fiber
The other characteristic of primary interest is the bandwidth of the fiber which is limited by the signal dispersion within the fiber. Once the attenuation is reduced to acceptable levels , attention is directed towards the dispersive properties of the fiber
•Dispersion
Dispersion with the fiber cause broadening of the transmitted
light pulses as they travel along the channel
-During an optical transmission of a digitally modulated signal, dispersion with the fiber cause broadening of the transmitted light pulses as they travel along the channel. As a result if we have a stream of digital pulses , each pulse broadens and overlapped with its neighbors and becomes indistinguishable at the receiver input
-Since the broadening increases with the distance traveled along the fiber, we define the parameter BW x length of the fiber:
Typical values: 20 MHz km (MMSI), 1GHz km (MMGI), 100 MHz km (SMSI)
-This phenomena is clear in the following example:

31. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 31
Consider the input digital pattern to the fiber shown and notice the output at a distance d1 and further distance d2
Amplitude
Input digital bit pattern
Time
Distinguishable pulses
Amplitude
Composite pattern
output at d1
Time
Indistinguishable pulses
Amplitude
no zero level
output at d2
Time
Intersymbol interference
Thus, pulse broadening causes overlapping between pulses and eventually the pulses can become indistinguishable

32. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 33
This limits the maximum bit rate βT to be carried by the optical fiber
A conservative estimate of which assumes a pulse duration of τ and that pulse
spreading can be up to τ (broadening) is given by (no overlap at all):
 1 2  T
A more accurate estimation of the maximum bit rate for an optical channel with dispersion can be obtained by taking into consideration that the light pulses at the output are Gaussian in shape with rms width σ . This allows a slight overlap while still avoiding any penalties and errors due to inter-symbol interference and low SNR The maximum bit rate in this case is
 (max)  0.2 bits / s T 
It is very important to point out that this formula gives a reasonable good approximation for other pulse shapes which may occur on the channel resulting from various dispersive mechanisms within the fiber and may be assumed to represent the rms impulse response for the channel

33. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 34
Example
A multimode graded index fiber exhibits total pulse broadening of 0.1us over a distance of 15km. Estimate:
The max. possible BW assuming no inter symbol interference;
The pulse dispersion per unit length;
The BW-length product of the fiber.
Solution a)
 1 2  T
= 1/(0.2x10-6)=5 MHz
Dispersion = dispersion /total length
= 0.1 x 10-6/15= 6.67 ns km-1
BW x length = 5 MHz x 15km=75 MHz km

34. Intramodal (Chromatic)
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 35
•Types of dispersion
Dispersion
Intramodal (Chromatic)
Intramodal: due to finite spectral line width of the optical source. The optical source emits a band of frequencies (LD emits fraction percent of the central frequency while LED emits significant percentage)
We know that light of different wavelengths is refracted by differing amounts
There will be a propagation delay differences between the different spectral components of the transmitted signal which in turn causes broadening of each transmitted mode and hence intramodal dispersion

35. Example Intramodal dispersion
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
Example Intramodal dispersion
Consider the source have a certain spectral width, the pulse generated will consist of a sum of identical pulses which are only different in their wavelengths. For simplicity consider we have only three wavelength components coming out of the source which constitute the pulse
Components of input pulse
Components of input pulse λ1 λ1
Input pulse
output pulse  λ2 λ2
   λ3 λ3
Source signal

36. therefore pulse broadening is solely due to the intramodal dispersion
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 37
Intermodal dispersion
Dispersion
Intramodal (Chromatic)
Intermodal
(mode)
Intermodal: due to the propagation delay differences between the modes within a multimode fiber. (MMSI fiber exhibits a large amount of mode dispersion which gives the greatest pulse broadening)
The single mode operation does not give intermodal dispersion and
therefore pulse broadening is solely due to the intramodal dispersion

37. Intermodal dispersion
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
Example
Intermodal dispersion

38. Intramodal (Chromatic) Intermodal (mode)
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES
-Material dispersion
Dispersion
Intramodal (Chromatic)
Intermodal
(mode)
Material
-Is the broadening due to different group velocities of the various spectral components launched from the source into the fiber
-It occurs when the phase velocity of the plane wave propagating in the dielectric medium varies nonlinearly with the wavelength (d2n/dλ2≠0), i.e., due to atomic structure
-Exists in all fibers and is a function of the source line width
Spectrum of I/P pulse
I/P pulse
O/P pulse

39. -We define material dispersion factor M as
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 40
-The group delay (per unit length) is the inverse of the group velocity; τg =1/vg
-The pulse delay due to material dispersion in a fiber of length L is given by
-For a source with rms spectral width σλ and a mean λ, the rms pulse broadening due to material dispersion σm is obtained as follows:
-We define material dispersion factor M as
M=(λ/c)|d2n1 /dλ2|
and the pulse broadening can be written as
σm= σc=σλLM

40. Material dispersion parameter M (Silica)
OPTICAL FIBER COMM. SYSTEM PROF. A.M.ALLAM
9/9/2014 LECTURES 41
We can observe from the graph of material dispersion of Silica that , to minimize the material dispersion:
-Longer wave length around 1.3um is used because it gives low material dispersion; tends to zero
-LD with narrow spectral is used rather than LED
Region of negligible material dispersion
Material dispersion parameter M (Silica)
λ in um

41. -The material dispersion parameter (factor)
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
Example
11- A glass fiber material dispersion expressed by λ2(d2n1/dλ2) of It is
used with a good LED source of rms spectral width 20 nm at a wavelength of 0.85um . Estimate
-The material dispersion parameter (factor)
-The rms pulse broadening per kilometer for the used source and also when the optical source is LD with relative spectral width of at the same wavelength
Solution
-Concerning the material dispersion parameter or factor M
M=(λ/c)|d2n1 /dλ2|= (1/λc)λ2|d2n1/dλ2|= 0.025/(3x105x0.85x10-6)= 9.8x10-2 s m-1km-1
-Concerning the material dispersion for LED and LD:
for LED
σm /1km =σλM = 20 x 10-9x M = 19.6x s km-1
for LD with σλ=0.0012λ = x 0.85 x 10 -6=1.02 x 10-9 m
σm /1km=σλM = 1.02 x 10-9x M = x s km-1 i.e., 20 times less than LED

42. -Waveguide dispersion Dispersion
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 43
-Waveguide dispersion
Dispersion
Intramodal
(Chromatic)
Intermodal (mode)
Material
Waveguide
-Is the broadening due to variation in the group velocity with wavelength for a particular mode
-It occurs when (d2β/dλ2≠0)
-Exists in multimode fibers but can be significant in single mode fibers

43. Intramodal (Chromatic) Intermodal (mode)
OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014
-Modal dispersion
Dispersion
Intramodal (Chromatic)
Intermodal (mode)
Material
Waveguide
Modal
High order mode
Lo w order mo de
Broadened light pulse
Cladding
Light pulse
Intensity
Core
Due to propagation delay differences between modes within the fiber. It has a greatest effect of pulse broadening in step index multimode fibers
Intensity
Axial
Spread,  t t
Schematic illustration of light propagation in a slab dielectric waveguide. Light pulse entering the waveguide breaks up into various modes which then propagate at diferent group velocities down the guide. At the end of the guide, the modes combine to constitute the output light pulse which is broader than the input light pulse.
© 1999 S.O. Kasap,Optoelectronics(P rentice Hall)

44. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 45
Assume the length of the fiber is L; the pulse spread due to intermodal dispersion is due to the difference in time between the two extreme rays shown in the previous figure : θc θ θi
Guide n1>n2
Cladding n2
but θc
but
in terms of NA
The rms broadening for MMSI fiber can be derived as
σnSI =
2√3c
NA2
In terms of NA it can be written as
σnSI = 4√3n c 1

45. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
Using mode theory analysis it can be shown that the intermodal dispersion in GI
fibers with parabolic index profile is given by :
σnGI =
This correspond to an increase in transmission
time for the slowest mode of Δ2/8 relative to the fastest mode
For optimum index profile, rms intermodal broadening is
σnGI =
20√3 c
The overall fiber dispersion in multimode is given by
where σc is the chromatic dispersion (which is all causes related to waveguide and material), σn is from intermodal dispersion
In most cases waveguide dispersion is ignored and the chromatic dispersion is mainly due to material dispersion

46. OPTICAL FIBER COMM. SYSTEM
PROF. A.M.ALLAM
9/9/2014 LECTURES 47
Example
An 11 km optical fiber link consisting of the optimum near parabolic profile graded
index fiber exhibits rms intermodal pulse broadening of 346 ps over its length. If the
fiber has a relative refractive index of 1.5%, estimate the core axis refractive index. Hence determine the numerical aperture for the fiber.
Solution

47. OPTICAL FIBER COMM. SYSTEM PROF. A.M.ALLAM
9/9/2014 LECTURES 48