optical fiber + noise

1. COMPONENTS OF
OPTICAL
COMMUNICATION
SYSTEMS-FIBRE-I

3. Optical Fibre
Optical fibers are used as the most popular transmission
medium in optical communication systems
Optical fibers exploit the principle of Total Internal Reflection
(TIR), where light entering the fiber at a certain angle remains
confined to the core due to reflections from the boundary of the
core
The reason for the reflection of light at the boundary of the core
is the significant change in the refractive index at the core
boundary

4. Optical Fibre
An optical fiber is made of silicon and it is cylindrical in shape,
consisting of two sections, the inner core and the outer cladding
The refractive index of the cladding is made significantly lower
than that of the core
Since a change in refractive index results in the reflection of
light, the light entered at a certain angle into the fiber remains
confined to the core
We will discuss the most common type of fiber used in optical
communications, namely the SMF

5. Single Mode Fibre
It is referred to as being single mode, since it allows only one
mode of light to pass through it, due to its small core radius
If the core radius is on the order of the wavelength of light
used, then only a single mode of light travels through it
following an almost a straight path without reflections
The refractive index profile for a SMF generally obeys a step-
index profile, since the refractive index of the core is a step
higher than that of the cladding, i.e. there is no gradual
transition between them

6. Single Mode Fibre

7. Single Mode Fibre

8. Single Mode Fibre
The core diameter of a typical SMF is 8 - 10 μm and its
cladding diameter is 125 μm
Since the core radius of SMF is comparable to the wavelength
of light used in optical communications, the TIR is no longer
responsible for the confinement of light to the SMF
Instead, it is the step-change in the refractive index of the SMF
that helps in confining the light to the fiber

9. Single Mode Fibre
In a transmission medium having a homogeneous refractive
index, light spreads due the phenomenon of diffraction
Therefore, the width of a beam of light traveling through a
homogeneous medium will increase, but fortunately the beam-
width may be controlled by carefully designing the refractive
index profile of the medium
If the refractive index of the medium near the center of the
beam is kept high compared to the periphery, then the light at
the center travels slower than at the periphery

10. Single Mode Fibre
The reduced speed of light at the center compared to that at
the periphery enables the medium to keep the light focused, by
preventing it from spreading out
The refractive index profile of the SMF shown in the Figure was
designed to keep the light focused, so that it travels along the
core for long distances

11. Impairments Induced by Fibre
Like any other transmission medium, optical fiber also imposes
impairments on the signal that is transmitted through it
The major impairments include:
a) Attenuation
b) Dispersion and
c) Nonlinear Effects

12. Attenuation of Fibre
The fiber attenuates any signal that passes through it
There are two main reasons for fiber attenuation, namely
material absorption and Rayleigh scattering
Material absorption can be further divided into two categories:
1. Intrinsic absorption and
2. Extrinsic absorption
Intrinsic absorption is due to the silica itself, which is used to
make the fiber, while extrinsic absorption is due to impurities in
silica.

13. Attenuation of Fibre
Material absorption exists due to the electronic or vibrational
resonances within the fiber material
The attenuation due to intrinsic absorption in silica occurs due
to electronic resonance occurring for wavelengths in the
ultraviolet region, while due to vibrational resonance for
wavelengths in the infrared region
The major impurity causing extrinsic absorption is the presence
of water vapors in silica
These vapors cause attenuation peaks near the 2.73 μm
wavelength region due to vibrational resonance of Oxygen and
hydrogen (OH) ions

14. Attenuation of Fibre

15. Attenuation of Fibre
The dependence of material absorption on the wavelength of
light can be observed from Figure shown, which shows the
amount of attenuation in dB/km versus the wavelength for
different sources of material absorption
It can be observed from the Figure that the intrinsic absorption
occurs only in the ultraviolet as well as infrared region and it
remains small in magnitude

16. Attenuation of Fibre – Rayleigh Scattering
The second major source of attenuation in optical fibers is
Rayleigh scattering, which is caused due to minor refractive
index variations within the fiber core
These refractive index inhomogeneties are due to variations in
the silica density within the core, which are caused by imperfect
manufacturing of the fiber
A small part of the light traveling through the fiber is reflected
every time a change in refractive index is encountered

17. Attenuation of Fibre – Rayleigh Scattering
Since the reflected light is not received at the other end,
Rayleigh scattering is a major cause of optical signal
attenuation
It can be observed from Figure that the attenuation caused by
Rayleigh scattering is considerably higher than that of material
absorption
The Rayleigh scattering induced attenuation increases in
inverse proportionately with the fourth power of the wavelength
Therefore, as observed from Figure, the attenuation due to
Rayleigh scattering is lower at higher wavelengths

18. Attenuation of Fibre
Figure also shows the total attenuation due to the combined
effect of all the sources of absorptions
The overall attenuation 𝛼 of the fiber may be written
mathematically as:
Here Pin and Pout are the input and output optical powers of a
fiber of length L

19. Attenuation of Fibre
The peaks observed in the experimental plots are due to the
extrinsic absorption caused by water vapors in silica
In order to keep the signal attenuation to a low value, the
wavelengths of light chosen in optical communications are in
the 1.3 μm and 1.5 μm bands
As observed in the Figure, the overall attenuation of the fiber is
as low as 0.2 dB/km in these regions

20. Fibre Dispersion
Fiber dispersion is a phenomenon where light of different
wavelengths travels at different speeds within the fiber
The reason for dispersion is the wavelength-dependence of the
refractive index of silica used for manufacturing the optical fiber
An optical signal, be it CW or pulsed, is always composed of a
finite range of wavelengths
Hence due to refractive index variations, each wavelength
travels at a different speed along the length of fiber

21. Fibre Dispersion
This phenomenon where different spectral components of the
pulse travel at slightly different group velocities is referred to as
group-velocity dispersion (GVD)
Its also called intramodal dispersion or simply fibre dispersion
Intramodal dispersion has two contributions:
1. Material dispersion and
2. Waveguide dispersion.

22. Group Velocity Dispersion
Consider a single-mode fiber of length L
A specific spectral component at the frequency ω would arrive
at the output end of the fiber after a time delay T = L/vg, where
vg is the group velocity, given as:
Here 𝛽 is the propagation constant given as:

23. Group Velocity Dispersion
From the previous equations, we get:
Where 𝑛𝑔 is the group index given by:
If Δω is the spectral width of the pulse, the extent of pulse
broadening for a fiber of length L is governed by:

24. Group Velocity Dispersion
The parameter β2 = d2β /dω2 is known as the GVD parameter
It determines how much an optical pulse would broaden on
propagation inside the fiber
Generally, the frequency spread Δω is determined by the range
of wavelengths Δλ emitted by the optical source
It is customary to use Δλ in place of Δω
We will use, ω = 2πc/λ and Δω = (−2πc/λ2)Δλ

25. Group Velocity Dispersion
Therefore, in terms of 𝜆, the pulse broadening may be written
as:
Where:
D is called the dispersion parameter and is and is expressed in
units of ps/(km-nm)

26. Material Dispersion
Material dispersion DM occurs because the refractive index of
silica, the material used for fiber fabrication, changes with the
optical frequency ω

27. Material Dispersion
Material dispersion DM is related to the slope of ng by the
relation:
It turns out that dng/dλ = 0 at λ = 1.276 μm
This wavelength is referred to as the zero-dispersion
wavelength λZD, since DM = 0 at λ = λZD
The dispersion parameter DM is negative below λZD and
becomes positive above that

28. Waveguide Dispersion
It should be stressed that λZD = 1.276 μm only for pure silica
It can vary in the range 1.27–1.29 μm for optical fibers whose
core and cladding are doped to vary the refractive index
The zero-dispersion wavelength of optical fibers also depends
on the core radius a and the index step Δ through the
waveguide contribution to the total dispersion
Main effect of waveguide dispersion is to shift λZD by an amount
30–40 nm so that the total dispersion is zero near 1.31 μm

29. Material, Waveguide and Total Dispersion
Figure below shows material, waveguide and total dispersion
for a conventional SMF

30. Waveguide Dispersion
Waveguide dispersion also reduces D from its material value
DM in the wavelength range 1.3–1.6 μm that is of interest for
optical communication systems
Typical values of D are in the range 15–18 ps/(km-nm) near
1.55 μm
This wavelength region is of considerable interest for lightwave
systems, the fiber loss is minimum near 1.55 μm
High values of D limit the performance of 1.55-μm lightwave
systems

31. Fibre Dispersion
Figure shows the variation of dispersion with wavelength of the
optical signal
It can be observed from the figure that dispersion is negative
for wavelengths below 1310 nm and becomes positive for
wavelengths higher than 1310 nm
However, the slope of the dispersion versus wavelength plot,
which is also called the dispersion slope, remains positive over
the complete range of wavelengths

32. Fibre Dispersion
The wavelength of 1310 nm, where the dispersion changes
sign is generally termed as the zero-dispersion wavelength
Dispersion is the derivative of group refractive index of silica
with respect to wavelength
The sign change indicates that the group index decreases with
an increase in wavelength until 1310 nm
And increases for wavelengths beyond 1310 nm

33. Fibre Dispersion
The effect of dispersion is different for CW and pulsed
communication systems
The CW signals have a narrow bandwidth, therefore the
wavelengths at the edges of the spectral width have a small
difference between them
Due to this small difference in the wavelengths, their speed in
the optical fiber is almost similar, hence avoiding the
broadening of the signal in the time domain

34. Fibre Dispersion
Optical pulses have a narrow but finite pulse width which
results in a broad spectrum
The effect of a fixed kilometric fiber dispersion is more
pronounced on narrower pulses having a wide spectrum
Due to the presence of a wide range of frequencies, the
frequency component at one end of a broad spectrum travels at
a different speed compared to the frequency component at the
other end
This broadens the pulses in the time domain, which might
hence overlap with the adjacent pulses

35. Fibre Dispersion

36. Fibre Dispersion
As observed in the Figure, after the signal was transmitted over
a dispersive fiber, each pulse broadens in the time domain
The tails of two adjacent pulses might overlap, thus potentially
imposing detection errors
Since high-bit rate Optical TDM systems require short pulse-
widths, they suffer from the effects of dispersion
Increasing the fiber length further degrades the signal due to
high overall dispersion