opto electronics syed abdul rehman rizvi the islamia university of bahawalpur

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Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

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Page 1: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Opto Electronics

Syed Abdul Rehman Rizvi

The Islamia University of Bahawalpur

Page 2: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Opt0 Electronics

INSTRUCTOR: Syed Abdul Rehman Rizvi

E-mail: [email protected]

OFFICE: New Building, U.C.E.T

PHONE: 03336371316

OFFICE HOURS: As per scedule

I encourage you to make an appointments if time table conflicts with your schedule.

REFERENCE TEXT: As indicated in the slides

LECTURES: As per time table

LABS: As per time table

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Page 3: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

GRADING: Assignments|Project : 3 Due at the beginning of class on due date.

Quizzes (9-10) : 10 Quizzes will be given at random dates.

Classroom participation : 2 Give full attenetion to ur teacher.

viva voce : 5 Comprehensive.

QUIZZES: Quizzes will be given at random dates throughout the term. Most of themwill be pop quizzes.

HOMEWORK: Late homework will be penalized with 20% of the grade for each day it is late.

VIVA: There will be no make-up viva.

ACADEMIC DISHONESTY:

Violations of academic dishonesty will be sanctioned. It involve the use of any method or technique enabling a student to misrepresent the quality and integrity of his or her own academic work or the work of a fellow student. Students committing academic dishonesty will be reported to the appropriate college official and an appropriate disciplinary action will be initiated against him/her.

3

Page 4: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Objective

To provide an understanding of the structure,

operating principles and underlying physical

concepts of optical communication systems

(particularly fiber links), having emphasis on

fundamental aspects, but taking care of

engineering issues as well.

Page 5: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Text Book/Reference Books

Fiber-Optic Communication Systems by Govind P. Agrawal

‡ Optical Fiber Communication, principles and practices (2nd

edition) by John M. Senior

Understanding optical communication by Harry Dutton.

‡ Optical communication (Willy series in telecommunication

and signal processing) by Robert M.Gagliardi, Sherman

Karp.

‡ Optical Communication Systems by John Gawar

Page 6: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

The starting point !

‡ For thousands of years we have used light to communicate.

‡ Even in these high-tech days of satellite communications, ships still

carry powerful lamps for signaling at sea.

It was a well known ‘fact’ that, as light travels in straight lines, it is

impossible to make it follow a curved path.

‡ Boston, USA, 1870. An Irish physicist by the name of John Tyndall

gave a public demonstration of an experiment which not only

disproved this belief but gave birth to a revolution in communications

technology.

Page 7: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Expected ! ‡ His idea was very

simple. He filled a container with water and shown a light into it in dark room.

‡ It was expected that the light would shine straight out of the hole and the water would

would Curve downwardas shown in Figure.

Page 8: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

what actually happened ! The light stayed inside the water

column and followed the curved path.

He had found a way to guide light!

The basic requirements still remain

the same today — a light source and

a clear material (usually plastic or

glass) for the light to shine through.

‡ The light can be guided around any

complex path as in Figure .

Page 9: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Applications of light guiding Road signs- A single light source can be used to power many

optic fibers.

Endoscopes.

Hazardous areas.

All at sea.

Flexible lighting.(marking escape routes for fire fighters,

mountain and mine rescue, underwater routes for divers,

helicopter landing zones, oil refineries, planes, ships, tunnels.

The list is almost endless)

Page 10: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Back ground - Need for Optical Fiber ‡ The development of worldwide telephone networks during 20th

Century necessitated the use of coaxial cables instead of pairs wires

for increased capacity.

‡ A 3-MHz system capable of transmitting 300 voice channels was put

in to use in 1940.

‡ Then arises the frequency-dependent cable losses, which increase

rapidly for frequencies beyond 10 MHz.

‡ This limitation led to the development of microwave communication

systems in which an electromagnetic carrier wave with frequencies in

the range of 1-10 GHz is used to transmit the signal by using suitable

modulation techniques.

Page 11: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Cont.

‡ The first microwave system operating at the carrier frequency of 4

GHz was put into service in 1948. Since then, both coaxial and

microwave systems have evolved considerably and are able to

operate at bit rates ~100 Mb/s.

‡ A severe drawback of such high-speed coaxial systems was their

small repeater spacing (~ 1 km) -- expensive to operate.

‡ Microwave communication systems -allow larger repeater spacing.

‡ Figure of merit for communication systems is the bit rate-distance

product, BL, where B is the bit rate and L is the repeater spacing

Page 12: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

BL Development

Page 13: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Cont ‡ An increase of several orders of magnitude in the BL product would be

possible if optical waves were used as the carrier -- But neither a

coherent optical source nor a suitable transmission medium was

available during the 1950s.

‡ The invention of the laser and its demonstration in 1960 solved the first

problem.

‡ Attention was then focused on finding ways for using laser light for

optical communications.

‡ It was suggested in 1966 that optical fibers might be the best choice, as

they are capable of guiding the light in a manner similar to the guiding

of electrons in copper wires

Page 14: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Cont.. ‡ The main problem was the

high losses of optical fibers.

‡ fibers available during the 1960s had losses in excess of 1000 dB/kmm.

‡ A breakthrough occurred in 1970 when fiber losses could be reduced to below 20 dB/km in the wavelength region near 1 µm.

‡ The reduction of loss made it possible to use optical fibers for communication. Which was further reduced to 0.2 Around 1975. The enormous progress

db/km in 1979. was realized !

Page 15: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Cont.. ‡

At about the same time, GaAs semiconductor lasers, operating at room temperature, were demonstrated . The simultaneous availability of compact optical sources and a low-loss optical fibers led to a worldwide effort for developing fiber-optic communication systems. Figure shows the increase in the capacity of lightwave systems realized after 1980 through several generations of development. The commercial deployment of lightwave systems followed the research and development phase closely. The progress has indeed been rapid as evident from an increase in the bit rate by a factor of 100,000 over a period of less than 25 years.

‡ Transmission distances have also increased from 10 to 10,000 km over the same time period. As a result, the bit

rate-distance product of modernlightwave systems can exceed by a factor of 107 compared with the first-generation lightwave systems.

Page 16: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Optical Comm Systems

Page 17: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Optical Communication Systems ‡ Optical communication systems differ in principle from microwave

systems only in the frequency range of the carrier wave used to carry the information i.e. 200 THz & 1 GHz respectively.

‡ An increase in the information capacity is expected i.e. 1o,ooo times.

‡ Optical communication system consists of a transmitter, a commmmunication channel and a receiver.

‡ Optical communication systems can be classified as guided and unguided.

‡ In the guided lightwave systems the optical beam emitted by the transmitter remains confined, using optical fibers.

‡ In the unguided optical communication systems the optical beam emitted by the transmitter spreads in space, similar to spreading of microwaves.

‡ Unguided optical systems are less suitable for broadcasting applications than microwave systems because optical beams spreads mainly in the forward direction because of their short wavelength.

Page 18: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Fiber-optic communication

This is a method of transmitting information from

one place to another by sending light through an

optical fiber.

The light forms an electromagnetic carrier wave

that is modulated to carry information.

Page 19: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Fiber-optic communication

The process of communicating using fiber-optics involves the following basic steps:

Creating the optical signal using a transmitter, relaying the signal along the fiber, ensuring that

the signal does not become too distorted or weak, and receiving the optical signal and converting it

into an electrical signal.

Page 20: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Evolution of Fiber

1880 – Alexander Graham Bell1930 – Patents on tubing1950 – Patent for two-layer glass wave-guide1960 – Laser first used as light source1965 – High loss of light discovered1970s – Refining of manufacturing process1980s – OF technology becomes backbone of long

distance telephone networks in NA.

Page 21: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

OPTICAL FIBER

An optical fiber (or fibre) is a glass or plastic fiber

that carries light along its length.

Light is kept in the "core" of the optical fiber by

total internal reflection.

Page 22: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Advantages of Optical Fibre

Thinner Less Expensive Higher Carrying Capacity Less Signal Degradation Light Signals Non-Flammable Light Weight

Page 23: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Advantages of fiber optics

Much Higher Bandwidth (Gbps) - Thousands of channels can be multiplexed together over one strand of fiber

Immunity to Noise - Immune to electromagnetic interference (EMI).

Safety - Doesn’t transmit electrical signals, making it safe in environments like a gas pipeline.

High Security - Impossible to “tap into.”

Page 24: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Advantages of fiber optics

Less Loss - Repeaters can be spaced 75 miles apart (fibers can be made to have only 0.2 dB/km of attenuation)

Reliability - More resilient than copper in extreme environmental conditions.

Size - Lighter and more compact than copper. Flexibility - Unlike impure, brittle glass, fiber is

physically very flexible.

Page 25: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Areas of Application

Telecommunications Computer network LA N,WAN Cable TV CCTV Optical Fiber Sensors Nuclear plant instrument Industrial process control

system

Page 26: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Fiber Optic Cable

Page 27: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

OPTICAL FIBER CONSTRUCTION

Core – thin glass center of the fiber where light travels.Cladding – outer optical material surrounding the coreBuffer Coating – plastic coating that protects the fiber.

Page 28: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

OPTICAL FIBER

• The core, and the lower-refractive-index cladding,

are typically made of high-quality silica glass,

though they can both be made of plastic as well.

Page 29: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Fiber Optic Layers

• consists of three concentric sections

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plastic jacket glass or plasticcladding fiber core

Page 30: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Fiber Optic Cable

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Page 31: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

App. Of Fiber Optic Cable

Relatively new transmission medium used by telephone companies

in place of long-distance trunk lines

Also used by private companies in implementing local data

networks

It require a light source with injection laser diode (ILD) or light-

emitting diodes (LED)

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Page 32: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Five Generations of Light wave Systems

‡ First generation „ Operating near 800 nm and used GaAs semiconducor

laser, commercially available in 1980 „ Operated at bit rate of 45 Mbps and repeater spacing of

about 10 km (larger compared that of coaxial cable) „ Dec the instl and maintenance cost

‡ Second generation „ Operating near 1300 nm where fiber loss is 1 db/km

(typically 0.5 db/km) and fiber exhibit minimumdispersion.

„ Uses InGaAsP semiconductor lasers and detectors. (newly developed)

„ Available in early 80s „ By 1987 commercially available systems were operating at

bit rates of up to 1.7 Gbps and repeater spacing of about 50 km(SMF).

Page 33: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Cont.. ‡ Third generation

„ Fiber has minimum loss at 1550 nm (realized in 1979 butdispersion was considerably large)

„ Displayed more dispersion arround 1550nm

„ Dispersion shifted fibers could overcome the dispersionproblem , designed to have minimum dispersion around 1550 nm.

„ In 1990 commercially available systems were operating at 2.5 Gbps and capable of operating at 10 Gbps. (DSF with single-longitudinal-mode lasers)

„ Typical repeaters spacing is around 60-70 km

Page 34: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Cont.. ‡ Fourth generation

„ A drawback of third generation 1.55µmis that the signal is regenerated periodically by using electronic repeater.

„ The fourth generation makes use of optical amplifiers(1989) for increasing the repeater spacing and WDM for increasing the bit rate.

„ It employs erbium-doped fiber amplifiers(1990), 60 - 100 kmapart.

„ Several WDM systems were deployed across the Atlantic and Pacific oceans during 1998-2001 in response to the Internet-induced increase in the data traffic; they have increased the total capacity by orders of magnitudes.

‡ Fifth generation

„ Concerned with finding the fiber dispersion problems „ Optical amplifiers have solved the loss problem but made the

dispersion problem worse „ Solution is based on the concept of optical solitons - optical pulses

that preserve their shape during propagation by counteracting the effect of dispersion through the fiber nonlinearity.

Page 35: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

DWDM System

Page 36: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Refraction ‡ Imagine shining a flashlight. The light waves spread out along its beam. ‡ As we move further from the light source, the wavefront gets straighter

and straighter.

‡ At a long distance from the light source, the wavefront would be virtually straight.

‡ In a short interval of time each end of the wavefront would move forward a set distance.

‡ If we look at a single ray of light moving through a clear material the distance advanced by the wavefront would be quite regular.There is a widely held view that light always travels at the same speed.

This ‘fact’ is simply not true. The speed of light depends upon the material through which it is moving. In free space light travels at its maximum possible speed, close to 300 million meters or nearly eight times round the world in a second

Page 37: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Refractive index !! ™ When it passesthrough a clear material, it slows down by an amount dependent upon a property of the material called itsRefractive index. ™ For most materials that we use in optic fibers, the refractiveindex is in the region of 1.5.

Refractive Index = Speed of light in free space/Speed of light in material

Lower refractive index = higher speed

Page 38: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

If a ray of light enters from a material of highrefractive index to another material with a lower index, in which it would move faster. W e can see that the distances between thesuccessive wave crests, or the wavelength, willincrease as soon as the light moves into the second material.

‡ The direction that the light approaches the boundary between the two materials is very significant.

Page 39: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Snell’s law Willebrord Snell, a Dutch astronomer, discovered that there was a relationship between the refractive indices of the materials and the sine of the angles. He made this discovery in the year 1621.

Snell’s law states the relationship as:

n1sin φ1 = n2sin φ2

Where: n1 and n2 are the refractive indices of the two materials, and sin φ1 and sin φ2

are the angles of incidence and refraction respectively.

Snell's law will apply to the refraction of light in any situation, regardless of what the two media are.

Page 40: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Example Calculate the angle shown as φ2 ,The first material has a refractive index of 1.51 and the angle of incidence is 38° and the second material has a refractive index of 1.46. Starting with Snell’s law: n1sinφ1 = n2sinφ2

Page 41: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur
Page 42: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Critical angle - Light Guiding As the angle of incidence in the first material is increased, there will come a time when, eventually, the angle of refraction reaches 90° and the light is refracted along the boundary between the two materials. The angle of incidence which results in this effect is called the critical angle.We can calculate the value of the critical angle by assuming the angle of refraction to be 90° and transposing Snell’s law:

n1sin φ1 = n2sin90°

As the value of sin90° is 1, we can now transpose to find sin φ1, and hence φ1, (which is now the critical angle):

φ Critical

⎛n 2 ⎞ = arcSin ⎜ ⎟

⎝ n 1 ⎠

Page 43: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

A worked example

Page 44: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Total internal reflection ‡

The critical angle is well-named as its value is indeed critical to the operation of optic fibers. At angles of incidence less than the critical angle, the ray is refracted. However, if the light approaches the boundary at an angle greater than the critical angle, the light is actually reflected from the boundary region back into the first material. The boundary region simply acts as a mirror. This effect is called total internal reflection (TIR). The effect holds the solution to the puzzle of trapping the light in the fiber. If the fiber has parallel sides, and is surrounded by a material with a lower refractive index, the light will be reflected along it at a constant angle -shown as ø in the Figure .

‡ Any ray launched at an angle greater than the critical angle will be propagated along the optic fiber

Page 45: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur
Page 46: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Electromagnetic spectrum

Page 47: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur
Page 48: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Numerical aperture ‡ The numerical aperture of a fiber is a figure which represents

its light gathering capability. ‡ The acceptance angle also determines how much light is able to

enter the fiber and so we must expect an easy relationship between the nummerical aperture and the cone of acceptance as they are both essentially measurements of the same thing.

‡ The formula for the numerical aperture is based on the refractive indices of the core and the cladding.

2 NA = n core 2 −n cladding

Aceptance angle=sin-1 NA

Page 49: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Example Let’s try the short cut and see how it works out using values of ncore = 1.5, and

n cladding = 1.48

What will happen if incident angle is more than cone of acceptance ? H1

Page 50: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Geometrical- Optics description In its simplest form an optical fiber consists of a cylindrical core of silica glass surrounded by a cladding whose refractive index is lower than that of the core.

Because of an abrupt index change at the core-cladding interface, such fibers are called step-index fibers. In a different type of fiber, known as graded-index fiber, the refractive index decreases gradually inside the core.

Page 51: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

NA - Step index fiber ‡ Numerical Aperture is a measure of the light gathering power of the fiber. ‡ The acceptance angle for an optical fiber is maximum angle to the axis at

which light may enter the fiber in order to be propagated.

‡ It gives a relationship between the acceptance angle and the refractive indices of the three media involved, namely the core, cladding and air.

‡ The ray enters the fiber from a medium (air) of refractive index n0 , and the fiber core has a refractive index n1 , which is slightly greater than the cladding refractive index n2.

using Snell’s law no sinθi = n1 sinθr

Details are in class lecture

Page 52: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur
Page 53: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Example. A silica optical fiber with a core diameter large enough to be considered by ray theory analysis has a core refractive index of 1.50 and a cladding refractive index of 1.47.

Determine: (a) The critical angle at the core-cladding interface. (b) The NA for the fiber. (c) The acceptance angle in air for the fiber.

Solution: (a)The critical angle φc at the core- cladding interface is given by Eq.

sinφc = n2 / n1

φc = sin-1n2 / n1

= sin-1 1.47/1.50 = 78.50

Page 54: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

(b); From Eq. The numerical aperture is

NA = (n12 - n22) ½

= (1.502 - 1.472) ½

=(2.25 - 2.16) ½

=0.30

(c): Considering Eq the acceptance angle in the air θa is given by:

θa=sin-1 NA

= sin-1 0.30

=17.40

Page 55: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Intermodel dispersion (Multimode dispersion)

The extent of pulse broadening can be estimated by considering the

longest and shortest ray paths. The shortest path occurs for θ = 0, and X i

is just equal to the fiber lenght 'L'.The longest path occurs

for

shown previously and has a lenght 'L/sin Φ . v = c / n ,

Φc

θ i

the time delay is given by ;

∆T =T −T

c 1

L Max Min

L n 1

−L X= L/SinΦc s x−L n Ln n −n2 1 1 2= = = v v c

n 2

= cn 2

1

n 1 n SinΦc= n2/n1 1

X = L n1/n2

= Ln 1 ∆

When ∆ <<1 cn 2

Page 56: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

The tim e delay between the two rays taking the shortest and longest paths is a measure of broadening experienced by an impulse launched at the fiber input.

We can relate ∆T to the information-carrying capacity of the fiber measured through the bit rate B.,

Requirement for minimal inter symbol interference: B ∆T < 1

where B = bit rate

Page 57: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Names given to different rays ‡

The position and the angle at which the ray strikes the core will determine the exact path taken by the ray. There are three possibilities, called the skew, meridional and the axial ray as shown in Figure . If light enters a fiber from a practical light source, all three rays tend to occur as well as those outside of the cone of acceptance .

The skew ray never passes through the center of the core. Instead it reflects off the core/cladding interface and bounces around the outside of the core. It moves forward in a shape reminiscent of a spiral staircase built from straight sections.

The meridional ray enters the core and passes through its center. Thereafter, assuming the surfaces of the core are parallel, it will always be reflected to pass through the center. The axial ray is a particular ray that just happens to travel straight through the center of the core.

Page 58: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Graded index fibers ‡ The refractive index - is not constant. ‡ Decreases gradually from its maximum value n1 at the core center to

its minimum value n2 at the core-cladding interface. Most graded-index fibers are designed to have a nearly quadratic

decrease and are analyzed by using α-profile, given by

• where ‘a’ is the core radius. ‘ρ’ is the radial distance.

• The parameter α determines the index profile.

• A step-index - large α. A parabolic-index fiber corresponds to α= 2.

Page 59: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

Cont… ‡ Intermodal or multipath dispersion is

reduced for graded-index fibers. ‡ Figure shows schematically paths for

three different rays. ‡ The path is longer for more oblique

rays. However, the ray velocity changes along the path because of variations in the refractive index.

‡ The ray propagating along the fiber axis takes the shortest path but travels most slowly as the index is largest along this path.

‡ Oblique rays have a large part of their path in a medium of lower refractive index.

‡ Suitable choice of the refractive-index profile leads to non-dispersive pulse propagation. The trajectory of a ray is obtained by

Page 60: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

where ρ is the radial distance of the ray from the axis. For ρ< a with α = 2, Eq. above reduces to an equation of harm onic oscillator and has the general solution;

where p = (2∆/a2)1/2 and ρ0 and ρ’0 are the position and the direction of the input ray, respectively. All rays recover their initial positions and directions at distances z = 2mπ/p, where m is an integer.

Such a complete restoration of the input implies that a parabolic-index fiber does not exhibit intermodal dispersion.

Page 61: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

The quantity ∆T/L, where ∆T is the maximum multipath delay in a fiber of length L, is found to vary considerably with α. Figure shows this variation for n1 = 1.5 and ∆ = 0.01. The minimum dispersion occurs for α= 2(1−∆) and depends on ∆ as

The limiting bit rate-distance product is obtained by using the criterion ∆T < 1/B and is given by

Page 62: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

• The BL product of such fibers is improved by nearly three orders of magnitude over that of step-index fibers.

• Indeed, the first generation of lightwave systems used graded-index fibers. Further improvement is possible only by using single-mode fibers..

• Graded-index fibers are rarely used for long-haul links. They have relatively large core, resulting in a high numerical aperture and high coupling efficiency - but exhibit high losses .

• They can be used to transmit data at bit rates >1 Gb/s over short distances of 1 km or less (LAN).

Page 63: Opto Electronics Syed Abdul Rehman Rizvi The Islamia University of Bahawalpur

α- Profile The figures below expressing the range of refractive index profile of the fiber core as a variation of α. Allows representation of the step index fiber when α = ∞, a parabolic profile when α =2 and a triangular profile when α =1.