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EC-7106 Fiber Optic Communication 1

INTRODUCTION

Communication Scientists all over the world were in an incessant search of a wideband and low-

loss medium of data communication which could be used at high data rates with the least amount

of lost possible. This constant search, for such a medium, led to development of optical fiber

communication.

HISTORY

The first revolution in the field of communication came when Sir Alexander Graham Bell

successfully converted voice signals into electrical signals which were transmitted on electrical

wires and then converted back to voice signals. This was the major break-through in the field of

communication. Right from this time there has been a continuously increasing need of

bandwidth for communication due to continuously increasing number of users. More people

wanted to communicate and thus large bandwidths were required thereby forcing communication

scientists to look for new possibilities. This increasing trend, of need of large bandwidths, even

continues today.

ELECTROMAGNETIC SPECTRUM

Initial communications started at lower operating frequencies of about 30MHz. The bandwidths

then required were also low. Since then the operating frequencies have drastically increased due

to large requirements in bandwidths. Let us take a look into the electromagnetic spectrum to get

an idea of our discussion.

The medium of transmission that were used for operating frequencies upto about 1GHz were

coaxial cables in which there was a centre conductor surrounded by a layer of dielectric material


and the dielectric material was surrounded by outer metallic layer. The electromagnetic energy

travelled, along the lengths of these cables and was confined in between the two metallic layers.

These cables had a loss figure of about 20db/km. When operating frequencies increased further

the coaxial cables proved to be inadequate and lossy, thereby giving rise to the need of another

medium called waveguides. These are basically hollow structures which guide the

electromagnetic energy from one point to another through them. But as the operating frequency

further increased to few hundreds of gigahertz these waveguides too proved to be inadequate as

there were no supporting electronic circuitry available that could operate at such high

frequencies. The reason behind this was that at such high frequencies, even the size of the

electronic component started to show some variations in the circuit behavior and the electronic

components could no longer be treated as lumped elements. Hence this led to a strong need of a

search for other alternatives because though there seemed to have appeared a halt in the available

technology, but there did not appear any halt in the ever increasing demand for bandwidth.

Scientist all over the world started to explore new possibilities and looked in the optical domain

which was already being used in laboratory experiments. The idea was that, if the already well-

established relationship between bandwidth (BW) and operating frequency (f0) held good at

optical frequencies then we would emerge with a new option for communication that would

increase the existing bandwidth by 1000 to 10,000 times. Thorough investigations showed that

optical domain had the potentiality to be used for communication. Two very obvious questions

then come to the mind that whether or not there are transmitters and receivers available for this

new communication technology and the second question as to whether or not there exists such a

wideband and loss-less medium for carrying optical signals.

On the very first look, both the questions seem trivial. This is because we already have a lot of

sources of light in our day to day life, for e.g. incandescent bulbs, gas bulbs, LEDs, fluorescent

lamps, etc. Then why worry about sources? Similarly, the second question also has a very

obvious answer. The bright light from the sun, that is millions of light-years away from us,

reaches us, even through vacuum (in space) and also the earth‟s atmosphere. Thus air seems to

be a very efficient medium for light propagation. Then why need a special medium for optical

signals? But though the questions seem simple to be answered, they are not so.

A normal incandescent bulb emits light in all directions. If we keep an incandescent bulb

glowing on the roof -top and slowly move away from it, we will see its glow from even a

kilometer or may be 10Km. But if we go beyond that we will observe its brightness fade away

and after some distance it practically becomes invisible from view. Thus we see that though we

feel that the air is a very efficient medium of light, its efficiency reduces to zero after a few

kilometers. Hence we cannot accept air medium as we earlier thought, because in the field of

communication we do not talk about only a hundred kilometers but about thousands of

kilometers. Thus this notion incurs the need for special medium to carry light over such long

distances. With this need in mind the next option in the list was glass which also appeared to be a

very transparent medium and was perhaps already put to use in laboratory experiments to carry


light. Physicists have already been using glass in the form of prisms or lenses for guiding and

focusing lights in different experiments in the laboratories. However, when glass was used in the

laboratory for guiding or focusing light, we again here are talking about distances which may be

of the order of few meters only, over which the light was carried. And whatever loss glass has,

it is reasonably small over such small distances. So the question is that if glass is used as a

medium to carry light over the distances that are required for communication will it provide a

low-loss medium and also satisfy the requirements of a reliable communication? A yes would

have eased job already. But unfortunately the answer to this question is no. The reason for such

disappointment is that when experiments were carried out over the loss characteristics of glass, it

was found that glass had a very high attenuation of about 1000 dB/Km. Thus glass, which

appears to be so transparent to us, is practically not so. This means that if light is sent over a

glass rod then it would attenuate by 1000 dB over a distance of just 1 Km. So on the first look,

glass seemed to be very inefficient in being used as a medium for optical communications

though it served the requirements of laboratory experiments. But deep study and

experimentations on the nature of glass brought a very interesting notion to the scientists that, the

loss figure of 1000 dB/Km of glass was not due to the intrinsic nature of glass. Or in other

words, high loss was not a characteristic of glass as a substance and was not because of the glass

molecules. In fact, the loss was due to the impurities present in the glass. These impurities were

not removed from the laboratory-used glass prisms and lenses because their presence did not

bring any error in the measurements. As soon as this was realized, glass began to be

manufactured to the best possible purity with the best possible available manufacturing

technology in the early 60‟s. On the first purification, glass that was manufactured had a loss

figure of about 20dB/Km. Although this loss today still seems to be large, but in those times it

was comparable to the other already available communication mediums like waveguides and

coaxial cables. That is to say, if we used a purified glass rod as a communication medium it

would provide almost the same loss (of about a factor of 100) as would a coaxial cable or a

waveguide too would do, but at bandwidths 1000 to 10000 times larger than them. Thus it

attracted scientists to explore this new medium further. Perhaps, this was the reason for moulding

glass into the form of fibers (called optical fibers) that are used for optical communication today.

The second question now to be answered was about the availability of a source of light.

Superficially, this is a very simple question to be even answered. This triviality is because we see

so many different sources of light in our day-to-day life that they seem almost omnipresent. For

example, incandescent bulbs, tube lights, fluorescent lights etc. The question now is, whether

or not an ordinary electric bulb can be used to carry or transmit information. Carrier signal in a

communication system carries information by virtue of a variation in one or more of its

characteristics like amplitude, frequency or time period. Thus if we have a source whose

amplitude and frequency do not change with time, this source cannot be used to carry

information. If we want to use the electric bulb as a source we need to change the amplitude or

the frequency (or both) of the light emitted by it. The question now, is how difficult it is to do so.

Investigations showed that the rate at which an electric bulb can be switched ON and OFF, in


accordance with the information signal, is not fast enough. In other words, the frequency of

operation can only be upto a few cycles. Clearly then, if we want our bandwidths to be large,

these bulbs and tube lights are not suitable sources.

The rate at which an optical signal source can be turned ON and OFF depends on the spectral

width of the source. This means, if we investigate a source which has a very large spectral width

(say for example, white light) we would find that this source has very small operating frequency.

In other words, in order to have a source which can be operated at optical signal frequencies its

spectral width should be as narrow as possible.

Co-incidentally enough, LASERs happened to be invented almost during the same time as the

search for narrow spectral sources was in progress. LASERs happened to have sufficiently

narrow spectral widths and high beam directivity, adequate to be used as optical signal sources.

Initial LASERs emitted lights of wavelengths of about 800 nm. And so, initial optical

communications started with 800 nm wavelength due to which it was called the “First Optical

Window” of optical communication.

The above discussion, hence, gives a very brief introduction to a very interesting and fascinating

communication technology called the Optical Communication. With this backdrop of

information, the next obvious query would be concerning the structure of an optical

communication link. An optical communication link is no different from any other

communication links. It too has the three basic modules transmitter, receiver and the channel or

medium of communication. A typical optical communication link is shown in figure 1.2


The electrical signal, which may be audio, video or any data signal, is fed into the transmitter

module as input to a driver circuitry. The internal circuitry of the transmitter module converts

the data signal from the electrical domain to a compatible optical domain and this optical signal

is then transmitted. This signal then travels through the optical medium which is optical fiber. In

order to recover the optical data signal from the attenuated signal on the fiber, repeaters are

provided to ensure high SNR at the output. This regenerated (recovered) signal is then

retransmitted through the fiber to reach the receiver module in the best possible form and in the

lowest possible time. The receiver module detects (receives) the transmitted signal in the optical

domain and then converts it back into the original electrical signal to reach the intended

destination.

If we take transmission media into consideration, we invariably have the following basic

transmission media: Twisted pair, Coaxial Cable and Waveguides.

TWISTED PAIR (point-to-point)

Fig. 1.3: Twisted pair

-mechanically twisted along throughout their length.

-used at low operating frequencies such as in telephone lines.

-low date rates of about few tens of Kbps

-very high electromagnetic interference (EMI).

-extremely lossy at radio frequencies (RF).

COAXIAL CABLE (point-to-point)

Fig. 1.4: Coaxial Cable

-electromagnetic energy propagates between the two conductors along the length of the wires.

-used within a frequency range of about 30 MHz – 3 GHz.

-low electromagnetic interference and show moderate loss,

-their bandwidths are low

-data rates are only upto a few Mbps.

-used as Local Area Network (LAN) cables, Television channel distribution cable, laboratory

microwave experiments, etc.


MICROWAVE LINK (point-to-point)

Fig. 1.5: Microwave Link

-large bandwidths of about a few hundred Megahertz

-used for long distance communication.

-line-of-sight communication.

-very high free-space

SATELLITE COMMUNICATION (point-multipoint)

Fig. 1.6: Satellite Communication

- point-to-multipoint type link.

-used in broadcast applications like radio television broadcasts.

-operates on microwave frequencies and hence has large bandwidths of about few Gigahertz.

-data monitoring capability

-large delays in signal transmissions

-allows the user to be mobile within the area of electromagnetic illumination by the satellite.

Satellite Communication Fiber Optics

Point-to-multipoint technology

Bandwidth ~ GHz

Maintenance-Free

Short Life (7 to 8 Years)

No Upgradeability

Has Mobility capability. User can be mobile, may be on land,

in water or air.

Point-to-point technology

Bandwidth ~ THz

Needs Maintenance

Long Life

Upgradeable

No mobility.


History of Attenuation graph

The search for a medium for transmission of light over long distances led the scientist to

investigate glass which was already in use for laboratory optical experimentations. But, it was

found that laboratory-used glass, either in the form of prisms or lenses, had a very high loss

figure of about 1000 dB/Km. However, investigations also showed that this high loss was not an

intrinsic characteristic of glass but was due to the impurities that were present in the glass. In

other words, the high loss of optical energy was not due to glass molecules but was caused by the

impurities in it that remained in it during its manufacture. So, with the best possible

manufacturing technology scientists prepared purified glass which was then found to have a loss

figure of only 20 dB/Km. Although in modern days this loss is in no way small, but in early

times it was very much comparable to the other available alternatives for wide band

communication medium like the coaxial cables. Gradually, technologies improved and highly

purified glass started t o be manufactured which had very low attenuation. So, let us just have a

glimpse of this improvement in the manufacture of glass in the last fifty years. A “History of

Attenuation” graph is shown in the figure 2.1 below.

Fig. 2.1: History of Attenuation graph in the manufacture of glass

The above figure shows the loss profiles of manufactured glass with the best possible available

technologies in the early 1970s, 80s and 90s. As is seen, it can be clearly concluded that

manufacture of purified glass has drastically improved due to which the loss figures have


become negligibly small in comparison to other alternatives. In the 1970s, manufactures glass

had a loss profile which showed a minimum loss at around wavelength of 800 nm (0.8µm). By

the time this study of glass was going on, LASERs also were invented which used a

semiconductor material named Gallium Arsenide (GaAs) for emission of light. GaAs

intrinsically is capable of emitting light of wavelength 800nm. So, coincidently we had glass

which had minimum loss at the wavelength that was emitted by LASERs, and so it proved to be

great combination. So initial optical communications were started at 800nm wavelength region

and hence it is called as the “First Window” of optical communication.

As technology improved, glass was further purified and it showed a region of minimum loss at

1300nm and 1550nm regions in the 1980s as shown in figure 2.1. There was no minimum in the

800nm window and hence GaAs LASERs could not be used as sources. But in this course of

time the semiconductor material technology had also improved simultaneously and we had

sources available which could emit light both in 1300nm and the 1550nm regions. So, optical

communications were now shifted to these regions and were called as the “Second Window” and

“Third Window” of optical communication. The 1300nm window not only has low loss but also

can support high data rates. But today, most of the optical transmission take place in the 1550nm

window because though the 1300nm window had high bandwidth, it also had higher loss which

significantly affected the performance of the communication system since distances became

considerable large. The 1550nm window allows the installation of optical amplifiers at regular

distance intervals that can amplify the light in the optical domain without converting it into

electrical signal. This leads to a more reliable communication and hence today most optical

communications lie in the third window.

ADVANTAGES OF OPTICAL COMMUNICATION

Optical Communication provides an ultra-high bandwidth for communication of the order of

Terahertz (THz). This advantage meets the first requirement of a high quality reliable

communication system.

The loss figure of optical communication is very low, about 0.2 dB/Km. So this system has

high SNR values. This advantage provides a reliable communication system. No other medium

today can provide such low loss figures as optical medium.

Optical communication systems have very low or even negligible electromagnetic interference

(EMI).

Optical Communication provides high security data transmission. This is because optical

signal travels through optical fibers which do not allow leakage of light energy. So tapping of

transmitted information is very difficult in optical communication.

Optical communication systems have very low manufacturing cost. Whatever cost is incurred

is only due to the technology. This is because optical medium-glass is made from silica, which is

freely abundant in nature. So, the only cost is in moulding it to a form of optical medium like

optical fiber. The cost per voice channel of an optical fiber is also very much smaller than cost

per voice channel of any other medium like coaxial cable though the two may have comparable

costs per kilometer. This is because the bandwidth of optical fiber is almost 1000 times larger


than a coaxial cable. So, cost per channel of an optical fiber would be one thousandth of that in a

coaxial cable.

Applications where space and weight are constraints, optical fiber serves adequately because

optical fibers have low weight and low volume compared to other media.

The only flaw, if at all to be pointed out, is that optical communication is a point-to-point

communication technology. We already saw that satellite communication technology in this

regard is advantageous in that it is a broadcast type of technology. But in modern scenario where

optical fibres are reaching to every home, atleast in an urban area, information can be

broadcasted to every home in a very short time. Thus we see that optical communication has a lot

of advantages over any other mode of communication, which make it the most desirable option

for communication today. These advantages were precisely the reasons behind the rapid

developments in the field of optical communication that revolutionized itself almost every 10

years and is still in a fast pace of developments. Today, most of the networks are composed of

optical fibers using the optical networking technology. New developments to increase the

capacity of an optical communication system have also taken place such as wavelength division

multiplexing (WDM) technology.

CHARACTERISTICS OF LIGHT

We know that light is a form of electromagnetic radiation. Basically, the nature of light depends

on the context of which we talk about. First we treat light in the context of the Ray Model and

study different phenomena based on the ray model of light. Proceeding further, when we find

the ray model is inadequate in explaining some phenomena, we depart from the ray model and

then adopt a higher model for light which is the wave-model where light is treated as an

electromagnetic wave. And in those situations where we find even the wave-model inadequate in

explain certain phenomena like interaction light with matter, we adopt the quantum model of

light where light will be treated as a photons. So we will treat light in the following three models:

Ray Model

Wave Model

Quantum Model

CHARACTERIZATION OF A LIGHT SOURCE

A source of light can be characterized by the following factors:

Intensity of the light: Intensity of light is defined as the power per unit solid angle. So for a

given power of the source, if the emitted light is scattered into a very wide solid angle then the

source has low intensity. If the emitted light is confined to very narrow cone, the source appears

to be very bright because its intensity increases. This happens in case of a LASER whose light

appears to be much brighter and travels long distance than a normal 60W bulb though the power

of the LASER is much smaller than 60W. The intensity of the source is indicative of how

focused is the emitted light.


Wavelength of Light (λ): The second characteristic on which a source is characterized is the

wavelength of the emitted light. The wavelength of light is indicative of the colour of the light

and so many a times it is also called as the colour of the source. The visible light lies within a

wavelength range of 400nm to 700nm. If we look into figure 2.1, we find that glass which

appears so transparent to us in daily life is not actually that transparent to wavelengths of 400nm

to 700nm. In fact, it is much more transparent to lights of wavelengths 1300nm and 1550nm,

which lie in the infrared region. Since these regions are not in the visible range, colour does not

have any meaning, yet we may retain the colour as one of the characteristic to categorize light.

Depending on the desired loss performance of the optical communication system λ can be chosen

either 1300nm or 1550nm. So, the choice of wavelength of transmission has a direct relation to

the SNR of the transmission.

Spectral Width of Source (∆λ): It is basically the wavelength range over which the emission

takes place. In other words, it is the range of wavelengths emitted by the source. Thus the

spectral width may be considered to be indicative of the purity of the colour of the light source.

That is, if we have a source with a wide spectral width, say for example if it emits all the

wavelengths ranging from blue to red, we get a light from the source which will look like white

light. If we reduce the spectral width to near red, we would get a sharp red colour light. If we

reduce it to near blue, we would get a blue coloured light and so on. Thus reducing the spectral

width increases the purity of the colour. Spectral width is a very important parameter of a source

because we would later discover that spectral width of a source is related to the data rate upto

which a source can be used as a transmitter of optical signal. Smaller the value of ∆λ more will

be the purity of the source and also higher would be the data rate of the source. In other words,

higher will be the bandwidth of the communication system. So, the choice of ∆λ has a direct

relation to the bandwidth of the transmission.

The above three characteristic treat light as sources of energy. Nowhere does the wave nature of

light is to be noticed. However to discuss the propagation of light in an optical fibre, this notion

of light as an energy source is inadequate and we have to treat light as an electromagnetic wave.

Under this adoption, if the dimensions of the medium of propagation are very large compared to

the wavelength of the light, light can be considered as a transverse electromagnetic (TEM) wave.

This means that the direction of electric field, direction of magnetic field and the direction of

propagation of light are mutually perpendicular to one another according to the right hand thumb

rule as shown in figure 2.2 (a) & (b).


The electric and magnetic fields of light are hence related to each other through the medium

parameter η which is called the intrinsic impedance of the medium. That is,

|E|

|H|= η (intrinsic impedance of medium) =

µ

ε ---- (2.1)

Where,

|E| = magnitude of electric field E.

|H| =magnitude of magnetic field H.

µ = Permeability of the medium.

ε = Permittivity of the medium.

So, if the electric field is known completely, the magnitude of magnetic field can be determined

using the above relation and its direction would be perpendicular to the direction of electric field.

Thus with the knowledge of electric field the magnetic field can also be determined. The

behavior of the electric field as a function of time is called the polarization of light. Polarization

is one of the very important parameters of any electromagnetic wave. It is a quantity which

illustrates the vector nature of light unlike other quantities like intensity, wavelength and spectral

width which show scalar nature of light. It shows that light is made up of varying electric and

magnetic fields which are vector quantities. If we look at the locus of the tip of the electric field

vector with respect to time, this locus gives the polarization of the wave. There may be different

shapes that the tip of the electric field vector can trace with respect to time. Based on these

shapes there are different types of polarization which are called as the states of polarization, viz.

Linear Polarization

Elliptical Polarization

Circular Polarization

Random Polarization

Fig. 2.3: Elliptical Polarization


Linear and circular polarizations are special cases of elliptical polarization. In general, the tip of

the electric field vector traces out an ellipse and the light is then said to be elliptically polarized.

This kind of polarization is shown in figure 2.3. From the figure we can clearly see that the

electric field vector E traces out an ellipse with respect to time and so the light is said to be

elliptically polarized. However, in some special cases, this ellipse can degenerate into a circle or

a straight line and the light is then said to be circularly polarized or linearly polarized

respectively. When the major axis and the minor axis of the ellipse become equal to each other,

the locus of E would be a circle and it is then said to be circularly polarized. When either of the

major axis or the minor axis of the ellipse becomes zero, the locus of E would be a straight line

and the light is then said to be linearly polarized.

So, in general, we can say that light which is transverse electromagnetic in nature has three states

of polarization, linear, circular or elliptical. If the light does not have a systematic behavior with

respect to time, i.e. if the electric field orients itself randomly as a function of time (which may

happen in case of a light from a source with large value of ∆λ) the light is said to be randomly

polarized. In this type of polarization either the amplitude or direction of E or both varies

randomly with respect to time. Incoherent lights in general do not have any definite polarization

and are said to be randomly polarized. So, polarization is another very important characteristic

that categorizes different sources of light. It represents and illustrates the vector nature of light.

RAY-MODEL OF LIGHT

Fundamentally, we have two main aspects of the ray nature of light. Light rays actually are

fictitious lines which in reality represent the direction of propagation of what are called as phase-

fronts of light as shown in figure 2.4. Phase-fronts are nothing but constant phase surfaces in

which the phase difference between any two points is zero. In reality they represent the spatial

nature of propagation of a wave and hence are also called as wave-fronts. These phase-fronts

may be either spherical or planar in nature and accordingly, we get two aspects of ray nature of

light. A line drawn perpendicular to a phase front at every point gives the direction of

propagation of light energy at that point and is conventionally called as a light-ray. So, light-rays

are actually imaginary lines that determine the direction of propagation of light energy. In other

words, what we actually have is not light ray but the direction of propagation of phase-fronts of

light energy that are represented by directed line segments called light rays.


If we have an isotropic source of light situated at finite distance, as in figure 2.4(a), we get

spherical phase-fronts because the light source would emit light in all directions and light waves

would travel spherically outwards from the source of light. If we now draw lines perpendicular to

these phase-fronts at any point, these lines would give the direction of flow of light energy at that

point and the line drawn would then be called a light ray. Due to their spherical nature, the light

waves can be called as spherical waves.

If the same source is now placed at a very large distance from the point of observation (ideally at

infinity) the wave-fronts would appear almost planar and parallel to each other as shown in

figure 2.4 (b). So the light rays too would now not look divergent, but appear parallel to each

other because they are perpendicular to the phase fronts at every point. The light waves now can

be called plane waves.

WAVE-MODEL OF LIGHT

The “Wave-Model” of light introduces light as an electromagnetic wave. If light is treated as an

electromagnetic wave then light must be expressible in terms of the generalized wave function,

which is given as:

𝜑 𝑥, 𝑡 = 𝐴𝑒𝑗 (ω 𝑡−𝛽𝑥 ) ------- (2.2)

Where, A= Amplitude of the wave.

ω = Angular Frequency of the wave (radian/second)

β = Phase Constant (Radian/metre)

The wave function is a generalized function of space (x) and time (t). The term (ωt-βx) is the

phase function of ψ(x, t). Thus the phase of the wave is a function of space and time. If we now

freeze space, i.e. take x=constant or in other words observe at a particular point, we see that there

is a sinusoidal variation of the wave amplitude as a function of time having an angular frequency

of ω rad/s. If we freeze time, i.e. take t=constant or in other words observe the whole wave

simultaneously, we see that the amplitude of the wave has a sinusoidal variation with a phase

constant β rad/m. So these two phenomena together constitute a wave phenomenon represented

by the generalized wave equation.

The phase constant β is defined as the phase change per unit distance. The wavelength (λ) of a

wave is the distance between two consecutive points on the wave which are in the same phase.

The phase difference between two points in the same phase is either zero or an integral multiple

of 2π. Thus the wavelength of a wave is measured between two points that have a phase

difference of 2π. Hence the phase constant β can be calculated as:

β =2π

λ ------- (2.3)

Treating light as an electromagnetic wave, let us now define an important optical parameter of a

medium called the refractive index of the medium. Refractive index of a medium is defined as

the ratio of the velocity of light in vacuum to the velocity of light in that medium. It is denoted

by n. Since refractive index is a ratio of two velocities, it is a pure number and has no unit.


Refractive index of medium, n(medium ) = velocity of light in vacuum (c)

velocity of light in the medium (ν) -- (2.4)

For most media, n(medium) < 1, i.e. the velocity of light reduces from its value in vacuum. In

fact, light travels fastest in vacuum and in any other medium it slows down. For example, the

refractive index of material glass is about 1.5, i.e. light travels 1.5 times faster in vacuum than in

glass. Similarly the refractive index of water is 1.33. In other words, refractive index of a

medium indicates the factor by which the speed of light reduces in the medium.

Spectral width of the source of light is the range of wavelengths that are emitted by a source of

light.

λ =v

f -------- (2.5)

Where, λ = wavelength of light in a medium.

v = velocity of light in the medium.

f = frequency of the light under study.

The spectral width can be calculated from (2.5) as,

Δλ = −v

f2 Δf -------- (2.6)

Or, Δλ = − v

f

Δf

f

Or, Δλ

λ= −

Δf

f

Constructional Details of an Optical Fiber

Constructionally, an optical fiber is a solid cylindrical glass rod called the core, through which

light in the form of optical signals propagates. This rod is surrounded by another coaxial

cylindrical shell made of glass of lower refractive index called the cladding. This basic

arrangement that guides light over long distances is shown in figure.

Fig. 3.1: Constructional Details of an Optical Fiber

The diameter of the cladding is of the order of 125 µm and the diameter of the core is even

smaller than that. Thus it is a very fine and brittle glass rod. In order to provide mechanical

strength to this core-cladding arrangement, other coaxial surrounding called the buffer coating

and jacketing layers are provided. They do not play any role in the propagation of light through

the optical fiber, but are present solely for providing mechanical strength and support to the

fiber.

The light energy in the form of optical signals propagates inside the core-cladding arrangement

and throughout the length of the fiber by a phenomenon called the Total Internal Reflection

(TIR) of light. This phenomenon occurs only when the refractive index of core is greater than the

refractive index of cladding and so the cladding is made from glass of lower refractive index. By


multiple total internal reflections at the core-cladding interface the light propagates throughout

the fiber over very long distances with low attenuation.

Figure 3.2: Launching of light into an optical fiber

Figure 3.2 shows a section of the core of an optical fibre. If a ray of light is incident on the core

of an optical fibre from the side, the ray of light simply refracts out from the fibre on the other

side. The ray shown in figure (in green) demonstrates the situation. No matter what the angle of

incidence of the light is, any light that enters the fiber from the side does not propagate along the

fiber. The only option thus available with us is to launch the light through the tip of the fiber.

That is, in order to guide light along the fiber, the light must be incident from the tip of the

optical fiber. The red ray of light in figure 3.2 explains this situation. In other words, if the tip of

the optical fiber is not exposed to light, no light will enter the fiber. Equivalently, if there was

propagation of light through the fiber, no light would emerge from the sides of the fiber. This

characteristic of the optical fiber imparts the advantage of information security to the Optical

Fiber Communication Technology.

For explaining propagation of light in an optical fiber, the Ray-Model of light is be used. The

Ray-Model of light obeys the Snell‟s laws. Following figure depicts a situation of a typical

refraction phenomenon taking place at the interface of two optically different media having

refractive indices n1and n2.

Figure 3.3: Refraction of light at a media interface


The angles measured in the expression for Snell‟s law are measured with respect to the normal to

the media interface at the point of incidence. If n2 > n1 , then the angle of refraction is greater

than the angle of incidence and the refracted ray is said to have moved away from the normal. If

the angle of incidence (θ1) is increased further, the angle of refraction (θ2) also increases in

accordance with the Snell‟s law and at a particular angle of incidence the angle of refraction

becomes 90ᵒ and the refracted ray grazes along the media interface. This angle of incidence is

called the critical angle of incidence (θc) of medium2 with respect to medium1. The same

optically denser medium may have different critical angles with respect to different optically

rarer media. If θ1 is increased beyond the critical angle, there exists no refracted ray and the

incident light ray is then reflected back into the same medium. This phenomenon is called the

total internal reflection of light. The word „total‟ signifies that the entire light energy that was

incident on the media interface is reflected back into the same medium. Total Internal Reflection

(TIR) obeys the laws of reflection of light. This phenomenon shows that light energy can be

made to remain confined in the same medium when the angle of incidence is greater than the

angle of reflection. Thus there are two basic requirements for a TIR to occur:

1. The medium from which light is incident, must be optically denser than the medium to which

it is incident.

2. The angle of incidence in the denser medium must be greater than the critical angle of the

denser medium with respect to the rarer medium.

LAUNCHING OF LIGHT INTO AN OPTICAL FIBER

Light propagates inside an optical fiber by virtue of multiple TIRs at the core-cladding interface.

The refractive index of the core glass is greater than that of the cladding. This meets the first

condition for a TIR. All the light energy that is launched into the optical fiber through its tip does

not get guided along the fiber. Only those light rays propagate through the fiber which are

launched into the fiber at such an angle that the refracted ray inside the core of the optical fiber is

incident on the core-cladding interface at an angle greater than the critical angle of the core with

respect to the cladding. Figure 3.4 shows one of the possibilities of launching light into an

optical fiber where the light ray lies in a plane containing the axis of the optical fiber. Such

planes which contain the fiber axis are called meridional-planes and consequently the rays lying

in a meridional-plane are called meridional-rays. Meridional rays always remain in the respective

meridional plane.

Figure 3.4: Launching of Meridional Rays


There may be infinite number of planes that pass through the axis of the fiber and consequently

there are an infinite number of meridional planes. This indirectly indicates that there are an

infinite number of meridional rays too, which are incident on the tip of the fiber making an angle

with the fiber-axis as shown in the above figure. In the figure the meridional plane is the plane of

the paper which passes through the axis of the fiber and the incident rays, refracted rays and the

reflected rays lie on the plane of the paper. Meridional rays are classified into bound and

unbound rays. The rays that undergo TIR inside the fiber core remain inside the core at all times

along the propagation and are called as bound rays. The rays that fail to undergo TIR inside the

core are lost into the cladding and are called unbound rays. The dotted ray shown in figure 3.4 is

an unbound meridional ray.

Another way of launching a light ray into an optical fiber is to launch it in such a way that it does

not lie in any meridional plane. These rays are called skew rays. A pictorial representation of

launching a skew ray is shown in the figure 3.5 below.

Figure 3.5: Launching of Skew Rays

Skew rays propagate without passing through the central axis of the fiber. In fact the skew rays

go on spiraling around the axis of the optical fiber. The light energy carried by them is

effectively confined to an annular region around the axis as shown in figure. Consequently, at the

output, skew rays will have minimum energy at the axis of the optical fiber and it will gradually

increase towards the periphery of the core.

Thus when light energy is launched into an optical fiber, there arises two possible energy

distributions; one, which has maximum intensity at the axis due to meridional rays and the other,

which has minimum intensity at the axis due to the skew rays. Thus, on the whole, there are two

ways of launching light into an optical fiber; light can be launched either as meridional or as

skew rays.


Assuming that light is launched as meridional rays into the optical fiber, let us now carry out a

simple analysis. The figure shows a cross-section of an optical fiber with a core of refractive

index n1 and a cladding of refractive index n2. The incident ray AO (shown by dotted line) is

incident at an angle ϕ with the axis of the fibre. The refracted ray for AO in the core (dotted line

ON1) fails to be incident on the core-cladding interface at angle greater or equal to the critical

angle of the core w.r.t. cladding and hence refracts out of the core and is lost to the cladding. In

other words, the angle of incidence of a refracted ray at the core-cladding interface in turn

depends on the initial angle at which the incoming ray was launched into the fiber. If this

launching angle (with the fiber axis) is decreased, the angle of incidence which the refracted ray

makes at the core -cladding interface increases. If this increase is such, as to exceed the critical

angle of the core-cladding interface, then total internal reflection of the refracted ray takes place

and the light remains in the core and is guided along the fiber. The ray CO is launched into the

fiber at such an angle „α‟ that its refracted ray is incident at the core-cladding boundary at its

critical angle „θc‟. If any light ray is launched at an angle more than α then the refracted ray just

refracts out to the cladding because the angle of incidence of its refracted ray at the core-cladding

interface is less than the critical angle. Thus the angle α is indicative of the maximum possible

angle of launching of a light ray that is accepted by the fiber. Consequently, the angle α is called

the angle of acceptance of the fiber core. Since the optical fiber is symmetrical about its axis, it is

very clear that all the launched rays, which make an angle α with the axis, considered together,

form a sort of a cone. This cone is called the acceptance cone of the fiber as shown in the above

figure. Any launched ray that lies within this cone is accepted by the fiber and the light of this

ray is guided along the fiber by virtue of multiple TIRs as shown by the red ray BO in the figure.


NUMERICAL APERTURE OF OPTICAL FIBER

With the same initial assumption of meridional launching of light into an optical fiber, the figure

shows a cross-section of a core of refractive index n1 and a cladding of refractive index n2 that

surrounds the core glass. An incident ray AO is incident from medium1 at the tip of the fiber

making an angle α with the axis of the fiber, which is the acceptance angle of the fibre. The

refracted ray for this incident ray in the core then is incident at the core-cladding interface at the

critical angle θc of the core with respect to the cladding. The angle of refraction for critical angle

of incidence is 90ᵒ and the refracted ray thus grazes along the core-cladding boundary along BC

as shown in the figure. Applying Snell‟s law at the medium1-core interface we get:

𝑛 𝑠𝑖𝑛𝛼 = 𝑛1 𝑠𝑖𝑛𝜃 (3.1)

From the figure it is clear that, 𝜃 =𝜋

2− θc and so substituting this in equation (3.1), we get:

𝑠𝑖𝑛𝛼 =𝑛1

𝑛 𝑐𝑜𝑠θc

𝑠𝑖𝑛𝛼 =𝑛1

𝑛 1 − sin2θc (3.2)

Applying Snell‟s law at the core-cladding interface we get:

𝑛1𝑠𝑖𝑛𝜃𝑐 = 𝑛2 sin 90

𝑠𝑖𝑛𝜃𝑐 = 𝑛2/𝑛1

Substituting this in equation (3.2) we get:

𝑠𝑖𝑛𝛼 = 𝑛1

2 − 𝑛22

𝑛

Since the initial medium1 from which the light is launched is air most of the times, n = 1. The

angle α is indicative of light accepting capability of the optical fiber. Greater the value of α, more

is the light accepted by the optical fiber. In other words, the optical fiber acts as some kind of


aperture that accepts only some amount of the total light energy incident on it. The light

accepting efficiency of this aperture is thus indicated by sin α and hence this quantity is called

as the numerical aperture (N.A.) of the optical fiber. Thus for an optical fiber in air, with core

refractive index n1 and cladding refractive index n2 and having an acceptance angle of α is given

by 𝑁.𝐴. = sin 𝛼 = 𝑛12 − 𝑛2

2 .

Numerical Aperture is one of the most fundamental quantities of an optical fiber. It indicates the

light collecting efficiency of an optical fiber. More the value of N.A. better is the fiber. For

greater values of N.A. the difference on the right hand side of equation has to be maximized. For

maximizing the difference, either the refractive index of the core (n1) has to be increased or the

refractive index of the cladding (n2) has to be reduced. Since the core used is always glass, the

value of its refractive index n1 is thus fixed (approximately 1.5). The only option thus available

with us is to reduce the value of n2. But it too has a limitation of the lowest value of 1 for air

because till date no material is known which has a refractive index lower than that. If we make

n2=1, we would then get the maximum possible N.A. for an optical fiber. But then we are

basically talking about removing the cladding because, if there is a cladding, the value of n2 will

always be greater than 1. Thus one can clearly say that from the point of view of light accepting

efficiency, the presence of a cladding is undesirable.

The above discussion suggests that although the optical fiber is made of core and cladding, the

presence of cladding is undesirable because it reduces the light accepting efficiency of the optical

fiber. However, one can realize that the prime concern behind prolonged research on optical

fibers was not just to put light inside an optical fiber with the best efficiency but also to

propagate the light over long distances with the least attenuation. That means if we have a source

of optical signal and an optical fiber with the highest light accepting efficiency but is incapable

of propagating the accepted light; the optical fiber is of no use in spite of its high N.A. Thus

judging the need of a cladding just on the basis of light launching efficiency would be highly

inappropriate. In other words, light launching efficiency is just one of the key characteristic

aspects of an optical fiber. There are other attributes too which have to be given importance

while determining the quality of an optical fiber. One of such attributes of an optical fiber is its

bandwidth. Large bandwidths are desirable for high data rates of transmission.

When optical fiber is used for transmission of information, light signal launched into it cannot be

of continuous nature. For a carrier signal to carry information, one or more of its characteristics

has to be altered in accordance to the data signal. In an optical fiber light is launched in the form

of optical pulses to transmit the required information. Light energy launched into the fiber may

be considered to travel in the form of numerous rays in accordance to the Ray-Model. These rays

travel different paths inside the core of an optical fiber because different light rays are incident

on the tip of the optical fiber at different angles within the acceptance cone itself. This causes

different light rays in the acceptance cone to travel along different paths in the core of the optical

fiber and accordingly take different time intervals to travel a given distance too, which leads to

a phenomenon of pulse broadening inside the core of the optical fiber. Thus the pulse of light

which might originally be of width T seconds now might be of T+∆T seconds inside the fiber


core. The figure 3.9 below depicts a pictorial description of how light pulse broadens inside the

core of the fiber.

Figure 3.9: Pulse-Broadening inside optical fiber core

Any incident ray that lies within the acceptance cone gets guided inside the optical fiber by

virtue of multiple total internal reflections. Since the angle of refraction different incident rays

are different, they travel along different paths in the optical fiber as shown in the above figure.

This causes the initially launched narrow light pulse to broaden as shown. The amount of

broadening is measured in terms of the increase in the pulse time width and is denoted by ∆T. the

value of ∆T is given by:

∆T = L

c n1(n1−n2)

n2 (3.6)

Where, ∆T= Pulse Broadening; c = velocity of light in free space; n1= refractive index of core

and n2= refractive index of the cladding.

The quantity L is the horizontal distance travelled before suffering the first total internal

reflection by the refracted ray OB which corresponds to the incident ray AO, incident at the

acceptance angle as shown in the figure. The amount of pulse broadening is effectively the

difference in time of travel between the ray travelling along the axis and the incident ray AO.

This pulse broadening effect signifies that if a second pulse is now launched into the fiber within

the time interval T+∆T, the two pulses will overlap and no identifiable data would be obtained

on the output. Thus for a given length L, there would be a corresponding value of ∆T (from

equation 3.6) which would limit the rate at which light pulses can be launched into the optical

fiber. In other words, it limits the rate at which data can be transmitted along the fiber. This

indirectly limits the bandwidth available o n the fiber. Thus we can say that more the pulse

broadening lower the bandwidth.

Bandwidth (BW) = 1/∆T (3.7)

Equation 3.7 suggests that for higher bandwidth of transmission the pulse broadening, ∆T should

be as low as possible. In equation 3.6, we see that the value of ∆T is dependent on the value of L,


the difference (n1 – n2) as well as the value of n1/n2. But reducing the value of L would signify

the reduction in the length of the optical fiber, which is not desirable. As 1<n2<n1, the ratio,

n1/ n2 is very close to 1. Thus for low ∆T values, the only option is to decrease the value (n1–n2)

or in other words, to increase the refractive index of the cladding n2. So a contradictory situation

has been generated as to whether the cladding should be removed for high NA or to use a

cladding of large refractive index value for higher bandwidth. The answer to this query is purely

application specific. That means if an optical fiber is used as a sensor, where lowest possible

light has to be accepted, we use fiber with low n2 values. When the optical fiber is used for data

communication, fibers with high values of n2 are used. For practical communication purposes

the value of (n1 – n2) is made of the order of about 10-3

to 10 -4

. If the cladding is removed, the

value of n2 becomes 1 and the value of the above difference becomes about 0.5. The bandwidth

corresponding to this value of n1- n2 is of the order of few Kilohertz, which is far worse than

that of a normal twisted pair of wires. Thus cladding is an extremely important requirement for

optical fiber when the bandwidth is the prime concern of the application and its refractive index

is made as close to that of the core as the available technology permits, but not made equal. This

is brought about by varying the amount of doping in a single glass rod. The differently doped

regions have different refractive indices and serve as core and cladding of the optical fiber.

PHASE-FRONT (WAVE-FRONT) BASED STUDY OF TIR

Wave-fronts are nothing but the constant phase planes of the light wave and are also called as

phase-fronts. They are perpendicular to the direction of propagation of the wave at every point.

Any light ray launched meridional within the acceptance cone will propagate along the fiber core

by virtue of multiple total internal reflections at the core-cladding interface. Thus in accordance

to the ray-model of light we may visualize a solid cone of light (having angle = double the

acceptance angle) that enters an optical fiber and propagates through the fiber by TIRs. Figure

3.10 below shows the phenomenon of total internal reflection of a ray of light at the core-

cladding boundary along with the wave-fronts of the incident and the reflected rays. The red and

green coloured dotted lines represent the wave fronts of the light rays which are perpendicular to

their direction of propagation. The light rays, actually, are fictitious lines which, in reality,

represent the direction of propagation of these wave-fronts.

Figure 3.10: Total Internal Reflection of Light inside a fiber core.


The distance between a red and a green wave-front corresponds to a phase difference of 180ᵒ.

The similar coloured wave-fronts have either 0ᵒ or 360ᵒ phase difference between them. Thus,

when two similar coloured wave-fronts meet, they interfere constructively and dissimilar

coloured wave-fronts interfere destructively. This is evident from the interference pattern that

sets up in the core as shown in the above figure. In the core, the interference between the incident

and the reflected wave-fronts constitutes a standing wave pattern of varying light intensity with

discrete maxima and minima in a direction normal to the core-cladding interface.

Total internal reflection is also accompanied by an abrupt phase change between the incident and

the reflected rays at the core-cladding boundary. This phase change depends on the angle of

incidence of the incident ray at the core-cladding boundary, the refractive index or the core and

cladding and various other parameters.

If we refer to the electromagnetic wave theory of light, it shows that at total internal reflection,

the light intensity inside the cladding is not completely zero. Instead, there exist some decaying

fields in the cladding, which do not carry any power but support the total internal reflection

phenomenon by satisfying the boundary conditions at the core-cladding interface. These fields

are called as evanescent fields. The Ray-model of light does not offer any explanation about the

evanescent fields, which indeed are as equally important as the fields in the core for total internal

reflection to occur. The importance of these evanescent fields in the TIR can be clearly

ascertained from the fact that even the slightest disturbance to these fields in the cladding could

lead to the failure of the TIR at the core -cladding boundary accompanied by leakage of optical

power to the cladding. This is one of the instances when the ray-model of light becomes

inadequate in explaining the phenomena exhibited by light. Though the evanescent fields are

decaying fields, they never become zero, atleast theoretically. In other words, they remain

present upto infinite distance from the core-cladding boundary. But in practice, these fields

decay down to a negligibly small value as we move away from the core-cladding boundary

deeper into the cladding. Larger the value of the angle of incidence of the incident ray at the

core-cladding boundary, sharper is the decay of the evanescent fields. Thus there must me a

sufficient thickness of cladding provided for these evanescent fields to be accommodated so that

they decay to a negligibly small value in the cladding and cannot be disturbed by external

sources.

Figure 3.11 below shows two parallel rays that are launched into an optical fiber and they

propagate as shown. The dotted lines represent the wave-fronts of the rays. The refractive indices

of core and cladding are n1 and n2 respectively. The diameter of the core is„d‟. The phase-front

AE is common to both Ray 1 and Ray 2. The phase -front DB is common to Ray 2 and BF. The

Ray 2 is thus common to both the phase-fronts. Hence for a sustained constructive interference,

the distance between these two phase-fronts must be multiples of 2𝜋. In other words, it can be

said that the phase difference between the phase change undergone by Ray 1 in travelling

distance s1 and the Ray 2 in travelling s2 must be 0 or integral multiples of 2 𝜋 .


Figure 3.11: Propagation of Light rays in an Optical fiber

Mathematically,

𝑠1 = 𝑑

𝑠𝑖𝑛𝜃 (3.8)

𝑠2 = 𝐴𝐷 𝑐𝑜𝑠𝜃 = (𝑐𝑜𝑠 2𝜃−𝑠𝑖𝑛 2𝜃)𝑑

𝑠𝑖𝑛𝜃 (3.9)

If δ is the phase change undergone in each TIR of Ray 1, then the total phase change undergone

by Ray 1 in travelling s1 is given by

𝜙1 =2𝜋𝑛1

𝜆 𝑠1 + 2δ (3.10)

Where n1 = refractive index of core; 𝜆 = Wavelength of the light in the core.

The phase change undergone by Ray 2 in travelling s2 is given by

𝜙2 =2𝜋𝑛1

𝜆 𝑠2 (3.11)

For a sustained constructive interference, both ϕ1 and ϕ2 must have a phase difference of either

0 or integral multiples of 2п. That is, for an integer m (=0,1,2,3,…) the following condition must

be satisfied:

𝜙1 − 𝜙2 = 2𝑚п

2𝜋𝑛1

𝜆 𝑠1 − 𝑠2 + 2δ = 2𝑚п

2𝜋𝑛1 𝑑 𝑠𝑖𝑛𝜃

𝜆+ δ = 𝑚п (3.12)

The significance of the equation 3.12 is that only those rays, which are incident on the tip of the

fiber at angles such that their angle of refraction in the core satisfies equation (3.12), can

successfully travel along the fiber. In equation (3.12), „m‟ can take only discrete integral values,

the value of angle θ is also discrete. There are only some discrete launching angles within the

acceptance cone (N.A. cone) for which the rays can propagate inside the fiber core. A 3D

visualization reveals the significance of this observation, i.e. the acceptance cone can no longer

be assumed as a solid cone of rays, launched at all possible angles (smaller than acceptance

angle), but has to be viewed as composed of discrete annular conical rings of rays which are

launched at the tip of the fiber core at angles which satisfy equation (3.12). Thus the condition

that the launching angle of the incident ray should be within the acceptance cone is necessary but

not sufficient. This angle has to be such that the equation (3.12) is satisfied. Thus light can only


be launched at certain discrete angles within the N.A. cone leading to a further decrease in the

light gathering efficiency of the optical fiber. Any ray that is not launched at these discrete

angles will not propagate inside the optical fiber. This discretization in the values of launching

angles lead to formation of what are called as modes in an optical fiber, which are nothing but

different patterns of light intensity distribution around the axis of the core.

Figure: Annular rings of different modes

The number of different values of „m‟ signifies the number of different possible launching angles

which can successfully propagate in the optical fiber core. The ray that is launched along the axis

of the fiber propagates without any phase condition requirement to be satisfied and corresponds

to the first mode of propagation, also called as the zero order mode of propagation. This is shown

by m=0 in the figure above and few other modes are shown by their respective annular rings

represented by different colours. There may be N possible modes of propagation for which the

rays successfully travel along the fiber creating unique light intensity patterns around the axis of

the core. The number allowable values of „m‟ depend on the acceptance angle of the optical

fiber. This is because although there are infinite integral values of „m‟ (according to equation

3.12) only those modes would propagate along the fiber whose launching angles lie within the

N.A. cone of the fiber. Any ray that is launched outside this cone does not propagate along the

fiber although it might correspond to a particular mode. This is shown in the figure above by the

ray AO. This ray simply refracts out of the core because its angle of incidence at the core-

cladding interface is smaller than the critical angle of the core with respect to the cladding. Thus

the N.A. cone can no longer be assumed as a solid cone of rays, but has to be viewed as

composed of annular rings of rays which correspond to particular modes of propagation that

satisfy basic phase conditions. In other words, the optical fiber too is selective in accepting only

those rays which satisfy the basic phase conditions and the other rays are rejected by the fiber

although they may lie within the acceptance cone of the fiber. Thus there are only a finite

number of modes that are allowed in an optical fiber and the other modes are rejected. This

leads to a further decrease in the light accepting efficiency of fiber.


Let us reconsider the propagation of the rays in the optical fiber in relevance to wave theory of

light. Treating light a transverse electromagnetic wave, we find that when meridional rays

propagate along the fiber, their electric and magnetic fields of all the rays superimpose to result

in electric and magnetic field distribution which may be either transverse electric (TEx) or

transverse magnetic (TMx) in nature. The subscript „x‟ denotes the definite number of maxima

and minima in the resultant light intensity pattern. The propagation of skew rays, on the other

hand, results in a particularly special form of modes which are neither TE nor TM in nature

and are called as Hybrid modes. When we refer to modal propagation in dielectric waveguides,

we find that unlike metallic waveguides, there is a special set of modes that exists in a dielectric

waveguide in addition to TE and TM modes. This set of modes is called as hybrid mode. The

optical fiber is actually a cylindrical dielectric waveguide and so it can exhibit hybrid modes as

well. Rigorous analysis shows that hybrid mode is in fact the lowest order mode that can

propagate in an optical fiber. Since hybrid mode is the lowest order mode, it can be analytically

shown that the mode of the ray that propagates in the fiber along the axis is hybrid in nature.

Let us now have a glimpse of the different types of modes that propagate inside an optical fiber

which may be TEx, TMx, or hybrid in nature. Figure below shows different intensity patterns

created by superposition of the wave-fronts of all the light rays for Transverse Electric modes

that propagate in an optical fiber.

Figure: Different TE modes in an optical fiber

The fields that are shown in the cladding region are actually the evanescent fields that exist in the

cladding owing to the boundary condition requirement at the core-cladding interface. For very

low launching angles with respect to the axis of the fiber, the intensity pattern created is the one

which is shown by TE0 in the above figure. There exists a maximum intensity region around the

axis of the core and as we move towards the periphery of the core the fields start to decay. These


fields eventually decay down to negligibly low value in the cladding as shown in the figure. If

the launching angle is increased further, we get the intensity patterns as that shown for TE1 and

TE2 in the above figure. The subscript of TE in fact indicates the number of destructive

interferences in the pattern where the field intensity crosses the zero level, or in other words,

creates an optically dark area. So, for TE0 we have no dark area, for TE1 we have one dark area

at the axis, for TE2 we have two dark areas and so on. This situation is well obvious from the

above figure which shows the number of times the field intensity pattern crosses the zero level

corresponding to the subscript of TE. This subscript is also termed as the index of the mode. As

we further increase the launching angle with respect to the axis, more zeros are crossed and we

get the higher indices of the mode. The above discussion is also true for TM mode as well.

The ray-model of light showed us that launching angle of the light ray must be smaller than the

acceptance angle of the optical fiber core. But the consideration of the wave-fronts showed us

that this condition of the launching angle is not enough to ensure a successful propagation of

light in an optical fiber. The launching angle must be such that the angle of refraction of the

launched ray into the fiber must satisfy the phase condition of equation 3.12 for sustained

propagation inside the optical fiber core. 2𝜋𝑛1 𝑑 𝑠𝑖𝑛𝜃

𝜆+ δ = 𝑚п (m=0,1,2,3,…)

The different discrete values of the angle θ indirectly signify the different allowable launching

angles of the light rays into the optical fiber. If we substitute the first value of m (i.e. m=0) in the

above equation we get θ=0ᵒ. This refers to the ray that propagates along the axis. This ray will

inevitably propagate inside the fiber because it does not require any phase condition to be

satisfied. Let us now substitute the next integral value of m to obtain the first order mode.

We get:

𝜃1 = 𝑠𝑖𝑛−1 𝜆(𝜋 − 𝛿)

2𝜋𝑑𝑛1

This value of θ1 signifies the first annular ring of rays that propagates inside the fiber. Similarly

we may obtain the other modes that propagate in the fiber by subsequent substitution of the

corresponding values of m until the condition θ≤ α is reached, where α is the N.A. of the fiber

core.

When a pulse of light is aligned onto the tip of the optical fiber core, the light energy in the pulse

divides into numerous rays which become incident on the tip of the optical fiber core. But only

those rays propagate which satisfy both the requirements for a successful propagation of light in

the core. Yet there numerous rays that enter the optical fiber core at all the allowed launching

angles. This causes different rays to travel by different paths which indeed lead to pulse

broadening of light in the core. Pulse broadening is also referred to as dispersion and is greatly

an undesirable phenomenon because it reduces the bandwidth of the fiber. The pulse broadening

is caused by the time delay in between the axially launched ray and the ray corresponding to the

largest order mode possible in the optical fiber because it is the largest order mode that travels


the longest path inside the fiber. If we do not allow any mode to get launched into the fiber

except the axial ray, this would ideally lead to a zero pulse broadening.

The propagation of next mode and the subsequent modes depends on many parameters. If by any

means of variation in these parameters we could make θ>α, the ray corresponding to this θ will

not get launched into the fiber. The different parameters that we can possibly vary are the

refractive index (n1) of core and the diameter of the core (d) for a given wavelength of light (λ).

But the refractive index n1 cannot be varied because we have already chosen the material glass

for the core which has a fixed refractive index of about 1.5. This leaves us with only one option

and that is to vary the diameter of the core. If we reduce the diameter of the core to a very low

value such that θ1 exceeds the numerical aperture of the fiber core, then the rays corresponding

to this θ1 cannot be launched into the fiber. Thus only the axial ray would be launched and any

higher mode would not be launched into the fiber thereby reducing the pulse broadening effect to

a negligibly low value. These types of fibers which allow only a single mode of light to

propagate inside them are called as Single Mode Optical Fibers (SMOF). And the optical fibers

which allow the propagation of multiple modes are called as Multimode Optical Fibers (MMOF).

Thus it is obvious that SMOF have very low pulse broadening in comparison to MMOF and thus

have higher bandwidths. But MMOF have higher N.A. than SMOF. SMOF and MMOF are also

called as step-index type optical fibers because the transition from cladding refractive index n2 to

core refractive index n1or vice versa is in the form of a step function.

By reducing the diameter of the core of the optical fiber, the pulse broadening can be decreased

and thus its bandwidth can be increased. That is why almost for all practical data communication

purposes single mode optical fibers are used. Though SMOF have high bandwidths, they have a

very low N.A. value, which makes it very difficult to launch light into a single mode optical

fiber. First of all, the source of light has to have a highly directional beam and secondly, the fiber

core has to be carefully aligned to the source. The slightest disturbance to this arrangement

would prevent any available light to enter the fiber even with a highly directional optical source.

Hence LASER like sources are used in case of single mode optical fibers.

LASERs have highly directional beams which are apt for SMOF. The only trouble is to align the

fiber to the LASER source and prevent any external disturbance to the arrangement. On the other

hand, MMOF, on account of their high N.A., accept large percentage of the incident light. Even

LEDs could serve as a source in case of MMOF because they do not require highly directional

sources.

Single mode optical fibers attain their high bandwidth at cost of light gathering efficiency. The

obvious question that may come is that, is it possible to make a multimode fiber to have both

high N.A. and low pulse broadening (or high bandwidth). The answer to this query again can be

derived from the very cause of the pulse broadening effect. All the rays of light for a given

wavelength propagate with the same velocity inside the core of the optical fiber. This causes


different rays to take different time intervals to propagate a particular length of the fiber because

they travel along different paths. The axially launched ray thus takes the lowest time to travel

and the rays corresponding to the largest allowed mode take the largest amount of time because

they travel the longest distance inside the fiber and suffer the most number of total internal

reflections. This difference in the time intervals is in fact the pulse broadening ∆T. If by some

means all the rays could be made to travel with different velocities so that they all take the same

time to travel a given length of the optical fiber, we could achieve our goal of having a

multimode optical fiber with high N.A. and low pulse broadening. This means that we have to

make the rays which travel the longest distance travel with the fastest velocity and the other rays

to travel with correspondingly lower velocities with the axial ray having the lowest velocity. To

achieve this we can refer back to the basic definition of refractive index of a material which says:

Refractive index of medium, n(medium ) = velocity of light in vacuum (c)

velocity of light in the medium (ν)

The above definition signifies that light travels faster in materials with lower refractive index.

That is, if we make the axial ray to travel through a region of highest refractive index so that it

travels with the lowest velocity and make the other rays to travel through regions of decreasing

refractive indices whose refractive indices decrease in the same proportion as the increase in

their distance of travel, then all the rays would travel with almost equal velocity along the axis

and thus would take the same time to travel a given length of a fiber. We actually are suggesting

of creating some sort of refractive index gradient that is symmetrical around the axis such that

the refractive index is maximum at the axis and it gradually decreases as we move towards the

periphery of the core and again constant in the cladding. This type of index grading is shown in

figure below. The way in which the launched rays would travel in such a fiber is also shown in

the figure.

The maximum refractive index of the core is at the axis of the optical fiber and it decreases

gradually towards the periphery of the core and then in the cladding it is constant at n2. These

types of fibers are called Graded Index Optical Fibers (GIOF). The axial ray travels through a


region of highest refractive index compared to the rest of the core and hence travels with the

lowest velocity. The velocities of the rays increase as their lateral displacement from the axis

increase because they encounter regions of lower refractive index. This causes them to travel

together without any delay between themselves and thus reduce the pulse broadening to a

considerably low value. The perfect profiling of the refractive index has not yet been possible

practically. Hence the delay between the rays is never practically zero though it may be very

small. So, GIOFs are not as better in bandwidth as SMOF but do have higher N.A. than SMOFs.

This is why, where light gathering is more a concern over bandwidth, GIOFs becomes the

appropriate choice. GIOFs are obviously better than MMOFs in terms of bandwidth.

Index Profile and Cross-sectional View of different types of fibers

Single mode fibers are the best choice when distance of communication is very large and also the

bandwidth requirement is the primary concern (for example in long distance high-speed

communications like WAN etc.). It has the best dispersion performance out of the three and

hence has the highest bandwidth out of the three. Next to single mode fibers is the multimode

graded index optical fiber which has N.A. higher than single mode fiber but its dispersion

performance is about 10 times poorer than that of a single mode fiber. Applications where the


distance of communication is short and the designer does not want to sacrifice much on the light

gathering efficiency, this type of optical fibers appropriately serve the purpose (for example in

local area communications like LANs, Intranet etc.). Multimode step index fibers are used in

laboratory demonstrations because though they have high N.A., their dispersion performance too

poor to be of any use in communication. They may be used in optical sensors for their high

N.A., but have very limited range of applications.

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