Photonics and Optical Communication, Spring 2007, Dr. D. Knipp
Photonics and Optical Communication
(Course Number 300352)
Spring 2007
Optical Fibers
Dr. Dietmar Knipp
Assistant Professor of Electrical Engineering
http://www.faculty.iu-bremen.de/dknipp/
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Photonics and Optical Communication, Spring 2007, Dr. D. Knipp
Photonics and Optical Communication
4 Optical Fiber
4.1 Light propagation in optical fibers
4.2 Optical Attenuation
4.3 Dispersion
4.3.1 Material dispersion (Chromatic dispersion)
4.3.2 Modal dispersion
4.3.3 Waveguide dispersion
4.4 Designing optical communication systems
4.5 Characteristic of a glass fibers
4.5.1 Absorption properties of glass fibers
4.5.2 Scattering
4.5.3 Multi-mode and Single-mode fibers
4.6 Fiber transmission windows
4.6.1 Short Wavelength Band (First Window)
4.6.2 Medium Wavelength Band (Second Window)
4.6.3 Long Wavelength Band (Third Window)
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Photonics and Optical Communication
4 Optical Fiber
4.7 Types of fibers
4.7.1 Propagation of light in a Multimode Step-Index Fiber
4.7.2 Propagation of light in a Graded-Index Multi-mode Fiber
4.7.3 Bending of multi mode fibers
4.7.4 Propagation of light in a Single Mode Fiber
4.7.5 Bending losses in Single-Mode Fibers
4.8 Dispersion
4.8.1 Modal Dispersion
4.8.2 Modal Dispersion
4.8.3 Material Dispersion
4.8.4 Dispersion in Single-Mode Fibers
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4.1 Light propagation in optical fibers
In this chapter we will discuss the optical fibers and the most important properties
of optical fibers. Most important requirements for the application of optical fibers in
optical communication networks:
• Low attenuation of the optical fiber
• Low dispersion
• Mechanical flexibility of the optical fiber
The properties of the transmission channel (fiber) has a direct impact of the overall
performance of the optical communication network. Attenuation and dispersion are
the major physical obstacles that limit the performance of silica fibers.
4.2 Optical Attenuation
The glass itself is transparent for the wavelength region we are interested in.
However, glass contains impurities, which lead to the absorption of light.
Furthermore, non-uniformities in the manufacturing process and mechanical stress
lead to scattering of the light inside of the fiber which limits the performance. Both
the absorption of light by impurities and the scattering of light is wavelength
dependent which complicates compensation and correction of these effects.
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4.2 Attenuation
The optical power that propagates through an optical fiber decreases
exponentially with the distance as a result of absorption and scattering. Therefore,
we can define an attenuation coefficient,
 P0
1
1 1
α = 10 log  = 10 log
L
 ℑ L
 PT



Attenuation coefficient
Where L is the length of the fiber in km and ℑ
is the power transmission ratio. The power
transmission ratio is defined as the ratio of the
transmitted versus the incident optical power.
Don’t forget that losses in dB are added,
whereas losses in terms of transmission ratios
are multiplied.
Relationship between the power transmission ratio and the attenuation
coefficient. Ref: Saleh and Teich, Fundamentals of Photonics
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4.3 Dispersion
Dispersion properties are even more important than the attenuation of a fiber.
Dispersion occurs when optical pulse spread out while they are transmitted. As
a consequence the pulses cannot be distinguished anymore at the end of the
fiber.
The
effect
of
dispersion on the
propagation of optical
pulses in an optical
fiber.
Ref: Harry J.R Dutton,
Understanding optical
communications
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4.3 Dispersion
In following we will discuss the three most important sources of dispersion:
4.3.1 Material dispersion (Chromatic dispersion)
A range of wavelengths (optical spectrum) is typically transmitted through an
optical fiber. As a consequence of the wavelength depend refractive index of
the fiber the light will travel at different speed in the fiber, which lead to a
spreading o the optical pulses. (Remember: In the case of normal dispersion:
“The red cars are faster.”)
Even in the case of a laser which has a very narrow spectral width a spreading
of the optical pulses is observed while traveling through a fiber. The problem
gets obviously more severe if an LED or another light source is used, which
emits a broader optical spectrum.
In DWDM (Dense-Wavelength-Division-Multiplex) communication systems the
chromatic dispersion is therefore an inherent problem as different wavelength
are used to transmit different channel. As a consequence dispersion
management is absolutely essential for DWDM networks. Dispersion
management will be covered later.
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4.3.2 Modal dispersion
Modal dispersion is related to the difference in propagation speed caused by
the propagation of different modes. This is of course only a problem for multimode fibers. The explanation is relatively simple. We already discussed - as
part of the lecture on waveguides - that different modes can propagate in
waveguides. Each mode is associated with a specific propagation angle and a
specific effective refractive index. With increasing mode number the effective
refractive index and the propagation angle are reduced.
Again, this effect is inherent to the propagation of modes in a multi-mode fiber.
Even though the difference in refractive index is very small between the core
and the cladding of the fiber (therefore the difference in effective refractive
index and the difference in the propagation angle is small) the effect cannot be
avoided.
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4.3.3 Waveguide dispersion
Waveguide dispersion is due to the waveguide structure itself meaning the
effect depends on the design of the fiber, the refractive index of the core and
the cladding and the wavelength of the transmitted light. Depending on the
design of the fiber and the mode propagating in the fiber a fraction of the light is
propagated in the cladding of the fiber. This effect is due to the fact that the
electric and the magnetic field a the interface of the core and the cladding has
to be continuous so that the field extends into the cladding. In the case of a
single mode fiber for example 20% of the light is transmitted in the cladding. As
a consequence of the field distribution in the fiber (different refractive indices in
the core and the cladding) the light propagates at different speed in the core
and the cladding. Such kind of pulse spreading is called waveguide dispersion.
Again, this effect is inherent to a waveguide structure, but the effect can be
controlled by the shape and the profile of refractive index inside of the fiber.
Interestingly, the waveguide dispersion can be used to counteract the material
dispersion. Such fibers are called compensated fibers.
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4.4 Designing optical communication systems
In general the design of an optical communication system is very complex,
however, three major obstacles exist which limit the performance of optical
communications. We only speak about DWDM (Dense Wavelength Division
Multiplex) system here, which are the standard communication systems
nowadays.
• Problems related to the signal level. The signal level is affected by the
transmitter power, the transmission system and the sensitivity of the
receiver.
• Control of dispersion
• Control of noise
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4.4 Designing an optical communication system
At the moment we are dealing mainly with the first problem. The issue of
controlling the dispersion (dispersion management) and the influence of noise
on the overall performance of the system will be discussed later on.
The performance of the transmission system is mainly affected by the following
parameters:
• The design of the actual fiber (e.g. thicknesses/diameters of the core and the
cladding and the refractive index.
• Wavelength of light
• Characteristics of the light source (transmitter)
• Characteristics of the light detector (receiver)
• Influence of the modulation scheme on the performance
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4.5 Characteristic of a glass fibers
Glass/silica fibers have the lowest available optical attenuation. Plastic fibers
and other fibers with higher attenuation are only of interest for short range
optical communication systems.
In general pure fused silica is used to fabricate glass fibers. Pure fused silica
consist only of silicon oxide (SiO2). There should be no other materials
imbedded in the silica. The silica should be as pure as possible.
Pure fused silica glass is quit different from ordinary window glass. Window
glass contains sodium carbonate, calcium carbonate and silicon dioxide.
Therefore, ordinary window glass is a mixture (alloy) of different elements.
In terms of structural properties try to imagine glass as an disordered material.
The material is melted and cooled afterwards to define its shape. The cooling
process is carried out very fast, so that the SiO2 molecules have no chance to
organize or rearrange themselves in a more ordered fashion. This is completely
different from the silicon oxide used in electronics.
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4.5 Characteristic of a glass fibers
In order to change the refractive index of glass we can add certain materials
(dopants) to the melt. This process can be controlled very well. This process
however requires a lot of knowledge. For example we are not only interested in
very pure materials for the core and the cladding with certain optical properties.
Mechanical aspects have to be considered as well like the thermal expansion
coefficient of the different materials.
The refractive index of the fused glass can be either increased or decreased.
Adding germanium oxide (GeO2) (4% to 10%) will increase the refractive index,
whereas adding boron trioxide (B2O3) will decrease the refractive index.
In general adding of impurities (dopants) will lead to an increase of the
attenuation.
Remark: As we are already adding a relatively large fraction of impurities to the
material it is somewhat appropriate to use the term alloy rather than doping.
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4.5 Characteristic of a glass fibers
A lot of research and development leads to the reduction of the attenuation of
glass fibers. During the 70’s the attenuation was still 20 dB/km. By 1980 the
performance was already improved by a factor of 20 down to 1 dB/km. During
the 90’s attenuation was again reduced down to 0.2 dB/km.
The attenuation of the a glass fiber is strongly wavelength dependent.
Attenuation coefficient of a
silica fiber as a function of
the wavelength. A local and
an absolute minima can be
observed at 1.31 µm and
1.55 µm.
Ref: Saleh and Teich,
Fundamentals of Photonics
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4.5 Characteristic of a glass fibers
In general the attenuation coefficient is limited by scattering and absorption.
4.5.1 Absorption properties of glass fibers
Two strong absorption bands are observed for glass fibers. The first absorption
band is an infrared absorption band caused by vibration transitions. The
second absorption band (ultraviolet absorption) is caused by electronic and
molecular transitions. Furthermore, two peaks of attenuation are measured
around 1250nm and 1400nm which are caused by OH-absorption. The OHabsorption is caused by water. These peaks were already significantly be
reduced throughout the last decades. The OH-absorption is considered to be
an extrinsic effect, whereas the other effects (absorption due to bands and
scattering) are intrinsic effects of the fused glass.
In general, the attenuation of fibers is not limited by impurities anymore. The
level of impurities is nowadays extremely low. Impurities do not have an
influence on the attenuation anymore. The level of impurities is nowadays
below a level of ppb (parts per billion).
In general the attenuation coefficient is limited by scattering and absorption.
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4.5.2 Scattering
Even more important than absorption is scattering (Rayleigh Scattering) of light
in a glass fiber. In our case we have to deal with Rayleigh scattering which is
intrinsic to glass. We already discussed that fused glass can be considered to
be an amorphous (randomly oriented) material. As a consequence of the
random variations in the positions of the molecules light is scattered. We speak
about scattering centers that are “tiny” (1/10th of the wavelength). The
scattering intensity scales with the inverse 4th power of the wavelength (∼1/λ4).
It simply means that shorter wavelengths (blue light) are scattered more than
longer wavelengths (red or infrared light). Rayleigh scattering is not minimized
for 1.55µm. The attenuation of a glass fiber is limited by two effect the Rayleigh
scattering and the infrared absorption of fused glass.
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4.5.3 Multi-mode and Single-mode fibers
The behavior of single and multi-mode fibers is very similar in terms of the
attenuation. Both types of fibers exhibit a similar shape of the attenuation
curve. In general, the attenuation of multi-mode fibers is higher. With increasing
mode number more and more light is guided in the cladding. However, the
cladding has to be doped or alloyed to achieve total internal refection.
Therefore, the attenuation of multi-mode fibers is slightly higher.
Attenuation coefficient of a
single and multi-mode fiber.
Ref: Saleh and Teich,
Fundamentals of Photonics
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4.6 Fiber transmission windows
We already discussed that we can
distinguish three transmission “windows”
for optical communication. All three
bands are shown in the graph.
Historically optical fiber communication
started by using the short wave band.
Over time (it took 2-3 decades) the
transmission window shifted to higher
wavelengths. It is important to think in
terms of the entire transmission system.
The fact that the attenuation of a fiber is
lower at 1.55µm does not mean it can be
exploited. At the same time reliable and
cost efficient light sources and detectors
have to be available. The development
of the fibers and the development of the
sources and receivers went hand in
hand.
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Transmission window of glass fibers.
The upper curve shows the
characteristic of a fiber during the
70’s.
Ref: H. Dutton, Understanding
optical communications
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4.6.1 Short Wavelength Band (First Window)
The first window covers the wavelength range from 800nm to 900nm. It was the
first band used in optical communication networks. It is not only true that the
fibers had a minimum of attenuation in this wavelength range. The first solid
state lasers based on AlGaAs were develop for operation at 860nm to 870nm.
The same is of course true for the receivers, but it is in general much easier to
develop receivers. Light receivers at 800nm-900nm were already around for
15-20 years. The combination of both technologies made the first generation of
optical network possible at the end of 1970s and early 1980s.
4.6.2 Medium Wavelength Band (Second Window)
Until the end of the 90’s of the last century long distance optical networks were
operated in the range of 1310nm. This band is called the medium wave band.
The medium wave range is still very attractive, because the dispersion of
optical fibers is the lowest for the three optical communication bands. In terms
of light sources and light detectors the medium wave range is less attractive.
The technological effort to develop lasers and detectors at these wavelengths
is significant.
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4.6.3 Long Wavelength Band (Third Window)
Nowadays the long wavelength window is the standard optical communication
band in particular for long distance transmission systems. We find the lowest
attenuation at about 0.26 dB/km. The realization of light source and detectors
at 1550nm to 1600nm is even more difficult than the realization at 1310nm, but
the invention of the fiber based optical amplifier, which allows the amplification
of optical signals without transforming it into an electrical signal, amplifying it
and transmitting it back into an optical signal leads to the development of the
4th generation of optical networks.
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4.7 Types of fibers
We might classify fibers in single and
multi-mode fibers. Furthermore, we can
classify fibers in terms of the refractive
index profile (e.g. step index or gradedindex profile). The most important
types of fibers are:
• Multimode Step-Index Fibers
• Multimode Graded-Index Fibers
• Single-Mode (Step-Index) Fibers
So far we used only the multi-mode
step-index fiber to derive the mode
equations and to discuss the
propagation of light in the fiber. Now
we will discuss the advantages and
disadvantages of the different types of
fibers.
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Cross section and side view of optical
fibers, (a) multi mode step index fiber,
(b) single mode step index fiber,
(c) multi mode graded-index fiber.
Ref: Saleh and Teich,
Fundamentals of Photonics
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4.7.1 Propagation of light in a Multimode Step-Index Fiber
We already discussed that only certain modes can propagate in an optical fiber.
We discussed how to derived these modes. For a fiber with a core diameter of
62.5µm using a wavelength of 1310 nm, the number of modes is around 400
depending on the difference in refractive index between the core and the
cladding. The difference in mode will lead to a difference in the phase velocity
which will cause modal dispersion.
Cross section and side view of a
multi mode step index fiber.
Ref: Saleh and Teich,
Fundamentals of Photonics
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4.7.1 Propagation of light in a Multimode Step-Index Fiber
We already used the mode chart to extract information regarding the
propagation of modes. The mode chart can be generalized by introducing an
normalized frequency, where a is the core radius, λ is the wavelength in free
space.
V =
2πa
λ
n12 − n22
Normalized frequency
Mode chart for step-index fiber.
Ref: Joseph C. Palais, Fiber
optic communication
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4.7.1 Propagation of light in a Multimode Step-Index Fiber
The typical diameter of a multi-mode fiber is nowadays
in the order of 50 µm - 62.5 µm. The overall diameter
of the fiber including the cladding (without other
coatings) is typically 125 µm. The core is alloyed with
4% of germanium oxide (GeO2), which leads to an
increase of the refractive index. As we already
discussed the cladding is usually pure silica which
leads to the lowest available attenuation.
In order to compare different communication systems
in terms of their performance we use the bandwidthdistance product. The bandwidth-distance product of a
step-index multimode fiber varies between 15 MHz⋅km
and 50 MHz⋅km depending on the wavelength in use,
the core diameter and the refractive index contrast
between core and cladding.
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Cross section of a
Multi mode step
index fiber.
Ref: Dutton,
Understanding
optical
communications
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4.7.2 Propagation of light in a Graded-Index Multi-mode Fiber
One way to overcome (modal) dispersion in multimode fiber is a modified
refractive index profile of the fiber. The modal dispersion is caused by the total
internal reflection. A gradual chance of the refractive index from the core to the
cladding can significantly improve the situation. The light is still traveling on
different paths, but the faster traveling light is traveling the longer distance so
that these effects compensate each other to a certain extend. Graded-index
fibers allow the implementation of long distance optical communication links by
using multi-mode fibers. Please consider that not the refractive index of the
entire fiber is graded. Only the refractive index of the core is graded.
Cross section and side view of a
graded-index fiber.
Ref: Saleh and Teich,
Fundamentals of Photonics
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4.7.2 Propagation of light in a Graded-Index Multi-mode Fiber
The dimensions of a graded index fiber are
comparable with a multi-mode step-index fibers.
However, the refractive index of the core is graded.
The fiber is realized by a gradual change of the
doping level across the diameter of the fiber. It is
obviously clear that the manufacturing of gradedindex fibers is more difficult and therefore
significantly more expensive.
The bandwidth-distance product approaches
1000MHz⋅km at 1310 nm, which is 10-50 times
higher than the bandwidth-distance product for a
step-index fiber (again at 1300 nm).
Cross section of a
Multimode graded
index fiber.
Ref: Dutton,
Understanding optical
communications
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4.7.3 Bending of multi mode fibers
In general bending of a fiber will not influence the wave guiding properties of a
fiber. The light will still be guided without a loss. However, this is only true if the
bending radius is relatively large. With decreasing bending radius (< 1cm) some
light will be lost. If a multi-mode fiber is bended too sharp, the light couples into
the cladding of the fiber which is then lost. How can light couple out of the core?
In the case of a bend the propagation might get smaller than the critical angle so
that the light is not totally reflected anymore.
In general, the loss of light due to bending is a more significant problem for
multi-mode fibers.
Propagation of light around a bend in a
multi mode fiber.
Ref: Harry J.R Dutton, Understanding
optical communications
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4.7.4 Propagation of light in a Single Mode Fiber
The modal dispersion of multi-mode fibers can be overcome by three way: The
dimensions of the core can be reduced so that only a single mode can propagate
in the fiber. As a consequence we get an single mode or a mono-mode fiber. As
an alternative the difference in refractive index between the cladding and the core
can be reduced. The critical angle is getting closer to 90°, so that the wave starts
to propagate in a straight line. As a third alternative the wavelength can be
increased. At a certain point only a single mode can propagate in the fiber. All
three options can be derived from the mode chart. The second and the third
options are not really alternatives to the first suggestion. It is not feasible to
minimize the refractive index between the core and the cladding until the
difference is almost zero. Furthermore, the wavelength can simply not be
adjusted, because optical sources are required to provide the necessary optical
power.
Cross section and side view of a
single mode fiber.
Ref: Saleh and Teich,
Fundamentals of Photonics
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4.7.4 Propagation of light in a Single Mode Fiber
The propagation of a wave in a single mode fiber is visualized on this slide. The
diameter of the core is small in comparison to the wavelength of the incident
light.
However, the realization of a single mode fibers is not as simple, because a
significant proportion (up to 20%) of the light propagates actually in the cladding
of the fiber. The extension of the fields can only be understood by the
electromagnetic theory, where the electric and the magnetic field at the interface
between the core and the cladding has to be continuous.
Single Mode Propagation in a
single mode fiber.
Ref: H. Dutton, Understanding
optical communications
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4.7.4 Propagation of light in a Single Mode Fiber
Therefore, the “real” core is wider than the fiber core. The region in which the
wave propagates is called the “mode field” and the mode field diameter is
quoted instead of the core diameter. The field decays exponentially in the
cladding of the fiber. Such kind of an exponentially decaying field is called
“evanescent field”.
Mode Field Distribution in a single
mode fiber. The mode field is defined
as the diameter between points
where the electric field decays down
to E0/e (37% of the electric field).
Ref: H. Dutton, Understanding
optical communications
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4.7.4 Propagation of light in a Single Mode Fiber
The mode field varies in diameter depending on the relative refractive indices of
core and cladding. Reducing the diameter of the core further and further is
therefore not an option to improve the performance of the transmission system
and reduce the dispersion.
Refractive index Profile of single mode fibers
The core diameter of a single-mode fiber is only 4µm -10µm depending on the
difference in refractive index and the wavelength. However, the mode-field
diameter is more important than the core diameter due to the extension of the
field in the cladding (evanescent field).
Bandwidth-distance product is not a relevant concept for single-mode fibers
because there is no modal dispersions (although there is chromatic dispersion).
The refractive index of fibers is controlled like the refractive index of multi-mode
fibers by alloying materials to increase or decrease the refractive index of the
fiber.
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4.7.5 Bending losses in Single-Mode Fibers
With decreasing diameter of the single mode fiber (typically 4-9µm) the critical
bending radius gets larger. The behavior of single mode and multi-mode fibers
is different. In general, multi-mode fibers are more sensitive to effects caused by
bending. That does not mean that the critical bending radius for single mode
fibers is smaller. It simply means that both kinds of fibers have a critical bending
radius. The critical bending radius for a single mode fibers is larger. However, if
the fiber is bended beyond the critical bending radius the effect on the multi
mode fiber is stronger, because light couples into the cladding of the fiber which
is associated with a loss of the light.
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4.7.5 Bending losses in Single-Mode Fibers
In the case of a single mode fiber the light simply propagates in a straight line.
The bending of the fiber leads to a distortion of the wave front, because the light
at the outer radius has to propagate a longer distance than the light at the inner
radius of the fiber.
Propagation of light around a bend in a
single mode fiber.
Ref: H. Dutton, Understanding optical
communications
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4.8 Dispersion
When a short light pulse travels through a fiber its power is „dispersed“ in time
so that the pulse spreads out over time. Three (four) different kind of dispersions
are known: Modal dispersion, Material dispersion, Wave guide dispersion,
(Nonlinear dispersion).
4.8.1 Modal Dispersion
A single pulse of light enters a multi-mode fiber (m-modes) and the pulse
spreads out in m-pulses with different delay times .
σq:
Width of the spreading pulse
τq:
Time delay
στ :
Overall pulse width or Pulse spreading
Pulse spreading caused by
modal dispersion.
Ref: Saleh and Teich,
Fundamentals of Photonics
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4.8.1 Modal Dispersion
Modal dispersion in multi-mode fibers is related to the difference in propagation
speed caused by the propagation of different modes.
In a step-index multi-mode fiber the number of modes is very high, so that the
following equation can be derived for the response time.
L n −n
στ ≈ ⋅ 1 2
c
2
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Pulse spreading over a time internal for a step
index multi mode fiber
(Response time for a step index multi mode fiber)
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4.8.2 Modal Dispersion
Modal dispersion in multi-mode fibers is related to the difference in propagation
speed caused by the propagation of different modes.
Modal dispersion is much smaller for graded-index multi mode fibers. It can be
shown that the response time results to
L (n − n )
στ ≈ ⋅ 1 2
4
c
2
Pulse spreading over a time internal for a graded
index multi mode fiber
(Response time for a graded index multi mode
fiber)
Therefore the response time for a graded index fiber is reduced
by
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(n1 − n2 ) 2 << 1.
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4.8.3 Material Dispersion (Chromatic dispersion)
We know that glass is a dispersive media due to the wavelength dependent
refractive index. Since a pulse in a wave package is composed of a spectrum of
components of different wavelengths each wavelength travels at a different
speed. The spreading of the pulse can be calculated by,
σ τ = Dλ ⋅ σ λ L
Pulse spreading due to material dispersion
(Response time due to material dispersion)
where σλ is the spectral width of the optical pulse and Dλ is the dispersion
coefficient.
Dispersion coefficient of silica glass.
Ref: Saleh and Teich, Fundamentals of
Photonics
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4.8.4 Dispersion in Single-Mode Fibers
Since modal dispersion cannot occur in single mode fibers the dominate source
of dispersion is material (chromatic) dispersion and waveguide dispersion.
It is possible to utilize the fact that these two forms of dispersion have opposite
signs, so that these effects can counteract one another. Interestingly, the two
forms of dispersion cancel one another at a wavelength of 1310 nm. Therefore,
the medium wavelength band is very attractive for DWDM network applications.
The overall dispersion of a single mode fiber is shown in the graph.
Dispersion of a single mode fiber.
Ref: H. Dutton, Understanding
optical communications
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4.8.4 Dispersion in Single-Mode Fibers
As a consequence of the fact that chromatic and the waveguide dispersion have
a different sign each single-mode fiber has a dispersion zero (null) point where
these two dispersions cancel one another out. This point is usually observed
around 1300nm, which makes the medium wave range very attractive for optical
communication systems, because the local minimum of the attenuation can be
combine with the zero or almost zero dispersion properties. Nevertheless,
current DWDM systems operate at 1550nm, because the fiber attenuation is
lower (absolute minimum of the attenuation), Erbium doped fiber amplifiers
(EDFA) are getting more and more cost efficient and the available bandwidth for
the longer wavelength region is higher.
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4.8.4 Dispersion in Single-Mode Fibers
Alternatively the refractive index profile of a fiber can be modified, so that the
zero-dispersion point is shifted towards higher wavelengths or the fiber exhibits
two zero-dispersion points (dispersion flattened fiber).
However, the manufacturing of such fiber is expensive.
Total, chromatic, and waveguide dispersion for a dispersion shifted single
mode fiber.
Ref: H. Dutton, Understanding optical communications
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Photonics and Optical Communication, Spring 2007, Dr. D. Knipp
References:
Stamatios V. Kartalopoulos, DWDM, Networks, Devices and Technology,
IEEE press and Wiley Interscience, 2003.
Eugene Hecht, Optics, Addison Wesly, 4th edition, 2002
John M. Senior, Optical Fiber Communications, Prentice Hall Series in
Optoelectonics, 2nd edition, 1992.
Bahaa E.A. Saleh, Malvin Carl Teich, Fundamentals of Photonics,
Wiley-Interscience (1991)
Harry J. R. Dutton, Understanding Optical Communications,
Prentice Hall Series in Networking, 1998. (Formerly freely available as a red
book on the IBM red book server.
Joseph C. Palais, Fiber Optic Communications,
Prentice Hall Series, 1998. 4th edition.
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