Download - Optical Full Units NOTES
-
8/12/2019 Optical Full Units NOTES
1/98
1
OPTICAL FIBER COMMUNICATION
UNITI
OPTICAL FIBERS-STRUCTURE
1.INTRODUCTION:
The communication medium is either wire conductor cable or freespace.
Nowadays a new medium is fiberoptic cable. Fiber is essentially a light pipe that is used to carry a light beam from
one place to another.
The transmitter & receiver operates at low frequency 103HZ , mediumfrequency 10
6HZ & high frequency 10
14HZ, depending upon the
requirement of communication at narrow band, medium band or broad
band frequencies. Optical fiber cables are working at 1300nm,1500nm. In future we will
go to higher wavelengths around 2500nm.
ADVANTAGES:
High speed. Low loss Flexibility Wide channel
Low size & weight Low interruption(interference & crosstalk) Broad bandwidth. Long distance communication.
DISADVANTAGES:
High cost Maintenance is difficult Brittleness.
WDM:
To use multiple sources operating at slightly different wavelengths to
transmit several independent information streams over the same fiber.
-
8/12/2019 Optical Full Units NOTES
2/98
2
1.1EVOLUTION OF FIBER OPTICS SYSTEMS:
In 1880, Alexander Graham Bell experimented with an apparatus called
Photophone. It was a device constructed from mirror that transmitted sound
waves over a beam of light.
There are three generations in fiber optics:
1.1.1 FIRST GENERATION:
In 1977 ,GTE in Los Angeles & AT & T in Chicago were introduced. Intransmitter side they used LASER, it has high output power, high
frequency of operation, wide bandwidth.
The operating wavelength is 800 to 900nm i.e., around 850nm. Fiber material is GaAS and bit rate is 45 to 140 Mbps and repeater
spacing is 10kms.
1.1.2SECOND GENERATION:
The operating wavelength is around 1300nm. Fiber material is Indium Gallium Arsenide, Phosphorus and bit rate is
155 to 622 Mbps and repeater spacing is 40kms.
Both single mode and multimode fibers are used in LAN, & its bit rateis 10 to 100Mbps.
In 1984, Single mode fibers were used for larger bandwidth.1.1.3 THIRD GENERATION:
The operating wavelength is around 1550nm. Bit rate is 2.5 Gbps and repeater spacing is 90kms. In 1970s start to use WDM to boost the transmission capacity. In
1990s combination of EDFA & WDM was used to boost fiber capacityto even higher levels & to increase the transmission distance.
In 1996 onwards bit rate is increased around 10 Gbps by using highquality lasers.
Introduce the optical amplifier in 1989 gave a major boost to fibertransmission capacity.
GaAlAs was first introduced but successful & widely used devices areErbium Doped Fiber Amplifier(EDFA) ->1500nm and Prascodymium
Doped Fiber Amplifier(PDFA)->1300nm.
The use of WDM offers a further boost in fiber transmission capacity. The basis of WDM is to use multiple sources operating at slightly
different wavelengths to transmit several independent information
streams over the same fiber.Mid-1990s, a combination of EDFAs &
-
8/12/2019 Optical Full Units NOTES
3/98
3
WDM was used to boost fiber capacity to even higher levels and to
increase the transmission distance.
1.2ELEMENTS OF AN OPTICAL FIBER TRANSMISSION
LINK:
The basic components in the optical fiber communication are lightsource, the light signal transmitter, the optical fiber & photodetecting
receiver.
The other elements include fiber and cable splices and connectors,regenerators, beam splitters and optical amplifiers.
Information source:
The information signal to be transmitted may be voice, video orcomputer data. The first step is to convert the information into a form
compatible with the communications medium.
-
Figure:1.2.1.Major elements of an Optical fiber transmission link
-
8/12/2019 Optical Full Units NOTES
4/98
4
1.3BASIC LAWS & DEFINITIONS:
1.3.1Refractive Index (or) Index of Refraction:
The ratio of speed of light in free space to the speed of light in medium
n= c/v
n-> 1.00 for air, 1.50 for glass, 1.33 for water, 2.42 for diamond
Figure:1.3.1.Law of reflection
1.3.2.Angle of incidence(1):
The angle at which light strikes a surface with respect to normal iscalled angle of incidence.
The angle of incident light ray determines whether the ray will bereflected or refracted.
1.3.3.Angle of Reflection(2):
The angle at which light is reflected from a surface is called angle of
reflection.The law of reflection is 1= 2
1.3.4.Snells law:
It states that how the light ray reacts when it meets the interface of two
media having different refactive indexes. Mathematically it can be expressed by
n1 sin1=n2 sin 2
n1 = sin 2
n2 sin 1
-
8/12/2019 Optical Full Units NOTES
5/98
5
Figure:1.3.4. Reflection of a light ray at material boundary
1.3.5.Critical angle:
The value of angle of incidence at which the angle of refraction is 90ois
called critical angle.
1= c, 2 =90o
n1 sinc=n2 sin 90o
sinc = n2
n1
1.3.6.Total Internal Reflection:
When the light ray strikes the interface at an angle greater than the
critical angle,the light ray does not pass through the interface into the glass.Whan this occurs, the angle of reflection 2 is equal to angle of incidence 1.
This action is known as total internal reflection.
Figure:1.3.6.Total internal Reflection
-
8/12/2019 Optical Full Units NOTES
6/98
6
Condition:
i. n1>n2ii. 1> 2
1.3.7.Numerical aperture:
It is used to describe the light gathering or light collecting ability of an
optical fiber. It is referred as figure of merit commonly used to measure the
magnitude of acceptance angle. The numerical aperture for light entering the
glass fiber from an air medium is described mathematically as
NA=sinin
Where in-> acceptance angle
Acceptance angle is the maximum angle to the fiber axis at which light
may enter the fiber axis in order to be propagated.
in(max)=sin-1(n12-n22)
no
where no is refractive index of air( no=1)
Therefore in (max)=sin-1(n12-n22)
NA = sinin
Therefore NA= (n1
2
-n2
2
)
Hence acceptance angle is in=sin-1(NA
NA=sin in =(n12-n22)
NA= (n1+n2)(n1-n2)
= 2n1(n1-n2) [n1=n2]
Substitute =n1-n2
n1
therefore NA=2n1(n1 )
NA=n12
-
8/12/2019 Optical Full Units NOTES
7/98
7
1.4.RAY OPTICS:
There are 2 types of rays in fiber.
i. Meridional rays.ii. Skew rays.
1.4.1Meridional rays:
These rays are confined to the meridian planes of fiber, which are theplanes the contain the axis of symmetry of the fiber.
It lies in a single plane , its path is easy to track as it travels along thefiber . It can be classified into
i. Bound rays.ii. Unbound rays.
1.4.1.1.Bound rays:
That are trapped in the core and propagate along the fiber axis accordind
to the laws of geometrical optics.
1.4.1.2.Unbound rays:
That are refracted out of the fiber core.
1.4.2.Skew rays:
These rays are confined to single plane , but instead tend to follow ahelical type path along the fiber.
These rays are more difficult to track as they travel along the fiber ,since do not lie in a single plane.
A greater power loss arises when skew rays are included in analysis, thatare actually leaky rays.These leaky rays are only partially confined to
the core of circular optical fiber and attenuate as light travels along the
optical waveguide.
1.4.3.Meridional rays for Step index fiber:
The light ray enters the fiber core from a medium of refractive index n atan angle o with respect to fiber axis and strikes the core claddinginterface at an normal angle .
If it strikes this interface at such an angle that it is totally internallyreflected, then meridional ray allows a zigzag path along the fiber core.
-
8/12/2019 Optical Full Units NOTES
8/98
8
Figure:1.4.3.Meridional ray optics representation of the propagation mechanism
in an optical waveguide
From Snells law, the minimum angle min that supports total internal reflectionfor meridional ray is
sinmin = n2
n1
The rays striking the core-cladding interface at angles less then minwill refract out of core and be lost in cladding. By applying Snells lawto the air-fiber face boundary, then the relationship is
nsinomax = n1 sinc =((n12-n22)
omax maximum entrance angle
Where c= -- c2
NA for step-index fiber for meridional rays
NA=nsin omax= (n12-n22) = n12
1.5.MODES:
The number of paths for the light rays in the fiber. The set of
electromagnetic waves propagate inside any wave guide. There are two types of
modes are.
i. Single mode fiber:
Only one signal can propagate inside along the optical fiber parallel to
core axis.
-
8/12/2019 Optical Full Units NOTES
9/98
9
ii. Multimode fiber:
The light takes many paths through the core. The number of paths
possible for multimode fiber cable depends on frequency of light signal,
refractive index of core and cladding and core diameter.
Index profile:
It is a graphical representation of value of refractive index of core
diameter. According to index profile we can divide the configuration into 3
types of modes.
i. Single mode step index fiber.ii. Multimode step index fiber.iii. Multimode graded index fiber.
Step index:Refractive index of core is uniform throughout & undergoes a abrupt
change at cladding is called step-index fiber.
Graded index:
The core of refractive index is made to vary as a function of radialdistance from the center of fiber.
Advantages of cladding:
Used to reduce the scattering loss. It protects the core from absorbing surface. It adds mechanical strength to the fiber.
Fiber structure:
INDEX PROFILE FIBER CROSS SECTION& RAY OPTICS
-
8/12/2019 Optical Full Units NOTES
10/98
10
STEP INDEX GRADED INDEX
Refractive index of core isuniform Not uniform & is made to varyas a function of radial distancefrom the center of fiber
Light rays are meridional Light rays are skew rays No distortion for single mode
fiber &signal distortion in
multimode fiber
Distortion is less because ofself focusing effect & light rays
reach the fiber at the same timedue to helical path or light
propagation
Attenuation :Single mode fiberless effect
Multimode fibermore effect
Less attenuation Numerical Aperture:
Single mode fiberless
efficiency
Multimode fiberhighefficiency
Less efficiency
Band width:Single mode fiber > (GHZ)
Multimode fiber 50 MHZ
Theoretically infinitebandwidth
1.6.MODE THEORY OF CIRCULAR WAVE GUIDE:
In optical fiber, the core cladding boundary conditions lead to couplingbetween electric & magnetic field components.
This gives rise to hybrid modes, which makes optical waveguideanalysis more complex than metallic waveguide analysis.
The hybrid modes are HE or EH modes depending on whether thetransverse electric or magnetic field is larger for that mode. The lower
order modes are 11HE and 01TE .
Fibers usually are constructed so that the difference in the core &cladding refractive index is very small, then only four field components
exists(n1-n2
-
8/12/2019 Optical Full Units NOTES
11/98
11
Each mLP0 mode is derived from mHE1 mode and each mLP1 modecomes from mTE0 , mTM0 and mHE0 modes. Thus the fundamental
01LP mode corresponds to 11HE mode.
1.6.1.OVERVIEW OF MODES:
1. Guided modeswaves should be propagated inside the core.2. Radiated modesunbounded rays.3. Leaky Modesmore amount of power in cladding region.
Figure:1.6.1.1.Electric field Distributions for several of the lower-order
guided modes in a symmetricalslab waveguide
The order of a mode is equal to number of field zeros across the guide. The order of mode is also related to the angle that the ray congruence
corresponding to this mode makes with the plane of waveguide or axis
of fiber.
The plot shows that electric field of guided modes are not completelyconfined to the central dielectric slab i.e., they do not go to zero at core
cladding interface & extends into the cladding. The field vary harmonically in core region of refractive index n1 and
decay exponentially outside of this region of refractive index n2.
-
8/12/2019 Optical Full Units NOTES
12/98
12
In lower- order modes, the fields are tightly concentrated near the centerof slab or axis of an optical fiber, with little penetration into cladding
region.
In higher-order modes, the fields are distributed more towards the edgeof guide and penetrate further into the cladding region.
Due to this penetration, radiated modes are propagated in claddingregion.
In the leaky modes the fields are confined partially in the fiber core &attenuated as they propagate along the fiber length due to radiation and
tunnel effect.
1.6.1.2.Tunnel effect:
The leaky modes are continuously radiating their power out of the coreas they propagate along the fiber. This power radiation out of the wave
guide results from quantum mechanical phenomenon known as tunnel
effect.
Therefore, in order to mode remains guided, the propagation factor satisfy the condition
n2K < < n1K
Where, n1refractive index of core
n2refractive index of cladding
K propagation constant =
2
The boundary between truly guided modes and leaky modes is defined by cutoff
condition.
1. =n2K cutoff condition2. < Kn2 leaky modes3. > Kn2 guided modes
When becomes smaller than n2K ( < Kn2 )power leaks out of coreinto cladding region.
Leaky modes can carry significant amounts of optical power in shortfibers.
1.7.KEYMODEL CONCEPTS:
An important parameter connected with cutoff condition is V number isV = 2a (n12-n22)1/2
-
8/12/2019 Optical Full Units NOTES
13/98
13
= 2a
It determines how many modes a fiber can support for the lowest order11HE mode, each mode can exist only for values of V that exceed
certain limiting value.
The modes are cutoff when =n2K . This occurs when V
-
8/12/2019 Optical Full Units NOTES
14/98
14
A cylindrical co-ordinate system (r,, Z)is defined with Z-axis. The
waveguide equation are ).2..(..........
).1..(..........
2
2
r
EH
rq
jH
r
HE
rq
jE
ZZ
ZZ
The solutions can be obtained in 2 cases.
Case(i):
In metallic wave guide
For TE modes ZE =0
For TM modes ZH =0
Case(ii):
For optical waveguide
Hybrid modes are exist. Both ZE and ZH are non-zero.
Waveguide equation for step-index fiber:
Using separation of variable method , we can find the guided modes in
step-index mode. The general equation for wave equation is
jv
Ztj
Z
eF
etFZF
AtFZFFrAFE
()
)()(
)..().........()()()(
2
)(
43
4321
because of circular symmetry of waveguide each field component must
not change when the co-ordinate is increased by 2.
The fields are harmonically varied in the core region & deceying incladding region.
The solutions are Bessels function of first time of order , for this
For core region
-
8/12/2019 Optical Full Units NOTES
15/98
15
).(..........).........()(
2&
1
11
22
1
2
IurJVrF
nKKu
For cladding region
).(..........).........()(
2&
1
22
2
2
2
1
2
IIrKVrF
nKK
Sub:all equations in ( A)
For core region
)3....(..........)()( )( ZtjjvZ ejurAJVarE
Similarly for magnetic component
)()( urBJVarHZ )4....(..........)( Ztjjv ej
For cladding region
)5....(..........)()( )( ZtjjvZ ejrCKVarE
)6....(..........)()( )( ZtjjvZ ejrDKVarH
The solution for must be find from boundary conditions E and zE arethe tangential components for inside and outside dielectric.
H and zH are the tangential components for inside and outsidedielectric.
At the inner core cladding boundary
1ZZ EE
When r=a,
)(
1 )(
Ztjjv
Z ejuaAJVE
At the outside of boundary
2ZZ EE
When r=a,
-
8/12/2019 Optical Full Units NOTES
16/98
16
)(
2 )( ZtjjvZ ejaCKVE
At boundary conditions
021 ZZ EE
)7......(..........0)()(0)()(
)(
aCKVuaAJVaCKVuaAJVee
Ztjjv
Inside the core q2=u
2using equation (3) and (4) sub: in (1) find
1E
]..)(.([..)(.(
]..)(.([..)(.(
..)('
..)(
..)(
..)(
)(')(
22
)(')(
21
)(
)(
)('
)(
ZtjjvZtjjv
ZtjjvZtjjv
ZtjjvZ
ZtjjvZ
ZtjjvZ
ZtjjvZ
eeaJVDejveaKVCa
jE
eueuaJVBejveuaJVAau
jE
eeaDKVr
H
ejveaCKV
E
eueuaBJVr
H
ejveuaAJVE
At boundary condition
021 EE
)8.......(..........0).(.)(.).(.)(. '2
'
2
aKVDaKV
a
jvC
juuaJVBuaJV
a
jvA
u
j
At boundary condition
)9......(..........0)(.)(.
.).(.
.).(.
0
)(
2
)(
1
21
aKVDuaJVB
eeaKVDH
eeuaJVBH
HH
Ztjjv
Z
Ztjjv
Z
ZZ
At boundary condition
-
8/12/2019 Optical Full Units NOTES
17/98
17
]..)(.([..)(.(
]..)(.([..)(.(
0
)(')(
22
)(')(
21
21
ZtjjvZtjjv
ZtjjvZtjjv
eeaJVCejveaKVDa
jH
eueuaJVAejveuaJVBau
jH
HH
At boundary condition
021 HH
)10.......(..........0).(.)(.).(.)(. '2
'
2
aKVCaKV
a
jvD
juuaJVAuaJV
a
jvB
u
j
Using equation 7,8,9,10. Find the unknown values A,B,C,D using determinant
method
)(.)(.)(.)(.
)(0)(0
)(.)(.)(.)(.
0)(0)(
2
'
2
'
'
2
'
2
aKVa
VaKV
juaJV
au
VuaJV
u
jaKVuaJV
aKVj
aKVa
VuaJV
u
juaJV
au
V
aKVuaJV
=0
Evaluation of this determinant gives the Eigen equation .
)12.(..................................................)(
)('&
)(.
)('
)11......(`....................11
)((
2
22
2
2
2
2
1
aKV
aKVKV
uaJVu
uaJVJV
where
ua
VKVKJVKKVJV
1.9.MODES IN STEP INDEX FIBER:
To describe the modes we should examine the behavior of J type Besselfunction. Bessel function is the harmonic function & its having
oscillatory behavior of JV.
M roots for a given V value. The corresponding modes are TEvm&TMvm, EHvm &HEvm. These are designated by the roots of vm. For a
-
8/12/2019 Optical Full Units NOTES
18/98
18
dielectric waveguide all modes are hybrid modes except those for which
v=0.
At v=0, substitute in equation 11.( 0) 02202100 KKJKKJ
From this
( 0)00 KJ (or) 0022021 KKJK
Using regression formula in equation 12 substitute v=0 & JV ischanged in terms of J
Therefore,
0)(
)(
)(
)(
0
1
0
1 aK
aK
uauJ
uaJ
Cutoff condition:
v Mode Cutoff condition
0
1
>=2
TE0m,TM0m,
HE1m, HM1m,
EHvm,
0J (ua)=0
0)(1 uaJ
JV(ua)=0
At cutoff condition, the mode is not longer bound to core of fiber. Thenormalized propagation constant is
2
2
2
1
2
2
2
nn
nK
b
The normalized value )(2 NAav
. It determines how many modes a
fiber can support. HE11 mode has not cutoff and stop only core diameter
=0. By choosing appropriately a, n1, n2 value v
-
8/12/2019 Optical Full Units NOTES
19/98
19
In a step-index the difference between the refractive index of core&cladding is very small that is
-
8/12/2019 Optical Full Units NOTES
20/98
20
)(
)(
)(
)(. 11
aK
aK
uaJ
uaJu
j
j
j
j
It shows that within the weakly guiding approximation all modescharacterized by common set of j & m satisfy the same characteristic
equation. This means that these modes are degenerate.
Parameters:
1. All linearly polarized modes are degenerate modes.2. If an HEv+1,m is degenerate with an EHv-1,m mode and then combination
of these modes will constitute a guided mode of the fiber.
3. Degenerate modes are also called as linearly polarized modes.4. i. Each LPoMmode is derived from HE1Mmode.
ii.Each LP1M mode comes from TEoM , TMoM , HE2M ,modes.
iii. LPVM , mode(V>=2 )is derived from HEv+1,m & EHv-1,m .
Merits:
1. It provides an ability to visualize a mode quickly and easily.2. It is used to analysize the transmission characteristics of optical fibers.
Demerits:
1. If is not very much less than 1, LP mode has no sense.2. It cant form linearly polarized mode.
1.11.SINGLE MODE FIBER:
For single mode fiber, core diameter of an operating wavelength is 8-12m & its having small index differences between the core & cladding
with V=2.4.
The core cladding difference varies between 0.2 to 1 percent.1.11.1.Mode field diameter:
The fundamental parameter of single mode fiber is mode fielddiameter(MFD) & it can be determined from the mode field distributionof LP01 mode.
The field is Gaussian distribution.
-
8/12/2019 Optical Full Units NOTES
21/98
21
Figure:1.11.1.Distribution of light in SMF above its cutoff
wavelength
Its distance betweene
1to
2
1
e. therefore MFD=2W0.
The Gaussian distribution is )/exp()( 2020 wrErE rradius, 0Efield at zero radius. 0w width of electric
field distribution.
The MFD width 2 0w of LP01 mode can be defined2
1
0
2
0
23
0
)(
)(.2
22
drrrE
drrEr
W
1.11.2. PROPAGATION MODES IN SMF:
There are 2 independent degenerate modes arei. Horizontal polarization modes.ii. Vertical polarization modes.
These modes are very similar but their polarization planes are orthogonal.
In general , the electric field of light propagating along the fiber is alinear superposition of these two polarization modes & depends on
polarization of light at launching point into the fiber.
In ideal fibers with perfect rotational symmetry, the modes aredegenerate with equal propagation constants yx KK .
Due to fiber imperfectionsyx
KK . The modes propagate with
different phase velocities & difference between their effective indices
is called fiber birefringence.
xyf nnB
The fiber birefringence is defined as
-
8/12/2019 Optical Full Units NOTES
22/98
22
2
)(
0
0
K
where
nnK xy
Two modes will beat at 2 radius & length over which this beatingoccurs in the fiber is called beat length.
2pL
1.12.GRADED INDEX FIBER:
In Graded index fiber, the core refractive index decreases continuoslywith increasing radial distance r from the fiber axis, but refractive index
for cladding is constant.
The refractive index variation in core is the power law relationship thatis
arfora
rnrn
0.....21)(
21
1
aforrnnn 2121
1 )1()21(
rradial distance, 1n refractive index of core, refractive indexdifference
2n refractive index of cladding , core radius defines the shape of index profile. The index difference for the
graded index fiber is
=1
21
n
nn
For = infinite, n(r)= 1n
Determining NA for GIF is more complex than for SIF. Light incidenton fiber core at position r, will propagate as guide mode only. NA at
that point is defined as
NA(r)= arfor
arforarNAnrn
......................................................0
......1)0()( 2
12
2
2
Where the axial NA is defined as
NA(0)= 21
2
2
2 )0( nn
-
8/12/2019 Optical Full Units NOTES
23/98
23
2121
2
2
2
1 nnn
NA decreases from NA(0) to zero as r moves from fiber axis to corecladding boundary.
The number of bounded or guided modes in GIF is
)2(....................)2(.
:
)1........(.2
21
.1
2
1
KanV
sub
KanM
Sub :equation 2 in 1
2.
2
2VM
For aparabolic refractive index profile core fiber. Sub =2
4
2VM
UNITII
SIGNAL DEGRADATION OPTICAL FIBERS
2.INTRODUCTION
Signal attenuation also known as fiber loss or signal loss is one of the most
important proprieties of an optical fiber because it largely determines the
maximum unamplified or repeaterless separation between txr and rxr.
2.1.ATTENUATION:
Attenuation of a light signal as it proaogates along a fiber is an
important consideration in design of optical of an optical communication
system, since it playes a major role in determining maximam txn distance
between txr and rxr .
-
8/12/2019 Optical Full Units NOTES
24/98
24
The basic three mechanisms are:
1. Absorption loss2. Scattering loss3. Radiation loss
Figure: 2.1.1.optical fiber attenuation as a function of wavelangth
Attenuation Units:
At origin Z=0 the parallel power is P(0) after the same distance Z, the
power is P(z).
)(
)0(10)/(
.)(
)0(1
)0()(
zp
pLog
zkmdb
f icientuationcoeff iberatten
neperszp
pLog
z
ePZP
p
p
p
zp
-
8/12/2019 Optical Full Units NOTES
25/98
25
)343.4( 1 kmp
Pout(db)=10 Log .1
)(
mw
wpout
For First Window:
.4
850
km
dbLoss
nm
For Second Window:
m
dbloss
nm
5.0
1300
Third Window:
km
dbloss
nm
3.0
1550
2.2.Absorption Loss:
It is caused bu 3 different mechanisms.
1. Atomic defects in fiber material.2. Extrinsic absorption.3. Intrinsic absorption.
2.2.1.Atomic defects:
Radiation damages in internal structure fiber. The damage effects depends
on energy of ioniziny particles at rays.
It occurs due to imperfection of atomic structure. For eg. Missing molecules, high- density clusters of atom groups or exygen
defeats in the glass structure.
The total dose a material receives is expressed in rad(si ), which is measure
and relation absorbed in bulk silicon. //this unit is defined by 1 rad
(si)=0.01J/Kg
2.2.2. Extrinsic Absorption loss:
-
8/12/2019 Optical Full Units NOTES
26/98
26
Due to impurity atoms present in fiber material then this loss will occur Due to transition of metal ions. Impurity absorption occurs either bze of electronic transition between
energy levels or charge transition between ions.
Its also due to Hydroxyl ion. OH impurities result from ox hydrogen frame used for hydrolysis
reaction in fiber fabrication.
It can be reduced by reducing the water content in the fiber 1 to 10PPb(Parts/bullion).
2.2.3Intrinsic Absorption:
Associated with fiber material. It occurs from electronic absorption band in uv region and atomic
vibration band in infrared region.
UV Absorption:
It takes place when a pboton interval with electron in valence bandexcited to higher energy level.
\it decreases exponentially by increasing warelength , the UV edge ofabsorption is calculated by 0.
EE
uv eC C, 0E -
Emperial constant
E-photon energy.
IR Absorption
Above 1.2 m , wave guide loss in determine presence of hydroxyl ions.
An interaction between vibrating band and electro magnetic field opticalsignal results in a transfer of energy from field to the band, there by
giving rise to absorption.
22
48.4811
1081.7 SioforGeoeX xIR
material.
2.3.Scattering loss:
It occurs due to vibration in material density from compositionalfluctuations and from structural in homogeneities or defects during
fiber manufacturing.
Types:
1. Linear Scattering
-
8/12/2019 Optical Full Units NOTES
27/98
27
2. Non Linear Scattering2.3.1.Linear Scattering
Optical power is transferred from 1 mode to other mode linearly. It is more Predominant in multimode fibers because of compositionalfluctuation and it has higher dopant concentration
It can be classified into
1. Rayleigh Scattering.
2 . MIE Scattering
Rayleigh Scattering:
Rayleigh Scattering is the Phenomenon that Scatters light from the sunin the atmosphere. there by giving rise to blue sky.
It arise due to variation in refractive index that is compositionfluctuation.
It is dominant in UV region and less in IR region and it is inverselyproportional to 4
90% of Scattering loss occur due to Rayleigh Scattering in OFC.
For single component glass. the scattering loss is
128
4
3
3
8 mKTPn fcsoat
n R.I
P Photoetastic coefficient
c Isothermal compressibility
fT fictive temperature
For Multicomponent
nentglasscompoionofiionflutuatconcentratc
p
cn
n
rn
th
i
m
i
icn
i
nflactuatiodensity
)()(
)(3
8
2
1
22
2
22
22
4
3
2
Fictive temperature:Temperature at which the glass reach to state of thermo equality.
MIE:
It arises due to structural inhomogenetis of fiber. It occurs in forward direction only. It is minimized by
-
8/12/2019 Optical Full Units NOTES
28/98
28
1. Proper coaling2. Check the quality of fiber (detect free method )3. Increasing the wave length4. Decreasing R.I value.
2.3.2.Non- linear Scattering:
It occurs at higher energy levels. Frequency shift is associated with thisloss. R.I of core depends upon optical signal intensity.
It is divided into1. SBS(Stimulated Brilliant Seattering )2. SRS(StimulatedRomans Seattering).
SBS:
It is defined as modulation of light signal through thermal molecularvibration within the fiber.
The scattered light contains USB and LSB with incident light frequency. The incident Photon having nonlinear interaction between vibrational
energy or phonon as well as scattered light or photons.
The scattered light is found to be frequency modulator by thermalenergy.
Frequency shift and strength of scattering signal vary as a function ofscattering angle (angle between scattered ray and cladding region).
Frequency shift is maximum in backward direction and forwarddirection is zero.
widthsourceband
changein
waltsdXP dbB
.104.4 223
SRS:
Scattered light consisting of high frequence phonon and a scatrteredphoton.
Scatters occurs in forward and backward direction. Light signal is Predominant in forward direction . Threshold opticalpower is 3 times greater than
SBS.
wattesdXP dbR 22109.5
It is minimized by threshold optical power is launched in a fiber beforeSBS Occur.
-
8/12/2019 Optical Full Units NOTES
29/98
29
2.4.BENDING LOSS;
Bending loss and core and cladding loss under tadiating loss twotypes of bends are;
Macroscopic bends; Fiber bends at corner having radius of curratureis large com[pared to fiber diameter.
Microscopic bends: that can arise when the fibers are incorporatedinto cables.
Figure:2.4.1.A compressible jacket extruded over a fiber reduces microbending
resulting from external forces
Macro:
Large curvature radiation loss is called macro bending loss. For slightbend the loss is small. As the radius of curvature decreases the loss increase
exponentially until at a certain critical becomes observable.
When a fiber is bend at critical distance cx from the center of fiber thefield tail an the far side of centre of curvature must move faster to keep up
with the field in the core for lower order fiber mode. Since this is not
possible the optical energy in the field tail beyond cx Radiates away.
The amount of optimal radiation from a bend fiber depends on thefield strength at cx on the radius of curvature R
Thus the total number of modes that can be supported by curved fiberis less than straight fiber
-
8/12/2019 Optical Full Units NOTES
30/98
30
The effective number of modes effN that are guided by curvedmultimode fiber is expressed by
32
22
32
2
21
KRnR
aNNeff
N Total number of modes in straight fiber
2
12
KaAN n
Micro:
An increase in attenuation results from micro bending because the fibercurvature causes repetitive coupling of energy between guided modes
and leaky modes in the fiber.
Micro bending loss is minimized by extending a compressible cover isthe fiber.
When the external forces are applied to this configuration, the cover willbe deformed but the fiber will tend to stay relatively straight.
For MMGIF having a core radius a outer radius b & index diff themicro bending loss M of a covered fiber is reduced from that of
uncovered fiber by the factor is 2421)(
Ej
E
a
bF
f
M
fE , Ej are youngs moduli of cover & fiber
2.5.Core & Cladding Loss
Core and cladding bare different indices of refraction and havingdifferent attenuation coefficients 21&
For SIF , the loss for the mode of order (V,M )P
P
P
P cladcorevm 21
P
Pclad = 1 -P
Pcore
P
P
P
P cladcladvm 21 1
-
8/12/2019 Optical Full Units NOTES
31/98
31
=P
Pclad112
For GIF both the Attenuation co efficient & model power tend to befunctions of radial coordinate. At a distance r from the core axis the loss
if 222
22
121 )(
)()(
nob
rnob
r
The complexity of multi mode ware guide has presented by correlation
with the model
0
0
rdrrp
drrpr
gi
2.6.SIGNAL DISTORTION IN OPTICAL WAVE GUIDES
Dispersion of txed optical signal causes dispersion for both digital &analog txn along optical fibers.
An optical signal is distorted as it travels along a fiber. This distortion isdue to intra modal d dispersion and intermodal delay effects.
Dispersion means spreading of light pulse as it propagates through fiber. It introduces intersymbol interference (ISI) . It limits the information
carrying capacity of fiber
Dispersion:
Types are
i. Intermodal dispersion
ii. Intramodal dispersion
Intramodal dispersion are
i. Material (or) chromatic dispersion
ii. Wave guide dispersion
iii. Group velocity dispersion
-
8/12/2019 Optical Full Units NOTES
32/98
32
Figure:2.6.1.Broadening and attenuation of two adjacent pulses as they
travel along a fiber
A light pulse will broaden as it travels along the fiber . This pulsebroadening will cause overlap with neighboring pulse.
At certain distance the pulse are not individually distinguished at thereceiver & error will occur.
Information capacity of an optical wave guide is usually specified byBandwidth Distance Product (BLP) IN MHZ-KM. As the length of optical cable increases, the bandwidth decrease in
proportion.
For S.I between distance produced is 20 MHZ.Km & for G.I is 2.5MHZ.Km.
The ICC can be determined by short light pulses propagating along thefiber.
2.6.1.PHASE VELOCITY
As a monochromatic light wares propagates along a fiber in Z-direction. This points of constant phase travel at a velocity.
pV ,
- angular velocity,
- propagation factor
)(2
xyo
pnnk
fV
If the propagation factor in an infinite medium of R.In
cnn
11
2
-
8/12/2019 Optical Full Units NOTES
33/98
33
11
nc
cn
Vp
2.6.2.GROUP VELOCITY
Group of waves with slightly different frequency are propagating alongthe fiber. This elocity is denoted as group velocity
.,1
1
11
1
1
1
1
1
1
g
g
gg
g
g
N
CV
IgroupRNNc
nnc
n
cn
c
cn
V
V
-
8/12/2019 Optical Full Units NOTES
34/98
34
d
dnnNg
d
dnnNg
d
d
d
dnnNg
d
dnnNg
d
d
dc
dcd
c
c
cnn
11
11
11
11
2
11
1
12
12
2
2
2
2.6.3.GROUP DELAY
Group of waves propagate along the fiber with different velocity so itproduces the time delay or group at the rxr side.
.2
12
2
11
2
2
cL
dc
c
cVL
g
g
g
Each modes tares a different amount of time to travel a certain distancedue to this pulse spreading will occur at rxr side.
-
8/12/2019 Optical Full Units NOTES
35/98
35
If the spectrum width of optical source is the delay difference per unitlength is represented by
d
dg
For spectrum components which are X apart and which lie in the2
above and below the central wave length 0 The total delay difference over a distance L
d
d
d
d
c
L
d
d
cL
d
d
d
d g
22
2
2
22
2
Total delay difference in terms of
2
2
2
2
2
d
dwhere
d
dL
d
dL
d
d
d
d g
Group velocity dispersion parameter
.. 2L
The spectrum width of an optical source is characterized by itsRMS value than the puise spreading is approximated by RMS pulse
width is presented by g .
d
d
d
d
c
L
d
dgg
2
2 2
22
The dispersion factor D is
-
8/12/2019 Optical Full Units NOTES
36/98
36
22
2
2
2
2
2
2
2
1
1
11
1
cD
c
d
d
c
d
dD
d
d
d
d
d
d
d
d
d
d
Vd
dD
dbydivideandmultiple
Vd
d
KVd
d
L
d
d
LD
g
g
g
g
It defines the pulse spread spectrum as a function of ware length and it ismeasured in picoseconds / nm .km. The total dispersion = material
dispersion + ware length dispersion
gDmatD=D .
It is calculated by one type of dispersion is in the absence of other.2.7.MATERIAL DISPERSION
It occurs due to variation in R.I as a function of wave length.
The group velocity gV of a mode is a function of R.I the various spectralcomponents of a given mode will travel at different speeds, depending
on the wave length.
To calculate the material dispersion, we consider a plane wavepropagating in an infinitely extended dielectric medium that bas R.I n
)( equal to that of fiber core.
-
8/12/2019 Optical Full Units NOTES
37/98
37
Propagation constant )(2
n
The group deals for material dispersion is
d
dnn
c
Ld
dnn
c
L
d
dnn
c
L
nd
d
c
L
nd
d
c
L
valuesub
d
d
c
L
VL
mat
mat
g
mat
)()(
)()(
)(1)(
1
)(1
)(2
2
2
1
2
2
2
2
2
For a source of spectrum width X and w, L, the VMS pulsebreading due to material dispersion m is given by
.)(1
)(
)()(
)(
)(
)(
)()()(
)(.)(
2
2
2
2
2
2
2
2
2
2
d
d
cD
DLd
d
c
L
DL
alsoand
d
d
c
L
d
d
c
L
d
d
d
d
d
d
c
L
ddXn
cL
dd
d
d
nmat
matn
matmat
nmat
n
nnn
n
mat
mat
-
8/12/2019 Optical Full Units NOTES
38/98
38
Material dispersion can be reduced either by choosing sources withnarrower spectral output widths orm by operating at longer wave
lengths.
2.8.WAVE GUIDE DISPERSION
Its also intramodal dispersion. Due to variation in group velocitywith wavelength for a particular mode , it will occur.
The effect of wave guide dispersion on pulse spreading can beapproximated by assuming that R.I of material is independent of
wave length L.
Group delay can be expressed in terms of normalize propagationconstant b is
2
2
2
1
2
22
2
nn
nkb
For small values of index difference1
21
n
nnD
21
21
21
221
221
221
221
21
2
,1
)(
)(
)(
)(
nkbnk
nn
nbnk
nnnbk
knnnbk
knnnbk
nk
nnb
nn
nkb
-
8/12/2019 Optical Full Units NOTES
39/98
39
Group delay for wave guide dispersion is
.2
.2
)(.
.
.
2
22
21
nKaV
NAKaNAa
V
isfrequencynormalisedThe
dk
bkdnnC
L
nkbnkdk
d
C
L
dk
d
C
LG
For field fiber,
dk
bkdnn
C
LkV
g
)(. 22
First term constant term
Second term group delay due to wave guide dispersion.
The factordv
bvd )( can be expressed by
)()(
)(21)( 2
uaJuaJ
uaJb
dv
bvd
vavH
v
where
radiusfibera
kfactorcoreu
2212
2.9.SIGNAL DISTENTION IN SMF
The pulse spread g occurs over a distance nb of wave length is
obtained from the derivative of group delay with respect to wave length
-
8/12/2019 Optical Full Units NOTES
40/98
40
2
2
2
2
2
2
2
2
2
2
2
2
22
2
)(.)(
)(
.)(
.
)(.
)(.0
)(.
.2
.2
.
&
dvvbdv
cDD
equationbothEquating
DL
v
dv
bvdDn
c
L
dv
bvdDn
c
L
dv
bvdDnc
L
dv
bvdDnn
c
L
d
d
dv
dI
v
d
dv
NAa
d
dv
NAa
d
d
d
dv
d
dv
dv
d
dvbydividemultiply
d
d
ng
gg
g
g
g
g
g
g
Consider the factor (ua) for the lowest order mode in the normalized property
constant
2
41
4
1
41
21
v
uab
vua
Sub (ua) in b
2
41
441
21
vb
-
8/12/2019 Optical Full Units NOTES
41/98
-
8/12/2019 Optical Full Units NOTES
42/98
42
2.11.INTERMODAL DISPERSION:
In multimode fiber, different modes arrive at the receiver at differentthings because of vibration in path & group velocity. It makes pulse
broadening in receiver side. This pulse broadening is called Intermodal
Dispersion.
Figure:2.11.1.Meridional ray optics representation of the propagation
mechanism in an ideal step-index optical waveguide
The time delay at receiver side is
cn
Ln
nc
nn
L
T
nnwhere
nc
L
V
DT
nc
L
V
DT
where
TTT
c
D
2
2
1
1
1
2
max
1
2
1
max
1
min
minmax
sincos,
cos
Therefore minmax TTTD
.
1
1
2
211
2
11
1
2
2
1
c
LnT
n
nn
c
Ln
n
n
c
Lnc
Ln
cn
Ln
D
-
8/12/2019 Optical Full Units NOTES
43/98
43
2.12.MODE COUPLING:
Two modes are coupled with each other is called mode coupling. Atbending or joining, mode coupling will occur.
Due to bending, mode coupling gives rise to conversion of energy fromlower order modes to higher order modes and form the radiated modes.
Due to coupling, power from this lower mode transfer to faster mode &tends to propagate at moderate speed.
It reduces the group delay & intermodal dispersion in transmission link.Group delay for mode coupling is
cn
NAL
2
2
2
)(.
After coupling length Lc, the pulse distortion will change from L to2
1
)( LLc dependence value.
Coupling length Lc is the critical length of fiber at which equilibrium
mode power distribution is reached. For practical Lc=1km.
Due to mode coupling there is an additional loss called coupling lossdenoted byh unit is db/km.
The improvement by pulse spreading is caused by mode coupling overthe distance
Z< Lc, .It is denoted to excess loss L.
chZ c
2
0
0
pulse width increase in absence of mode coupling.
c pulse broadening in presence of strong mode coupling.
hZexcess attenuation.
cdepends upon the fiber profile shape & mode coupling strength
for practical purpose.
For strong mode coupling bandwidth of signal is reduced.2.13.DESIGN OPTIMIZATION OF SM FIBER:
The attributes of SMF are long time, very low attenuation, high qualitysignal transfer due to absence of modal noise.
Largest bandwidth-distance produce. The basis design optimization includes cutoff wavelength, dispersion,
mode field diameter & bending loss.
-
8/12/2019 Optical Full Units NOTES
44/98
44
SMF are used for long distance telecommunication network at 1320nmdispersion is low & attenuation is high & at 1550nm dispersion is high
& attenuation is low.
For long distance communication we should prefer D & A both shouldbe low.
To achieve this, adjust the basic parameters of fiber to zero dispersionfor longer wavelength.
For suitable design of refractive index profile we can get zerodispersion. To achieve zero dispersion to make waveguide
dispersion=material dispersion.
Figure:2.13.1.Typical waveguide dispersions and the common material
dispersion of three different fiber designs & resultant total dispersions
-
8/12/2019 Optical Full Units NOTES
45/98
45
2.13.1.R.I.PROFILE DESIGN:
There are 4 ways of shaping the SMFs.i. 1300nm optimized fiber.ii. Dispersion shifted fiber.iii. Dispersion flattened fiber.iv. Large effective core area fibers.
1.1300nm optimized fiber.
In matched cladding, R.I. of cladding & core region are uniform andmode field diameter MFD=9.5m.
In depressed cladding, R.I. of cladding portion next to core region is lessthan the outer region. MFD=9m..
This is to optimize the waveguide dispersion to get zero dispersion at1300nm.
2. Dispersion Shifted fiber.
At 1550nm, we have to increase the waveguide dispersion=materialdispersion, then we can get zero dispersion at that point.
Waveguide dispersion is function of core radius & value & shape ofrefractive index profile. Adjust the above factor we can get the zero
dispersion at 1550nm.
R.I. profile is shaped with steeper increasing R.I. of core with small coreradius & with large difference R.I. of core & cladding.
For triangular, R.I. profile is designed to get the zero dispersion at1550nm.
3. Dispersion flattened fiber.
The dispersion flattened fiber have minimum dispersion over a range of from 1.3m to 1.55m such that zero dispersion points lies at 1.3mto 1.55m. This fiber only used for WDM network.
R.I. profile is slightly modify from dispersion shifted fiber to get zerodispersion for wide range.
4. Large effective core area fiber.
For distance communication a SMF with large effective core area shouldbe design.
It is used to reduce the system capacity of the fiber & also reduce thenon-linearity in the fiber. Standard SMF have effective core about
55m2. A profile having values greater than 100m
2.
-
8/12/2019 Optical Full Units NOTES
46/98
46
2.13.4.Dispersion Compensating fiber:
For dispersion shifted fiber the cost is high. So we have to usecompensating fiber for same application.
It have negative waveguide dispersion at 1.55m. In optical networkevery 100km replace the 1km length of fiber by 1km conventional
fiber. So we can achieve minimum loss & zero dispersion.
2.13.5.Cutoff wavelength:
The normalized frequency,
405.2.2
.2
VNAa
At
NAa
V
c
Cutoff wavelength of SMF is minimum wavelength from thetransmission takes place. Above cutoff wavelength all the wavelength
can be transmitted. If 405.2V only LP01, HE11 mode is propagated
along the fiber. So generally for SIMMF,
SS
MSV
,
,405.2
Cutoff wavelength of MMF is defined as wavelength at which itbehaves as a SMF.2.14.PULSE BROADENING IN GIF:
In GIF, core R.I. is different according to the radial distance from thecentre of axis. In MMF, due to path difference intermodal dispersion
occurs. But this dispersion is reduced by GIF.
Group delay for GIF:
cLn
g8
2
1
Relationship between GIF, SIF.
sg x8
2
-
8/12/2019 Optical Full Units NOTES
47/98
47
Improvement factor for GIF for theoretical way is 1000, but due todifferent R.I. profile shape we cannot achieve this. The RMS pulse
broadening of GIF for parabolic profile is
sgD
.
s pulse broadening in SIF
g pulse broadening in GIF
Dconstant value & lies between 4 to 10.\
If D=0 & =1, then
sg 1.0
For GIF, core R.I. is optimum then loss is
5
122
opt
g is expressed in terms of 1n , L thenc
Lns
32
1
Therefore,
c
Ln
c
Ln
c
Ln
D
g
g
320
32.
10
32.
21
1
1
Profile Dispersion:
If wavelength propagating along optical fiber cable changed, alpha
value is also changed which leads to pulse broadening.
-
8/12/2019 Optical Full Units NOTES
48/98
48
UNIT- III
OPTICAL SOURCES
3.CHARACTERISTICS OF LIGHT:
High intensity,wavelength, narrow spectrum, less expensive, durable,
flexible, modulation speed should be high.
LEDs:
LEDs are used in optical systems that require bit rates less thanapproximately 100-200 mb/s. It is mostly coupled with multimode fiber.
LEDs require less complex drive circuitry than laser diode since nothermal or optical stabilization circuits are needed.
Principles of Operation:
LEDs must have.
1.High radiance output or brightness
It is a measure of optical power radiated into a unit solid angle per
unit area of emitting surface. Its unit is watts. High radiances are required tocouple sufficiently high optical power levels into a fiber.
2. Fast emission response time:
It is a time delay between the application of a current pulse and onset
of optical emission. This time delay is the factor limiting BW with which the
source can be modulated directly by varying the injected current.
Quantum efficiency:
It is related to fraction of injected electron hole pairs that recombine
radiately.
3.1.LEDS STRUCTURE:
LEDs should provide high radiance and high quantum efficiency, itmust achieve carrier and optical confinement.
Carrier confinement is used to achieve a high level of radiativerecombination in the active region of the device, which yields a highquantum efficiency.
Optical confinement is used for preventing absorption of emittedradiation by material surrounding the pn junction.
Heterojunction structures are used to achieve optical and carrierconfinement.
Heterojunction consists of two adjoining semiconductor materials withdifferent band- gap energies. It is also known as double hetero structure
-
8/12/2019 Optical Full Units NOTES
49/98
-
8/12/2019 Optical Full Units NOTES
50/98
50
A well is etched in a substrate to avoid the heavy absorption of emittedradiation and the fiber is connected to accept the emitted light.
The circular active area in surface emitters is 50m in diameter and upto 2.5m thick. The emission pattern is isotropic with 120 half power
beam width.
Isotropic pattern from a surface emitter is called lambertian pattern.
The source is equally bright when viewed from any direction but powerdiminishes as cos . Where is the angle b/w viewing direction &normal to the surface.
Power is exactly 50 % down of its peak when =600. so that the total half power beam width is 1200
3.1.2.EDGE EMITTING LED.
Figure:3.1.2.Edge-emitting doubleheterojunction LED
EELEDs emit a more directional light pattern than the surface emittingLEDs.
In order to reduce the losses caused by absorption in active layer and tomake the beam more directional the light is collected from the edge of
LED. So it is called EELED.
The EELED has transparent guiding layers with very thin active layer of50 to 100 m in order that the light produced in active layer spreads into
-
8/12/2019 Optical Full Units NOTES
51/98
51
the transparent guiding layers reducing self absorption in the active
layer.
The guiding layers have R.I lower than action region but higher thanouter surrounding material.
This structure forms a waveguide channel that directs the opticalradiation towards the fiber core.
3.2.LASER diodes.
Light amplification by stimulated emission of radiation. For optical fiber systems the laser sources used are almost exclusively
are semiconductor laser diodes. The o/p radiation is highly
monochromatic and light beam is very directional.
Semiconductor laser diodes are performed over LED for the OFCsystems requiring BW > 200 MHZ.
Laser diodes have response time is < 1ns. Optical B.W is 2nm or less.High coupling efficiency.
Principles of Operation:
1. Photon absorption2. Spontaneous emission3. Stimulated emission.
Photon absorption:
When photon with energy E2-E1 is incident on the atom. The atom isinitially in E1. The atom excited into higher energy state e2 through theabsorption of photon. This process is referred to as stimulated
absorption. These dimensions are commonly referred to as longitudinal, lateral and
dimensions of the cavity respectively.
DFB Laser:
In DFB Laser, lasing action is obtained by periodic variations of R.I,which are incorporated into the multiplayer structure along the length of
diode, here optical fiber is not required. The optical radiation within the resonance cavity of laser diode sets up
a pattern of electric and magnetic field lines called modes of cavity. The modes are seperated into two independent sets of TE and TM
modes. Each set of modes can be described in terms of longitudinal,
lateral And traverse modes.
Longitudinal modes.
It is related to length L of cavity and determines the principle structureof frequency of emitted radiation.
Since L is much layer then the lasing W.L of appro 1 um, manylongitudinal modes can exit.
Spontaneous emission:
An atom returns to lower energy state in random manner.
-
8/12/2019 Optical Full Units NOTES
52/98
52
Stimulated emission:
When a photon having equal energy to the difference b/w the two statesinteracts with the atom causing it to the lower state with the creation of
second photon.
Population inversion:
Most photons incident on the system will be absorbed so the stimulatedemission is essentially negligible. Stimulated emission will exceed
absorption onlf if the population of excited states is greater than that of
ground state. This condition is known as population inversion. The
population inversion can be achieved by various pumping techniques.
Fabry- Perot resonator cavity
Lasers are oscillators operations at optical frequency. The oscillator isformed by resonant cavity providing a selective f/b. The cavity is
normally used is fabry-perot resonator.
This cavity is much smaller,250-500 m long, 5.15 m wide, and 0.1-0.2m thick.
Lateral modes.
It lies in the plane of pn junction. These modes depend on the side wallpreparation and width of cavity and determine the shape of lateral
profile of laser beam.
Transverse modes:
It is associated with electromagnetic field and bean profile in thedirection perpendicular to the plane of pn junction.
These modes determine the laser characteristic such as the radiationpattern and threshold current density i.e, the point at which lasing starts.
3.2.1.Lasing conditions and resonant frequency.
The electromagnetic wave propagating in the longitudinal direction is expressed
as
E(z,t)= )()( ZtjeZI
I(z)optical field intensity
- optical radian frequency &
BPropagation constant
Lasing is the condition at which light amplification becomes possiblein layer diode. The condition for lasing is that population inversion be
achieved.
-
8/12/2019 Optical Full Units NOTES
53/98
53
The stimulated emission rate for particular mode is proportional tointensity of radiation in that mode.
The radiation intensity at a photon energy h varies exponentiallywith the distance Z that it transverse along the lasing cavity according to
the relationship.
I(z)=I(0) )()(exp hhg
effective absorption coefficient of material in optical path.
optical field confinement factor or fraction of optical power in activelayer.
ggain coefficient, Zdistance traverses along the lasing cavity,
hphoton energy.
Lasing occurs when the gain of guided modes exceeds above the opticalloss during one round trip through the cavity i.e,z=2L.
If R1,R2 are reflectivities of 2 ends of mirror during 1 round trip thenFresnel reflection coefficient is given by
R=
2
21
21
_
nn
nn
The lasing condition becomes I(2L) is
LRRILL 2exp)0()2( 21 )()( hhg
At threshold condition,For amplitude I(2L)=I(0)
For phase 1 Lje
The condition to reach the lasing threshold is the point at which theoptical gain is equal to total loss t in the cavity.
Total loss present in layer cavity.
endtth
th
th
RRLg
g
g
21
1ln21
end mirror loss in lasing cavity.
For lasing action, the gain g thg . i.e.,threshold gain.
-
8/12/2019 Optical Full Units NOTES
54/98
54
For strong carrier confinement the threshold current density for stimulated
emission Jthcan be related with lasing threshold gain is given by
thth gJ
Figure:3.2.1.Relationship between optical output power & laser diode drive
currents
3.2.2.Laser diode Rate equation:
The relationship b/w optical power & diode drive current can be foundby rate equation.
Total carrier population=carrier injection + Spontaneous recombn +
stimulated emission
Total active region with a carrier confinement region of depth d rateequation is given by
No of photons():
ph
spRCndt
d
= stimulated emission +spontaneous emission+photon loss
-
8/12/2019 Optical Full Units NOTES
55/98
55
No.0f electrons(n):
Cnn
qd
J
dt
dn
sp
=Injection + spontaneous recombination + Stimulated emission
where,
ccoefficient describing the strength of optical absorption &
emission interactions
Rsprate of spontaneous emission into lasing diode
ph photon lifetime
sp spontaneous recombn life time
Jinjection current density
For steady state condition ,0&0 dt
dn
dt
d when n & have non
zero values. Assume Rsp is negligible and nothing thatdt
dmust be
positive when is small. At threshold point sthnn & .therefore,
01
0
01
)2......(....................0
)1....(....................0
ph
ths
ph
ths
sth
sp
th
ph
s
spsth
Cnor
Cn
Cnn
qd
J
RCn
is always positive, so 01 ph
thCn
& s=0.
-
8/12/2019 Optical Full Units NOTES
56/98
56
sp
thth
sp
th
n
qd
J
thresholdAt
n
qd
J
n must exceed threshold value nth then only we can get is positive.Using equation 1 & 2.find the sIn equation 1
ph
sspsth RCn
From equation 2
sthth Cn
qd
J
qd
J0
Substitute thCn :
phspthph
s
sp
th
ph
s
ph
s
sp
th
RJJ
qd
Rqd
JJ
Rqd
J
qd
J
.
0
3.2.3External quantum efficiency:
It is defined as number of photons emitted per radiative electron holepair recombination above threshold.
th
thiex t
g
g
For high quality laser
i =(0.6-0.7)%
ex t =(30-40)%
3.3.MODULATION OF LASER DIODE:
The process of imposing information on a light stream is called
modulation. There are 2 types of modulation.
-
8/12/2019 Optical Full Units NOTES
57/98
57
1.Analog Modulation:
It is carried out when the drive current above the threshold current isdirectly proportional to information signal & there should be linear withi/p and o/p.
2. Digital modulation:
It is affected by photon and carrier lifetime. The photon life time isth
phgC
n
.
Threshold current Ithis the minimum value of direct to start the lasingaction. so in carrier life time
thBp
p
dIII
It
ln.
Where,
IBbias current, I
P=pulse current.
The total current flow in laser cavity isI= IP+ IB
Therefore the frequency of oscillation is
21
21
1..
1.
2
1
thphspI
If
3.3.1.TEMPERATURE EFFECTS IN LASER DIODE:
Threshold current I th(T) of laser diodes is temperature dependent. Ith(T)increases with temperatures in all types of semiconductor laser becauseof various complex temperature dependent factors.
Empirical expression that shows the relationship between I th(T) &temperature is given as
0)( T
T
Zth eITI
T0measure of relative temperature insensitivity.
IZconstant, Tdevice absolute temperature.
Experimental values of T0for 1300nm InGaAsp lasers are typically 60-80k(333-353
0c)
For GaAlAs T0=1200c to 1650c For quantum well laser T0=4370c
Using temperature compensation circuit we get the constant laser o/p.
-
8/12/2019 Optical Full Units NOTES
58/98
58
3.4.POWER LAUNCHING & COUPLING:
Lensing schemes for coupling improvement.
If the source emitting area is larger than the fiber core area thenmaximum optical power is coupled into the fiber. This is a result offundamental energy & radiance conservation principles. It is also known
as law of brightness. If the emitting area of source is smaller than the core area, miniature
lens may be placed between the source and fiber to improve the powercoupling efficiency.
The function of micro lens is to magnify the emitting area of the sourceto match exactly the core area of fiber end face.
If the emitting area is increased by magnification factorM then thesolid angle within which optical power is coupled to the fiber from LEDsource is also increased by same factor.
General possible lensing schemes are
1. Rounded- end fiber:The fiber itself rounded known as rounded end fiber. Here whole radiation from
LED emitting area is incident falls on the fiber end surface.
2.Non imaging microsphere:
A small glass sphere is contact with both fiber and source.
3. Imaging sphere:
A large spherical lens is used to image the source on the core area of teh source.
4. Cylindrical sphere:
Cylindrical lenses are generally formed from a short section of fiber.
5. Taper- ended fiber.
If the width of taper ended fiber is equal to width of emitting surface ofLED, the maximum coupling efficiency is achieved.
An the above techniques can improve the source to fiber couplingefficiency, they also create additional complexities.
One problem is that tha lens size is similar to source & fiber coredimensions which introduces fabrication and bandling difficulties.
Non Imaging Micro sphere:
Non imaging micro sphere is one of the most efficiency lensing methods.
-
8/12/2019 Optical Full Units NOTES
59/98
59
The spherical lens has R.I is 2.0 and outer medium is 1.0 and emittingarea is circular.
To collimate the output from LED, the emitting surface should belocated at focal point of lens,the focal point can be found from Gaussian
lens formula
r
nn
q
n
s
n ''
where
S Object distance,Q Image distance
S&Q are measured from lens surface
nR.I of lens
nR.I of outside medium
rradius of curvature if lens surface.
To find the focal point for right hand surface of lens is by some sign
conversions are :
1.Light travels from left to right
2.object distances are measured as +ve to left of vertex and -ve to the
right.
3.Images distances are measured as +ve to right vertex andve to the
left.
4.All convex surfaces encountered by light have +ve radius of curvature
and concave surfaces have -ve radius of curvature.
When s is measured from point B.At q= , r=-RL,n=2.0 & n=1.0.
L
L
Rs
Rs
r
nn
q
n
s
n
2
0.10
0.2
''
Thus the focal point is located in the lens surface at point A. If LED is placed to lens surface,thus results in magnification M of
emitting area .2
2
2
s
L
s
L
r
R
r
RM
-
8/12/2019 Optical Full Units NOTES
60/98
60
With the lens the optical power PLthat can be coupled into full apertureangle 2 is given by
22
sin.
s
LsL
r
RPP
Where
Pstotal output power from LED without lens.
The maximum coupling efficiency n max is determined by fiber size
NAa
rfor
NAa
rfor
NAr
a
s
s
s
1
)(
2
max
When the radius of emitting area is larger than the fiber radius noimprovement in coupling efficiency is efficiency is possible with a lens.3.5.SOURCE TO FIBER POWER LAUNCHING:
A measure of amount of optical power emitted from a source that can be
coupled into fiber is called coupling efficiency.
s
F
P
P
FPpower coupled into the fiber
sPpower emitted from fiber.
Many source suppliers offer devices with short length of optical fiber(1m or Less) already attached in an optimum power couplingconfiguration .this selection of fiber is referred to as flylead.
3.5.1.Source output pattern:
To determine the optical power accepting capability of fiber the spatialradiation pattern of source must be known.
The spherical coordinate system characterized R,Q, with normal toemitting surface.
The radiance may be function of both & s&also vary from point topoint on emitting surface.
Surface emitting LED s are characterized by their lambertian outputpattern which means the source is equally bright when viewed from any
direction.
The power delivered at an angle measured relative to normal toemitting surface, varies as cos
The emission pattern for lambertial source is
-
8/12/2019 Optical Full Units NOTES
61/98
61
cos.),( 0BB
Where
0B radiance along the normal to radiating surface.
Edge emitting LEDs & laser diodes have more complex emissionpattern. These devices have radiances B(,00) & B(,900) in the planesparallel & normal to emitting junction plane of device.
LT BBB cos
cos
cos
sin
,(
1
0
2
0
2
T & L are transverse & lateral power distribution coefficients.
3.5.2.Power coupling calculations:
To calculate, the maximum optical power coupled into a fiber,considerthe symmetric source of brightness B(As,s) where As& sarethe area & solid emission angle of source.
The coupled power can be found using the relationship
drrsdddB
ABsddAP
rm
f
ss
Af
s
2
0
2
0
max0
00
sin),(
),(.
Here emitting surface is taking as circular. If source radius rs is less thancore radius a, then rm=rs& assume surface emitting LED of radius rslessthan a then
rs
rs
rs
drrsdNAB
drrsdB
drrsddBP
0
2
0
2
0
0
2
0
0
2
0
2
0
max0
0
0
0
..
..maxsin
sincos2
For SIF, the NA is independent of positions s& r on the fiber end.
2
10
22
2
0
22
2
)(,
nBr
NABrPP
s
sstepLED
Consider now the total optical power Psthat is emitted from source ofarea Asinto hemisphere.
-
8/12/2019 Optical Full Units NOTES
62/98
62
arforNAPr
astepP
arforNAPstepP
Br
dBr
ddBAP
ss
s
LED
ssLED
s
s
ss
2
2
2
0
22
2/
0
0
2
2
0
2/
0
)(,
)(,
sincos2
sin),(
For Graded Index Fiber:
a
rnP
a
rnBr
drrnrnBP
s
s
ss
rs
gradedLED
2
212
2212
)(2
2
1
210
22
0
2
2
2
0
2
,
3.5.3.Power launching versus wavelength:
The Optical power launched into fiber does not depend on thewavelength of the source but only on its brightness.
The no of modes that can propagate in GIF of core size a & indexprofile is
2
12
2
anM
twice as many modes propagate in a given fiber at 900nm than at 1300nm
The radiated power per mode,Ps/M ,from a source at a particularwavelength is given by radiance multiplied by the square of nominal
source wavelength.
2
0BM
Ps
Thus twice as much power is launched into a given mode at 1300 nmthan at 900nm.
Hence two identically sized sources operating at different wavelengthsbut having identical radiances will launch equal amounts of optical fiber
power into same fiber.
-
8/12/2019 Optical Full Units NOTES
63/98
63
3.6.LED COUPLING TO SMF.
LED were considered only for MMF systems. However, around 1985,researchers recognized that edge-emitting LEDs can launch sufficientoptical power into SMF for transmission at data rates up to 560 mb/s
over several kms.
Edge-emitting LEDs are used since they have a larger like o/p pattern inthe direction perpendicular to junction plane.
Coupling analyses of o/p from an edge emitting LED electromagnetictheory are interpreted which involves defining a NA for SMP.
The two cases for coupling isi. Direct coupling of an LED into SMF &ii. Coupling into SMF from multimode fly lead attached to LED.
Edge emitting LEDs have Gaussian near o/p profiles with ye2 full widthof approximately 0.9 & 22 m in the direction perpendicular
¶llel to junction plane.
The x(parallel) & y(perpendicular)directions, & let x & y be the x& y power transmissivities.
We can find the maximum LED to fiber coupling efficiency from therelation
yx
s
in
P
P
inPoptical power launched into the fiber, sPtotal source output power
-
8/12/2019 Optical Full Units NOTES
64/98
64
UNIT-IV
OPTICAL RECEIVERS
4.1.PIN PHOTODETECTOR:
Figure:4.1.1.Schematic representation of a pin photodiode circuit with an
applied reverse bias
The device consists of p and n regions separated by very lightlyn-doped intrinsic(i) region. A large reverse bias voltage is
applied across the device so that the intrinsic region is fully
depleted of carriers.
When an incident photon has an energy is greater than or equalto bandgap energy, the photon can give up its energy & excite anelectron from valence band to conduction band. This process
generates electron-hole pair is known as photocarriers.
Normally these carriers are generated mainly in depletion regionwhere most of the incident light is absorbed.
-
8/12/2019 Optical Full Units NOTES
65/98
65
The high electric field present in the depletion region causes thecarriers to separate & be collected across the reverse biased
junction.
This gives rise to current flow in every external circuit, with oneelectron flowing for every carrier pair generated. This current
flow is known as photocurrent.
The charge carriers move a distance Ln or Lp for electrons &holes. This distance is known as diffusion length.
The time it takes for an electron or hole to recombine is knownas carrier lifetime & is represented by n & p . The lifetime &diffusion lengths are related by
2121 & pppnnn DLDL
nD & pD electron & hole diffusion coefficients.
Optical radiation is absorbed in semiconductor materialaccording to exponential law.xsePxP )(01)(
)(s
absorption coefficient at which wavelength .
P0 incident optical power level.
P(x)optical power absorbed in a distance x.
The cutoff wavelength is expressed by)(
24.1)(
evEE
hcm
gg
c
The cutoff wavelength is about 1.06m for Si & 1.6m for Ge .
For longer wavelength, the photon energy is not sufficient to
excite on electron from valence to conduction band.
If the depletion region has a width w, then the total powerabsorbed in the distance w is
wsePwP 1)( 0 The primary photocurrent Ip resulting from power absorption is
given by
)1(10 fwp RePh
qI s
Where, fR reflectivity
two important characteristics of photo detector are
i. Quantum efficiency.
ii. Response speed.
-
8/12/2019 Optical Full Units NOTES
66/98
66
The quantum efficiency is the number of electronhole carrier pairsgenerated per incident photon of energy h & is given by
hP
q
Ip
0
The performance of photodiode is characterized by responsivity R. thisis related to quantum efficiency
h
q
P
IR
p
0
4.2.PHOTODETECTOR NOISE:
powernoiseAmplifierpowernoiseectorphoto
ntphotocurrefrompowersignal
N
S
det
To achieve high SNR
i. Quantum efficiency should be high to generate large signal power.
ii. Photodetector & amplifier noises should be kept as low .
4.2.1.NOISE SOURCES:
Fig:4.2.1.1.Photodetector receiver model Fig:4.2.1.2Equivalent
circuit
The photodiode has series resistance Rs, total capacitance Cd,&bias resistor RL.
The primary photocurrent ip(t) is generated when modulatedsignal optical power P9t) falls on the detector.
)()( tPh
qtiph
-
8/12/2019 Optical Full Units NOTES
67/98
67
For pin photodiode, the mean square signal current is
ianceistii ppinss var)(22
,
2
For Avalanche photodiode,
222
,
2
.)( Mtii pAPDss
Mavalanche multiplication factor.
< >ensemble average
The signal component 2pi > for sinusoid ally varying input signal of
modulation index m is
22
22.
2 ppp I
mi
The noise associated with photodiode that have no internal gain arei. Quantum noise or shot noise.
ii. Dark current noise.
iii. Bulk dark current
iv.Surface dark or surface leakage current noise.
1. Quantum noise.
It arises from statistical nature of production & collection of photo-electrons, when the optical signal is incident on a photodiode.
The quantum noise current has a mean square value in bandwidth Bwhich is proportional to average value of photocurrent Ip.
)(2 222
MFqIpBMI QQ
Where, F(M)noise figure arised with random nature of avalanche
process(for pin P.D M=1)
F(M)=Mx
2. Dark current noise:
The current that flows through the bias circuit when no light is incidenton the diode is known as dark current.
3.Bulk dark current:
It is due to thermally generated electrons & holes in the pn junction ofP.D.The mean square of bulk current is given by
BMFMqII DDBDB ).(2 222
-
8/12/2019 Optical Full Units NOTES
68/98
68
DI primarly (unmultiplied)detector bulk dark current
4.Surface leakage current:
It is due to surface defects, cleanliness, bias voltage & surface area.
The mean square value
BqII LDSDS 222
The total mean square P.D. noise current is
BqIBMFMIIq
iiii
LDP
DSDBQ
DSDBQNN
2)(2 2
222
22222
Thermal noise(Amplifier noise):
The P.D. load resistor gives thermal noise
L
BTT
R
TKi
422
SNR:
L
BLDP
P
R
TKBqIBMFMIIq
MI
N
S
42)(2 2
22
For sinusoidally modulated signal with m=1 & F(M) approximat4ed by
Mxgives
)(
42
2
DP
L
BL
X
optIIXq
R
TKqI
M
4.3.DETECTOR RESPONSE TIME:
4.3.1.Depletion layer photocurrent:
The electron hole pairs generated due to absorption of incident photonswill be separated by reverse bias voltage induced by electric field.
Under steady-state conditions, the total current density throughdepletion layer is
diffdrtot JJJ
The drift current density is expressed as
-
8/12/2019 Optical Full Units NOTES
69/98
69
wPdr seqA
IJ
10
Aphotodiode area , 0 incident photon flux per unit area
Ah
RP f
100 fR surface reflectivity
The hole diffusion can be determined by one dimensional diffusion
equation
0)(02
2
xG
PP
x
PD
p
nnnp
pD hole diffusion co-efficient, nPhole concentration in n-type material
0nP equlilbrium hole density, p excess hole life time
G(x)electron-hole generation rate & is given by
xs sexG 0)( Therefore the diffusion current density is
P
Pn
w
Ps
Ps
diffL
DqPe
L
LqJ s 00
1
The total current density = diff dr JJ
P
Pn
Ps
w
P
Pn
Ps
w
Ps
w
Ps
w
Ps
P
Pn
w
Ps
Psw
P
Pn
w
Ps
Psw
tot
L
DqPL
eq
L
DqP
L
eLeLeLq
L
DqPe
L
Leq
L
DqPe
L
LqeqJ
s
sss
ss
ss
00
00
00
000
11
1
1
11
11
4.3.2.RESPONSE TIME:
The response time of photodiode are depends on
1. Transit time of photocarriers within the depletion region.
-
8/12/2019 Optical Full Units NOTES
70/98
70
2. Diffusion time of photocarriers outside the depletion region.
3. RC time constant of photodiode & its associated circuit.
1. TRANSIT TIME:
The response speed of photodiode is primarily limited by time taken by
photo generated carriers travel across the depletion region.
d
dv
wt
dv carrier drift velocity, wdepletion layer width
2. DIFFUSION TIME:
i. Rise time:
The rise time r is measured from 10 to 90% of leading edge of outputpulse.
ii. Fall time:
f is measured from 90 to 10% of falling edge of output pulse.
For fully depleted photodiodes the rise time r& fall time f are same. Approximately within 1ns, the fast carriers allow the device output rise
to 50% of its maximum value but slow carriers cause a relatively long
delay before the output reaches its maximum value.
3.RC TIME CONSTANT:
To achieve high quantum efficiency, the depletion layer width mustlarger than
s
1[inverse of absorption coefficient] so that most of light
will be absorbed.
Junction Capacitance:
If the width of depletion region is too thin, the junction capacitance willbecome high & is given by
w
AC sj
s permittivity of semiconductor material = sK0
sK semiconductor dielectric constant, Adiffusion layer area
The detector behaves like a simple RC low pass filter with pass band is
given by
-
8/12/2019 Optical Full Units NOTES
71/98
71
TTCRB
2
1
TR combination of load & amplifier input resistance
TC sum of photodiode & amplifier capacitances.
4.3.3.AVALANCHE MULTIPLICATION NOISE:
Every photogenerated carriers donot undergo the same multiplicationand hence the avalanche process is statistical in nature.
Excess noise factor(F):
tionmultiplicaavalancheofsquare
tionmultiplicaavalancheofsquaremeanF
M
m
m
m
2
22
Mean square gain is greater than average gain i.e., if m denotes thestatiscally varying gain, then
> 2=M2 The noise in avalanche process is relatively high because it depends on
mean square gain
=M
2+x, 0
-
8/12/2019 Optical Full Units NOTES
72/98
72
)1(1
2
)1(1
)1(2
122
221
22111
22111
21111
1111
22
22
2
2
eff
e
effee
eff
e
effeffe
e
eff
e
effeffe
eff
e
eff
effe
e
e
eff
e
eff
eff
ee
e
e
eff
e
eff
eff
ee
e
ee
effe
e
effee
KM
KMF
KM
KKM
M
K
MKKM
KM
KKM
M
M
K
M
KK
MMM
M
K
M
KK
MMM
MMKM
MKMF
For injected holes
effheffeff
h
h
heffheffeffhh
h
heffheffeffhh
h
hheff
h
heffhh
KMKK
M
M
MKMKKMMM
MKMKKMMM
MMKM
MKMF
'
2
'
1
'2
1
'
2
'
1
'
12111
'
2
'
1
'
12111
211
'
111
1
1'
1
11
22
22
2
2
-
8/12/2019 Optical Full Units NOTES
73/98
73
1"12"
1'
112
'
'
11
12
'
'
11
1
'
112
'
'
11
'
22
'
eff
h
effhh
effheff
h
effheff
h
effheffeff
h
heffheffeff
h
KM
KMF
KMK
M
KMK
M
KMKK
M
MKMKK
M
Where,
effK" =effK'1
The effective ionization rate ratios are
2
1
2
2
1
2
2
2
12
'
1
K
K
K
KK
KK
KKK
eff
eff
eff
It shows that Fe as a function of average electron gain Me for variousvalue of effective ionization rate ratio Keff.
If the ionization rates are equal , the excess noise is at its maximum thenFe = Me
Smaller value of Keff gives smaller excessive noise factor. Keff rangesbetween 0.015 to 0.035 for silicon & 0.6 to 1.0 for germanium.
For excess noise factor can be approximated asF=M
x
4.4.FUNDAMENTAL RECEIVER OPERATION
A decision circuit compares the solution in each time slot with a certainreference voltage known as threshold level.
(i) Received signal > Threshold Level = 1
(ii) Received signal < Threshold Level = 0
-
8/12/2019 Optical Full Units NOTES
74/98
-
8/12/2019 Optical Full Units NOTES
75/98
75
This equation is approximated by empirical expression
10)( xMMF x
4.4.2.RECEIVER CONFIGURATION:
The rectangular digital pulse falls on P.D is found by)()( b
n
pn nTthbtP
nb Rec