Optics and Optical Communication: Amanuel Admassu, Mtu-Ece

Optics and
Optical Communication
SHECAT
Amanuel Admassu, mtu-ece

SHECAT
Light Propagation in Fibers

CRITICAL ANGLE and SHECAT
TOTAL INTERNAL REFLECTION
The critical angle is the minimum angle of

incidence at which light ray may strike the
interface of two media and result in an angle
of refraction of 90o or greater. This definition
pertains only when the light ray is traveling
from a more dense medium into a less dense
medium.
n2
 c  1  sin ( )
1
n1>n2
n1

If the light hits the interface at any angle
larger than this critical angle, it will not
pass through to the second medium at all.
Instead, all of it will be reflected back into
the first medium, a process known as total
internal reflection.

Example: What striking angle in the fiber

surface is needed to produce a minimum
angle of incidence (critical angle) between
the core-clad boundary that will effectively
confine the light signals within the fiber if
n1=1.55 and n2=1.45?
Ans.: θc=69.3o and θ0=33.21o

SHECAT
ACCEPTANCE ANGLE
The acceptance angle or acceptance cone half-

angle defines the maximum angle (θmax) in
which external light rays may strike the
air/fiber interface and still propagate down the
fiber
sin  max  (n  n ) 2
1
2
2
SHECAT
ACCEPTANCE ANGLE
sin  max  (n  n )
2
1
2
2
1
 max  sin ( NA)
SHECAT
ACCEPTANCE ANGLE
SHECAT
ACCEPTANCE ANGLE
SHECAT
NUMERICAL APERTURE (NA)
The Figure of Merit used to describe the light

gathering or light-collecting ability of an
optical fiber. The larger the magnitude of NA,
the greater the amount of light accepted by the
fiber from an external light-source
NA  (n  n ) 2
1
2
2
THE STRUCTURE OF AN OPTICAL SHECAT
FIBER
Composition of Optical Fibers:

FIBER
Core – inner part of the fiber, which guides

light
FIBER
Cladding – surrounds the core completely

Note: the refractive index of the core is
higher than that of the cladding, the light in
the core that strikes the boundary with the
cladding at an angle shallower than critical
angle will be reflected back into the core
through total internal reflection.
FIBER
Buffer Coating – provides mechanical

protection and bending flexibility for the fiber.
Made of soft or hard plastic such as acrylic or
nylon. Diameter: 250μm to 1000μm.
FIBER
FIBER
SHECAT
Common Optical Fiber Types:
1550 nm single mode fiber
850 nm multimode fibers
1300 nm multimode fibers
Core diameters for these types range from

8 – 62.5μm and a cladding of 125μm
SHECAT
Plastic fibers are more flexible and, consequently,

more rugged than glass. Therefore, plastic cables
are easier to install, can better withstand stress, are
less expensive, and weigh approximately 60% less
than glass. However, plastic fibers have higher
attenuation characteristics and do not propagate
light as efficient as glass. Therefore, plastic fibers
are limited to relatively short cable runs, such as
within a single building.
SHECAT
Fibers with glass cores have less attenuation than

plastic fibers, with PCS being slightly better than
SCS. PCS fibers are also less affected by
radiation and, therefore, are more immune to
external interference. SCS fibers have the best
propagation characteristics and are easier to
terminate than PCS. Unfortunately, SCS fibers
are the least rugged, and they are more susceptible
to increases in attenuation when exposed to
radiation.
SHECAT
The selection of a fiber for a given application

is a function of the specific system
requirements. There are always trade-offs
based on economics and logistics of a
particular application.
OPTICAL FIBER SHECAT
MODE OF PROPAGATION
An optical fiber guides light waves in distinct

patterns called modes.
Mode – describes the distribution of light

energy across the fiber
MODE OF PROPAGATION
1. Single Mode Fibers
Fibers having very small diameter core that

can carry only one mode which travels as a
straight line at the center of the core
MODE OF PROPAGATION
2. Multimode Fibers
Fibers that carry more than one mode at a

specific light wavelength.
MODE OF PROPAGATION
MODE OF PROPAGATION
How to calculate the number of modes in a fiber
DxNA 2
Nm  0.5( )

Where: D is the core diameter

λ is the operating wavelength
NA is the numerical aperture
MODE OF PROPAGATION
Normalized Frequency (V-parameter):
General Solution
D
V  NA

MODE OF PROPAGATION
Normalized Frequency (V-parameter):
Alternative Solution
D
V  n1 2

MODE OF PROPAGATION
So that, the Number of Modes can be calculated as:
1
Nm  V 2
2
MODE OF PROPAGATION
Example: Compute the number of modes for

a fiber whose core diameter is 50μm, given
n1=1.48, n2=1.46, and λ=0.82μm.
Ans.: 1,079 modes

SHECAT
OPTICAL FIBER INDEX PROFILE
Index Profile
A graphical representation of the value of the

refractive index across the fiber
SHECAT

STEP-INDEX PROFILE
The step-index fiber has a central core with a

uniform refractive index. The core is
surrounded by an outside cladding with a
uniform refractive index less than that of a
central core. There is a sharply defined step in
the index of refraction where the fiber core
and the cladding interfaced.
SHECAT

STEP-INDEX PROFILE
SHECAT

STEP-INDEX PROFILE
 n1 r  a : core
n( r )  
n 2 r  a : cladding
Where: n1 = refractive index of core

n2 = refractive index of cladding
a = radius of core
SHECAT

GRADED-INDEX PROFILE
A multimode optical fiber in which the
refractive index of the core declines from its
highest value at the center of the core to a
value at the edge of the core that equals the
refractive index of the cladding. This design
compensates for modal dispersion by allowing
light rays in the outer zones of the core to
travel faster than those in the center of core.
SHECAT

SHECAT

 1
 
 2


 r 
n1 1  2   ; for  0  r  a
n( r )     a  
 1 for  r  a : cladding
n1 (1  2) 2  n1 (1   )  n 2 ;
Where: Δ = relative refractive index difference

a = core radius
n1 = refractive index of core axis
n2 = refractive index of cladding
α = profile parameter which defines the shape of index profile
SHECAT
OPTICAL FIBER CONFIGURATION

SINGLE-MODE STEP-INDEX
The single-mode step-index fiber has a central

core that is sufficiently small so that there is
essentially only one path (monomode fiber)
that light may take as it propagates down the
cable. The light rays that enter the fiber
propagate straight down the core or maybe are
reflected once.
SHECAT

SHECAT

Maximum Radius for Single-mode
Propagation:
General Solution Alternative Solution

0.383 r 0.383
rmax  max 
NA n1 2
SHECAT

Where: Δ = fractional index change – the normalized
difference between the index of the core and cladding
GENERAL SOLUTION APPROXIMATE SOLUTION
( n12  n 22 ) ( n1  n 2 )
 
2n12 n1
SHECAT

Example: Calculate the maximum core radius

to support single mode operation for a fiber
with a NA of 0.15 and λ = 0.82μm. answer :
2.1μm
SHECAT

Advantages:
• Minimum dispersion
• Higher accuracy in reproducing transmitted
pulses at the receive end
• Larger bandwidth
• Higher transmission information rates
SHECAT

Disadvantages:
• Difficulty in coupling light into the fiber
(due to the smallness of the central core)
• Requires highly directive light source (like
ILD)
• Expensive
• Difficult to manufacture
SHECAT

MULTIMODE STEP-INDEX
The multimode step-index is similar to single-

mode configuration except that the center core
is much larger. This type of fiber has a larger
light-to-fiber aperture and consequently,
allows more light to enter the cable.
SHECAT

SHECAT

There are many paths that a light ray may

follow as it propagates down the fiber. As a
result, all light rays do not follow the same
path and hence do not take the same amount of
time to travel the length of the fiber.
SHECAT

Advantages:
• Inexpensive
• Simple to manufacture
• Coupling the light into the fiber is easy
SHECAT

Disadvantages:
• Maximum dispersion
• Smaller bandwidth
• Lower information transmission rates
SHECAT

Key Formulas:
Number of Modes Power Distribution
V-number
for V>>2.045 Bet. Core and Cladding
D 1 2 Pcladding 4
V  NA Nm  V 
 2 Pcore 3 Nm
SHECAT

MULTIMODE GRADED-INDEX
It is characterized by a central core that has a

refractive index that is not uniform; it is
maximum at the center and decreases
gradually toward the outer edge. Light is
propagated down this type of fiber through
refraction.
SHECAT

SHECAT

Advantages:
• Light can be easily coupled into this fiber

than single mode step index fiber
• Intermodal dispersion is less than in
multimode step index fiber
SHECAT

Disadvantages:
• Light can not be easily coupled into this

fiber than multimode step index fiber
SHECAT

Key Formulas:
V-number
D
V  NA

SHECAT

Key Formulas:
Number of Modes for V>>2.405

Where:
 g  4a  n    g  V
2 2 2 2
 g = graded fiber gradient
Nm      
1
 
 g  2     g  2  2 = 2 (parabolic profile)
2

= 1 (triangular profile)
= ∞ (step index profile)
SHECAT

COMPARISON SIMPLIFIED
SHECAT
OPTICAL FIBER LOSSES
1. Material Absorption Losses
The absorption losses are analogous to power

dissipation in copper cables; impurities in the
fiber absorb the light and convert it to heat.
SHECAT

The factors that contribute to the material
absorption losses are:
Infrared Absorption
This is a result of photons of light that are absorbed by the
atoms of the glass core molecules. The absorbed photons are
converted to random mechanical vibrations typical of
heating.
SHECAT

Ultraviolet Absorption
This is caused by valence electrons in the silica material from
which fibers are manufactured. Light ionizes the valence
electrons into conduction. The ionization is equivalent to a
loss in the total light field and, consequently, contributes to
the transmission losses of the fiber.
SHECAT

Ion Resonance Absorption
This is caused by OH- ions in metallic material like iron, copper, and
chromium. The source of OH- ions is water molecules that have been
trapped in the glass during the manufacturing process.
SHECAT

Hydrogen Effects
The hydrogen either can interact with the glass to produce
hydroxyl ions and their losses or it can infiltrate the fiber and
produce its own loss. The solution is to eliminate the
hydrogen-producing source or to add coating to the fiber that
is impermeable to hydrogen.
SHECAT
2. Scattering Losses
These occur when a wave interacts with a

particale in a way that removes energy in the
directional propagating wave and transfer it to
other directions
SHECAT
Linear Scattering Losses
Primarily characterized by having no change
in frequency in the scattered wave. Also, the
amount of light power that is transferred from
a wave is proportional to the power of the
wave
SHECAT
Rayleigh Scattering Losses
Results from light interacting with the inhomogeneities
(submicroscopic irregularities or impurities formed in the
fiber during the manufacturing process) in the medium that are
much smaller than the wavelength of the light. When light
rays propagating down a fiber strike one of these impurities,
they are diffracted.
SHECAT
0.887
L Where:
 4 λ = signal wavelength in µm
SHECAT
Example: Calculate the Rayleigh scattering loss in dB for a

50/125 step-index fiber operating at 1200nm. Also compute
for the attenuation in neper. Note: 1 N = 8.686 dB
Answer: 3.68dB; 0.423N

SHECAT
Mie Scattering Losses
Occurs at inhomogeneities that are comparable in size to a
wavelength and can be reduced by carefully controlling the
quality and cleanliness of the manufactured process.
Mie scattering is caused by inhomogeneity in the surface of

the waveguide
- Mie scattering is typically very small in optical fibers
SHECAT
Rayleigh and Mie Scattering Losses
SHECAT
Non-linear Scattering Losses
These scattering losses cause significant power to be scattered
in the forward, backward or sideways directions, depending on
the nature of interactions. These losses are accompanied by a
frequency shift of the scattered light.
SHECAT
Brillouin Scattering Losses
This is modeled as a modulation of the light by the thermal
energy in the material mainly in the backward directions. The
incident photon of light undergoes the nonlinear interaction to
produce vibrational energy (or phonons) in the glass as well as
scattered light (as photons)
SHECAT

PB  17.6 x10 3
 a     
2 2
SHECAT
Where:λ = signal wavelength in μm

a = core radius in μm
α = signal attenuation
Δυ = line frequency in GHz
SHECAT
Example: Consider a single-mode fiber operating at 1300nm

with a loss of 0.8 dB/km. The line width of the source is 0.013
nm. The core radius is 4 μm. Calculate the Brillouin scattering
threshold
Hint: use Δv=(c/λ2)(Δ λ)
Ans.: PB = 0.879W
SHECAT
Raman Scattering Losses
In this scattering, the nonlinear interaction produces a high-

frequency phonon and a scattered photon of Brillouin Scattering.
The scattering is predominately in the forward direction hence
the power is not lost to the receiver.
SHECAT
  a   
Where:
2
PR  23.6 x10 2 2
λ = signal wavelength in μm
a = core radius in μm
α = signal attenuation
SHECAT
Example: Consider a single-mode fiber operating at 1300nm
with a loss of 0.8 dB/km. The line width of the source is 0.013
nm. Calculate the ratio of the Brillouin scattering threshold to
the Raman scattering threshold.
Ans: 17.2%
SHECAT

Absorption and Scattering Losses
SHECAT

Absorption and Scattering Losses Graphs
SHECAT
3. Macrobending
Refers to a large-scale bending, such as that occurs
intentionally when wrapping the fiber on a pool or pulling it
around a corner
SHECAT
4. Microbending
Occurs when a fiber is sheathed within a
protective cable. The stresses set up in the
cabling process cause small axial distortions
to appear randomly along the fiber.
Microbending also occurs as a result of
differences in the thermal contraction rates
between the core and the cladding.
SHECAT
4. Microbending
Developed during deployment of the fiber, or can be due to
local mechanical stresses placed on the fiber often referred to
as cabling or packaging losses
SHECAT
4. Microbending
Critical Radius of Curvature:
3n 
2
0.24n 
2
rcritical  1
 1
4 ( NA) 3
( NA)3
Example: Calculate the critical radius of curvature for a

multimode 50/125 fiber with an NA of 0.2, n1 of 1.48 and
operating at 850 nm.
SHECAT
5. Coupling/Connector Losses
The coupling losses occur because of the

presence of optical junctions like:
• light source-to-fiber connections

• fiber-to-fiber connections
• fiber-to-photodetector connections
SHECAT
Losses Due to Misalignment Effects
Lateral Misalignment
This is the lateral or axial displacement between
two pieces of adjoining fiber cables. The amount of
loss can be from a couple of tenths of a decibel to
several decibels. This loss is generally negligible if
the fiber axis is aligned to within 5% of the smaller
fiber’s diameter.
SHECAT
SHECAT
Assumptions:
• Uniform power distribution over the fiber core

(suitable for multimode step index fiber).
• The lateral misalignment loss is due only to the non-
overlap of transmission and receiving cores.
SHECAT
SHECAT
The coupling efficiency η is defined as the ratio of the
overlapping area to the core area.

2  1 d d d  
2
  cos  1   
 2a 2a  2a  
 
SHECAT
The small displacements d/2 a < 0 . 2
2d
  1
a
SHECAT
The inversed cosine is calculated in radians.
The loss in dB is:
L  10 log10 
SHECAT
Lateral misalignment loss for

a multimode SI fiber
SHECAT
Gap Misalignment
This is sometimes called end separation.

When splices are made in optical fibers, the
fibers should actually touch. The farther
apart the fibers are, the greater the loss of
light
SHECAT
Angular Misalignment
This is sometimes called

angular displacement. If the
angular displacement is less
than 2o, the loss will be less
than 0.5dB.
SHECAT
The coupling loss due to angular misalignment can be
calculated using:
Where:
 n o 
L( dB)  10 log1   θ = misalignment angle in radians
  ( NA)  no = refractive index of the material
filling the groove
SHECAT
Example: Calculate the coupling loss for a fiber facility

with a misalignment angle of 2.4o and 2.4 NA.
Ans: 0.248 dB
SHECAT
Imperfect Surface Finish (Non Flat Ends)

This results when the ends of the two adjoining fibers are not
highly polished. If the fiber ends are less than 3o off from
the perpendicular, the losses will be less than 0.5 dB
PULSE SPREADING IN FIBER SHECAT
The modal dispersion or pulse spreading is caused by

the difference in the propagation times of light rays
that take different paths down a fiber. It can only be
seen in multimode fibers.
This can be reduced considerably by using
graded-index fibers and almost entirely eliminated by
using single-mode step-index fibers.
Intersymbol Interference
The overall effect of dispersion on the performance of a
fiber optic system is known as intersymbol
interference . Intersymbol interference occurs when the
pulse spreading caused by dispersion causes the output
pulses of a system to overlap, rendering them
undetectable. If an input pulse is caused to spread such
that the rate of change of the input exceeds the
dispersion limit of the fiber, the output data will become
indiscernible.
Intersymbol Interference
Dispersion
• The spreading (in time-domain) of light pulses as it
propagates down the fiber end
1. Material Dispersion
• Pulses at different wavelengths have different

velocities.
• Due to wavelength dependency on the index of
refraction
t MAT
 DM x
km
Where: DM = dispersive coefficient in ps / nm-km
Δλ = -3 dB wavelength (line or spectral

width) in nm
t MAT
 DM x
km
Example: For a step-index fiber 12.5 km long is to
be used with a 0.8µm light source with a spectral
width of 1.5nm. What value of material dispersion
might be expected assuming DM = 0.15 ns/nm-km.
Ans.: 2.81 ns
2. Waveguide Dispersion
• Pulses at different wavelengths (but propagating in

the same mode) must travel at slightly different
angles.
• Due to the physical structure of the waveguide
• e.g.: LED or laser have finite bandwidths which
means they emit more than one wavelength
tWAVE
 DW x
 km
Where:DW = peak waveguide dispersive coefficient in ps / nm-km
= 6.6 ps / nm-km
Δλ = -3 dB wavelength (line or spectral width) in nm
tWAVE
 DW x
 km
Example: A 12.5km single-mode fiber is used with a
1.3 µm light source which has a spectrum width of
6nm. Find the total expected waveguide dispersion.
Ans.: 495 ps
Material and Waveguide Dispersion
They are called Chromatic Dispersions

Material dispersion and waveguide dispersion can
have opposite signs depending on the transmission
wavelength
@SMSI Fiber, these two effectively cancel each
other @1310nm yielding zero dispersion
Material and Waveguide Dispersion

However, the drawback is that, even though dispersion is
minimized at 1310 nm, attenuation is not. Glass fiber exhibits
minimum attenuation at 1550 nm. Coupling that with the fact
that erbium-doped fiber amplifiers (EDFA) operate in
the 1550-nm range makes it obvious that, if the zero-
dispersion property of 1310 nm could be shifted to coincide
with the 1550-nm transmission window, high-bandwidth
long-distance communication would be possible. With this in
mind, zero-dispersion-shifted fiber was developed.
3. Modal Dispersion (Modal Delay Spreading)

A pulse at a single wavelength splits power into
modes that travel at different axial velocities because
of the path differences.
Pulse spreading caused by the time delay between the
low order modes and high order modes
3. Modal Dispersion (Modal Delay Spreading)
Ln1  Ln1 
t MODAL  
c 1    c
Example: Consider a 50/125 step-index fiber

(L=12.5km) with n1=1.47 and Δ=1.5%. Calculate the
group delay (modal dispersion) for this fiber at an
operating wavelength of 850 nm. Ans.: 918.75 ns
4. Total Dispersion
At any wavelength, the total dispersion is the root-

mean-square combination of material, modal, and
waveguide dispersions.
 2
tTOTAL  t MAT  t MODAL  tWAVE
2 2

Facts to Remember: Modal dispersion is only present for
multimode fiber
4. Total Dispersion
 2
tTOTAL  t MAT  t MODAL  tWAVE
2 2

Example: A single-mode fiber operating at 1.3 µm is
found to have a total material dispersion of 2.81 ns and a
total waveguide dispersion of 0.495ns. Determine the
receive pulse width and approximate bit rate for a fiber if
the transmitted pulse has a width of 1.5 ns. Ans.: 2.85
ns; 175.44 Mbps (RZ); 350.5 Mbps (NRZ)
RECEIVER RISE TIME AND SHECAT
BANDWIDTH
1. System Rise Time (ts)
The rise time is the time for the detector output (e.g. current)
to change from 10 to 90% of its final value when the optic
input power variation is a step.
Note:
The fiber rise time is equal to the total dispersion within the
fiber
BANDWIDTH
1. System Rise Time (ts)
2 2 2
t s  t tx  t f  t rx
Where: ts = system rise time in ns

ttx = source rise time in ns
trx = receiver rise time in ns
tf = fiber rise time in ns
BANDWIDTH
2. Maximum Data Rate
1 1
UPRZ fb  fb 
2t s 2t
1 1
fb  fb 
t
UPNRZ
ts
BANDWIDTH
3. Bandwidth
0.35
Electrical BWe 
t
BWo  2  BWe 
Optical
1
BWo 
2 t
BANDWIDTH
4. Bandwidth-Distance Product
1
BWx  x km
2t
Example: A fiber optic system uses a detector with a rise time

of 1.5 ns and a source with a rise time of 4ns. If an RZ code is
used with a data rate of 100Mbps over a distance of 20 km,
calculate the maximum acceptable dispersion for the fiber and
the equivalent BW-Distance product.
Ans. Dispersion per unit length = 0.13 ns/km
BW-Distance Product = 3.846 GHz - km
SHECAT
THANK YOU!
***end***

Optics and Optical Communication: Amanuel Admassu, Mtu-Ece

Uploaded by

Copyright:

Available Formats

Optics and Optical Communication: Amanuel Admassu, Mtu-Ece

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Optics and Optical Communication: Amanuel Admassu, Mtu-Ece

Uploaded by

Copyright:

Available Formats

Optics and

Amanuel Admassu, mtu-ece

Light Propagation in Fibers

TOTAL INTERNAL REFLECTION

The critical angle is the minimum angle of

TOTAL INTERNAL REFLECTION

TOTAL INTERNAL REFLECTION

TOTAL INTERNAL REFLECTION

TOTAL INTERNAL REFLECTION

Example: What striking angle in the fiber

Ans.: θc=69.3o and θ0=33.21o

The acceptance angle or acceptance cone half-

NUMERICAL APERTURE (NA)

The Figure of Merit used to describe the light

Composition of Optical Fibers:

Composition of Optical Fibers:

Core – inner part of the fiber, which guides

Composition of Optical Fibers:

Cladding – surrounds the core completely

Composition of Optical Fibers:

Buffer Coating – provides mechanical

Common Optical Fiber Types:

1550 nm single mode fiber

850 nm multimode fibers

1300 nm multimode fibers

Core diameters for these types range from

Common Optical Fiber Types:

Plastic fibers are more flexible and, consequently,

Common Optical Fiber Types:

Fibers with glass cores have less attenuation than

Common Optical Fiber Types:

The selection of a fiber for a given application

An optical fiber guides light waves in distinct

Mode – describes the distribution of light

1. Single Mode Fibers

Fibers having very small diameter core that

Fibers that carry more than one mode at a

Where: D is the core diameter

Normalized Frequency (V-parameter):

Normalized Frequency (V-parameter):

Example: Compute the number of modes for

Ans.: 1,079 modes

OPTICAL FIBER INDEX PROFILE

A graphical representation of the value of the

OPTICAL FIBER INDEX PROFILE

The step-index fiber has a central core with a

OPTICAL FIBER INDEX PROFILE

OPTICAL FIBER INDEX PROFILE

Where: n1 = refractive index of core

OPTICAL FIBER INDEX PROFILE

OPTICAL FIBER INDEX PROFILE

OPTICAL FIBER INDEX PROFILE

Where: Δ = relative refractive index difference

OPTICAL FIBER CONFIGURATION

The single-mode step-index fiber has a central

OPTICAL FIBER CONFIGURATION

OPTICAL FIBER CONFIGURATION

General Solution Alternative Solution