modern trends in telecom & information superhighway

Modern Trends in Telecom & Information Superhighway

Institute of Information & Communication Technologies (IICT), Mehran UET, Jamshoro

2

Modern Trends in Telecom & Info. Superhighway

I2CT, Mehran UET, Jamshoro Sindh Pakistan

Objectives • Understand optical fiber propagation characteristics and transmission

properties.• An understanding of the theory of optical sources including light-emitting

diodes and laser diodes, and the methods for using these devices in optical fiber communication systems

• Design such fiber optic links and relate the limitations in the performance to the limitations of the components and subsystems used;

• Understand the modeling of photo detectors, including shot noise and avalanche noise.

• Understand optical amplifiers and in particular their noise characteristics.• Understanding the principles and methods for constructing optical fiber

communication systems, including techniques to increase the data rate and decrease transmission impairments.

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Background of Optical Communications

Age of Smoke Signals and semaphores!

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Why Optical Communication?

• Optical Fiber is the backbone of modern communication networks– Voice (SONET/Telephony) - The largest traffic– Video (TV) over Hybrid Fiber Coaxial (HFC)– Fiber Twisted Pair for Digital Subscriber Loops (DSL)– Multimedia (Voice, Data and Video) over DSL or HFC

Information revolution wouldn’t have happened without the Optical Fiber

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Information revolution

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• Physical limits for the bandwidth– Wire ~ 1 MHz = 106 Hz

– Coaxial Cable ~ 10 GHz = 1010 Hz

– Microwave (Wireless) ~ 100 GHz = 1011 Hz

– Optical Fiber ~ 100 THz = 1014 Hz

– Free space Optics ~ 1000 THz = 1015 Hz

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Why Optical Communication?• Lowest attenuation attenuation in the optical fiber (at 1.3 µm and

1.55 µm bands) is much smaller than electrical attenuation in any cable at useful modulation frequencies– Much greater distances are possible without repeaters– This attenuation is independent of bit rate

• Highest Bandwidth (broadband) high-speed– Single Mode Fiber (SMF) offers the lowest dispersion highest

bandwidth rich content

• Upgradability: Optical communication system can be upgraded to higher bandwidth, more wavelengths by replacing only the transmitters and receivers

• Low Cost for fiber

9



Light in History• Light in Greek Times

– In Greek times many believed that light came from visible objects toward the eye. However, Plato and many other Greeks believed that vision issued out from the eye.

– Empedocles correctly believed that light traveled with finite speed.

– Aristotle explained rainbows as a sort of reflection off of raindrops.

– The mathematician Euclid worked with mirrors and reflection but did not know how to express it mathematically.

– Ptolemy is the first recorded person to experiment with optics and collect data, but he believed in Plato's mistaken thought.

• Light in Arabian Times – Ptolemy's work was further developed by the Egyptian scientist

Ibn al Haythen, who was known to Europeans as Alhazen.– Alhazen who first drew ray diagrams – The Arabian mathematician Alhazen studied the refraction of

light and disputed the ancient theory that visual rays emanated from the eye. He believed that the angles of incidence and refraction are related, but was unable to determine how they are related.

– This relationship, now known as Snell's law, was established six hundred years later.

http://en.wikipedia.org/wiki/File:Parthenon_from_west.jpg

http://en.wikipedia.org/wiki/File:Libr0310.jpg

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Light in Modern Times • Many advances in the study of light based on Alhazen work were made in the 16th and 17th

centuries by such renowned scientists as Galileo Galilei, Johannes Kepler, and Renes Descartes.

• The Snell's law was discovered.• During the late 17th century, a debate grew over whether light behaved as a particle or a

wave. Sir Isaac Newton and Laplace. • However, there were some who believed in a wave theory of light. The most notable among

these was the Dutch scientist Christiaan Huygens who first wrote of light as a wave. • It was not until the early 19th century that the wave theory of light became widely accepted.

This acceptance came in large part due to the work of the English doctor Thomas Young. (1801, “double-slit experiment”)

• In the 1850s Fizeau and Foucault showed through measurements that light traveled slower through denser media.

• In the same century, Augustin Fresnel and later James Clerk Maxwell, working on a wave theory of light explained phenomena such as polarization, interference, and diffraction. They also determined which part of the light will be reflected and which transmitted when light is reflected at a surface such as glass or water.

• Maxwell's work seemed to have finally settled the issue of whether light was a wave or a particle, but the whole debate was reopened in the 20th century.

• Scientists such as Albert Einstein, who described the Doppler effect for light, brought the particle theory back into the picture with quantum theory.

• This time they postulated that light did not just behave as a particle or a wave, but had properties of both.

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Properties of LightDefinition of light:

That agent, force, or action in nature by the operation of which objects are rendered visible or luminous. Or light is an electromagnetic radiation that can produce a visual sensation.

Properties of Light• Propagation Matter is not required for the propagation of light. • Reflection occurs at the surface, or boundary, of a regular medium.• Refraction, or bending, may occur where a change of speed is experienced.• Interference is found where two waves are superposed.• Diffraction, or bending around corners, takes place when waves pass the edges of

obstructions. • Scattering occurs at the surface, or boundary, of irregular medium.• Absorption change of light into heat energy.

Dual nature of light• Particle (or Corpuscular) Theory: Sir Isaac Newton believed that light consists of streams

of tiny particles, which he called "corpuscles," emanating from a luminous source. • Wave theory: Christian Huygens - The wave theory treats light as a train of waves having

wave fronts perpendicular to the paths of the light rays. Wave effects are insignificant in an incoherent, large scale optical system because the light waves are randomly distributed and there are plenty of photons.

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The Electromagnetic Theory • The James Clerk Maxwell in 1865 predicted that heat, light, and electricity are

propagated in free space at the speed of light as electromagnetic disturbances.

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The Electromagnetic Spectrum • EM-Spectrum extend from 10 Hz to 1025 Hz. • All EM radiations travel in free space with constant velocity of 3 x 108 m/s. • Optical radiation lies between radio waves and x-rays on the spectrum.

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Visible Spectrum/Visible Light• At x-ray and shorter wavelengths, electromagnetic radiation tends to be

quite particle like in its behavior, whereas toward the long wavelength end of the spectrum the behavior is mostly wavelike. The visible portion occupies an intermediate position, exhibiting both wave and particle properties in varying degrees.

• Their wave lengths range from approximately 7600 A to 4000 A. • The optical spectrum also extends into the near infrared and into the near

ultraviolet. Although our eyes cannot see these radiations, they can be detected by means of photographic film.

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Ultraviolet (UV) light

– UV-A (or black light) is the least harmful and most commonly found type of UV light, because it has the least energy. It is used for its relative harmlessness and its ability to cause fluorescent materials to emit visible light - thus appearing to glow in the dark. Most phototherapy and tanning booths use UV-A lamps.

– UV-B is typically the most destructive form of UV light, because it has enough energy to damage biological tissues, yet not quite enough to be completely absorbed by the atmosphere. UV-B is known to cause skin cancer. Since most of the extraterrestrial UV-B light is blocked by the atmosphere, a small change in the ozone layer could dramatically increase the danger of skin cancer.

– Short wavelength UV-C is almost completely absorbed in air within a few hundred meters. When UV-C photons collide with oxygen atoms, the energy exchange causes the formation of ozone. UV-C is almost never observed in nature, since it is absorbed so quickly. Germicidal UV-C lamps are often used to purify air and water, because of their ability to kill bacteria.

Common UV band designations

Short wavelength UV light exhibits more quantum properties than its visible and infrared counterparts. UV light is arbitrarily broken down into three bands:

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Infrared (IR) Light• Infrared light contains the least amount of energy per photon of any other band and

therefore, an IR photon often lacks the energy required to pass the detection threshold of a quantum detector. IR is usually measured using a thermal detector such as a thermopile, which measures temperature change due to absorbed energy.

• Since heat is a form of infrared light, far infrared detectors are sensitive to environmental changes - such as a person moving in the field of view. Night vision equipment takes advantage of this effect, amplifying infrared to distinguish people and machinery that are concealed in the darkness.

• Infrared is unique in that it exhibits primarily wave properties. This can make it much more difficult to manipulate than UV and visible light. IR is more difficult to focus with lenses, refracts less, diffracts more, and is difficult to diffuse.

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The most important ideasThe most important ideas to note are: • Light travel slower through denser media. • Propagation Matter is not required for the propagation of light. • Reflection occurs at the surface, or boundary, of a regular medium.• Refraction, or bending, may occur where a change of speed is experienced.• Interference is found where two waves are superposed.• Diffraction, or bending around corners, takes place when waves pass the edges

of obstructions. • Scattering occurs at the surface, or boundary, of irregular medium.• Absorption change of light into heat energy. • Electromagnetic waves span over many orders of magnitude in wavelength (or

frequency). • The frequency of the electromagnetic radiation is inversely proportional to the

wavelength. • The visible spectrum is a very small part of the electromagnetic spectrum. • Photon energy increases as the wavelength decreases. The shorter the

wavelength, the more energetic are its photons.

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Wavelength Standards• Frequency multiples of 50 GHz or 100 GHz• λ = c/f c = 299792458 m/s• λ [nm] = 299792.458/f [THz]

– f = 195 THz → λ = 1537.397 nm– f =195.1 THz → λ = 1536.609 nm– f =195.2 THz → λ = 1535.822 nm– f =193.4 THz → λ = 1550.116 nm

f

50 or 100 GHz ITU grid

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Wavelength Ranges available for Communication

Band Name Range

O-band Original 1260 – 1360 nm

E-Band Extended 1360 – 1460 nm

S-Band Short 1460 – 1530 nm

C-Band Conventional 1530 – 1565 nm

L-Band Long 1565 – 1625 nm

U-Band Ultra-long 1625 – 1675

Different types of sources/detectors/amplifiers are used in different bands

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Example of a ProblemHow many 100 GHz-ITU Grid channels are covered by the conventional band (1530 – 1560 nm)?

λ = 1530 nm → f = 195.943 THzλ = 1560 nm → f = 192.174 THz

192.2 192.3192.4...195.7195.8195.9

3813711.0

2.1929.195

N

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Fiber Optic Communication System• Generic System

• Transmitter and receiver module

• Fiber-optic communication channel

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OFC System• An optical fiber communication (OFC) system is similar in basic

concept to any type of communication system, the function of which is to convey the signal from the information source over the transmission medium, to the destination.

• For OFC, the information source (usually, an LED or laser) provides an electrical signal to a transmitter comprising an electrical stage which drives an optical source to give modulation of the light wave carrier.

• The transmission medium consists of an optical fiber cable and the receiver consists of an optical detector which drives a further electrical stage and hence provides demodulation of the optical carrier.

• Photodiodes (p-n, p-i-n, or avalanche) and, in some instances, phototransistors and photoconductors are used as detectors.

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Networks • Local area networks (LAN) L ≤ 1 km • Metropolitan area networks (MAN) L ≤ 10 km • Wide area networks (WAN) L ≥ 100 km

• LAN: provides communication access to users. Bit-rate requirement is relatively low. Main issue: scalable and reconfigurable architecture.

• MAN: provides communication access within a city. Moderate Bit-rate requirements. Fixed architecture acceptable in many access

• WAN: provides communication over long distances. High-bit rate is required. Use of multiplexing techniques. Compensation for optical losses and dispersion is major problem.

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First Generation Fiber Optic Systems

Purpose:• Eliminate repeaters in T-1 systems used in inter-office trunk linesTechnology:• 0.8 µm GaAs semiconductor lasers• Multimode silica fibers• All the switching and processing is handled by electronicsLimitations:• Fiber attenuation• Intermodal dispersionDeployed since 1974• Examples

– SONET (synchronous optical network), USA– SDH (synchronous digital hierarchy), international – FDDI (Fiber distributed data network)

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Second Generation Fiber Optic SystemsOpportunity:• Development of low-attenuation fiber (removal of H2O and other

impurities)• Eliminate repeaters in long-distance lines

Technology:• Use optics for switching and routing • 1.3 µm multi-mode semiconductor lasers• Single-mode, low-attenuation silica fibers• DS-3 signal: 28 multiplexed DS-1 signals carried at 44.736 Mbps

Limitation:• Fiber attenuation (repeater spacing ≈ 6 km)

Deployed since 1978

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Third Generation Fiber Optic Systems

Opportunity:• Deregulation of long-distance market

Technology:• 1.55 µm single-mode semiconductor lasers• Single-mode, low-attenuation silica fibers• OC-48 signal: 810 multiplexed 64-kb/s voice channels carried at

2.488 Gbps

Limitations:• Fiber attenuation (repeater spacing ≈ 40 km)• Fiber dispersion

Deployed since 1982

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Fourth Generation Fiber Optic Systems

Opportunity:• Development of erbium-doped fiber amplifiers (EDFA)

Technology (deployment began in 1994):• 1.55 µm single-mode, narrow-band semiconductor lasers• Single-mode, low-attenuation, dispersion-shifted silica fibers• Wavelength-division multiplexing of 2.5 Gb/s or 10 Gb/s signals

Nonlinear effects limit the following system parameters:• Signal launch power• Propagation distance without regeneration/re-clocking• WDM channel separation• Maximum number of WDM channels per fiber

Polarization-mode dispersion limits the following parameters:• Propagation distance without regeneration/re-clocking

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Evolution of Optical Networks

1.55 μm DFB Laser Receiver

0.85 LED or LD Receiver

Regenerators/repeaters

Multimode fibers

1.3 μm FP Laser Receiver

Single mode fibers

T3

T2

T1

MU

XDE

MU

X

T3

T2

T1Single mode fibers

Optical amplifiers

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History of Attenuation

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Three windows based on Wavelengths

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Multiplexing Technologies

• Time division multiplexing Low-speed data streams

High-speed data streams

Bit rate 10 to 40 Gbps

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Wavelength Division Multiplexing

MU

X

λ1

λN

λ3

λ2

λ1 λNλ3λ2

.

.

...Essentially the same as frequency division multiplexing

WDM: 32 wavelengths, 2.5 Gbps each → 80 Gbps commercially available now.

Combination of WDM and TDM demonstrated to provide 2 Tbps over single mode fiber

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What is Fiber Optics • Fiber optics (optical fibers) are long, thin strands of

very pure glass about the diameter of a human hair. • They are arranged in bundles called optical cables. • If you look closely at a single optical fiber, you will see

that it has the following parts: – Core (n1) - is a cylindrical rod of dielectric

material. Light propagates mainly along the core of the fiber.

– Cladding (n2)- Outer optical material surrounding the core that reflects the light back into the core. The index of refraction of the cladding material is less than that of the core material (n2 < n1). The cladding performs the following functions:

• Reduces loss of light from the core into the surrounding air

• Reduces scattering loss at the surface of the core• Protects the fiber from absorbing surface contaminants• Adds mechanical strength

– Buffer coating -. For extra protection, the cladding is enclosed in an additional layer called the coating or buffer. It is a layer of material used to protect an optical fiber from physical damage and moisture.

Refractive Index (n): The ratio of velocity of light in air ‘c’ to the ratio of velocity of light in any medium ‘v’.

vcn

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Types of Optical Fiber• Single mode

– Single mode step index• Multi mode

– Multimode step index– Multimode graded index

• Dispersion Shifted/Non-dispersion shifted

• Silica/fluoride/Other materialsMode: A set of electromagnetic wave

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Types of Fibersst

ep-in

dex

mul

timod

e nc

nc

n1

nc

nc

nc

nc

step

-inde

xsin

glem

ode

GRIN

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Single Mode Step Index• A small-core optical fiber through which only one mode will

propagate. • The typical diameter is about 3.5 x 10-4 inches or 9 microns. • Step-index Fiber: Fiber that has a uniform index of refraction

throughout the core that is a step below the index of refraction in the cladding.

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Multi-mode Fiber• Multimode (MM) Fiber: An optical fiber that has a core large

enough to propagate more than one mode of light. The typical diameter is about 2.5 x 10-3 inches or 62.5 microns.– Multimode Step-Index Fiber: Fiber that has a uniform index of refraction

throughout the core that is a step below the index of refraction in the cladding and allows more than one mode of light.

– Multimode Graded-Index Fiber: A multimode graded-index fiber has a core of radius (a). Unlike step-index fibers, the value of the refractive index of the core (n1) varies according to the radial distance (r). The value of n1 decreases as the distance (r) from the center of the fiber increases.

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Multimode Graded Index Fiber

Step-index Single mode fiber

Graded-index Multi mode fiber

Step-index Multi mode fiber

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Typical dimensions

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Transmission of Light through Optical Fibers

• The transmission of light along optical fibers depends not only on the nature of light, but also on the structure of the optical fiber.

• Two theories are used to describe how light is transmitted along the optical fiber.

– Ray theory, uses the concepts of light reflection and refraction and treat light as a simple ray. The advantage of the ray approach is that you get a clearer picture of the propagation of light along a fiber. The ray theory is used to approximate the light acceptance and guiding properties of optical fibers.

– Mode theory, treats light as electromagnetic waves. The mode theory describes the behavior of light within an optical fiber. The mode theory is useful in describing the optical fiber properties of absorption, attenuation, and dispersion.

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Ray theory

• Two types of rays can propagate along an optical fiber, meridional rays and skew rays.

• Meridional rays pass through the axis of the optical fiber. – Meridional rays are used to illustrate the basic transmission

properties of optical fibers.

• Skew rays are rays that travel through an optical fiber without passing through its axis.

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Refractive index • The refractive index is the ratio of the speed of light in a vacuum, c, to the speed of

light in the medium, v.

• Since the speed of light in a medium is always less than it is in a vacuum, the refractive index is always greater than one. In air, the value is very close to 1.

• The refractive index varies with the wavelength of light. • In a homogeneous medium, that is, one in which the refractive index is constant,

light travels in a straight line. Only when the light meets a variation or a discontinuity in the refractive index will the light rays be bent from their initial direction.

• The light travelling into an optically denser medium (with higher refractive index) would be bent toward the normal, while light entering an optically rarer medium would be bent away from the normal.

vcn

44



Light in optical fibers • If one were to use a fiber consisting of only a single strand of glass or

plastic, light could be lost at any point where the fiber touched a surface for support.

• To eliminate this possibility, the central light carrying portion of the fiber, called the core, is surrounded by a cylindrical region, called the cladding.

• Since the refractive index difference between the core and the cladding is less than in the case of a core and air, the critical angle is much bigger for the clad fiber. The index of the cladding n2, is still less than the index of the core n1, because total internal reflection will occur only when n1 > n2.

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Total Internal Reflection • The light in a fiber-optic cable travels through the core (hallway) by

constantly bouncing from the cladding (mirror-lined walls), a principle called Total Internal Reflection.

• When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". The exit angle will then approach 90° for some critical incident angle θc , and for incident angles greater than the critical angle there will be total internal reflection.

What is Frustrated TIR? And where it is useful?

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Ray theory

Snell’s Law• The angle of incidence θ1 and refraction θ2 are

related to each other by Snell’s law, which states:

Critical Angle• The critical angle can be calculated from Snell's law

by setting the refraction angle equal to 90°.

2211 sinsin nn

1

2sinnn

c

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Total internal reflection

Incident ray

Exit ray

Partial internalreflection

Low index n2(air)

2

1

High index n1(glass)

n2

n1

(a) refraction (b) the limiting case of refraction showingthe critical ray at an angle

c

c

(c) total internal reflection where c

n1

n2

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Transmission of light through perfect optical fiber

Low index cladding

High index core

The transmission of a light ray in a perfect optical fiber

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Phase change due to TIR• In addition, when light is totally internally reflected, a phase

change δ occurs in the reflected wave. This phase change depends on the angle θ1 ˂ θc according to the relationships

here δN and δp are the phase shits of the wave components normal and parallel to the place of incidence, respectively, and n = n1/n2.

1

122

1

122

sin1cos

2tan

sin1cos

2tan

nn

nn

p

N

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Relative refractive index

• It defines the difference in the core and cladding refractive indices.

1

2121

22

21

2 nnn

nnn

51



Acceptance Angle• The acceptance angle (a) is the largest incident angle ray that

can be coupled into a guided ray within the fiber

The acceptance angle is related to the refractive indices of the core, cladding, and medium surrounding the fiber. This relationship is called the numerical aperture of the fiber.

The numerical aperture (NA) is a measurement of the ability of an optical fiber to capture light.

The NA is also used to define the acceptance cone of an optical fiber.

Numerical Aperture

22

210 sin nnnNA a

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Meridional Rays

• Meridional rays can be further classified as bound or unbound rays.

• Bound rays remain in the core and propagate along the axis of the fiber. Bound rays propagate through the fiber by total internal reflection.

• Unbound rays are refracted out of the fiber core. Figure 2-3 shows a possible path taken by bound and unbound rays in a step-index fiber. In general, meridional rays follow the laws of reflection and refraction.

Meridional Rays

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Skew Rays• Skew rays propagate without passing through the center axis

of the fiber. • The θas (for skew rays) ˃ θa (meridional rays). • Skew rays are often used in the calculation of light

acceptance in an optical fiber. • The addition of skew rays increases the amount of light

capacity of a fiber. • In a multimode fiber, most rays are skew rays.• The addition of skew rays also increases the amount of loss in

a fiber. Skew rays tend to propagate near the edge of the fiber core.

• The acceptance angle is:

• where γ = change in direction/2

cossin 1 NA

as

Skew Rays

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Mode Theory

• The mode theory uses electromagnetic wave behavior to describe the propagation of light along a fiber.

• A set of guided electromagnetic waves is called the mode of the fiber.

• Depending on the boundary conditions, two types of modes are to be distinguished: – If the electromagnetic field is zero at infinity, the mode is

guided;. This implies that the guided mode spectrum is discrete.

– If not, it is a radiation mode. They exist in a continuum.

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Limitations of Ray Theory

• Ray theory describes only the direction a plane wave takes in a fiber. In reality, plane waves interfere with each other. Therefore, only certain types of rays are able to propagate in an optical fiber.

• Optical fibers can support only a specific number of guided modes. In small core fibers, the number of modes supported is one or only a few modes.

• Mode theory is used to describe the types of plane waves able to propagate along an optical fiber.

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Plane Wave• The mode theory suggests that a light wave can be represented as a

plane wave. • A plane wave is a wave whose surfaces of constant phase are infinite

parallel planes normal to the direction of propagation. • A plane wave is described by its direction, amplitude, and wavelength

of propagation.• The planes having the same phase are called the wavefronts. • The wavelength, λ, of the plane wave is given by:

• Where c is the speed of light in a vacuum, f is the frequency of the light, and n is the index of refraction of the plane-wave medium.

nfcwave ,length

http://upload.wikimedia.org/wikipedia/commons/2/20/Plane_wave_wavefronts_3D.svg

57



Plane Wave• The plane waves repeat as they travel along the fiber axis.

– At distance:– At a periodic frequency:

• The quantity β is defined as the propagation constant along the fiber axis. It is a function of the wave's wavelength and mode.

• As the wavelength (λ) changes, the value of the propagation constant must also change.

• For a given mode, a change in λ can prevent the mode from propagating along the fiber. The mode is no longer bound to the fiber. The mode is said to be cut off.

sin/ /sin2

58



Plane Waves• Modes that are bound at one wavelength may not exist at

longer wavelengths. • The wavelength at which a mode ceases to be bound is

called the cutoff wavelength for that mode. Or the wavelength that prevents the next higher mode from propagating is called the cutoff wavelength of the fiber.

• However, an optical fiber is always able to propagate at least one mode. This mode is referred to as the fundamental mode of the fiber. The fundamental mode can never be cut off.

• Single mode fiber operates @/above cutoff wavelength. • Multimode fiber operates below the cutoff wavelength.

59



Modes • A set of guided electromagnetic waves is called the modes of

an optical fiber.• Maxwell's equations describe electromagnetic waves or

modes as having two components; – the electric field, E(x, y, z), and – the magnetic field, H(x, y, z).

• The electric field, E, and the magnetic field, H, are perpendicular to each other.

60



Modes • Modes traveling in an optical fiber are said to be transverse. The transverse

modes propagate along the axis of the fiber. • In TE modes, the electric field is perpendicular to the direction of

propagation. • In TM modes, the magnetic field is perpendicular to the direction of

propagation. • The modes ain’t confined to the core of the fiber - extend partially into

cladding. • Low-order modes penetrate the cladding only slightly. In low-order modes,

the electric and magnetic fields are concentrated near the center of the fiber.

• However, high-order modes penetrate further into the cladding material. In high-order modes, the electrical and magnetic fields are distributed more toward the outer edges of the fiber.

61



Modes • This penetration of low-order and high-order modes into the cladding region

indicates that some portion is refracted out of the core. Cladding Mode• The refracted modes may become trapped in the cladding due to the dimension of

the cladding region. The modes trapped in the cladding region are called cladding modes.

Mode coupling• As the core and the cladding modes travel along the fiber, mode coupling occurs.

Mode coupling is the exchange of power between two modes. Mode coupling to the cladding results in the loss of power from the core modes.

• A mode remains bound if the propagation constant β meets the following boundary condition:

12 22 nn

62



Normalized Frequency • The normalized frequency (a dimensionless quantity)

determines how many modes a fiber can support. Normalized frequency (V) is defined as:

• Where n1 is the core index of refraction, n2 is the cladding index of refraction, ‘a’ is the core radius, and λ is the wavelength of light in air.

• The number of modes that can exist in a fiber is a function of V. As the value of V increases, the number of modes supported by the fiber increases.

22

21

2 nnaV

63



Example of # of Modes @ 850nm• Silica step-index fiber has n1 = 1.452, n2 = 1.442 (NA = 0.205)

• SELFOC graded index fiber with same NA

• From the V parameter, we see that we can reduce the number of modes in a fiber by reducing: (1) NA (2) diameter (wrt )

• This is exactly the case in single mode fibers.

diameter (microns) 2.5 50 200 400 1000

# step-index modes 2 1.4 E3 22 E3 92 E3 2.4 E6

# GRIN modes 1 716 11 E3 46 E3 1.2 E6

64



Phase & Group Velocity Phase Velocity• Plane waves form a surface with constant phase points called wavefronts.

As a monochromatic light wave propagates along a waveguide in the direction of propagation these points of constant phase travel at a phase velocity vp given by:

• where ω is the angular frequency of the wave.Group Velocity• Often the situation exists where a group of waves with closely familiar

frequencies propagate so that their resultant forms a packet of waves. This wave packet does not travel at the phase velocity of the individual waves but is observed to move at a group velocity given by:

pv

gv

65



Goos – Haenchen Shift

Penetrationdepth

Vertical reflecting plane

d

Lateral shift

1 1

n2

n1 > n2

66



Single Mode Step-Index Fibers• The optical fiber with a core of radius ‘a’ and a constant refractive

index n1 and a cladding of slightly lower refractive index n2 is known as step index fiber.

• There are two basic types of single mode step-index fibers: matched clad and depressed clad. – Matched cladding means that the fiber cladding consists of a single

homogeneous layer of dielectric material.– Depressed cladding means that the fiber cladding consists of two regions:

the inner and outer cladding regions.

a for ,a for ,

2

1

rnrn

rn n1n2

n(r)

ab

67



SM Fiber cutoff wavelength

• Single mode fiber cutoff wavelength is the smallest operating wavelength when single mode fibers propagate only the fundamental mode.

• At this wavelength, the 2nd-order mode becomes lossy and radiates out of the fiber core.

• As the operating wavelength becomes longer than the cutoff wavelength, the fundamental mode becomes increasingly lossy.

68



Single Mode Step-Index Fibers• A SM step-index fiber has

– low attenuation – low intermodal dispersion (broadening of transmitted light pulse), as

only one mode is transmitted, and – high bandwidth properties.

• Present applications for single mode fibers include – Long-haul, high-speed telecommunication systems.– Future applications include single mode fibers for sensor systems.

• However, the current state of single mode technology makes installation of single mode systems expensive and difficult.

69



Multi-mode Step-Index Fiber• Multimode step index fibers allow the propagation of a finite

number of guided modes along the channel. • A multimode step-index fiber has a core of radius ‘a’ and a

constant refractive index n1. A cladding of slightly lower refractive index n2 surrounds the core.

• The difference in the core and cladding refractive index is the parameter Δ, given by:

Δ is the relative refractive index difference.

21

22

21

2nnn

70



Multi-mode Step-Index Fiber• In a typical MM step-index fiber, there are hundreds of

propagating modes. • Most modes in multimode step-index fibers propagate far from

cut-off wavelength λc. – Modes away from the λc concentrate most of their light energy into

the fiber core. – Modes close to λc have a greater percentage of their light energy

propagate in the cladding.– Since most modes propagate far from cutoff, the majority of light

propagates in the fiber core. – Therefore, in multimode step-index fibers, cladding properties such

as cladding diameter, have limited effect on mode (light) propagation.

71



Multi-mode Step-Index Fiber• The total number of guided modes or mode volume Ms for a

step index fiber is related to the normalized frequency, V, by the approximate expression:

• This allows an estimate of the number of guided modes propagating in a particular multimode step index fiber.

• Only for large number of modes (V >> 2.4), the number of modes can be given by V2/2. Under this condition the ratio between power travelling in the cladding and in the core is given by

2V 2

sM

72



Multi-mode Step-Index Fiber

• Multimode step-index fibers have relatively large core diameters and large numerical apertures.

• A large core size and a large numerical aperture make it easier to couple light from LED into the fiber.

• Unfortunately, multimode step-index fibers have limited bandwidth capabilities. Dispersion, mainly modal dispersion, limits the bandwidth or information-carrying capacity of the fiber. Short-haul, limited bandwidth, low-cost applications typically use multimode step-index fibers.

73



Multimode Graded-Index Fiber• In multimode (MM) graded-index fiber with core of radius ‘a’, unlike step-index

fibers, the value of the refractive index of the core n1 varies according to the radial distance ‘r’ i.e., such fibers do not have constant refractive index in the core.

• The value of n1 decreases as the distance r from the center of the fiber increases.• The index variation may be represented as:

• where Δ is the relative refractive index difference and is profile parameter which determines the shape of the core's profile.

• The relative refractive index difference (Δ) is determined using the maximum value of n1 and the value of n2.

)( 21)( /21)(

22/1

1

2/1

1

claddingarnncoreararnrn

74



Graded Index Fibernc

nc

n va

ries

quad

ratic

ally

like a “restoring” force !

75



MM Graded-Index Fiber• Multimode graded-index fibers exhibit far less intermodal

dispersion than multimode step index fivers due to their refractive index profile. This results in the transmission bandwidths which may be orders of magnitude greater than multimode step index fiber bandwidths.

• Multimode graded-index fibers accept less light than multimode step-index fibers with the same core & Δ.

76



MM Graded-Index Fiber

• The total number of guided modes or mode volume Mg for a graded-index fiber is related to the normalized frequency, V, by the approximate expression:

• Hence, for a parabolic refractive index profile core ( = 2),

2V

2

2

gM

4V2

gM

77



Applications of Optical Fiber • Applications

– Most present day applications that use multimode fiber use graded-index fibers. – LAN

• Advantages– In most applications, a multimode graded-index fiber with a core and cladding size of

62.5/125 μm offers the best combination of the following properties: – Relatively high source-to-fiber coupling efficiency– Low loss– Low sensitivity to microbending and macrobending– High bandwidth– Expansion capability

• Disadvantages– In LAN type environment, macrobends and microbands losses are hard to predict.– Cable tension, bends, and local tie-downs increase macrobend and microbend losses.

78



Summary

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