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Optical Fibre Fundamental idea of optical fibre:

John Tyndall in 1870 demonstrated that light can be guided along a curved stream of water.

Owing to total internal reflection, light gets confined to the water stream and the stream appears luminous.

A luminous water stream was the precursor of an optical fibre.

Historically the first technical effort to use light waves as vehicle of communication was done by Alexander Bell.

In 1960, it has been established that light could be guided by a glass fibre.

Commercial communication system based on optical fibre cables made their appearance in late 70’s.

Optical fibers are glass or plastic conduits as thin as human hair, designed to guide light waves along their length.

An optical fibre works on the principle of total internal reflection.

When light enters one end of the fibre, it under goes successive total internal reflections from sidewalls and

travels down the length of the fibre along a zig- zag path.

A small fraction of light may escape through sidewalls but a major fraction emerges out from the other end of the fibre.

Mostly the optical fibers are made of silica.

If the basic material silica is doped with Germania (GeO2) or phosphorous pentaoxide, (P2O5) the refractive index of the

material increases.

Such materials are used as core materials and pure silica is used as cladding material.

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When pure silica is used as core material then material with decreased refractive index, i.e. silica doped with B2O3 or

fluorine is used for cladding.

The cladding and support structure of optical fibers are sometimes made of polymer.

Construction:

A practical optical fibre has in general three coaxial regions. The inner most region is the light guiding region known as

the core.

It is surrounded by a coaxial middle region known as the cladding. The outer most region is called sheath.

CORE

CLADDING

Core

Cladding

Buffer Coating n1

n2

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The refractive index of cladding is always lower than that of the core.

The purpose of cladding is to make the light to be confined to the core.

Light launched into the core and striking the core to cladding interface at greater than critical angle will be reflected back

into the core.

Since the angle of reflection and incidence are equal, the light will continue to rebound and propagate through the fibre.

The sheath protects the cladding and the harmful influence of moisture. Hence increases the mechanical strength of the

fibre.

Optical fibers are constructed as either as a single fibre, or a flexible bundle, or a cable.

A fibre bundle is a jacket of no. of fibers. Each fibre carries light independently.

The cross sectional view of cable is

125μm 50μm

150μm

CLADDING

CORE

SHEATH

Cross Sectional View

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It contains six fibers and has an insulated steel cable at the centre for providing tensile strength.

Each optical fibre consists of a core surrounded by a cladding, which in turn is coated with an insulating jacket.

Thus, fibers are individually buffered and strengthened.

Six insulated copper wires are distributed in the space between the fibers.

They are used for electrical transmission.

The fibers are wrapped with Mylar tape to bind the assembly. The assembly is then fitted in a corrugated aluminum sheath,

which acts as a shield.

A polythene jacket is applied over the top.

Types of Fibre: Optical fibers can be classified into following

three categories:

1. Single mode step index fibre 2. Multimode step index fibre 3. Graded index fibre

Insulated steel strength member

Aluminum FPA shield

Insulated 22 Gauge conductor

Insulated fibre optic strand and

protective tube

Red polythene 1.5 mm jacket

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1. Single mode step index fibre:

A single mode step index fibre has a very fine thin core of uniform refractive index of a higher value, which is

surrounded by a cladding of lower refractive index.

The refractive index changes abruptly at the core cladding boundary, because of which it is known as a step index fibre.

An opaque protective sheath surrounds the fibre. A typical SMF has a core diameter of 4μm, which is of the order of a

few wavelength of light.

Light travels in SMF along a single path that is along the axis. It is the zero order mode that is supported by an SMF.

An SMF is characterized by a very small value of Δ. It is of the order of 0.002.

CABLE

n1

n2

Refractive Index Profile

n1

n2

Cross Section

n1

n2

Side view showing mode of propagation

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2. Multimode Step Index Fibre:

A multimode fibre is very much similar to the single mode step index fibre except that its core is of larger diameter.

A typical MMF has a core diameter of 100µm, which is very large compared to the wavelength of light being transmitted.

Light follows zigzag paths inside the fibre. Many such zigzag paths of propagation are permitted in MMF.

The NA of a MMF is larger as the core diameter of the fibre is larger. It is of the order of 0.3.

CABLE

n1

n2

Refractive Index Profile

n1

n2

Cross Section

Side view showing mode of propagation

n1

n2

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3. Graded Index Fibre:

A graded index fibre is a multimode fibre with a core consisting of concentric layers of different refractive indices.

Therefore the refractive index of the core varies with distance from the fibre axis.

It has a value at the centre and falls off with increasing radial distance from the axis.

The typical index profile causes a periodic focusing of the light propagating through the fibre.

In case of GRIN fibers, the acceptance angle and numerical aperture decreases with radial distance from the axis.

For fibers of parabolic index profile, the numerical aperture is

given by 2

21

1 12

a

rnNA

Typical size of GRIN fibers are 50/125,62.5/125 and 85/125.

The manner of denoting the size is core diameter/ cladding diameter.

2a n n1 n2

r

Refractive Index Profile

n(r)

n2

Cross section

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Acceptance angle and cone:

Let we have an optical fibre into which light is launched. The end at which light enters the fibre is called the launching end.

Let the refractive index of the core be n1 and the refractive index of the cladding be n2.( n1> n2).

Let n0 be the refractive index of the medium from which light is launched into the fibre.

2a

Side view showing typical ray paths along a GRIN fibre

θr Ør Ør

θi A

B

C

Axis of the fibre

Totally internally reflected ray

Launching

zone n0

Refracted ray normal

n1

n2

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Let a light ray enters the fibre at an angle θi to the axis of the fibre. The ray refracts at an angle θr and strikes the core

cladding interface at an angle Ø.

If Ø is greater than critical angle ØC, the ray undergoes total internal reflection.

Since n1> n2, as long as the angle Ø is greater ØC the light will stay within the fibre.

Now applying the Snell’s law, to the launching face of the fibre we get,

0

1

sin

sin

n

n

r

i

If θi is increased beyond a limit, Ø will drop below the critical value ØC and the ray escapes from the sidewalls of the fibre.

The largest value of θi occurs when Ø = ØC.

From Δ ABC we have

cos90sinsin r

Hence cossin0

1

n

ni

When C

Cin

n cosmaxsin

0

1

But 1

2sinn

nC

Hence1

2

2

2

1cos

n

nnC

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Hence

1

2

2

2

1

0

1maxsinn

nn

n

ni

0

2

2

2

1maxsin

n

nni

For air n0= 1

Hence 2

2

2

1maxsin nni

Let 0(max) i then

The angle θ0 is called the acceptance angle of the fibre. It may be

defined as the max. angle that a light ray can have relative to the

axis of the fibre and propagate down the fibre.

222110 sin nn

Acceptance Cone

θ0(max)

Fibre Axis

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Light rays contained within the cone having a full angle 2θ0 are

accepted and transmitted along the fibre. Therefore the cone is

called the acceptance cone.

Light incident beyond at an angle θ0 refracts through the cladding

and the corresponding optical energy is lost. It is obvious that the

larger the diameter of the core, the larger the acceptance angle.

Fractional refractive index change: The fractional difference

between the refractive indices of the core and the cladding is

known as fractional refractive index change. It is defined as

1

21

n

nn

It is always positive as n1 must be larger than n2 for the total

internal reflection condition. Typically, Δ is of the order of 0.01.

Numerical Aperture: The numerical aperture is defined as the

sine of acceptance angle. i.e.

0sinNA

2

2

2

1 nnNA

21212

2

2

1 nnnnnn

12121 2

22n

nnnn

Let 121

2n

nn

We have 2

1

2

2

2

1 2nnn

12

Hence 21nNA NA determines the light gathering ability of the fibre. It is a

measure of the amount of the light that can be accepted by a fibre.

It depends only on the refractive indices of the core and cladding

material. Its value ranges from 0.13 to 0.50. A large NA implies

that a fibre will accept large amount of light from the source.

V-No.: V- No. is more generally called the normalized frequency

of the fibre. It is given by:

22212

nna

V

Where a is the radius of core and λ is the free space wavelength.

Again NAa

V

2

As 2

2

2

1 nnNA

And 22

1na

V

Now the path through which light wave propagates is a function

of its angle of incidence. Since the angle of incidence can vary so

that the paths also vary. These paths are called modes.

The no. of modes that can be propagated through the fibre may be

related to an important parameter and that is V-No. The max. no.

of modes supported by SMF is 2

2

1VM n

For SMF 405.2V and for MMF 405.2V

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The wavelength corresponding to value 405.2V is called the

cut off wavelength λC of the fibre i.e. 405.2

VC

In case of GRIN 4

2VNm

Losses in Fibers:

Pulse dispersion: A light pulse launched into a fibre decreases in amplitude as it travels along the fibre, due to

losses in the fibre. The pulse received at the output is wider

than input pulse. It means that the pulse becomes distorted as

it propagates through the fibre. Such a distortion arises due to

dispersion effect. It is measured in ns/km.

There are three mechanisms, which contributes to the distortion of

light pulse in a fibre:

1. Material Dispersion 2. Waveguide Dispersion 3. Intermodal Dispersion

Broadening of the signal due to Dispersion

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1. Material dispersion: Light waves of different wavelengths travel at different speeds in a medium. The short wavelength

wave’s travel slower than long wavelength waves,

consequently narrow pulses of light tend to broaden as they

travel down the optical fibre. This is known as material

dispersion.

The spectral width of the source determines the

extent of material dispersion. It is given by:

2

2

d

ndL

cm

Where λ = peak wavelength

Δλ= spectral wavelength

L= length of core

n = refractive index of core

c= velocity of light

It can be reduced by using monochromatic source.

2. Waveguide Dispersion: It arises from the guiding property of the fibre. The effective refractive index for any mode varies

with wavelength, which causes pulse spreading just like the

variations in refractive index does. This is known as waveguide

λ1

λ2

Material Dispersion

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dispersion. It is small compared to material dispersion and can

be ignored in MMF.

3. Intermodal Dispersion: A ray of light launched into a fibre follows different zigzag paths. When numerous modes are

propagating in a fibre, they travel with different net velocities

with respect to fibre axis. Parts of the wave arrive at the output

before other parts leading to a spread of the input pulse. It is

known as Intermodal dispersion. It does not depend on the

spectral width of the source.

Dispersions limit the bandwidth of a fibre. The bandwidth of

optical fibre is obtained from knowledge of dispersion:

kmnsdispersionBandwidth

/

310

The bandwidth –distance product specifies the information

capacity of an optical fibre. The max. bit rate allowed is given by

λ1 λ2

Wave guide Dispersion

Modal Dispersion

λ1 λ2

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A

B

C

Dl/2 l/2

a

?i

?r

DELAY DUE TO MODAL DISPERSION

DispersionB

5

1max

Attenuation: An optical fibre propagating through a fibre will get

progressively attenuated. The signal attenuation is defined as the

ratio of the optical output power from a fibre of the length L to

the input optical power. It is expressed in decibel per km (dB/km).

Attenuation,o

i

P

P

Llog

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Time Delay due to modal dispersion: The total delay between

the arrival of axial ray and the slowest ray, the one traveling the

longest distance is:

minmax ttt

Referring to the fig.

The time taken by a refracted ray to traverse the distance ABC of

the fibre will be:

v

BCABt

'

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rc

ACnt

cos' 1

r

r

BC

DC

AB

AD

cos

cos

hence

BCDC

ABAD

r

r

cos

cos

Also 1n

cv

Since the ray path will repeat itself the time taken by a ray to

traverse length of the fibre is

rc

Lnt

cos1

The above relation shows theat time taken by a ray in the core is a

function of r , for axial ray 00r hence,

c

Lnt 1min

For longest path,

As cr 90 so that )90cos(

1max

cc

Lnt

Or, cn

Lnt

2

2

1max

Hence from minmax ttt

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1

2

11

n

n

c

Lnt

Or

1

1

c

Lnt

Time Delay Due to Material Dispersion: Plane wave can be

expressed as:

)exp( tkx

0

0

22k

nk0

2

nc

k2

nc

k

also c

22

For a wave packet

dk

dg

c

n

d

d

d

dk

g

1

d

dn

cc

n

g

1

But

d

d

d

dn

d

dn

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d

dn

cd

dn

2

2

d

dn

cn

cg 2

11 2

d

dnn

cg

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As the signal propagates through the fibre each spectral

component can be assumed to travel independently and undergo a

time delay in the direction of propagation, i.e.

g

mat

Lt

d

dnn

c

Ltmat

Pulse spread Δtmat for a source of spectral width Δλ will be given

as:

d

dtt matmat

2

22

d

nd

c

Ltmat

matmatt hence

2

2

d

nd

c

Lmat

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Propagation of light ray through fibre (SIMPLE RAY MODEL)

(Optical fiber with core, cladding and total internally reflected ray)

For propagation of light inside the core there are two possibilities.

1. A light ray is launched in a plane containing the axis of the fiber. We can then see the light ray after total

internal reflection travels in the same plane i.e., the ray is confined to the plane in which it was launched and

never leave the plane. In this situation the rays will always cross the axis of the fiber. These are called the

Meridional rays shown in the fig. above.

2. The other possibility is that the ray is not launched in a plane containing the axis of the fiber.

For example if the ray is launched at some angle such that it does not intersect the axis of the fiber, then after

total internal reflection it will go to some other plane. We can see that in this situation the ray will never

intersect the axis of the fiber. The ray essentially will spiral around the axis of fiber. These rays are called the

Skew rays.

So it can be concluded that if the light is to propagate inside an optical fiber it could be through two types of

rays

a) Meridional rays: The rays which always pass through the axis of fiber giving high optical intensity at the

center of the core of the fiber.

b) Skew Rays: The rays which never intersect the axis of the fiber, giving low optical intensity at the center

and high intensity towards the rim of the fiber.

Principle of light propagation in optical fiber An optical fiber consists of a core that is surrounded by a cladding. The core and cladding is normally made of silica glass, although polymer materials are also in use. The function of the core is to transmit an

optical signal while the purpose of the cladding is to guide the light within the core, in effect to confine the

light within the core. A fiber is sometimes called an optical waveguide because light is guided through the

fiber. The basic construction of a fiber is shown in figure 1(a). In order to confine the optical signal to the core

of the fiber the core and cladding materials are deliberately given different refractive indices, so that the

refractive index of the core (n1) is higher than that of the cladding (n2). The refractive index of a material

decides whether the material transmits or reflects a light ray that intersects the surface of the material. The

simplest type of fiber is called a step index fiber, since in such a fiber there is a step in the value of the

refractive index at the boundary between the core and the cladding. This is shown in figure 1(b) which graph

which shows how the refractive index varies with distance from the centre of the fiber. In a step index fiber

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the refractive index is constant at n1 until the core cladding boundary is reached, where the refractive index

falls to n2 The core diameter of step index multimode fiber is typically 200nm, with a cladding diameter of

300nm. A light ray that enters the fiber does not merely travel straight down through the centre of the core.

Instead light rays within the core are continually reflected at the core/cladding boundary so that the rays

remain within the core. This process is called total internal reflection and is the means by which an optical

signal is confined to the core of a fiber. Fig (2) illustrates the process for a step index fiber. Fig (1) Core with

refractive index n1 and n2Fig(2) Propagation of light in an optical fiber profile for a step index optical fiber

Fig(3) Propagation of light in an optical fiber3In order to understand the process in more detail consider in

fig(2) a light ray (i) entering the core at point A and then travelling through the core until it reaches the core

cladding boundary at point B. As long as the light ray intersects the core/cladding boundary at a small enough

angle the ray will be reflected back into the core to travel on to point C where the process of reflection is

repeated. If a ray enters the fiber at a steep angle, for example light ray (ii), then when this ray intersects the

core/cladding boundary the angle of intersection is too large and reflection back in to the core does not take

place and the light ray is lost in the cladding. This means that to be guided through a fiber a light ray must

enter the core with an angle that is less than the so called acceptance angle for the fiber. A ray which enters

the fiber with an angle greater than the acceptance angle will be lost in the cladding. By convention the

acceptance angle for a fiber can also be described by the term "numerical aperture". The fiber acceptance

angle o can be calculated from the refractive indices of the core and cladding using the formula:

222110 sin nn