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�� UNIT IV OPTICS WITH LASER AND�OPTICAL FIBRE �

CHAPTER-16

Optical Fibre

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Introduction

Communication is defined as the transfer of information from one point to another.

Main constraints in the communication are transmission fidelity, data rate,

distortions, and distance between relay stations.

In order to meet out the demands of telecommunication companies worldwide,

optical fibers are used as a dominant transmission system.

This optical communication system consists of hair-thin glass fibers that guide light

signals with minimum losses over long distances.

An optical fiber is a cylindrical waveguide system consisting of three regions. The

centre is a the core, the middle region is a cladding and the outer region is a

protective sheath.

Fibers fabricated with recently developed technology are characterized by extremely

low losses (less than 0.2 dB/km) as a consequence of which, the distance between

two successive repeaters could be as large as 250 km.

Due to the low cost and better response, optical fibers are replacing the traditional

copper cables.

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Why we use optical fibers?

There are many advantages of optical fibers over conducting wires. The main advantages are:

Cheaper:
Silicon (Si) is the main component in the manufacturing of optical fibers.
It is one of the most abundant materials on earth.
Due to this the overall cost of optical fiber is lower than that of an equivalent cable

used in communication.

(2) Not hazardous:

In optical fiber cables there is no chance of sparking and short circuit.
This removes the risk of high damage.

(3) Immune to RFI and EMI:

The information is carried by photons in the optical fiber communication.
Due to this signals propagating through fibers suffer less loss and are immune to

electromagnetic interference and radio frequency interference.

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(4) Small size, light weight, flexible, and strong:

The size of optical fiber is very small. It is of the order of few hundred microns.
Its weight is very less .
Optical fibers are flexible. They can be molded at any place with the help of suitable

connectors and splices.

An optical fiber has an outer jacket, which protects it from any outer damage and hence,

makes it strong.

(5) No crosstalk:

There is no chance of crosstalk in the optical fiber communication because the

information propagating through the optical fiber is trapped within the fiber and cannot

leak out.

.

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(6) High information-carrying capacity:

A light source, acting as a carrier wave is capable of carrying far more information than

radio waves and microwaves.

It has been observed that the light signals used instead of electric signals in the process of communication can transmit 45 million pulses per second

(7) Low loss:

Optical fibers are characterized by extremely low losses (less than 0.2 dB/km) as a

consequence of which, the distance between two successive repeaters can be as large

as 250 km.

(8) Higher data-rate transmission:

Optical fiber communication permits the transmission of data over longer distances

and at higher data rates than other forms of wired and wireless communications.

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FUNDAMENTALS OF OPTICAL FIBERS:

What is an optical fiber?

Optical fibers are dielectric waveguides which are fabricated from glass or plastic and are operated on optical frequencies.

Structure of an optical fiber:

Optical fibers are normally of cylindrical form. It has three principal sections:
Core
Cladding
Jacket

Fig1: An optical fiber waveguide showing core, cladding, and protective jacket

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(i) Core

It is the innermost region of the fiber which has specific property of conducting an

optical beam.

Core is usually made of glass or plastic.
It is covered with another layer of glass or plastic having slightly different chemical

composition known as cladding.

(ii) Cladding

It is the region just above the core region of the optical fiber.
It has lower refractive index than the core region.
The optical fiber may have an abrupt boundary between the core and the cladding or there may be a gradual change in the material between the two.

(iii) Jacket

The outermost section of the optical fiber is known as jacket.
It is made up of plastic or special kind of polymer and other materials usually opaque in nature.
It protects the core from abrasion, interaction with environment, moisture, absorption, crushing, and other adversities of the terrestrial atmosphere and thus, enhances its tensile

strength.

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PROPAGATION OF LIGHT THROUGH OPTICAL FIBER:

In the optical fiber, the arrangement of core and cladding regions is done in such a way that the core acts like a continuous layer of two parallel mirrors.
The message which has to be sent through fiber is first encoded into a light wave and then fed into the fiber where it is propagated as a result of multiple internal reflections.

Fig2: Propagation of light in an optical fiber

The end at which the light enters the fiber is known as the launching end.

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Let

n₁ = the refractive index of the core and

n₂= the refractive index of cladding (n₂ < n₁).

n₀= refractive index of outside medium from where the light is launched

And

θ_ibe the angle made by light with the axis of fiber at launching end and

θ_r be the angle made by the refracted ray with the axis

Φ be the angle at which refracted ray strikes the core–cladding interface

If Φ > critical angle (θ_c), then the ray undergoes total internal reflection at the interface. As long as the angle Φ > θ_c the light remains within the fiber.

Applying Snell’s law at the launching face of the fiber, we get

(1)

Now, the largest value of θ_i will be at Φ = θ_c

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From the right-angled triangle ABC, we have

sin θ_r = sin (90°– Φ) = cos Φ

From Eq. (1), we know that

By putting the value of sin θ_r , we get

When Φ = θ_c , θ_i = θ_max

Now,

(2)

Using Snell’s law at point B or cladding boundary,

or, (because for total internal reflection, reflection angle will be 90°)

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So, (3)

Using the value of cos θ_c from Eq. (3) in Eq. (2), we get

(4)

For the conditions when for all values of angle of incidence, total internal reflection will occur. For special condition, when n₀= 1, the maximum value of angle of incidence (θ_i) for the ray to be guided is given by

(5)

In the above expression, θ_m is known as the acceptance angle of the fiber.

Acceptance angle is defined as the maximum angle which incident light makes with the axis of fiber at which the ray is propagated (guided) through the fiber.
The light rays contained within the cone having a full angle are accepted and transmitted along the fiber. This cone is known as acceptance cone.

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16.6 FRACTIONAL REFRACTIVE INDEX CHANGE

Fractional refractive index change is defined as the ratio of the difference between the refractive indices of the core and the cladding to the refractive index of the core. It is denoted by  and is given as

−=nnn121 (16.6)

The value of  is always positive and less than one because n1 > n2 (always), otherwise the phenomena of total internal reflection will not be fulfilled.

16.7 NUMERICAL APERTURE

Numerical aperture (NA) is a number, which defines the light acceptance or light propagating capacity of a fiber. Sometimes, it is also known as figure of merit. Numerical aperture is defined as the sine of maximum angle (acceptance angle) from the fiber axis at which the light may enter in the core of optical fiber and propagate through it by several internal reflections. It is expressed as

NA = sin qm = nnn12220−

Usually n0 is the refractive index of the air and is given as n0 = 1. Hence, the value of NA can be given as

NA==sinqmnn1222− (16.7)

where n1 and n2 are the refractive indices of core and cladding, respectively.

Numerical aperture can also be expressed in terms of fractional refractive index change () as follows:

FRACTIONAL REFRACTIVE INDEX CHANGE

Fractional refractive index change is defined as the ratio of the difference between the refractive indices of the core and the cladding to the refractive index of the core. It is denoted by Δ and is given as

(6)

The value of Δ is always positive and less than one because n₁> n₂ (always), otherwise the phenomena of total internal reflection will not be fulfilled.

WHAT IS NUMERICAL APERTURE?

Numerical aperture (NA) is a number, which defines the light acceptance or light propagating capacity of a fiber. It is also known as figure of merit. It is expressed as

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Usually n₀ is the refractive index of the air and is given as n₀ = 1. Hence, the value of NA can be given as

(7)

where n₁ and n₂ are the refractive indices of core and cladding, respectively.

Numerical aperture can also be expressed in terms of fractional refractive index change (Δ)as follows:

Since the difference in n₁ and is n₂ small, so we can write

Hence Δ

or, (8)

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FIBER FABRICATION:

Double crucible method is used to fabricate an optical fiber produced by the liquid phase technique.
It is much suitable for the fabrication of graded index optical fibers.
In this method, the material glass for core and cladding is fed to two separate concentric platinum crucibles as shown in Fig 3.

Fig 3: The double crucible method for fiber fabrication

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The assembly is placed in a furnace capable of heating the crucible contents to a temperature between 80°C and 1200°C.

Clad fiber is drawn directly from the melt through the nozzles in the bases of crucibles. Index grading is achieved by the diffusion of mobile ions across the core–cladding interface within the molten glass.

Graded index fibers produced by this technique are subsequently less dispersive than step index fibers.

TYPES OF FIBERS:

On the basis of refractive index profile and modes propagated through core, optical fibers are classified mainly into two categories. These are as follows:

(i) Step index (SI) optical fiber

(ii) Graded index (GI) optical fiber

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Step Index Optical Fiber:

In step index optical fiber, there is a step discontinuity of the refractive index profile at the core–cladding interface.
The refractive index of these fibers is defined as

n(r) = n₁ when r < a (where n₁ > n₂)

n₂ when r > a

where n₁ and n₂ are the refractive indices of core and cladding respectively, and a is the core radius.

SI optical fibers can be further classified into two categories:

(i) Single-mode step index (SMSI) optical fiber

(ii) Multimode step index (MMSI) optical fiber

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Single-Mode Step Index Optical Fiber:

In the SMSI optical fiber the refractive index difference between core and cladding is very small.
Due to this, only a single mode is propagated through the core of fiber (Fig. 16.4). These fibers are also known as mono mode fibers.
In general, the mono mode optical fiber has a core diameter of 8 mm to 10 mm and is designed for use in the infrared region.
Single-mode optical eliminates the modal dispersion because only single mode can travel through the core.
Hence, the information transmission capacity of a single-mode fiber is much larger than that of a multimode fiber.

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Such fibers are used for communication longer than 200 m, and these are frequently used under sea water.

Fig.4 (a) Structure of a single-mode optical fiber, (b) refractive index profile,

(c) input pulse, (d) pulse propagation, and (e) output pulse

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(ii) Multimode Step Index Optical Fiber

In general, an MMSI optical fiber has larger core diameter than an SMSI optical fiber.
The diameter of core is about 20 mm–100 mm and the diameter of cladding is about 100 mm–200 mm. The standard overall diameter of the MMSI optical fiber is about 125 mm.
In order to achieve the minimum angle for total internal reflection, the difference between the refractive index of core and cladding material is kept relatively large.
The interface between the core and the cladding acts as a cylindrical mirror at which the reflection of the transmitted light takes place.
Due to this structure, there are many paths available for light signals to travel through the fiber.

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Since the refractive index of the core is constant, so all the rays making an angle equal to or greater than critical angle travel with the same velocity in the core.
They take different times to reach the output end of the fiber as their path lengths are different (shown in Fig.5).
Due to the time difference between the rays arriving at the end of the optical fiber, modal dispersion takes place.
It reduces the information carrying capacity of the fiber.
Hence, Multimode optical fibers are used for short distances (less than 200 m), where high power transmission is needed.

Fig.5 (a) Structural view of MMSI, (b) refractive index profile, (c) input pulse,

(d) pulse propagation, and (e) output pulse

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2. Graded Index Optical Fiber

In graded index optical fiber, refractive index of the core region decreases with the radial distance from the maximum value of n₁ at the starting boundary (inner side) to a constant value n₂ beyond the core radius (a). The index variation may be given as

Where,

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Multimode Graded index(MMGI) Optical Fiber

In the multimode graded index optical fiber, the index of refraction in the core decreases continuously in a parabolic manner from a maximum value at the centre of the core to a minimum constant value of the core–cladding interface (Fig. 16.6).

The rays travelling close to the fiber axis have shorter paths in comparison to the rays travelling into the outer regions of the core.

Since, the velocity of light ray is inversely proportional to the refractive index and the axial rays are transmitted through a region of higher refractive index, so they travel with a lower velocity than the extreme rays.

This compensates for the shorter path lengths and reduces the dispersion in the fiber. MMGI optical fibers have the advantage of large core diameters (greater than 30 mm) coupled with the bandwidths suitable for long-distance communication.

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Fig.6 (a) Structural view of MMGI, (b) refractive index profile, (c) input pulse

(d) pulse propagation, and (e) output pulse

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The numerical aperture (NA), relative refractive index difference (D), profile parameter (α), and normalized frequency (v) determine the number of propagating modes in MMGI fibers.
When a fine value of α(most commonly α = 2) is used, then the number of supported modes for a large number of modes is reduced according to the expression

(9)

Where ,a is core radius and λ is the wavelength.

The maximum number of modes supported by GI fiber is

(10)

Where V is referred to as V- number, known as normalized frequency of cut-off.

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Where n₁(r) is the varying refractive index of the core as the function of r, n₂ is the refractive index of the cladding, a is the radius of the core, x is the parameter describing the refractive index profile variation, and NA(r = 0) is the numerical aperture at the centre of the fiber core.

NUMERICAL APERTURE FOR GRADED INDEX OPTICAL FIBER

In a GI fiber, the numerical aperture is a function of position across the core.
So it can be expressed in terms of local numerical aperture NA(r), which is a function of radius of the core. NA(r) at the position r is expressed as

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V-NUMBER AND CUT-OFF PARAMETERS OF FIBERS

The number of modes supported by an optical fiber is given in terms of some cut-off parameters such as normalized frequency of cut-off, referred to as V-number. V-number is mathematically expressed as;

(12)

Where λ₀ is the wavelength of the light propagating in the multimode glass fiber, d = 2a is the diameter of the core, and NA is the numerical aperture.

If the external medium around the fiber has the refractive index n₀, then Eq. (12) can be given as

(13)

The approximate total number of modes, which the fiber can support is expressed as

(13a)

Where V-parameter is considerably larger than unity.

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COMPARISON OF SINGLE-MODE AND MULTIMODE INDEX FIBRES

Table 1 Comparison of single-mode and multimode index fibers

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DIFFERENCES BETWEEN STEP INDEX AND GRADED INDEX FIBERS

Table 2 Differences between step index and graded index fibers

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COMMUNICATION THROUGH OPTICAL FIBERS

Light propagates within the fiber due to the total internal reflection.
For explaining the communication process through optical fibers, let us consider two types of rays propagating through multimode optical fiber. They are

Meridional rays and (ii) Skew rays.

1. Propagation Mechanism of Meridional Rays

The meridional ray is shown in Fig.16.7 for the SI fiber.

Fig.16.7 Ray diagram of a meridional ray propagating through SI fiber

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In Fig.16.7, the light ray is entering the fiber core from a medium of refractive index n₀ at an angle with respect to the core–cladding interface at a normal angle Φ. If it strikes this interface at such an angle which is totally internally reflected, then meridional rays follow a zigzag path along the fiber core. These rays pass through the axis of the waveguide after each reflection.

According to Snell’s law, the minimum angle Φ_min that supports the total internal reflection for the meridional ray is obtained as

Where n₁ and n₂ are the refractive indices of core and cladding, respectively.

The rays which are striking at core–cladding interface at angle less than Φ_min will refract out of the core and will be lost in the cladding. From Fig. 16.7, it is clear that

Hence corresponding to ,we have

And correspondingly

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Using Snell’s law at the air–fiber interface AB, we get

Hence, we can conclude that the rays having entrance angle θ_iless than θ_{i max}will be totally internally reflected at the core–cladding interface.

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2. Propagation Mechanism of Skew Rays

Skew rays do not pass through the centre and follow a three-dimensional path in the fiber.

Fig. 7 The helical path of skew rays: (a) skew ray path in core of fiber and

(b) cross sectional view of the fiber

The point of emergence of skew rays from the fiber in air will depend upon the number of reflections they undergo rather than the input conditions of the fiber. When the light input on the fiber is non-uniform, skew rays will tend to achieve a smoothing effect on the distribution of the light.
The amount of smoothing depends on the number of reflections encountered by the skew rays.

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The ray diagram of a skew ray propagating through an optical fiber is shown in Fig.8 with a skew ray incident on the fiber core at point A, at an angle θ to the normal at air–core interface.
At point B, ray is incident at an angle Φ and is reflected at the same angle, where Φ is greater than the critical angle of core–cladding interface.

Fig.8 The path of skew ray in the fiber core, incidenting at an angle θ_i

If we consider the ray between A and B, then it is necessary to resolve the direction of ray path AB to the core radius at point B.
As the incident and reflected rays at point B are in same plane, then this is simply

Cos Φ.

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However, if the two perpendicular planes through which the ray AB traverses are considered, then γ is the angle between the core radius and the projection of the ray on the plane BRS normal to the axis of the core.

θ is the angle between the ray and the line AT drawn parallel to the core axis. Thus, to resolve the ray path AB relative to the radius BR in these two perpendicular planes requires multiplication by cos γ and sin θ.

Hence, the reflection at point B at an angle Φ may be given as

(14)

For total internal reflection

(15)

Using Snell’s law at point A, we have

(16)

Where θ_imax is maximum input axial angle for meridional rays and θ is the internal axial angle.

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Putting the value of sin θ from Eq. (16) in Eq. (15), we get

(17)

Where θ_imax represents the maximum input angle or acceptance angle for skew rays. The condition at which skew rays are accepted by the fiber core can be given as

(18)

If n₀ = 1 for air, then

(19)

Skew rays are accepted at larger axial angles in a given fiber than the meridional rays, depending upon the value of cos γ.

Skew rays propagate only in the annular region near the outer surface of the core and do not fully utilize the core as a transmission medium.

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OPTICAL FIBER TRANSMISSION LINK

The block diagram of an optical communication system is shown in Fig.9. The system has:

(i) Information source: It is the source of input signals which are to be transmitted through the optical fiber up to the destination.

(ii) Electrical transmitter: It is the next part of the communication system where the information signals are produced in the form of electrical signals.

(iii) Optical source: Optical source is capable of generating an optical signal at desired frequencies. Basically LASER or LEDs are used as the source of light.

Fig.9 Optical fibre communication system

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(iv) Optical fiber cable: The optical signal is launched into the optical fiber which is contained inside the cable. The cable provides mechanical and environmental protection to the hair-thin optical fiber.

(v) Optical detector: At the receiving end, photo detector is the main component. It is capable of converting the received modulated wave back to the original signal, which has the same wave shape as the optical wave envelope.

(vi) Electrical receiver: It is the part of the communication system where original signal is recovered in its suitable form. Usually, electronic amplifiers and signal restorers consisting of signal processor circuits are used in this section of communication system.

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FIBER ATTENUATION (LOSSES)

Attenuation is defined as the reduction in the signal strength or power when it is transmitted (or guided) through an optical fiber.

Signal attenuation within an optical fiber is usually expressed in terms of logarithmic unit of the decibel (dB).

Decibel is defined for a particular optical wavelength as the ratio of the input optical power P_i into a fiber to the output optical power P_o from the fiber. Mathematically, it is expressed as

(20)

In optical fiber communications, attenuation is usually expressed in decibels per unit length (i.e., dB/km) as

(21)

Where α_dB is the signal attenuation per unit length in decibel and L is the fiber length.

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On the basis of several mechanisms which are responsible for signal attenuation within optical fibers, we can categorize the losses in terms of the following points:

(i) Absorption losses

(ii) Scattering losses

(iii) Bending losses

(iv) Dispersion losses

1) Absorption Losses

The absorption of light by core and cladding materials of a fiber during wave propagation is the main source of attenuation. Absorption of light is caused by the following three different mechanisms:

(i) Atomic imperfection in the glass composition

(ii) Intrinsic absorption

(iii) Extrinsic absorption

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Atomic Imperfections

Atomic defects or imperfections in the atomic structure of fiber materials is due to the missing of molecules, high density clusters of atom groups, or oxygen defects in the glass structure. These losses increase up to a significant value if the fiber is exposed to ionizing radiations.
Radiations damage a material by changing its internal structure. Up to what extent a material is damaged depends on the energy of ionizing particles, rays, and radiation flux.
The basic response of a fiber to ionizing radiation is an increase in the attenuation, owing to the creation of atomic defects that absorb optical energy.
The higher the radiation level, the larger the attenuation.

Intrinsic Absorption

It is caused by interaction of the propagating light wave with one or more major components of the glass which is used in the composition of the fiber.
A pure silicate glass has small intrinsic absorption due to its basic material structure in the near infrared region. However, it does have two major intrinsic absorption mechanisms at optical wavelengths which leave a low intrinsic absorption window over 0.8 mm–1.7 mm wavelength range as shown in Fig.10.

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Fig. 10 The attenuation spectra for the intrinsic loss mechanism in pure GeO₂—SiO₂ glass

The absorption due to the strong electronic and molecular transition band is characterized by peak loss in the ultraviolet and diminishing loss as the visible region is approached.

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Extrinsic Absorption

It is caused by the presence of minute quantity of metallic ions and the hydroxyl ion from the water dissolved in glass.

In the fabrication of various types of fibers, GeO2, P2O5, B2O3, etc., are used as dopants in silica to modify its refractive index.

B2O5 produces strong absorption at 3.2 mm and P2O5 at 3.8 mm wavelength. However, in both the cases, absorption tails extend below 1.3 mm

Loss increases considerably when the operating wavelength is beyond 1.55 mm.

The Hydroxyl ion absorption in optical fibers is due to the presence of trapped hydroxyl ions remaining in water as a contaminant. Hydroxyl ion absorption produces a significant attenuation of discrete wavelength, e.g., centered at 1.383 mm.

Impurities such as Fe+3, Cr+2, and copper, present in the glass may create unacceptable losses within the usable portion of the spectrum. However, these impurities can be reduced considerably by using a good refining technique for purifying the raw materials for silica.

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2) Scattering Losses

Scattering is another parameter for optical attenuation. Such losses in glass arise due to microscopic variation in material density, random variation in refractive index, and structural in homogeneities or defects occurring during fiber manufacturing.
Depending upon the various factors responsible for scattering losses, we can classify them in the following two types:

(i) linear scattering losses and

(ii) non-linear scattering losses.

Linear scattering losses

Linear scattering mechanisms cause the transfer of some or all of the optical power contained within one propagating mode to be transferred linearly (proportionally to mode power) into a different mode. This process tends to result in attenuation of the transmitted light.
This transfer may be to a leaky or a radiation mode, which does not continue to propagate within the fiber core, but is radiated from the fiber. There is no change in the frequency on scattering.
Linear scattering may be categorized into two major types:

(a) Rayleigh and

(b) Mie scattering.

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(ii) Nonlinear Scattering Losses

It is observed that in optical waveguide the output optical power does not always increase in the proportion of the input power.
Several nonlinear effects occur, which in the case of scattering cause disproportionate attenuation, usually at high optical power levels. This nonlinear scattering depends critically upon the optical power density within the fiber and hence, becomes significant only above threshold power levels.
There are two types of nonlinear scattering:

Stimulated Brillouin scattering (SBS):

Stimulated Brillouin scattering may be regarded as the modulation of light through thermal molecular vibrations within the fiber.
In this scattering, the incident photon produces a phonon of acoustic frequency as well as a scattered photon, which produces an optical frequency shift according to the variation in the scattering angle.
If the polarization state of the transmitted light is not maintained, then the threshold power density can be given as;

(22)

where d is the core diameter, λ is the operating wavelength (both are measured in μm), α_dBis the fiber attenuation in db/km, and ν is the source bandwidth in GHz.

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(b) Stimulated Raman scattering (SRS):

Stimulated Raman scattering is similar to stimulated Brillouin scattering except that a high frequency optical phonon rather than an acoustic phonon is generated in the scattering process.
Similar to Brillouin scattering threshold, the threshold optical power for SRS in a long single-mode fiber is given as

(23)

where P_SRS is the threshold optical power for SRS, d is the core diameter, λ is the operating wavelength, and α_dB is the fiber attenuation in decibels.

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3) Bending Losses

Bending losses occur due to imperfections and deformations present in the fiber structure. Generally, there are two types of bending losses: micro bending losses and macro bending losses.

Micro bending losses:
These losses occur when the core surface has small variations in shape. These variations change the angle at which light strikes the core–cladding interface and can cause the light to refract into the cladding rather than reflect into the core.

(ii) Macro bending losses:

Macro bending losses depend on the core radius and the bend radius.
As the radius of curvature decreases, the loss increases exponentially until at a certain critical radius.
If the bend radius is made a little bit smaller, then a threshold point may be reached at which losses suddenly become extremely large. But practically, we never reach this critical value. The critical value of radius of curvature R_c is expressed as

(16.24)

where all the symbols have their usual meanings.

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4)Dispersion Losses

Dispersion loss is defined as the spreading of light pulse as it travels down along the length of the fiber causing the pulses to overlap and thus making the pulses undetectable at the receiving end. Mainly, there are two types of dispersions:

(i) Intramodal dispersion and (ii) Intermodal dispersion.

(i)Intramodal Dispersion

Intramodal or chromatic dispersion occurs in all types of fibers.
It is further divided in two categories:

(a) material dispersion and (b) waveguide dispersion.

Material dispersion:

Material dispersion is based on the wavelength of the optical signal and its interaction with the glass of which the fiber is made.
Every laser source has a range of optical wavelengths. The refractive index of silica is different for different wavelengths of wave.
Hence, different spectral components of an optical pulse have different speeds which lead the pulse to spread out in time after travelling some distance in the fiber.

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(b) Waveguide dispersion:

Waveguide dispersion can occur for waves propagating through any inhomogeneous structure, whether or not waves are confined to some region.
Waveguide dispersion depends on the refractive index difference between core and cladding. The effective refractive index is very close to the refractive index of the core.
Waveguide dispersion is always positive and is not strongly wavelength-dependent. It depends strongly on the core diameter (increases with decrease in core diameter) and on the fiber distance (increases with distance).

(ii) Intermodal Dispersion

Intermodal dispersion occurs due to the propagation delay differences between the modes propagating in a multimode fiber.
The higher-order modes travel a longer distance and arrive at the receiver end later than the lower-order modes. Hence, different modes have different group velocities.
The effect of intermodal dispersion can be reduced by taking the parabolic refractive index profile, usually as it is in the case of a GI optical fiber.

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In order to calculate the delay difference time between axial and meridional rays propagating through MMSI fibers (shown in Fig. 16.12), let us take a fiber of length L.

The time taken by the axial ray to travel along the fiber of length L gives the minimum delay time t_min which can be given as

(25)

where n₁ is the refractive index of the core and c is the velocity of light.

The extreme meridional ray takes the maximum delay time t_max which can be given as

(26)

Using Snell’s law of refraction at the core–cladding interface,

(27)

where n₂ is the refractive index of cladding.

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Fig. 12 Path taken by axial and extreme meridional ray in a perfect MMSI fiber

Putting the value of cos θ in Eq. (26), we get

(28)

The delay difference δ_TSI between the extreme meridional ray and the axial ray will be given as

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where Δ is the relative refractive index difference. Since Δ<< 1, so it may also be given approximately by

Putting the value of Δ in terms of numerical aperture, we get

(30)

where NA is the numerical aperture of the fiber. The approximate expression for the delay difference given in Eq. (30) is usually employed to estimate the maximum pulse broadening in time due to the intermodal dispersion in an MMSI fiber.

(29)

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ATTENUATION CONSTANT

Attenuation losses in optical fibers are generally measured in terms of decibel.
To obtain the expression for attenuation constant, let us consider that P_out is the output power at the end of 1 km of optical fiber, which is equal to the input optical power (P_in), reduced by a fraction k (say), i.e.,

Similarly, after 2 km of optical fiber, the output power is

Hence, after L kilometer of optical fiber, the above expression can be given as

Or,

Taking log on both sides and then multiplying by 10 gives power loss in decibel as

where α (10 log10 k) is the attenuation coefficient of the fiber in decibel/kilometer.

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Therefore, (31)

Sometimes, the number of decibel loss is expressed with negative sign and hence, the above equation can also be given as

(32)

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FIBER SPLICES AND CONNECTORS

Splices and connectors are used for the interconnection of fibers with minimum loss.

Splices and connectors may be required between individual single fibers or they may involve a number of fibers in a multifiber cable.

Besides this, interconnectors are also required for optical source in a transmitter and for photo detector in a receiver.

The particular technique for joining depends on whether a permanent bond or easily remountable connection is required.

According to the requirement, where permanent joints are needed, fiber splicing is used, and where easily remountable connection is required, connectors are used.

Each splice or connector gives rise to additional attenuation, therefore, there is a need to minimize such losses.

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OPTICAL FIBER CABLES

Since optical fibers are sensitive to external environment and effects, so it became necessary to cover the fibers to improve their tensile strength and to protect them against external influences.

This is usually achieved by surrounding the fibers with a series of protective layers, which is referred to as coating and cabling.

There are four main functions of optical cables, which are as follows:

The major function of optical cables is to protect fibers against damage and breakage during installation and working, throughout their life.

(ii) Optical fiber cables have good stable transmission characteristics. The optical attenuation due to cabling are quite usual and must be minimized within the cable design.

(iii) Optical cables have similar mechanical properties such as tension, torsion, compression, bending, squeezing, and vibration, as of electrical transmission cables. Hence, the cable strength will be improved.

(iv) Splicing and joining of optical fibers are very easy within the cable.

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OPTICAL CABLE DESIGN

There are several types of arrangements for designing optical cables. The simplest designs are one- or two-fiber cables intended for indoor use. Hypothetical two-fiber design is shown in Fig. 16.13.
In this design, fiber is first coated with a buffer material and placed loosely in a tough, oriented polymer tube such as polyethylene.
For strength purposes, this tube is surrounded by strands of aramid yarn and, in turn, is encapsulated in a polyurethane jacket.
A final outer jacket of a polyurethane, a polyethylene, or a nylon binds the two encapsulated fiber units together.
Larger cables can be created by stranding several basic fiber building blocks around a central strength member.

Fig.13 A hypothetical two-fiber cable design. The basic building block on the left-hand fiber is exactly same as it is shown on right-hand fiber

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APPLICATIONS OF OPTICAL FIBERS

Optical fibers have wide range of applications in the field of optical communication, medical science, illumination technology, optical sensor, etc. Some important applications of optical fiber are as follows:

(i) Optical fibers are widely used in broadcast television, cable TV, remote monitoring, and surveillance.

(ii) Fibers are most commonly used for transmission of digital data.

(iii)It is frequently used in military operations such as for secret communications, command and control links on ship and aircrafts, data links for satellites, etc.

(iv) It is widely used in cable TV network and closed circuit TV (CCTV) systems.

(v) Fibers are frequently used in illumination technology.

(vi) Fibers have a variety of applications in medical services.

(vii) Fibers are frequently used for decorative applications.

(viii) A coherent bundle fiber is used, sometimes along with lens, for a long, thin imaging device called endoscope.

(ix) Fibers are used to transfer infrared energy from the source to the point of application of heat.

(x) Fibers are used to form sensors to measure physical and chemical parameters.