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EC2402 OPTICAL COMMUNICATION AND NETWORS
UNIT 1 INTRODUCTION Optical Communication is the most modern
mode of wired communication. Optical communication is also the
youngest mode of communication. However its
capabilities supersede all other modes of communication. Before
optical communication the most of the communication was in radio
and
microwave domain which has frequency range orders of magnitude
lower than the optical see Fig for the electromagnetic spectrum
For good communication a system needs to have following
things.
Good signal to noise ratio (SNR) i.e. low loss Since the
bandwidth of a system is more or less proportional to the frequency
of operation, use of
higher frequency facilitates larger BW. The BW at optical
frequencies is expected to be 3 to 4 orders of magnitude higher
than that at the
microwave f frequencies (1GHz to 100GHz). Transmission media
Alternative to the Optical Communication There are various wired
and wireless media used for long and short distance
communication.
Their broad characteristics are summarized in the following.
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The first two media have a very limited bandwidth.
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Microwave links and Satellite communication has comparable
bandwidths as in principle their mode of operation is same but the
spatial reach of satellite is far greater.
Before Fiber optic communication became viable, satellite
communication was the only choice for long distance communication.
Hence Fiber optic communication may be achieved using an
electromagnetic carrier which is selected from the optical range of
frequency (1.76 x 1015 Hz to 3.75 x 1015 Hz). Therefore
communication at optical wavelengths (0.8m to 1.7m or 850nm to
1700nm) offer an increase in bandwidth by a factor of 104
Advantages of Optical Communication
Ultra high bandwidth (THz) Low loss (0.2 dB/Km) Low EMI Security
of transmission Low manufacturing cost Low weight, low volume Point
to Point Communication
1.1 EVOLUTION OF OPTICAL COMMUNICATION SYSTEM Initially in early
1970s due to technology limitation, the optical fiber had a low
loss
window around 800nm. Also the semiconductor optical sources were
made of GaAs which emitted light at 800nm. Due to compatibility of
the medium properties and the sources, the optical communication
started in 800nm band so called the First window' .
As the glass purification technology improved, the true silica
loss profile emerged in 1980s. The
loss profile shows two low loss windows, one around 1300nm and
other around 1550nm. In 1980s the optical communication shifted to
1300nm band , so called the Second Window' . This window is
attractive as it can support the highest data rate due to lowest
dispersion.
In 1990s the communication was shifted to 1550nm window, so
called Third Window' due to invention of the Erbium Doped Fiber
Amplifier (EDFA). The EDFA can amplify light only in a narrow band
around 1550nm. Also this window has intrinsically lowest loss of
about 0.2 dB/Km . This band has higher dispersion, meaning lower
bandwidth. However, this problem has been solved by use of so
called dispersion shifted fibers'. To summarize: 1ST OPERATING
WINDOW: centered at 850nm Fiber silica ( MM fiber) Sources LEDs,
GaAlAs Photo detector silicon
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Appln : Initial telephone field trials were carried out in USA
in 1977 by GTE in Los Angeles and By AT & T in Chicago).
Intercity applications ranged from 45 140 Mbps with repeater
spacing of around 10Km. Long window 1300nm to 1700nm,
attenuation
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In 1998 a new ultrahigh purifying process patented by Lucent
technologies eliminated virtually all water molecules from the
glass fiber material. The resultant fiber produced, after reducing
the OH content of silica is called All wave fiber. With these
fibers the attenuation was reduced at 1550nm. 1.2 Elements of an
optical fiber transmission link The key sections are transmitter
consisting of a light source and its associated drive circuitry,
fiber and a receiver consisting of a photo detector plus
amplification & signal restoring circuitry. Additional
components include optical amplifiers, connectors, splices,
couplers and regenerators( for restoring the signal shape
characteristics).The cabled fiber is one of the most important
elements in an optical link.
Splice is permanent or semi-permanent joint b/w two fiber
segments.
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Let us now understand how information (voice, data and video) is
transmitted on a light beam through
fiber cables. Once the fiber cable is installed, a source of
light that is dimensionally compatible with the fiber core is
used to launch the optical power into the fiber. LEDS and LASERS
are used for this purpose since; their output can be modulated
rapidly at the desired
transmission rate, thereby producing an optical signal. The
electric signals to the transmitter circuitry for the optical
source can be either in analog or digital
form. For high rate systems (usually greater than 1 Gb/s),
direct modulation of the source can lead to
unacceptable signal distortion. In this case, an external
modulator is used the amplitude of a continuous light output from a
laser diode source.
In the 800-900 nm region the light sources are generally alloys
of GaAlAs. At longer wavelengths(1100-1600 nm) an InGaAsP alloy is
the principal optical source material.
After the optical signal is launched into the fiber, it will
become progressively attenuated and distorted with increasing
distance because of scattering, absorption and dispersion
mechanisms in the glass material.
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At the receiver, a photodiode will detect the weakened optical
signal and convert into an electrical current called as
photocurrent. The design of an optical receiver is inherently more
complex than that of the optical transmitter, since it has to
interpret the content of weakened signal received by the photo
detector. Wavelength Division Multiplexing(WDM)
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. The longest link is SEA ME WE 3 cable system. It runs
from Germany to
Singapore connecting many countries in between. 1.3 BASIC
OPTICAL LAWS& DEFINITIONS: The fundamental parameter of a
material is its refractive index n. The ratio of speed of light in
vacuum to that in matter is the index of refraction n of the
material given by n = c / v n = 1 for ain = 1.3 for water n = 1.55
for glass Representation of a critical angle and total internal
reflection at a glass air interface. 1 angle of incidence 2 angle
of refraction Using snells law n1 sin 1 = n2 sin 2, at 1 = c n1 sin
c = n2 sin 90
sin c = n2 / n1 c = sin
-1(n2/n1) when 1> c min total internal reflection takes
place. CRITICAL ANGLE OF INCIDENCE C: If the angle of incidence 1
is increased, a point will eventually be reached where the light
ray in air is parallel to the glass surface. This point is known as
critical angle of incidence c.
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1.4 Optical fiber
Optical fiber is basically a solid glass rod. The diameter of
rod is so small that it looks like a fiber.
Optical fiber is a dielectric waveguide. The light travels like
an electromagnetic wave inside the waveguide.
The dielectric waveguide is different from a metallic waveguide
which is used at microwave and millimeter wave frequencies.
In a metallic waveguide, there is a complete shielding of
electromagnetic radiation but in an optical fiber the
electromagnetic radiation is not just confined inside the fiber but
also extends outside the fiber.
The light gets guided inside the structure, through the basic
phenomenon of total internal reflection.
The optical fiber consists of two concentric cylinders; the
inside solid cylinder is called the core and the surrounding shell
is called the cladding. (See Fig 1)
Figure1: Schematic of an optical fiber
For the light to propagate inside the fiber through total
internal reflections at core-cladding interface, the Refractive
index of the core must be greater than the refractive index of the
cladding. That is .
1.4.1 Different types of fibers: By refractive index profile
step-index fiber : the refractive index profile of fiber core is
a step function graded-index fiber : the refractive index of fiber
core depends on the radius distance.
By sustainable propagation mode single-mode fiber : support only
single propagation mode. multi-mode fiber : support multiple
propagation mode.
By dispersion characteristics non-dispersion-shifted fiber
(NDSF) : standard single-mode fiber
with zero dispersion at 1.3m. [ITU-T G.652] dispersion-shifted
fiber (DSF) : zero dispersion at 1.55m. [ITU-T G.653] non-zero
dispersion
shifted fiber (NZDSF) : small but non-zero dispersion at 1.55m.
[ITU-T G.655] By polarization characteristics
polarization maintaining fiber : polarization preserved
fiber
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1.4.1.1 STEP INDEX FIBER
Step Index Fiber (Refractive index profile)
For this fiber the refractive index of the core is constant (see
Fig 5). Since refractive index profile looks like a pulse or step,
this kind of fiber is called the STEP INDEX FIBER. This structure
is useful for analyzing propagation of light inside an optical
fiber. 1.4.1.2 GRADED INDEX FIBER In a step index fiber since the
refractive index is constant inside the core, the velocity of all
the rays is constant and hence there is travel time difference
between different rays. If we develop a system where the rays which
travel longer distances travel with higher velocities and the rays
which travel shorter distances travel with lower velocities, the
pulse spread on the fiber can be reduced and consequently the
bandwidth can be increased. The ray which is at a higher angle,
should speed up and the ray which is along the axis of the fiber
should travel with the slowest possible velocity. Since velocity is
inversely proportional to the refractive index, it can be
manipulated by changing the refractive index of the core. The
refractive index of outer layers of the core should be smaller
compared to that of the inner layers, so the rays that go in the
outer layers, travel faster. So we find that for reducing
dispersion, the refractive index at the center should be maximum
and it should gradually decrease from the center to the
core-cladding interface. The rays that go at higher angles speed up
and the dispersion gets reduced. In this fiber we grade the
refractive index profile of the core and consequently it is called
the graded index fiber.
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A graded index fiber and the ray propagation is shown in the
figure :
(Graded Index Profile) er the profile optimally, we get the
dispersion reduction compared to that for a step index fiber,
factor of thousand. The data rate of a typical graded index
fiber is typically 10 to 100 times higher compared to a step index
fiber.
Therefore, in practice, even for LANs, we use GIF (Graded Index
Fiber) instead of SIF \ (Step Index Fiber). Both the SI and GI
fibers can be further divided into single mode and multimode
fibers.
1.4.1.3 SINGLE MODE OPTICAL FIBER This fiber has one fundamental
mode of propagation. It is a high capacity link used for long
distance communication. Having smaller radii, Lasers are used as
optical sources which
is quiet expensive. The optical fiber in which only one ray
travels along the axis of fiber is called the single mode optical
fiber . Single mode optical fiber is the best amongst the three
types of fibers, namely the step index fiber, GI fiber and the
single mode fiber. In a long distance communication, we use single
mode optical fiber, whereas in LANs we generally use graded index
optical fiber.
Note: For single mode optical fiber however we have to use a
source like laser because the diameter of the fiber is very small
and without a highly collimated beam, sufficient light cannot be
launched inside the fiber. The three types of fibers have typical
diameters as follows: Core diameter: SM - 50-60 micrometre GI -
50-60 micrometre Single mode fiber-5-10 micrometre Cladding
diameter (Standarised for all fibers)-125 micrometre
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1.4.1.4 Multi-mode fiber : larger core area easier for power
coupling between source and fiber or fiber to fiber. can use LEDs
as the light source; LED are easy to make, Less expensive, require
simpler circuitry, and have longer life time. This fiber has many
modes of propagation. As the optical pulse is launched into this
fiber, the optical power in the pulse is distributed over all of
the modes of the fiber .Each of the modes that can propagate in a
multimode fiber travels at a different velocity. This means that
the modes arrive at different times, thus causing pulse broadening
as it travels along the fiber. This effect is known as Intermodal
dispersion. This is the main disadvantage of multimode fibers. This
effect can be reduced by using Graded index profile in a fiber
core. Comparison of single mode and multimode step index and graded
index optical fibees.
1.5 Ray Optics Representation 1.5.1 Rays and Modes
The propagation of light along a waveguide can be described in
terms of a set of guided electromagnetic waves called the modes of
the waveguide.
These guided modes are confined to the core which is also
referred as bound modes. Family of plane waves corresponding to a
particular mode forms a set of rays called Ray Congruence.
The two types of rays that can propagate through a fiber are
meridional rays and skew rays.
1.5.2 Meridional rays The Meridional rays are confined to the
meridional planes of the fiber, the planes that has the axis of
symmetry of the fiber (core axis). They are of two types of
meridional rays:
o Bound Rays that propagate along the fiber axis and are trapped
in the core. o Unbound Rays are refracted out of the core.
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1.5.3 Skew Rays The Skew rays are not confined to a single
plane, but tend to follow a helical type path along the fiber.
These rays are more difficult to track as they travel along the
fiber, since they do not lie in a single plane.
The Meridional ray is as shown in the fig for a step index
fiber. The light ray enters the fiber core from a medium of
refractive index n at an angle o with respect
to the fiber axis and strikes the core cladding interface at a
normal angle . If it strikes the interface at such an angle that it
is totally internally reflected, then the meridional ray allows a
zigzag path along the core, passing through the axis after each
reflection.
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From snells law, the minimum angle that supports total internal
reflection is given by sin Cmin = n2 / n1
At pt A, snells law is given as nsin0max = n1sinc ----(1) At pt
B, snells law is given as n1sinc = n2 sin 90
----(2) c = sin
-1(n2/n1) From (1 ) nsin0max = n1sin (90 c)
nsin0max = n1cos c 2
= n11 sin c = n1 1 n22/n12
= n1 n12 n22/n12 nsin0max = n1
2 n2
2 Numerical aperture is defined as
Thus those rays having entrance angles c< 0max are said to be
totally internally reflected at the core cladding interface. 1.6
Mode Theory of circular waveguides The different types of modes
are
Guided (Or) Bound Modes Refracted (Or) Cladding Modes Leaky
Modes
In optical fibers, the boundary condition at the core cladding
interface lead to a coupling between electric and magnetic field
component that results in hybrid modes designated as the HE or EH
modes.
NA = nsin 0 max = n 1 2 n 2
2
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Since n1 n2
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the cladding, some of this radiation gets trapped in the
cladding, thereby causing cladding modes to appear. In addition to
guided and refracted modes, third category of modes are called
leaky modes is present in fibers..These leaky modes are partially
confined to the core region, and attenuate by continuously
radiating their power out of the core as they propagate along the
fiber. This power radiation out of the waveguide results from a
quantum mechanical phenomenon known as the tunnel effect.
A mode remains guided as long as satisfies the condition n2k
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cylindrical coordinate system used for analyzing EM wave
propogation in an optical fiber.
For this fiber a cylindrical coordinate system(r, , z ) is
defined with the x axis lying along the axis of the waveguide
If the EM waves are to propagate along the z axis they will have
the functional dependence of the form
E = E0 ( r, ) ej(t-z) H = H0 ( r, ) ej(t-z)
where is the z component of the propagation constant k = 2/
These are harmonic in time t and coordinate z when these
equations are substituted in maxwells equations, the wave equations
in cylindrical coordinates is given as
2 Ez/ r2 + 1/r (Ez/ r) + 1/r
2 ( 2Ez/ 2)+ q2Ez = 0 (1)
|||ly 2 Hz/ r
2 + 1/r (Hz/ r) + 1/r2 (Hz/
2)+ q2Hz = 0 (2) where q2 = k2 2 where K free space propagation
constant.
o If the boundary conditions do not lead to coupling between the
field components, the modes are either TE or TM modes.
o If they are non zero ( Ez 0, Hz 0 ) that results in hybrid
modes, HE (or) EH modes.
1.8.1 WAVE EQUATION FOR SI FIBERS: The above results are used to
find the no of modes in SI fiber. The solution of (1) is of the
form
Ez = AF1(r) F2 ( ) F3 (z) F4 (t) (3) A -arbitrary constant The
time and the Z dependent factors are given by
F3 (z) F4 (t) = ej(t-z) (4) since the waves are
sinusoidal in time and propagates in the Z direction. Because of
circular symmetry of the waveguide, each field component must not
change when coordinate is increased by a factor of 2.
Assuming a periodic function of the form F2 () = e
jv (5)
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where v can be positive or negative ,it should be an integer
since the fields must be periodic with a period of 2 . sub (4)
& (5) in (3) Ez = A F1 ( r ).e jv . ej (t-z) (6) Sub eqn (6) in
(1) eqn (1 )becomes 2 F1/ r
2 + 1/r ( F1/ r) + (q2 v2 /r2 ) F1 = 0 (7)
This equation (7) is the differential equation for Bessel
functions.
The reason for assuming an infinitely thick cladding is that the
guided modes in the core have exponentially decaying fields outside
the core which must have insignificant values at the outer boundary
of the cladding.
The fields vary harmonically in the guiding region of refractive
index n and decay exponentially outside of this region.
Equation (6) must be solved for regions inside and outside the
core. Inside the core, the solutions must remain infinite as r 0.
whereas , the solutions must decay to 0 as r .Thus for r 0. This in
turn implies that K2 (since 2 = 2 K2
2 ) which represents the cutoff condition. A second condition of
can be deduced from the behavior of Jv(ur). Inside the core, the
parameter u should be real for F1 to be real from which it follows
that k1 ( since u
2 = K12 2 )
Therefore the permissible range of for bound solutions is
where K = 2/ 1.8.2 MODES IN SI FIBERS:
To describe the modes, the behavior of J type Bessel functions
Jv are examined and they are plotted for the first 3 orders. ( v =
0,1,2)
n 2 K = K 1 K 1 = n 1 K
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As these functions are oscillatory in nature there will be m
roots of modal equation for a given value of v. These roots are
designated as vm
The modal equation is given as ( Jv +Kv) ( K1
2Jv + K22Kv) = ( v/ a)
2 ( 1/u2 + 1/ w2) 2 (8) where Jv = Jv(ua) / uJv (ua) or
JV+1 ( ua) / u Jv (ua) ( 9) Kv = kv
,(wa) / w Kv(wa) or Kv+1 (wa) / wKv (wa) (10) The different
roots are designated as vm and the corresponding modes are
represented as TEVM, TMVM, HEVM or EHVM For the dielectric fiber
waveguide, all modes are hybrid modes expect for those for which v
= 0. If v = 0 then the R.H.S of (8) becomes 0 and therefore two
equations result which are
given as J0 + K0 = 0 (11) J1(ua ) / uJ0 (ua) + K1 (wa) / wK0
(wa) =0 (12)
which corresponds to TEOM mode K1
2J0 + K22K0 = 0 (13)
K12 J1 (ua ) / u (J0 wa) + K2
2 K1(wa) / wK0 (wa) =0 (14) which corresponds to TMOM mode
An important parameter connected with the cutoff condition is
the normalized frequency V given as V2 =( u2 +2 ) a2 V2 = ( k12 2 +
2 k22 ) a2 V2 = ( k1
2 k22 ) a2
V2 = ( (2a/)2n12 (2/)2 n2
2) a2 V2 = (2a/)2 (n1
2 n22)
V2 = (2a/)2 (NA)2
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The normalized propagation constant b = a2 2 / V2
substituting for and V, we get b= (/k)2 n2
2/ (n12-n2
2).
1.9 LINEARLY POLARISED MODES The exact analysis for the modes of
a fiber is very complex. However a simpler approximation can be
used based on this assumption. In SI fibers,
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Each LP1m mode comes from TEom , TMom , & HE2m modes. Each
LPvm mode (v 2) is from an HEv+1,m mode & on EHv-1,m mode.
Table represent the composition of lower order linearly polarized
modes
LP mode designation
Traditional mode designation and no of modes
No. of total degenerate modes
LP01 HE11 2
LP11 TE01, TM01, HE21 4
LP21 HE31, EH11 4
LP02 HE12 2
LP31 HE41, EH21 4
LP12 TE02, TM02, HE22 4
1.10 SINGLE MODE FIBERS: 1.10.1 MODE FIELD DIAMETER (MFD) For
single mode fibers, the geometric distribution of light in the
propagating mode( rather than core diameter and numerical aperture)
is important in predicting the performance characteristics of these
fibers.Thus a fundamental parameter of a single mode fiber called
Mode Field Diameter (MFD )is defined. This can be determined from
the mode field distribution of electric field of the fundamental
mode LP01 mode.The main consideration in measuring the MFD is
approximating the electric field distribution. let us assume that
the electric field distribution is Gaussian in nature given as E(
r) = Eo exp ( - r
2 / wo2)
Eo - electric field at zero radius r - radial distance wo -
width of the electric field distribution Figure shows the
distribution of light a SI fiber
, For Gaussian distribution MFD is given by 2 wo. Then MFD =
1/e2 of Eo (which is equivalent to the e
-2 radius of the optical power) 1.10.2 PROPOGATION MODES IN SM
FIBERS: In any ordinary single mode fiber there are actually two
independent, degenerate propagation modes.
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These modes are very similar but their propagation planes are
orthogonal. These are chosen as Horizontal (H) and vertical(V)
polarizations as shown in the fig. Either one of these two
polarization modes constitutes the fundamental HE11 mode .In
general, the electric field of the light propagating along the
fiber is a linear superposition of these polarization modes and
depends on the polarization of the light at the launching point
into the fiber. One of the mode have transverse electric field
polarized along the x direction and the other to be polarized in
the y direction. In the case of ideal fibers with perfect
rotational symmetry, the two modes are degenerate With equal
propagation constants(kx=ky), and any polarization state into the
fiber will propagate Unchanged. In actual fibers, there are
imperfections in practical fibers are such as
non circular cores asymmetrical lateral stresses variations in
refractive index profiles.
These imperfections break the circular symmetry of the ideal
fiber and lift the degeneracy of the two modes.so the two
degenerate modes propagate with different phase velocities.
Therefore the and the difference between the effective refractive
indices is called fiber birefringence.
Bf = l ny nx l Defining the birefringence = Ko ( ny nx) , Where
K0 = 2 / -free space propagation constant.
BEAT LENGTH: If light is injected into the fiber so that both
the modes are excited, then one will be delayed in phase relative
to the other as they propagate. When this phase difference is an
integral multiple of 2, the two modes will beat at this point and
the input polarization state will be reproduced. The length over
which the beating occurs is called fiber beat length given as Lp =
2 /
1.11 GRADED INDEX FIBER STRUCTURE: In this fiber design, the
core refractive index decreases continuously with increasing
radial
distance r from the centre of the fiber, but is generally
constant in the cladding. The most commonly used construction for
the refractive index variation in the core is given by
the power law relation
n(r) = { n1 [1 2 (r/a) ] for 0 r a
{ n1 [1 2 ] = n1 (1 ) for r > a
~ n2 where is the shape of the refractive index profile = 1 if
triangular profile = 2 if parabolic profile = for SI fiber for
graded index fiber, the relative refractive index difference =
(n1
2 n22 ) / n1
2 ~ n12 n2
2 / n1 For = n(r) = n1 that corresponds to a step index fiber
The NA for GI fiber is a function of radial distance r given as NA(
r) = { [ n2 (r) n2
2 ]1/2 ~ NA (0) 1 ( r/a) for r a 0 r > a
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Where NA( 0) is the axial NA. o The number of bound modes in GI
fiber is given by the expression o M = /+2 a2k2n12 1 o For