Optical Fibers - 1st Edition - ISBN: 9780125252607, 9780323141482

Optical Fibers

1st Edition

Authors: Takanori Okoshi
eBook ISBN: 9780323141482
Imprint: Academic Press
Published Date: 28th April 1982
Page Count: 314
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Optical Fibers describes the theoretical basis—electromagnetic theories—of transmission characteristics of optical fibers. The material and fabrication technologies are not described systematically, but only briefly where necessary to assist comprehension of the transmission characteristics.
This book comprises 11 chapters, with an introductory chapter that discusses such topics as optical communications before the advent of optical fibers, a technical background of the subject matter, and a summary of its history. Succeeding chapters then discuss basic concepts and equations; ray theory of optical fibers; wave theory of uniform-core fibers; wave theory of nonuniform-core fibers; and classification and comparison of various analysis methods. Other chapters cover optimum refractive-index profile of optical fibers; optical fibers having structural fluctuations; measurement of refractive-index profile of optical fibers; measurement of transmission characteristics of optical fibers; and finally, some concluding remarks. This book will be of interest to practitioners in the fields of electronic engineering and electrical communications.

Table of Contents



1 Introduction

1.1 Technical Background

1.2 Optical Communications Before the Advent of Optical Fibers

1.3 Summary of the History

1.4 Purpose and Organization of This Book


2 Basic Concepts and Equations

2.1 Introduction

2.2 Wave Equation

2.3 Solution of Wave Equation

2.4 Classification of Wave Equation Solutions

2.5 Phase Velocity and Group Velocity

2.6 Propagating Power

2.7 Eikonal Equation

2.8 Ray Equations

2.9 Refraction and Reflection at a Boundary between Two Media

2.10 Transmission Loss Mechanisms in Optical Fibers

2.11 Optical Fiber Manufacture


3 Ray Theory of Optical Fibers

3.1 Introduction

3.2 Ray Theory of Uniform-Core Fibers

3.3 Ray Theory Analysis of Nonuniform-Core Fibers

3.4 Summary


4 Wave Theory of Uniform-Core Fibers

4.1 Introduction

4.2 Derivation of Basic Equations

4.3 Wave Phenomena in Uniform-Core Fibers

4.4 Dispersion Characteristics

4.5 Summary


5 Wave Theory of Nonuniform-Core Fibers

5.1 Introduction

5.2 Basic Equations and Mode Concepts in Nonuniform-Core Fibers

5.3 Analysis of Nonuniform-Core Fibers by the WKB Method

5.4 Computation of Propagation Characteristics of Multimode Fibers Based on WKB Analysis

5.5 Analysis of Nonuniform-Core Fibers by Rayleigh-Ritz Method

5.6 Analysis of Fibers Having a-Power Index Profiles by Power-Series Expansion Method

5.7 Suggestions on the Optimum Index Profile for Multimode Fibers

5.8 Analysis of Nonuniform-Core Fibers by Finite Element Method

5.9 Analysis of Nonuniform-Core Fibers by Staircase-Approximation Method

5.10 Summary


6 Classification and Comparison of Various Analysis Methods

6.1 Introduction

6.2 Various Wave Theories

6.3 Relation between Wave and Ray Theories

6.4 Summary


7 Optimum Refractive-Index Profile of Optical Fibers

7.1 Introduction

7.2 Optimum Refractive-Index Profile for Single-Mode Fibers

7.3 Optimum Refractive-Index Profile for Multimode Fibers


8 Optical Fibers Having Structural Fluctuations

8.1 Introduction

8.2 Mode Conversion Due to Axial Fluctuation

8.3 Summary


9 Measurement of Refractive-Index Profile of Optical Fibers

9.1 Introduction

9.2 Scattering-Pattern Method

9.3 Interference Methods

9.4 Reflection Method

9.5 Other Methods

9.6 Summary


10 Measurement of Transmission Characteristics of Optical Fiber

10.1 Introduction

10.2 Classification of Dispersion-Measurement Techniques

10.3 Pulse Method

10.4 Swept-Frequency Modulation Method

10.5 Spectrum Analysis Method

10.6 Shuttle-Pulse Method

10.7 Measurement of Multimode Dispersion for Each Mode Group

10.8 Summary


11 Concluding Remarks

11.1 Development of Practical Single-Mode Fibers

11.2 Development of Long-Wavelength (1.0-1.6 µm) Optical-Fiber Communications Systems

11.3 Development of FDM (Frequency-Division Multiplexing) Optical-Fiber Communications Systems

11.4 Development of Low-Cost, Large-Diameter, Large-Numerical-Aperture Fibers

11.5 Development of Economical Methods for Manufacturing Optical Fibers


2A.1 Derivation ofEqs. (2.68) and (2.69)

3A.1 Derivation of Eqs. (3.16)

3A.2 Derivation of Eq. (3.24)

3A.3 Derivation of Eqs. (3.27) and (3.28)

3A.4 Derivation of Eq. (3.30)

3A.5 Derivation of Eq. (3.39)

3A.6 Derivation of Eq. (3.49)

4A.1 Derivation of Wave Equations in Cyclindrical Coordinates

4A.2 Derivation of Proper Equations for Hybrid Modes under the Weakly Guiding Approximation

5A. 1 Derivation of Eqs. (5.7)-(5.12)

5A.2 Derivation of Eq. (5.23)

5A.3 Definitions and Properties of Airy Functions Ai(x) and Bi(x)

5A.4 Derivation of Eqs. (5.136)-(5.139) (Determination of Constants A-G, f, and ß1)

5A.5 Derivation of Eq. (5.193)

5A.6 Proof of Eq. (5.198)

5A.7 Derivation of Eq. (5.199)

5A.8 Derivation of Eq. (5.200)

5A.9 Table of Exact Normalized Cutoff Frequencies

5A. 10 Proof of the Validity of the Functional [Eq. (5.242)]

5A. 11 Proof That Eq. (5.258) Gives the Scalar Wave Equations

5A. 12 Propagation Matrix Components

8A. 1 Mode Degeneration in a Quadratic-Profile Fiber

8A.2 Derivation of Eq. (8.27)

8A.3 Nature of Parameters Used in Eq. (8.36)

9A.1 The Induced Dipole Method

9A.2 Sampling Theorem for Hankel Transform

9A.3 Derivation of Eq. (9.50)



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© Academic Press 1982
Academic Press
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Takanori Okoshi

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