Advanced Electronic Communications Systems PDF

Advanced Electronic Communications Systems ications Advanced Electronic Commun...

Advanced Electronic Communications Systems ications Advanced Electronic Commun Systems Wayne Tomasi Sixth Edition Tomasi Sixth Edition ISBN 978-1-29202-735-7 9 781292 027357 Pearson New International Edition Advanced Electronic Communications Systems Wayne Tomasi Sixth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk © Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. ISBN 10: 1-292-02735-5 ISBN 10: 1-269-37450-8 ISBN 13: 978-1-292-02735-7 ISBN 13: 978-1-269-37450-7 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Printed in the United States of America  P E A R S O N C U S T O M L I B R A R Y Table of Contents 1. Optical Fiber Transmission Media Wayne Tomasi 1 2. Digital Modulation Wayne Tomasi 49 3. Introduction to Data Communications and Networking Wayne Tomasi 111 4. Fundamental Concepts of Data Communications Wayne Tomasi 149 5. Data-Link Protocols and Data Communications Networks Wayne Tomasi 213 6. Digital Transmission Wayne Tomasi 277 7. Digital T-Carriers and Multiplexing Wayne Tomasi 323 8. Telephone Instruments and Signals Wayne Tomasi 383 9. The Telephone Circuit Wayne Tomasi 405 10. The Public Telephone Network Wayne Tomasi 439 11. Cellular Telephone Concepts Wayne Tomasi 469 12. Cellular Telephone Systems Wayne Tomasi 491 13. Microwave Radio Communications and System Gain Wayne Tomasi 529 I  14. Satellite Communications Wayne Tomasi 565 Index 609 II  Optical Fiber Transmission Media CHAPTER OUTLINE 1 Introduction 8 Optical Fiber Configurations 2 History of Optical Fiber Communications 9 Optical Fiber Classifications 3 Optical Fibers versus Metallic Cable Facilities 10 Losses in Optical Fiber Cables 4 Electromagnetic Spectrum 11 Light Sources 5 Block Diagram of an Optical Fiber 12 Optical Sources Communications System 13 Light Detectors 6 Optical Fiber Types 14 Lasers 7 Light Propagation 15 Optical Fiber System Link Budget OBJECTIVES Define optical communications Present an overview of the history of optical fibers and optical fiber communications Compare the advantages and disadvantages of optical fibers over metallic cables Define electromagnetic frequency and wavelength spectrum Describe several types of optical fiber construction Explain the physics of light and the following terms: velocity of propagation, refraction, refractive index, critical angle, acceptance angle, acceptance cone, and numerical aperture Describe how light waves propagate through an optical fiber cable Define modes of propagation and index profile Describe the three types of optical fiber configurations: single-mode step index, multimode step index, and mul- timode graded index Describe the various losses incurred in optical fiber cables Define light source and optical power Describe the following light sources: light-emitting diodes and injection diodes Describe the following light detectors: PIN diodes and avalanche photodiodes Describe the operation of a laser Explain how to calculate a link budget for an optical fiber system From Chapter 1 of Advanced Electronic Communications Systems, Sixth Edition. Wayne Tomasi. Copyright © 2004 by Pearson Education, Inc. Published by Pearson Prentice Hall. All rights reserved. 1  Optical Fiber Transmission Media 1 INTRODUCTION Optical fiber cables are the newest and probably the most promising type of guided trans- mission medium for virtually all forms of digital and data communications applications, in- cluding local, metropolitan, and wide area networks. With optical fibers, electromagnetic waves are guided through a media composed of a transparent material without using elec- trical current flow. With optical fibers, electromagnetic light waves propagate through the media in much the same way that radio signals propagate through Earth’s atmosphere. In essence, an optical communications system is one that uses light as the carrier of information. Propagating light waves through Earth’s atmosphere is difficult and often im- practical. Consequently, optical fiber communications systems use glass or plastic fiber ca- bles to “contain” the light waves and guide them in a manner similar to the way electro- magnetic waves are guided through a metallic transmission medium. The information-carrying capacity of any electronic communications system is di- rectly proportional to bandwidth. Optical fiber cables have, for all practical purposes, an in- finite bandwidth. Therefore, they have the capacity to carry much more information than their metallic counterparts or, for that matter, even the most sophisticated wireless commu- nications systems. For comparison purposes, it is common to express the bandwidth of an analog com- munications system as a percentage of its carrier frequency. This is sometimes called the bandwidth utilization ratio. For instance, a VHF radio communications system operating at a carrier frequency of 100 MHz with 10-MHz bandwidth has a bandwidth utilization ratio of 10%. A microwave radio system operating at a carrier frequency of 10 GHz with a 10% bandwidth utilization ratio would have 1 GHz of bandwidth available. Obviously, the higher the carrier frequency, the more bandwidth available, and the greater the information- carrying capacity. Light frequencies used in optical fiber communications systems are be- tween 1  1014 Hz and 4  1014 Hz (100,000 GHz to 400,000 GHz). A bandwidth utiliza- tion ratio of 10% would be a bandwidth between 10,000 GHz and 40,000 GHz. 2 HISTORY OF OPTICAL FIBER COMMUNICATIONS In 1880, Alexander Graham Bell experimented with an apparatus he called a photophone. The photophone was a device constructed from mirrors and selenium detectors that trans- mitted sound waves over a beam of light. The photophone was awkward and unreliable and had no real practical application. Actually, visual light was a primary means of communi- cating long before electronic communications came about. Smoke signals and mirrors were used ages ago to convey short, simple messages. Bell’s contraption, however, was the first attempt at using a beam of light for carrying information. Transmission of light waves for any useful distance through Earth’s atmosphere is im- practical because water vapor, oxygen, and particulates in the air absorb and attenuate the signals at light frequencies. Consequently, the only practical type of optical communica- tions system is one that uses a fiber guide. In 1930, J. L. Baird, an English scientist, and C. W. Hansell, a scientist from the United States, were granted patents for scanning and trans- mitting television images through uncoated fiber cables. A few years later, a German sci- entist named H. Lamm successfully transmitted images through a single glass fiber. At that time, most people considered fiber optics more of a toy or a laboratory stunt and, conse- quently, it was not until the early 1950s that any substantial breakthrough was made in the field of fiber optics. In 1951, A. C. S. van Heel of Holland and H. H. Hopkins and N. S. Kapany of En- gland experimented with light transmission through bundles of fibers. Their studies led to the development of the flexible fiberscope, which is used extensively in the medical field. It was Kapany who coined the term “fiber optics” in 1956. 2  Optical Fiber Transmission Media In 1958, Charles H. Townes, an American, and Arthur L. Schawlow, a Canadian, wrote a paper describing how it was possible to use stimulated emission for amplifying light waves (laser) as well as microwaves (maser). Two years later, Theodore H. Maiman, a sci- entist with Hughes Aircraft Company, built the first optical maser. The laser (light amplification by stimulated emission of radiation) was invented in 1960. The laser’s relatively high output power, high frequency of operation, and capability of carrying an extremely wide bandwidth signal make it ideally suited for high-capacity communications systems. The invention of the laser greatly accelerated research efforts in fiber-optic communications, although it was not until 1967 that K. C. Kao and G. A. Bock- ham of the Standard Telecommunications Laboratory in England proposed a new commu- nications medium using cladded fiber cables. The fiber cables available in the 1960s were extremely lossy (more than 1000 dB/km), which limited optical transmissions to short distances. In 1970, Kapron, Keck, and Maurer of Corning Glass Works in Corning, New York, developed an optical fiber with losses less than 2 dB/km. That was the “big” breakthrough needed to permit practical fiber optics com- munications systems. Since 1970, fiber optics technology has grown exponentially. Re- cently, Bell Laboratories successfully transmitted 1 billion bps through a fiber cable for 600 miles without a regenerator. In the late 1970s and early 1980s, the refinement of optical cables and the development of high-quality, affordable light sources and detectors opened the door to the development of high-quality, high-capacity, efficient, and affordable optical fiber communications systems. By the late 1980s, losses in optical fibers were reduced to as low as 0.16 dB/km, and in 1988 NEC Corporation set a new long-haul transmission record by transmitting 10 gigabytes per second over 80.1 kilometers of optical fiber. Also in 1988, the American National Standards Institute (ANSI) published the Synchronous Optical Network (SONET). By the mid-1990s, optical voice and data networks were commonplace throughout the United States and much of the world. 3 OPTICAL FIBERS VERSUS METALLIC CABLE FACILITIES Communications through glass or plastic fibers has several advantages over conven- tional metallic transmission media for both telecommunication and computer networking applications. 3-1 Advantages of Optical Fiber Cables The advantages of using optical fibers include the following: 1. Wider bandwidth and greater information capacity. Optical fibers have greater in- formation capacity than metallic cables because of the inherently wider bandwidths avail- able with optical frequencies. Optical fibers are available with bandwidths up to several thousand gigahertz. The primary electrical constants (resistance, inductance, and capaci- tance) in metallic cables cause them to act like low-pass filters, which limit their transmis- sion frequencies, bandwidth, bit rate, and information-carrying capacity. Modern optical fiber communications systems are capable of transmitting several gigabits per second over hundreds of miles, allowing literally millions of individual voice and data channels to be combined and propagated over one optical fiber cable. 2. Immunity to crosstalk. Optical fiber cables are immune to crosstalk because glass and plastic fibers are nonconductors of electrical current. Therefore, fiber cables are not sur- rounded by a changing magnetic field, which is the primary cause of crosstalk between metallic conductors located physically close to each other. 3. Immunity to static interference. Because optical fiber cables are nonconductors of electrical current, they are immune to static noise due to electromagnetic interference (EMI) caused by lightning, electric motors, relays, fluorescent lights, and other electrical 3  Optical Fiber Transmission Media noise sources (most of which are man-made). For the same reason, fiber cables do not ra- diate electromagnetic energy. 4. Environmental immunity. Optical fiber cables are more resistant to environmen- tal extremes (including weather variations) than metallic cables. Optical cables also oper- ate over a wider temperature range and are less affected by corrosive liquids and gases. 5. Safety and convenience. Optical fiber cables are safer and easier to install and maintain than metallic cables. Because glass and plastic fibers are nonconductors, there are no electrical currents or voltages associated with them. Optical fibers can be used around volatile liquids and gasses without worrying about their causing explosions or fires. Opti- cal fibers are also smaller and much more lightweight and compact than metallic cables. Consequently, they are more flexible, easier to work with, require less storage space, cheaper to transport, and easier to install and maintain. 6. Lower transmission loss. Optical fibers have considerably less signal loss than their metallic counterparts. Optical fibers are currently being manufactured with as lit- tle as a few-tenths-of-a-decibel loss per kilometer. Consequently, optical regenerators and amplifiers can be spaced considerably farther apart than with metallic transmission lines. 7. Security. Optical fiber cables are more secure than metallic cables. It is virtually impossible to tap into a fiber cable without the user’s knowledge, and optical cables cannot be detected with metal detectors unless they are reinforced with steel for strength. 8. Durability and reliability. Optical fiber cables last longer and are more reliable than metallic facilities because fiber cables have a higher tolerance to changes in environ- mental conditions and are immune to corrosive materials. 9. Economics. The cost of optical fiber cables is approximately the same as metallic cables. Fiber cables have less loss and require fewer repeaters, which equates to lower in- stallation and overall system costs and improved reliability. 3-2 Disadvantages of Optical Fiber Cables Although the advantages of optical fiber cables far exceed the disadvantages, it is impor- tant to know the limitations of the fiber. The disadvantages of optical fibers include the following: 1. Interfacing costs. Optical fiber cable systems are virtually useless by themselves. To be practical and useful, they must be connected to standard electronic facilities, which often require expensive interfaces. 2. Strength. Optical fibers by themselves have a significantly lower tensile strength than coaxial cable. This can be improved by coating the fiber with standard Kevlar and a protective jacket of PVC. In addition, glass fiber is much more fragile than copper wire, making fiber less attractive where hardware portability is required. 3. Remote electrical power. Occasionally, it is necessary to provide electrical power to remote interface or regenerating equipment. This cannot be accomplished with the opti- cal cable, so additional metallic cables must be included in the cable assembly. 4. Optical fiber cables are more susceptible to losses introduced by bending the ca- ble. Electromagnetic waves propagate through an optical cable by either refraction or re- flection. Therefore, bending the cable causes irregularities in the cable dimensions, result- ing in a loss of signal power. Optical fibers are also more prone to manufacturing defects, as even the most minor defect can cause excessive loss of signal power. 5. Specialized tools, equipment, and training. Optical fiber cables require special tools to splice and repair cables and special test equipment to make routine measurements. Not only is repairing fiber cables difficult and expensive, but technicians working on opti- cal cables also require special skills and training. In addition, sometimes it is difficult to lo- cate faults in optical cables because there is no electrical continuity. 4  Optical Fiber Transmission Media Ultraviolet light FM radio and Gamma rays Infrared light Cosmic rays satelite and Visible light microwave Ultrasonic Terrestrial television AM radio Subsonic X-rays Audio radar Hz 100 101 102 103 104 105 106 107 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 kHz MHz GHz THz PHz EHz (kilo) (mega) (giga) (tera) (penta) (exa) Frequency FIGURE 1 Electromagnetic frequency spectrum 4 ELECTROMAGNETIC SPECTRUM The total electromagnetic frequency spectrum is shown in Figure 1. From the figure, it can be seen that the frequency spectrum extends from the subsonic frequencies (a few hertz) to cos- mic rays (1022 Hz). The light frequency spectrum can be divided into three general bands: 1. Infrared. The band of light frequencies that is too high to be seen by the human eye with wavelengths ranging between 770 nm and 106 nm. Optical fiber systems generally operate in the infrared band. 2. Visible. The band of light frequencies to which the human eye will respond with wave- lengths ranging between 390 nm and 770 nm. This band is visible to the human eye. 3. Ultraviolet. The band of light frequencies that are too low to be seen by the hu- man eye with wavelengths ranging between 10 nm and 390 nm. When dealing with ultra-high-frequency electromagnetic waves, such as light, it is common to use units of wavelength rather than frequency. Wavelength is the length that one cycle of an electromagnetic wave occupies in space. The length of a wavelength depends on the frequency of the wave and the velocity of light. Mathematically, wavelength is c λ (1) f where λ  wavelength (meters/cycle) c  velocity of light (300,000,000 meters per second) f  frequency (hertz) With light frequencies, wavelength is often stated in microns, where 1 micron  106 meter (1 μm), or in nanometers (nm), where 1 nm  109 meter. However, when describ- ing the optical spectrum, the unit angstrom is sometimes used to express wavelength, where 1 angstrom  1010 meter, or 0.0001 micron. Figure 2 shows the total electromagnetic wavelength spectrum. 5 BLOCK DIAGRAM OF AN OPTICAL FIBER COMMUNICATIONS SYSTEM Figure 3 shows a simplified block diagram of a simplex optical fiber communications link. The three primary building blocks are the transmitter, the receiver, and the optical fiber ca- ble. The transmitter is comprised of a voltage-to-current converter, a light source, and a source-to-fiber interface (light coupler). The fiber guide is the transmission medium, which 5  μm 0.01 2 3 3.9 4.55 4.92 5.77 5.97 6.22 7.7 15 60 400 1000 Å 100 2000 3000 3900 4550 4920 5770 5970 6220 7700 15,000 60,000 400,000 1,000,000 nm 10 200 300 390 455 492 577 597 622 770 1500 6000 40000 10000 Extreme Far Near Vio Blue Green Yel Orng Red Near Middle Far Far Far Ultraviolet Visible light Infrared Long electrical Gamma rays oscillations Radio waves Cosmic rays X-rays Microwaves -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Hz 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Wavelength FIGURE 2 Electromagnetic wavelength spectrum Source Analog or digital interface Transmitter Voltage-to- Source-to- Light current fiber source converter interface Optical fiber cable Optical fiber cable Signal regenerator Fiber-to- Current-to- Light light detector voltage detector interface converter Receiver Analog or digital interface Destination FIGURE 3 Optical fiber communications link 6  Optical Fiber Transmission Media is either an ultrapure glass or a plastic cable. It may be necessary to add one or more re- generators to the transmission medium, depending on the distance between the transmitter and receiver. Functionally, the regenerator performs light amplification. However, in real- ity the signal is not actually amplified; it is reconstructed. The receiver includes a fiber-to- interface (light coupler), a photo detector, and a current-to-voltage converter. In the transmitter, the light source can be modulated by a digital or an analog signal. The voltage-to-current converter serves as an electrical interface between the input circuitry and the light source. The light source is either an infrared light-emitting diode (LED) or an injection laser diode (ILD). The amount of light emitted by either an LED or ILD is pro- portional to the amount of drive current. Thus, the voltage-to-current converter converts an input signal voltage to a current that is used to drive the light source. The light outputted by the light source is directly proportional to the magnitude of the input voltage. In essence, the light intensity is modulated by the input signal. The source-to-fiber coupler (such as an optical lens) is a mechanical interface. Its function is to couple light emitted by the light source into the optical fiber cable. The opti- cal fiber consists of a glass or plastic fiber core surrounded by a cladding and then encap- sulated in a protective jacket. The fiber-to-light detector-coupling device is also a mechan- ical coupler. Its function is to couple as much light as possible from the fiber cable into the light detector. The light detector is generally a PIN (p-type-intrinsic-n-type) diode, an APD (ava- lanche photodiode), or a phototransistor. All three of these devices convert light energy to current. Consequently, a current-to-voltage converter is required to produce an output volt- age proportional to the original source information. The current-to-voltage converter trans- forms changes in detector current to changes in voltage. The analog or digital interfaces are electrical interfaces that match impedances and signal levels between the information source and destination to the input and output cir- cuitry of the optical system. 6 OPTICAL FIBER TYPES 6-1 Optical Fiber Construction The actual fiber portion of an optical cable is generally considered to include both the fiber core and its cladding (see Figure 4). A special lacquer, silicone, or acrylate coating is gen- erally applied to the outside of the cladding to seal and preserve the fiber’s strength, help- Polyurethane outer jacket Strength members Buffer jacket Protective coating Fiber core FIGURE 4 Optical fiber cable and cladding construction 7  Optical Fiber Transmission Media ing maintain the cables attenuation characteristics. The coating also helps protect the fiber from moisture, which reduces the possibility of the occurrence of a detrimental phenome- non called stress corrosion (sometimes called static fatigue) caused by high humidity. Moisture causes silicon dioxide crystals to interact, causing bonds to break down and spon- taneous fractures to form over a prolonged period of time. The protective coating is sur- rounded by a buffer jacket, which provides the cable additional protection against abrasion and shock. Materials commonly used for the buffer jacket include steel, fiberglass, plastic, flame-retardant polyvinyl chloride (FR-PVC), Kevlar yarn, and paper. The buffer jacket is encapsulated in a strength member, which increases the tensile strength of the overall cable assembly. Finally, the entire cable assembly is contained in an outer polyurethane jacket. There are three essential types of optical fibers commonly used today. All three vari- eties are constructed of either glass, plastic, or a combination of glass and plastic: Plastic core and cladding Glass core with plastic cladding (called PCS fiber [plastic-clad silica]) Glass core and glass cladding (called SCS [silica-clad silica]) Plastic fibers are more flexible and, consequently, more rugged than glass. Therefore, plastic cables are easier to install, can better withstand stress, are less expensive, and weigh approximately 60% less than glass. However, plastic fibers have higher attenuation charac- teristics and do not propagate light as efficiently as glass. Therefore, plastic fibers are lim- ited to relatively short cable runs, such as within a single building. Fibers with glass cores have less attenuation than plastic fibers, with PCS being slightly better than SCS. PCS fibers are also less affected by radiation and, therefore, are more immune to external interference. SCS fibers have the best propagation characteristics and are easier to terminate than PCS fibers. Unfortunately, SCS fibers are the least rugged, and they are more susceptible to increases in attenuation when exposed to radiation. The selection of a fiber for a given application is a function of the specific system re- quirements. There are always trade-offs based on the economics and logistics of a particu- lar application. 6-1-1 Cable configurations. There are many different cable designs available today. Figure 5 shows examples of several optical fiber cable configurations. With loose tube con- struction (Figure 5a), each fiber is contained in a protective tube. Inside the tube, a polyurethane compound encapsules the fiber and prevents the intrusion of water. A phe- nomenon called stress corrosion or static fatigue can result if the glass fiber is exposed to long periods of high humidity. Silicon dioxide crystals interact with the moisture and cause bonds to break down, causing spontaneous fractures to form over a prolonged period. Some fiber cables have more than one protective coating to ensure that the fiber’s characteristics do not alter if the fiber is exposed to extreme temperature changes. Surrounding the fiber’s cladding is usually a coating of either lacquer, silicon, or acrylate that is typically applied to seal and preserve the fiber’s strength and attenuation characteristics. Figure 5b shows the construction of a constrained optical fiber cable. Surrounding the fiber are a primary and a secondary buffer comprised of Kevlar yarn, which increases the tensile strength of the cable and provides protection from external mechanical influences that could cause fiber breakage or excessive optical attenuation. Again, an outer protective tube is filled with polyurethane, which prevents moisture from coming into contact with the fiber core. Figure 5c shows a multiple-strand cable configuration, which includes a steel central member and a layer of Mylar tape wrap to increase the cable’s tensile strength. Figure 5d shows a ribbon configuration for a telephone cable, and Figure 5e shows both end and side views of a PCS cable. 8  Optical Fiber Transmission Media FIGURE 5 Fiber optic cable configurations: (a) loose tube construction; (b) constrained fiber; (c) multiple strands; (d) telephone cable; (e) plastic-silica cable As mentioned, one disadvantage of optical fiber cables is their lack of tensile (pulling) strength, which can be as low as a pound. For this reason, the fiber must be rein- forced with strengthening material so that it can withstand mechanical stresses it will typi- cally undergo when being pulled and jerked through underground and overhead ducts and hung on poles. Materials commonly used to strengthen and protect fibers from abrasion and environmental stress are steel, fiberglass, plastic, FR-PVC (flame-retardant polyvinyl chlo- ride), Kevlar yarn, and paper. The type of cable construction used depends on the perfor- mance requirements of the system and both economic and environmental constraints. 7 LIGHT PROPAGATION 7-1 The Physics of Light Although the performance of optical fibers can be analyzed completely by application of Maxwell’s equations, this is necessarily complex. For most practical applications, geomet- ric wave tracing may be used instead. 9  Optical Fiber Transmission Media In 1860, James Clerk Maxwell theorized that electromagnetic radiation contained a series of oscillating waves comprised of an electric and a magnetic field in quadrature (at 90° angles). However, in 1905, Albert Einstein and Max Planck showed that when light is emitted or absorbed, it behaves like an electromagnetic wave and also like a particle, called a photon, which possesses energy proportional to its frequency. This theory is known as Planck’s law. Planck’s law describes the photoelectric effect, which states, “When visible light or high-frequency electromagnetic radiation illuminates a metallic surface, electrons are emitted.” The emitted electrons produce an electric current. Planck’s law is expressed mathematically as Ep  hf (2) where Ep  energy of the photon (joules) h  Planck’s constant  6.625  1034 J  s f  frequency of light (photon) emitted (hertz) Photon energy may also be expressed in terms of wavelength. Substituting Equation 1 into Equation 2 yields Ep  hf (3a) hc or Ep  (3b) λ An atom has several energy levels or states, the lowest of which is the ground state. Any energy level above the ground state is called an excited state. If an atom in one energy level decays to a lower energy level, the loss of energy (in electron volts) is emitted as a photon of light. The energy of the photon is equal to the difference between the energy of the two energy levels. The process of decaying from one energy level to another energy level is called spontaneous decay or spontaneous emission. Atoms can be irradiated by a light source whose energy is equal to the difference be- tween ground level and an energy level. This can cause an electron to change from one en- ergy level to another by absorbing light energy. The process of moving from one energy level to another is called absorption. When making the transition from one energy level to another, the atom absorbs a packet of energy (a photon). This process is similar to that of emission. The energy absorbed or emitted (photon) is equal to the difference between the two energy levels. Mathematically, Ep  E2  E1 (4) where Ep is the energy of the photon (joules). 7-2 Optical Power Light intensity is a rather complex concept that can be expressed in either photometric or radiometric terms. Photometry is the science of measuring only light waves that are visible to the human eye. Radiometry, on the other hand, measures light throughout the entire elec- tromagnetic spectrum. In photometric terms, light intensity is generally described in terms of luminous flux density and measured in lumens per unit area. Radiometric terms, how- ever, are often more useful to engineers and technologists. In radiometric terms, optical power measures the rate at which electromagnetic waves transfer light energy. In simple terms, optical power is described as the flow of light energy past a given point in a speci- fied time. Optical power is expressed mathematically as d1energy2 P (5a) d1time2 10  Optical Fiber Transmission Media dQ or  (5b) dt where P  optical power (watts) dQ  instantaneous charge (joules) dt  instantaneous change in time (seconds) Optical power is sometimes called radiant flux (φ), which is equivalent to joules per second and is the same power that is measured electrically or thermally in watts. Radio- metric terms are generally used with light sources with output powers ranging from tens of microwatts to more than 100 milliwatts. Optical power is generally stated in decibels relative to a defined power level, such as 1 mW (dBm) or 1 μW (dBμ). Mathematically stated, P 1watts2 dBm  10 logB R 0.001 1watts 2 (6) P 1watts 2 dbμ  10 logB R 0.000001 1watts 2 and (7) Example 1 Determine the optical power in dBm and dBμ for power levels of a. 10 mW b. 20 μW Solution a. Substituting into Equations 6 and 7 gives 10 mW dBm  10 log  10 dBm 1 mW 10 mW dBμ  10 log  40 dBμ 1 μW b. Substituting into Equations 6 and 7 gives 20 μW dBm  10 log  17 dBm 1 mW 20 μW dBμ  10 log  13 dBμ 1μW 7-3 Velocity of Propagation In free space (a vacuum), electromagnetic energy, such as light waves, travels at ap- proximately 300,000,000 meters per second (186,000 mi/s). Also, in free space the ve- locity of propagation is the same for all light frequencies. However, it has been demon- strated that electromagnetic waves travel slower in materials more dense than free space and that all light frequencies do not propagate at the same velocity. When the ve- locity of an electromagnetic wave is reduced as it passes from one medium to another medium of denser material, the light ray changes direction or refracts (bends) toward the normal. When an electromagnetic wave passes from a more dense material into a less dense material, the light ray is refracted away from the normal. The normal is sim- ply an imaginary line drawn perpendicular to the interface of the two materials at the point of incidence. 11  Optical Fiber Transmission Media FIGURE 6 Refraction of light: (a) light refraction; (b) prismatic refraction 7-3-1 Refraction. For light-wave frequencies, electromagnetic waves travel through Earth’s atmosphere (air) at approximately the same velocity as through a vacuum (i.e., the speed of light). Figure 6a shows how a light ray is refracted (bent) as it passes from a less dense material into a more dense material. (Actually, the light ray is not bent; rather, it changes direction at the interface.) Figure 6b shows how sunlight, which contains all light frequencies (white light), is affected as it passes through a material that is more dense than air. Refraction occurs at both air/glass interfaces. The violet wavelengths are refracted the most, whereas the red wavelengths are refracted the least. The spectral separation of white light in this manner is called prismatic refraction. It is this phenomenon that causes rain- bows, where water droplets in the atmosphere act as small prisms that split the white sun- light into the various wavelengths, creating a visible spectrum of color. 7-3-2 Refractive Index. The amount of bending or refraction that occurs at the in- terface of two materials of different densities is quite predictable and depends on the re- fractive indexes of the two materials. Refractive index is simply the ratio of the velocity of propagation of a light ray in free space to the velocity of propagation of a light ray in a given material. Mathematically, refractive index is c n (8) v 12  Optical Fiber Transmission Media where n  refractive index (unitless) c  speed of light in free space (3  108 meters per second) v  speed of light in a given material (meters per second) Although the refractive index is also a function of frequency, the variation in most light wave applications is insignificant and, thus, omitted from this discussion. The indexes of refraction of several common materials are given in Table 1. 7-3-3 Snell’s law. How a light ray reacts when it meets the interface of two trans- missive materials that have different indexes of refraction can be explained with Snell’s law. A refractive index model for Snell’s law is shown in Figure 7. The angle of incidence is the angle at which the propagating ray strikes the interface with respect to the normal, and the angle of refraction is the angle formed between the propagating ray and the nor- mal after the ray has entered the second medium. At the interface of medium 1 and medium 2, the incident ray may be refracted toward the normal or away from it, depending on whether n1 is greater than or less than n2. Hence, the angle of refraction can be larger or Table 1 Typical Indexes of Refraction Material Index of Refractiona Vacuum 1.0 Air 1.0003 (≈1) Water 1.33 Ethyl alcohol 1.36 Fused quartz 1.46 Glass fiber 1.5–1.9 Diamond 2.0–2.42 Silicon 3.4 Gallium-arsenide 2.6 a Index of refraction is based on a wavelength of light emitted from a sodium flame (589 nm). FIGURE 7 Refractive model for Snell’s law 13  Optical Fiber Transmission Media FIGURE 8 Light ray refracted away from the normal smaller than the angle of incidence, depending on the refractive indexes of the two materi- als. Snell’s law stated mathematically is n1 sin θ1  n2 sin θ2 (9) where n1  refractive index of material 1 (unitless) n2  refractive index of material 2 (unitless) θ1  angle of incidence (degrees) θ2  angle of refraction (degrees) Figure 8 shows how a light ray is refracted as it travels from a more dense (higher refractive index) material into a less dense (lower refractive index) material. It can be seen that the light ray changes direction at the interface, and the angle of refraction is greater than the angle of incidence. Consequently, when a light ray enters a less dense material, the ray bends away from the normal. The normal is simply a line drawn per- pendicular to the interface at the point where the incident ray strikes the interface. Similarly, when a light ray enters a more dense material, the ray bends toward the normal. Example 2 In Figure 8, let medium 1 be glass and medium 2 be ethyl alcohol. For an angle of incidence of 30°, determine the angle of refraction. Solution From Table 1, n1 (glass)  1.5 n2 (ethyl alcohol)  1.36 Rearranging Equation 9 and substituting for n1, n2, and θ1 gives us n1 sin θ1  sin θ2 n2 1.5 sin 30  0.5514  sin θ2 1.36 θ2  sin1 0.5514  33.47° The result indicates that the light ray refracted (bent) or changed direction by 33.47° at the interface. Because the light was traveling from a more dense material into a less dense material, the ray bent away from the normal. 14  Optical Fiber Transmission Media FIGURE 9 Critical angle refraction 7-3-4 Critical angle. Figure 9 shows a condition in which an incident ray is strik- ing the glass/cladding interface at an angle (1) such that the angle of refraction (θ2) is 90° and the refracted ray is along the interface. This angle of incidence is called the critical an- gle (θc), which is defined as the minimum angle of incidence at which a light ray may strike the interface of two media and result in an angle of refraction of 90° or greater. It is impor- tant to note that the light ray must be traveling from a medium of higher refractive index to a medium with a lower refractive index (i.e., glass into cladding). If the angle of refraction is 90° or greater, the light ray is not allowed to penetrate the less dense material. Conse- quently, total reflection takes place at the interface, and the angle of reflection is equal to the angle of incidence. Critical angle can be represented mathematically by rearranging Equation 9 as n2 sin θ1  sin θ2 n1 With θ2  90°, θ1 becomes the critical angle (θc), and 112  n2 n2 sin θc  sin θc  n1 n1 n2 and θc  sin1 (10) n1 where θc is the critical angle. From Equation 10, it can be seen that the critical angle is dependent on the ratio of the refractive indexes of the core and cladding. For example a ratio n2 /n1  0.77 produces a critical angle of 50.4°, whereas a ratio n2 /n1  0.625 yields a critical angle of 38.7°. Figure 10 shows a comparison of the angle of refraction and the angle of reflection when the angle of incidence is less than or more than the critical angle. 7-3-5 Acceptance angle, acceptance cone, and numerical aperture. In previous discussions, the source-to-fiber aperture was mentioned several times, and the critical and acceptance angles at the point where a light ray strikes the core/cladding interface were ex- plained. The following discussion addresses the light-gathering ability of a fiber, which is the ability to couple light from the source into the fiber. 15  Optical Fiber Transmission Media FIGURE 10 Angle of reflection and refraction FIGURE 11 Ray propagation into and down an optical fiber cable Figure 11 shows the source end of a fiber cable and a light ray propagating into and then down the fiber. When light rays enter the core of the fiber, they strike the air/glass in- terface at normal A. The refractive index of air is approximately 1, and the refractive index of the glass core is 1.5. Consequently, the light enters the cable traveling from a less dense to a more dense medium, causing the ray to refract toward the normal. This causes the light rays to change direction and propagate diagonally down the core at an angle that is less than the external angle of incidence (θin). For a ray of light to propagate down the cable, it must strike the internal core/cladding interface at an angle that is greater than the critical angle (θc). Using Figure 12 and Snell’s law, it can be shown that the maximum angle that exter- nal light rays may strike the air/glass interface and still enter the core and propagate down the fiber is 16  Optical Fiber Transmission Media FIGURE 12 Geometric relationship of Equations 11a and b 2n21  n22 θin1max2  sin1 (11a) no where θin(max)  acceptance angle (degrees) no  refractive index of air (1) n1  refractive index of glass fiber core (1.5) n2  refractive index of quartz fiber cladding (1.46) Since the refractive index of air is 1, Equation 11a reduces to θin1max2  sin1 2n21  n22 (11b) θin(max) is called the acceptance angle or acceptance cone half-angle. θin(max) defines the maximum angle in which external light rays may strike the air/glass interface and still propagate down the fiber. Rotating the acceptance angle around the fiber core axis de- scribes the acceptance cone of the fiber input. Acceptance cone is shown in Figure 13a, and the relationship between acceptance angle and critical angle is shown in Figure 13b. Note that the critical angle is defined as a minimum value and that the acceptance angle is de- fined as a maximum value. Light rays striking the air/glass interface at an angle greater than the acceptance angle will enter the cladding and, therefore, will not propagate down the cable. Numerical aperture (NA) is closely related to acceptance angle and is the figure of merit commonly used to measure the magnitude of the acceptance angle. In essence, nu- merical aperture is used to describe the light-gathering or light-collecting ability of an op- tical fiber (i.e., the ability to couple light into the cable from an external source). The larger the magnitude of the numerical aperture, the greater the amount of external light the fiber will accept. The numerical aperture for light entering the glass fiber from an air medium is described mathematically as NA  sin θin (12a) and NA  2n21  n22 (12b) Therefore θin  sin1 NA (12c) where θin  acceptance angle (degrees) NA  numerical aperture (unitless) n1  refractive index of glass fiber core (unitless) n2  refractive index of quartz fiber cladding (unitless) 17  Optical Fiber Transmission Media FIGURE 13 (a) Acceptance angle; (b) acceptance cone A larger-diameter core does not necessarily produce a larger numerical aperture, al- though in practice larger-core fibers tend to have larger numerical apertures. Numerical aperture can be calculated using Equations 12a or b, but in practice it is generally measured by looking at the output of a fiber because the light-guiding properties of a fiber cable are symmetrical. Therefore, light leaves a cable and spreads out over an angle equal to the ac- ceptance angle. 8 OPTICAL FIBER CONFIGURATIONS Light can be propagated down an optical fiber cable using either reflection or refraction. How the light propagates depends on the mode of propagation and the index profile of the fiber. 8-1 Mode of Propagation In fiber optics terminology, the word mode simply means path. If there is only one path for light rays to take down a cable, it is called single mode. If there is more than one path, it is called multimode. Figure 14 shows single and multimode propagation of light rays down an optical fiber. As shown in Figure 14a, with single-mode propagation, there is only one 18  Optical Fiber Transmission Media FIGURE 14 Modes of propagation: (a) single mode; (b) multimode path for light rays to take, which is directly down the center of the cable. However, as Figure 14b shows, with multimode propagation there are many higher-order modes possible, and light rays propagate down the cable in a zigzag fashion following several paths. The number of paths (modes) possible for a multimode fiber cable depends on the fre- quency (wavelength) of the light signal, the refractive indexes of the core and cladding, and the core diameter. Mathematically, the number of modes possible for a given cable can be approximated by the following formula: πd 2 N⬇¢ 2n21  n22≤ (13) λ where N  number of propagating modes d  core diameter (meters) λ  wavelength (meters) n1  refractive index of core n2  refractive index of cladding A multimode step-index fiber with a core diameter of 50 μm, a core refractive index of 1.6, a cladding refractive index of 1.584, and a wavelength of 1300 nm has approximately 372 possible modes. 8-2 Index Profile The index profile of an optical fiber is a graphical representation of the magnitude of the refractive index across the fiber. The refractive index is plotted on the horizontal axis, and the radial distance from the core axis is plotted on the vertical axis. Figure 15 shows the core index profiles for the three types of optical fiber cables. There are two basic types of index profiles: step and graded. A step-index fiber has a central core with a uniform refractive index (i.e., constant density throughout). An outside cladding that also has a uniform refractive index surrounds the core; however, the refractive index of the cladding is less than that of the central core. From Figures 15a and b, it can be seen that in step-index fibers, there is an abrupt change in the refractive index at the core/cladding interface. This is true for both single and multimode step-index fibers. 19  Optical Fiber Transmission Media FIGURE 15 Core index profiles: (a) single-mode step index; (b) multimode step index; (c) multimode graded index In the graded-index fiber, shown in Figure 15c, it can be see that there is no cladding, and the refractive index of the core is nonuniform; it is highest in the center of the core and decreases gradually with distance toward the outer edge. The index profile shows a core density that is maximum in the center and decreases symmetrically with distance from the center. 9 OPTICAL FIBER CLASSIFICATIONS Propagation modes can be categorized as either multimode or single mode, and then mul- timode can be further subdivided into step index or graded index. Although there are a wide variety of combinations of modes and indexes, there are only three practical types of opti- cal fiber configurations: single-mode step-index, multimode step index, and multimode graded index. 9-1 Single-Mode Step-Index Optical Fiber Single-mode step-index fibers are the dominant fibers used in today’s telecommunications and data networking industries. A single-mode step-index fiber has a central core that is sig- nificantly smaller in diameter than any of the multimode cables. In fact, the diameter is suf- ficiently small that there is essentially only one path that light may take as it propagates down the cable. This type of fiber is shown in Figure 16a. In the simplest form of single- mode step-index fiber, the outside cladding is simply air. The refractive index of the glass core (n1) is approximately 1.5, and the refractive index of the air cladding (n2) is 1. The large 20  Optical Fiber Transmission Media FIGURE 16 Single-mode step-index fibers: (a) air cladding; (b) glass cladding difference in the refractive indexes results in a small critical angle (approximately 42°) at the glass/air interface. Consequently, a single-mode step-index fiber has a wide external ac- ceptance angle, which makes it relatively easy to couple light into the cable from an exter- nal source. However, this type of fiber is very weak and difficult to splice or terminate. A more practical type of single-mode step-index fiber is one that has a cladding other than air, such as the cable shown in Figure 16b. The refractive index of the cladding (n2) is slightly less than that of the central core (n1) and is uniform throughout the cladding. This type of cable is physically stronger than the air-clad fiber, but the critical angle is also much higher (approximately 77°). This results in a small acceptance angle and a narrow source-to- fiber aperture, making it much more difficult to couple light into the fiber from a light source. With both types of single-mode step-index fibers, light is propagated down the fiber through reflection. Light rays that enter the fiber either propagate straight down the core or, perhaps, are reflected only a few times. Consequently, all light rays follow approximately the same path down the cable and take approximately the same amount of time to travel the length of the cable. This is one overwhelming advantage of single-mode step-index fibers, as explained in more detail in a later section of this chapter. 9-2 Multimode Step-Index Optical Fiber A multimode step-index optical fiber is shown in Figure 17. Multimode step-index fibers are similar to the single-mode step-index fibers except the center core is much larger with the multimode configuration. This type of fiber has a large light-to-fiber aperture and, con- sequently, allows more external light to enter the cable. The light rays that strike the core/cladding interface at an angle greater than the critical angle (ray A) are propagated down the core in a zigzag fashion, continuously reflecting off the interface boundary. Light 21  Optical Fiber Transmission Media FIGURE 17 Multimode step-index fiber FIGURE 18 Multimode graded-index fiber rays that strike the core/cladding interface at an angle less than the critical angle (ray B) en- ter the cladding and are lost. It can be seen that there are many paths that a light ray may follow as it propagates down the fiber. As a result, all light rays do not follow the same path and, consequently, do not take the same amount of time to travel the length of the cable. 9-3 Multimode Graded-Index Optical Fiber A multimode graded-index optical fiber is shown in Figure 18. Graded-index fibers are char- acterized by a central core with a nonuniform refractive index. Thus, the cable’s density is maximum at the center and decreases gradually toward the outer edge. Light rays propagate down this type of fiber through refraction rather than reflection. As a light ray propagates di- agonally across the core toward the center, it is continually intersecting a less dense to more dense interface. Consequently, the light rays are constantly being refracted, which results in a continuous bending of the light rays. Light enters the fiber at many different angles. As the light rays propagate down the fiber, the rays traveling in the outermost area of the fiber travel a greater distance than the rays traveling near the center. Because the refractive index de- creases with distance from the center and the velocity is inversely proportional to refractive index, the light rays traveling farthest from the center propagate at a higher velocity. Conse- quently, they take approximately the same amount of time to travel the length of the fiber. 9-4 Optical Fiber Comparison 9-4-1 Single-mode step-index fiber. Advantages include the following: 1. Minimum dispersion: All rays propagating down the fiber take approximately the same path; thus, they take approximately the same length of time to travel down the cable. Consequently, a pulse of light entering the cable can be reproduced at the receiving end very accurately. 22  Optical Fiber Transmission Media 2. Because of the high accuracy in reproducing transmitted pulses at the receive end, wider bandwidths and higher information transmission rates (bps) are possible with single-mode step-index fibers than with the other types of fibers. Disadvantages include the following: 1. Because the central core is very small, it is difficult to couple light into and out of this type of fiber. The source-to-fiber aperture is the smallest of all the fiber types. 2. Again, because of the small central core, a highly directive light source, such as a laser, is required to couple light into a single-mode step-index fiber. 3. Single-mode step-index fibers are expensive and difficult to manufacture. 9-4-2 Multimode step-index fiber. Advantages include the following: 1. Multimode step-index fibers are relatively inexpensive and simple to manufacture. 2. It is easier to couple light into and out of multimode step-index fibers because they have a relatively large source-to-fiber aperture. Disadvantages include the following: 1. Light rays take many different paths down the fiber, which results in large dif- ferences in propagation times. Because of this, rays traveling down this type of fiber have a tendency to spread out. Consequently, a pulse of light propagating down a multimode step-index fiber is distorted more than with the other types of fibers. 2. The bandwidths and rate of information transfer rates possible with this type of cable are less than that possible with the other types of fiber cables. 9-4-3 Multimode graded-index fiber. Essentially, there are no outstanding advan- tages or disadvantages of this type of fiber. Multimode graded-index fibers are easier to cou- ple light into and out of than single-mode step-index fibers but are more difficult than mul- timode step-index fibers. Distortion due to multiple propagation paths is greater than in single-mode step-index fibers but less than in multimode step-index fibers. This multimode graded-index fiber is considered an intermediate fiber compared to the other fiber types. 10 LOSSES IN OPTICAL FIBER CABLES Power loss in an optical fiber cable is probably the most important characteristic of the ca- ble. Power loss is often called attenuation and results in a reduction in the power of the light wave as it travels down the cable. Attenuation has several adverse effects on performance, including reducing the system’s bandwidth, information transmission rate, efficiency, and overall system capacity. The standard formula for expressing the total power loss in an optical fiber cable is Pout A1dB2  10 log¢ ≤ (14) Pin where A(dB)  total reduction in power level, attenuation (unitless) Pout  cable output power (watts) Pin  cable input power (watts) In general, multimode fibers tend to have more attenuation than single-mode cables, primarily because of the increased scattering of the light wave produced from the dopants in the glass. Table 2 shows output power as a percentage of input power for an optical 23  Optical Fiber Transmission Media Table 2 % Output Power versus Loss in dB Loss (dB) Output Power (%) 1 79 3 50 6 25 9 12.5 10 10 13 5 20 1 30 0.1 40 0.01 50 0.001 Table 3 Fiber Cable Attenuation Core Diameter Cladding Diameter NA Attenuation Cable Type (μm) (μm) (unitless) (dB/km) Single mode 8 125 — 0.5 at 1300 nm 5 125 — 0.4 at 1300 nm Graded index 50 125 0.2 4 at 850 nm 100 140 0.3 5 at 850 nm Step index 200 380 0.27 6 at 850 nm 300 440 0.27 6 at 850 nm PCS 200 350 0.3 10 at 790 nm 400 550 0.3 10 at 790 nm Plastic — 750 0.5 400 at 650 nm — 1000 0.5 400 at 650 nm fiber cable with several values of decibel loss. A 1-dB cable loss reduces the output power to 50% of the input power. Attenuation of light propagating through glass depends on wavelength. The three wavelength bands typically used for optical fiber communications systems are centered around 0.85 microns, 1.30 microns, and 1.55 microns. For the kind of glass typically used for optical communications systems, the 1.30-micron and 1.55-micron bands have less than 5% loss per kilometer, while the 0.85-micron band experiences almost 20% loss per kilometer. Although total power loss is of primary importance in an optical fiber cable, attenu- ation is generally expressed in decibels of loss per unit length. Attenuation is expressed as a positive dB value because by definition it is a loss. Table 3 lists attenuation in dB/km for several types of optical fiber cables. The optical power in watts measured at a given distance from a power source can be determined mathematically as P  Pt  10Al/10 (15) where P  measured power level (watts) Pt  transmitted power level (watts) A  cable power loss (dB/km) l  cable length (km) Likewise, the optical power in decibel units is P(dBm)  Pin(dBm)  Al(dB) (16) where P  measured power level (dBm) Pin  transmit power (dBm) Al  cable power loss, attenuation (dB) 24  Optical Fiber Transmission Media Example 3 For a single-mode optical cable with 0.25-dB/km loss, determine the optical power 100 km from a 0.1-mW light source. Solution Substituting into Equation 15 gives P  0.1mW  10{[(0.25)(100)]/(10)}  1  104  10{[(0.25)(100)]/(10)}  (1  104)(1  102.5)  0.316 μW 0.316 μW and P1dBm2  10 log¢ ≤ 0.001  35 dBm or by substituting into Equation 16 ≤  3 1100 km2 10.25 dB>km2 4 0.1 mW P1dBm2  10 log¢ 0.001 W  10 dBm  25 dB  35 dBm Transmission losses in optical fiber cables are one of the most important characteristics of the fibers. Losses in the fiber result in a reduction in the light power, thus reducing the sys- tem bandwidth, information transmission rate, efficiency, and overall system capacity. The predominant losses in optical fiber cables are the following: Absorption loss Material, or Rayleigh, scattering losses Chromatic, or wavelength, dispersion Radiation losses Modal dispersion Coupling losses 10-1 Absorption Losses Absorption losses in optical fibers is analogous to power dissipation in copper cables; im- purities in the fiber absorb the light and convert it to heat. The ultrapure glass used to man- ufacture optical fibers is approximately 99.9999% pure. Still, absorption losses between 1 dB/km and 1000 dB/km are typical. Essentially, there are three factors that contribute to the absorption losses in optical fibers: ultraviolet absorption, infrared absorption, and ion res- onance absorption. 10-1-1 Ultraviolet absorption. Ultraviolet absorption is caused by valence elec- trons in the silica material from which fibers are manufactured. Light ionizes the valence electrons into conduction. The ionization is equivalent to a loss in the total light field and, consequently, contributes to the transmission losses of the fiber. 10-1-2 Infrared absorption. Infrared absorption is a result of photons of light that are absorbed by the atoms of the glass core molecules. The absorbed photons are converted to random mechanical vibrations typical of heating. 10-1-3 Ion resonance absorption. Ion resonance absorption is caused by OH ions in the material. The source of the OH ions is water molecules that have been trapped in the glass during the manufacturing process. Iron, copper, and chromium molecules also cause ion absorption. 25  Optical Fiber Transmission Media FIGURE 19 Absorption losses in optical fibers Figure 19 shows typical losses in optical fiber cables due to ultraviolet, infrared, and ion resonance absorption. 10-2 Material, or Rayleigh, Scattering Losses During manufacturing, glass is drawn into long fibers of very small diameter. During this process, the glass is in a plastic state (not liquid and not solid). The tension applied to the glass causes the cooling glass to develop permanent submicroscopic irregularities. When light rays propagating down a fiber strike one of these impurities, they are diffracted. Dif- fraction causes the light to disperse or spread out in many directions. Some of the dif- fracted light continues down the fiber, and some of it escapes through the cladding. The light rays that escape represent a loss in light power. This is called Rayleigh scattering loss. Figure 20 graphically shows the relationship between wavelength and Rayleigh scat- tering loss. 10-3 Chromatic, or Wavelength, Dispersion Light-emitting diodes (LEDs) emit light containing many wavelengths. Each wavelength within the composite light signal travels at a different velocity when propagating through glass. Consequently, light rays that are simultaneously emitted from an LED and propagated down an optical fiber do not arrive at the far end of the fiber at the same time, resulting in an impairment called chromatic distortion (sometimes called wavelength dispersion). Chromatic distortion can be eliminated by using a monochromatic light source such as an injection laser diode (ILD). Chromatic distortion occurs only in fibers with a single mode of transmission. 10-4 Radiation Losses Radiation losses are caused mainly by small bends and kinks in the fiber. Essentially, there are two types of bends: microbends and constant-radius bends. Microbending occurs as a result of differences in the thermal contraction rates between the core and the cladding ma- terial. A microbend is a miniature bend or geometric imperfection along the axis of the fiber and represents a discontinuity in the fiber where Rayleigh scattering can occur. Mi- crobending losses generally contribute less than 20% of the total attenuation in a fiber. 26  Optical Fiber Transmission Media FIGURE 20 Rayleigh scattering loss as a function of wavelength Constant-radius bends are caused by excessive pressure and tension and generally occur when fibers are bent during handling or installation. 10-5 Modal Dispersion Modal dispersion (sometimes called pulse spreading) is caused by the difference in the propagation times of light rays that take different paths down a fiber. Obviously, modal dis- persion can occur only in multimode fibers. It can be reduced considerably by using graded- index fibers and almost entirely eliminated by using single-mode step-index fibers. Modal dispersion can cause a pulse of light energy to spread out in time as it propa- gates down a fiber. If the pulse spreading is sufficiently severe, one pulse may interfere with another. In multimode step-index fibers, a light ray propagating straight down the axis of the fiber takes the least amount of time to travel the length of the fiber. A light ray that strikes the core/cladding interface at the critical angle will undergo the largest number of internal reflections and, consequently, take the longest time to travel the length of the cable. For multimode propagation, dispersion is often expressed as a bandwidth length product (BLP) or bandwidth distance product (BDP). BLP indicates what signal frequen- cies can be propagated through a given distance of fiber cable and is expressed mathemat- ically as the product of distance and bandwidth (sometimes called linewidth). Bandwidth length products are often expressed in MHz  km units. As the length of an optical cable increases, the bandwidth (and thus the bit rate) decreases in proportion. Example 4 For a 300-meter optical fiber cable with a BLP of 600 MHzkm, determine the bandwidth. 600 MHz  km Solution B  0.3 km B  2 GHz Figure 21 shows three light rays propagating down a multimode step-index optical fiber. The lowest-order mode (ray 1) travels in a path parallel to the axis of the fiber. The middle-order mode (ray 2) bounces several times at the interface before traveling the length 27  Optical Fiber Transmission Media FIGURE 21 Light propagation down a multimode step-index fiber FIGURE 22 Light propagation down a single-mode step-index fiber FIGURE 23 Light propagation down a multimode graded-index fiber of the fiber. The highest-order mode (ray 3) makes many trips back and forth across the fiber as it propagates the entire length. It can be seen that ray 3 travels a considerably longer dis- tance than ray 1 over the length of the cable. Consequently, if the three rays of light were emitted into the fiber at the same time, each ray would reach the far end at a different time, resulting in a spreading out of the light energy with respect to time. This is called modal dispersion and results in a stretched pulse that is also reduced in amplitude at the output of the fiber. Figure 22 shows light rays propagating down a single-mode step-index cable. Be- cause the radial dimension of the fiber is sufficiently small, there is only a single transmis- sion path that all rays must follow as they propagate down the length of the fiber. Conse- quently, each ray of light travels the same distance in a given period of time, and modal dispersion is virtually eliminated. Figure 23 shows light propagating down a multimode graded-index fiber. Three rays are shown traveling in three different modes. Although the three rays travel differ- ent paths, they all take approximately the same amount of time to propagate the length of the fiber. This is because the refractive index decreases with distance from the center, and the velocity at which a ray travels is inversely proportional to the refractive index. 28  Optical Fiber Transmission Media FIGURE 24 Pulse-width dispersion in an optical fiber cable Consequently, the farther rays 2 and 3 travel from the center of the cable, the faster they propagate. Figure 24 shows the relative time/energy relationship of a pulse of light as it propa- gates down an optical fiber cable. From the figure, it can be seen that as the pulse propa- gates down the cable, the light rays that make up the pulse spread out in time, causing a cor- responding reduction in the pulse amplitude and stretching of the pulse width. This is called pulse spreading or pulse-width dispersion and causes errors in digital transmission. It can also be seen that as light energy from one pulse falls back in time, it will interfere with the next pulse, causing intersymbol interference. Figure 25a shows a unipolar return-to-zero (UPRZ) digital transmission. With UPRZ transmission (assuming a very narrow pulse), if light energy from pulse A were to fall back (spread) one bit time (tb), it would interfere with pulse B and change what was a logic 0 to a logic 1. Figure 25b shows a unipolar nonreturn-to-zero (UPNRZ) digital trans- mission where each pulse is equal to the bit time. With UPNRZ transmission, if energy from pulse A were to fall back one-half of a bit time, it would interfere with pulse B. Con- sequently, UPRZ transmissions can tolerate twice as much delay or spread as UPNRZ transmissions. The difference between the absolute delay times of the fastest and slowest rays of light propagating down a fiber of unit length is called the pulse-spreading constant ( t) and is gener- ally expressed in nanoseconds per kilometer (ns/km). The total pulse spread (T) is then equal to the pulse-spreading constant (t) times the total fiber length (L). Mathematically, T is T(ns)  t(ns/km)  L(km) (17) For UPRZ transmissions, the maximum data transmission rate in bits per second (bps) is expressed as 1 fb1bps2  (18) ¢t  L 29  Optical Fiber Transmission Media FIGURE 25 Pulse spreading of digital transmissions: (a) UPRZ; (b) UPNRZ and for UPNRZ transmissions, the maximum transmission rate is 1 fb1bps2  (19) 2¢t  L Example 5 For an optical fiber 10 km long with a pulse-spreading constant of 5 ns/km, determine the maximum digital transmission rates for a. Return-to-zero. b. Nonreturn-to-zero transmissions. Solution a. Substituting into Equation 18 yields 1 fb   20 Mbps 5 ns>km  10 km b. Substituting into Equation 19 yields 1 fb   10 Mbps 12  5 ns>km2  10 km The results indicate that the digital transmission rate possible for this optical fiber is twice as high (20 Mbps versus 10 Mbps) for UPRZ as for UPNRZ transmission. 30  Optical Fiber Transmission Media FIGURE 26 Fiber alignment impairments: (a) lateral misalignment; (b) gap displacement; (c) angular misalign- ment; (d) surface finish 10-6 Coupling Losses Coupling losses are caused by imperfect physical connections. In fiber cables, coupling losses can occur at any of the following three types of optical junctions: light source-to-fiber connections, fiber-to-fiber connections, and fiber-to-photodetector connections. Junction losses are most often caused by one of the following alignment problems: lateral misalign- ment, gap misalignment, angular misalignment, and imperfect surface finishes. 10-6-1 Lateral displacement. Lateral displacement (misalignment) is shown in Figure 26a and is the lateral or axial displacement between two pieces of adjoining fiber ca- bles. The amount of loss can be from a couple tenths of a decibel to several decibels. This loss is generally negligible if the fiber axes are aligned to within 5% of the smaller fiber’s diameter. 10-6-2 Gap displacement (misalignment). Gap displacement (misalignment) is shown in Figure 26b and is sometimes called end separation. When splices are made in 31  Optical Fiber Transmission Media optical fibers, the fibers should actually touch. The farther apart the fibers, the greater the loss of light. If two fibers are joined with a connector, the ends should not touch because the two ends rubbing against each other in the connector could cause damage to either or both fibers. 10-6-3 Angular displacement (misalignment). Angular displacement (misalign- ment) is shown in Figure 26c and is sometimes called angular displacement. If the angular displacement is less than 2°, the loss will typically be less than 0.5 dB. 10-6-4 Imperfect surface finish. Imperfect surface finish is shown in Figure 26d. The ends of the two adjoining fibers should be highly polished and fit together squarely. If the fiber ends are less than 3° off from perpendicular, the losses will typically be less than 0.5 dB. 11 LIGHT SOURCES The range of light frequencies detectable by the human eye occupies a very narrow segment of the total electromagnetic frequency spectrum. For example, blue light occupies the higher frequencies (shorter wavelengths) of visible light, and red hues occupy the lower fre- quencies (longer wavelengths). Figure 27 shows the light wavelength distribution produced from a tungsten lamp and the range of wavelengths perceivable by the human eye. As the figure shows, the human eye can detect only those lightwaves between approximately 380 nm and 780 nm. Furthermore, light consists of many shades of colors that are directly re- lated to the heat of the energy being radiated. Figure 27 also shows that more visible light is produced as the temperature of the lamp is increased. Light sources used for optical fiber systems must be at wavelengths efficiently propa- gated by the optical fiber. In addition, the range of wavelengths must be considered because the wider the range, the more likely the chance that chromatic dispersion will occur. Light Ultraviolet Infrared wavelengths wavelengths 1 Yellow 2000°k Normalized human eye response 0.8 Orange 2500°k Green Tungsten lamp 0.6 radiation spectrums for different temperatures 3400°k 0.4 Eye response GaAs 0.2 Blue Red 0 200 400 600 800 1000 1200 1400 Wavelength (nanometers) FIGURE 27 Tungsten lamp radiation and human eye response 32  Optical Fiber Transmission Media sources must also produce sufficient power to allow the light to propagate through the fiber without causing distortion in the cable itself or in the receiver. Lastly, light sources must be constructed so that their outputs can be efficiently coupled into and out of the optical cable. 12 OPTICAL SOURCES There are essentially only two types of practical light sources used to generate light for op- tical fiber communications systems: LEDs and ILDs. Both devices are constructed from semiconductor materials and have advantages and disadvantages. Standard LEDs have spectral widths of 30 nm to 50 nm, while injection lasers have spectral widths of only 1 nm to 3 nm (1 nm corresponds to a f