Photonics and Optical Communication - Jacobs … Optical... · Optical Fibers 3 Photonics and...

Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

1Optical Fibers

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

4 Optical Fiber4.1 Light propagation in optical fibers4.2 Optical Attenuation4.3 Dispersion

4.3.1 Material dispersion (Chromatic dispersion)4.3.2 Modal dispersion4.3.3 Waveguide dispersion

4.4 Designing optical communication systems4.5 Characteristic of a glass fibers

4.5.1 Absorption properties of glass fibers4.5.2 Scattering4.5.3 Multi-mode and Single-mode fibers

4.6 Fiber transmission windows4.6.1 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 Fiber4.7 Types of fibers

4.7.1 Propagation of light in a Multimode Step-Index Fiber4.7.2 Propagation of light in a Graded-Index Multi-mode Fiber4.7.3 Bending of multi mode fibers4.7.4 Propagation of light in a Single Mode Fiber4.7.5 Bending losses in Single-Mode Fibers

4.8 Dispersion 4.8.1 Modal Dispersion 4.8.2 Modal Dispersion 4.8.3 Material Dispersion4.8.4 Dispersion in Single-Mode Fibers


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4.1 Light propagation in optical fibersIn this chapter we will discuss the optical fibers and the most important propertiesof 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 AttenuationThe 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 AttenuationThe 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,

=

ℑ

=TPP

LL0log1011log101α Attenuation coefficient

Where L is the length of the fiber in km and ℑis 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 DispersionDispersion 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 DispersionIn 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. Dispersionmanagement will be covered later.


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4.3.2 Modal dispersionModal dispersion is related to the difference in propagation speed caused by the propagation of different modes. This is of course only a problem for multi-mode 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 dispersionWaveguide 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 systemsIn 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 systemAt 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 thecladding 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 fibersGlass/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 fibersIn 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 fibersA 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 fibersIn general the attenuation coefficient is limited by scattering and absorption.

4.5.1 Absorption properties of glass fibersTwo 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 OH-absorption 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 ScatteringEven 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 Rayleighscattering and the infrared absorption of fused glass.


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4.5.3 Multi-mode and Single-mode fibersThe 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.



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4.6 Fiber transmission windowsWe 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.

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 fibersWe 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 graded-index 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.

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.



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4.7.1 Propagation of light in a Multimode Step-Index FiberWe 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.



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4.7.1 Propagation of light in a Multimode Step-Index FiberWe 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.

22

21

2 nnaV −=λπ 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

Cross section of a Multi mode step

index fiber.

Ref: Dutton, Understanding

optical communications

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 bandwidth-distance product. The bandwidth-distance product of a step-index multimode fiber varies between 15 MHz⋅kmand 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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4.7.2 Propagation of light in a Graded-Index Multi-mode FiberOne 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.



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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 graded-index 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

4.7.2 Propagation of light in a Graded-Index Multi-mode Fiber


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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 FiberThe 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.



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4.7.4 Propagation of light in a Single Mode FiberThe 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.



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4.7.4 Propagation of light in a Single Mode FiberTherefore, 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).



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4.7.4 Propagation of light in a Single Mode FiberThe 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 FibersWith 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 FibersIn 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.



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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.

221 nn

cL −⋅≈τσ

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

Therefore the response time for a graded index fiber is reduced

by

( )4

221 nn

cL −⋅≈τσ

Pulse spreading over a time internal for a graded index multi mode fiber

(Response time for a graded index multi mode fiber)

( ) .1221 <<− nn


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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,

where σλ is the spectral width of the optical pulse and Dλ is the dispersion coefficient.

LD λλτ σσ ⋅=Pulse spreading due to material dispersion

(Response time due to material dispersion)

Dispersion coefficient of silica glass.Ref: Saleh and Teich, Fundamentals of Photonics


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4.8.4 Dispersion in Single-Mode FibersSince 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.



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4.8.4 Dispersion in Single-Mode FibersAs 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 FibersAlternatively 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.



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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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