Fiber Optic Communications (eBook)

Fundamentals and Applications

Shiva Kumar, M. Jamal Deen (Autoren)

eBook Download: EPUB

2014
John Wiley & Sons (Verlag)
978-1-118-68344-6 (ISBN)

Infos

Fiber-optic communication systems have advanced dramatically over the last four decades, since the era of copper cables, resulting in low-cost and high-bandwidth transmission. Fiber optics is now the backbone of the internet and long-distance telecommunication. Without it we would not enjoy the benefits of high-speed internet, or low-rate international telephone calls.

This book introduces the basic concepts of fiber-optic communication in a pedagogical way. The important mathematical results are derived by first principles rather than citing research articles. In addition, physical interpretations and real-world analogies are provided to help students grasp the fundamental concepts.

Key Features: 

• Lucid explanation of key topics such as fibers, lasers, and photodetectors.
• Includes recent developments such as coherent communication and digital signal processing.
• Comprehensive treatment of fiber nonlinear transmission.
• Worked examples, exercises, and answers.
• Accompanying website with PowerPoint slides and numerical experiments in MATLAB.

Intended primarily for senior undergraduates and graduates studying fiber-optic communications, the book is also suitable as a professional resource for researchers working in the field of fiber-optic communications.

Shiva Kumar, Department of Electrical and Computer Engineering, McMaster University, Canada

M. Jamal Deen, Department of Electrical and Computer Engineering, McMaster University, Canada

Rezensionen

"The detailed, worked examples and first-principles
derivations of key results are helpful pedagogical features.
Students seeking their first exposure to this field who also wish
to learn about advanced topics will find their requirements met by
this book." (Optics and Photonics News, 28
August 2014)

Textauszug

Chapter 1
Electromagnetics and Optics

1.1 Introduction

In this chapter, we will review the basics of electromagnetics and optics. We will briefly discuss various laws of electromagnetics leading to Maxwell's equations. Maxwell's equations will be used to derive the wave equation, which forms the basis for the study of optical fibers in Chapter 2. We will study elementary concepts in optics such as reflection, refraction, and group velocity. The results derived in this chapter will be used throughout the book.

1.2 Coulomb's Law and Electric Field Intensity

In 1783, Coulomb showed experimentally that the force between two charges separated in free space or vacuum is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The force is repulsive if the charges are alike in sign, and attractive if they are of opposite sign, and it acts along the straight line connecting the charges. Suppose the charge is at the origin and is at a distance as shown in Fig. 1.1. According to Coulomb's law, the force on the charge is

1.1

where is a unit vector in the direction of and is called the permittivity that depends on the medium in which the charges are placed. For free space, the permittivity is given by

1.2

For a dielectric medium, the permittivity is larger than . The ratio of the permittivity of a medium to the permittivity of free space is called the relative permittivity, ,

1.3

It would be convenient if we could find the force on a test charge located at any point in space due to a given charge . This can be done by taking the test charge to be a unit positive charge. From Eq. (1.1), the force on the test charge is

1.4

The electric field intensity is defined as the force on a positive unit charge and is given by Eq. (1.4). The electric field intensity is a function only of the charge and the distance between the test charge and .

Figure 1.1 Force of attraction or repulsion between charges.

For historical reasons, the product of electric field intensity and permittivity is defined as the electric flux density ,

1.5

The electric flux density is a vector with its direction the same as the electric field intensity. Imagine a sphere of radius around the charge as shown in Fig. 1.2. Consider an incremental area on the sphere. The electric flux crossing this surface is defined as the product of the normal component of and the area .

1.6

where is the normal component of . The direction of the electric flux density is normal to the surface of the sphere and therefore, from Eq. (1.5), we obtain . If we add the differential contributions to the flux from all the incremental surfaces of the sphere, we obtain the total electric flux passing through the sphere,

1.7

Since the electric flux density given by Eq. (1.5) is the same at all points on the surface of the sphere, the total electric flux is simply the product of and the surface area of the sphere ,

1.8

Thus, the total electric flux passing through a sphere is equal to the charge enclosed by the sphere. This is known as Gauss's law. Although we considered the flux crossing a sphere, Eq. (1.8) holds true for any arbitrary closed surface. This is because the surface element of an arbitrary surface may not be perpendicular to the direction of given by Eq. (1.5) and the projection of the surface element of an arbitrary closed surface in a direction normal to is the same as the surface element of a sphere. From Eq. (1.8), we see that the total flux crossing the sphere is independent of the radius. This is because the electric flux density is inversely proportional to the square of the radius while the surface area of the sphere is directly proportional to the square of the radius and therefore, the total flux crossing a sphere is the same no matter what its radius is.

Figure 1.2 (a) Electric flux density on the surface of the sphere. (b) The incremental surface on the sphere.

So far, we have assumed that the charge is located at a point. Next, let us consider the case when the charge is distributed in a region. The volume charge density is defined as the ratio of the charge and the volume element occupied by the charge as it shrinks to zero,

1.9

Dividing Eq. (1.8) by where is the volume of the surface and letting this volume shrink to zero, we obtain

1.10

The left-hand side of Eq. (1.10) is called the divergence of and is written as

1.11

Eq. (1.11) can be written as

1.12

The above equation is called the differential form of Gauss's law and it is the first of Maxwell's four equations. The physical interpretation of Eq. (1.12) is as follows. Suppose a gunman is firing bullets in all directions, as shown in Fig. 1.3 [1]. Imagine a surface that does not enclose the gunman. The net outflow of the bullets through the surface is zero, since the number of bullets entering this surface is the same as the number of bullets leaving the surface. In other words, there is no source or sink of bullets in the region . In this case, we say that the divergence is zero. Imagine a surface that encloses the gunman. There is a net outflow of bullets since the gunman is the source of bullets and lies within the surface , so the divergence is not zero. Similarly, if we imagine a closed surface in a region that encloses charges with charge density , the divergence is not zero and is given by Eq. (1.12). In a closed surface that does not enclose charges, the divergence is zero.

Figure 1.3 Divergence of bullet flow.

1.3 Ampere's Law and Magnetic Field Intensity

Consider a conductor carrying a direct current . If we bring a magnetic compass near the conductor, it will orient in the direction shown in Fig. 1.4(a). This indicates that the magnetic needle experiences the magnetic field produced by the current. The magnetic field intensity is defined as the force experienced by an isolated unit positive magnetic charge (note that an isolated magnetic charge does not exist without an associated ), just like the electric field intensity is defined as the force experienced by a unit positive electric charge.

Figure 1.4 (a) Direct current-induced constant magnetic field. (b) Ampere's circuital law.

Consider a closed path or around the current-carrying conductor, as shown in Fig. 1.4(b). Ampere's circuital law states that the line integral of about any closed path is equal to the direct current enclosed by that path,

1.13

The above equation indicates that the sum of the components of that are parallel to the tangent of a closed curve times the differential path length is equal to the current enclosed by this curve. If the closed path is a circle () of radius , due to circular symmetry, the magnitude of is constant at any point on and its direction is shown in Fig. 1.4(b). From Eq. (1.13), we obtain

1.14

or

1.15

Thus, the magnitude of the magnetic field intensity at a point is inversely proportional to its distance from the conductor. Suppose the current is flowing in the -direction. The -component of the current density may be defined as the ratio of the incremental current passing through an elemental surface area perpendicular to the direction of the current flow as the surface shrinks to zero,

1.16

The current density is a vector with its direction given by the direction of the current. If is not perpendicular to the surface , we need to find the component that is perpendicular to the surface by taking the dot product

1.17

where is a unit vector normal to the surface . By defining a vector , we have

1.18

and the incremental current is given by

1.19

The total current flowing through a surface is obtained by integrating,

1.20

Using Eq. (1.20) in Eq. (1.13), we obtain

1.21

where is the surface whose perimeter is the closed path .

In analogy with the definition of electric flux density, magnetic flux density is defined as

1.22

where is called the permeability. In free space, the permeability has a value

1.23

In general, the permeability of a medium is written as a product of the permeability of free space and a constant that depends on the medium. This constant is called the relative permeability ,

1.24

The magnetic flux crossing a surface can be obtained by integrating the normal component of magnetic flux...

Produkt-Details

• Erscheint lt. Verlag: 12.6.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Backbone • BASIC • Benefits • Book • Cables • Concepts • Copper • decades • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • ERA • fiber • fiberoptic communication • First • Four • Glasfaseroptik • Highspeed • important • Internet • Last • lowcost • Materials Science • Materialwissenschaften • Optical and Non-Linear Optical Materials • Optical Communications • Optics • Optics & Photonics • Optik u. Photonik • Optische Nachrichtentechnik • Optische u. Nichtlineare Optische Materialien • pedagogical • Physics • Physik • Systems • Telecommunication • Way
• ISBN-10: 1-118-68344-7 / 1118683447
• ISBN-13: 978-1-118-68344-6 / 9781118683446