Chapter 3
`
`telephone
`c.
`d. wireless radio transmission
`2. Which of the following statements are true for analog signals?
`a. They vary continuously in intensity.
`b. They are transmitted in parts of the telephone network.
`c. They are compatible with human senses.
`d. They can be processed electronically.
`e. All of the above
`3. Which of the following statements are true for digital signals?
`a. They can encode analog signals.
`b. They are transmitted in parts of the telephone network.
`c. They can be processed electronically.
`d. They are used in computer systems.
`e. All of the above
`4. You digitize a 10-kHz signal by sampling it at twice the highest frequency
`(i.e., 20,000 times a second) and encoding the intensity in 8 bits. What is the
`resulting data rate?
`a. 20 kbit/s
`b. 64 kbit/s
`c. 144 kbit/s
`d. 160 kbit/s
`e. 288 kbit/s
`5. What part of the telephone network is connected directly to your home
`telephone if you get your telephone service from a local telephone company?
`a. subscriber loop
`b.
`feeder cable
`c.
`trunk line
`d. backbone system
`6. What part of the telephone network carries the highest-speed signals?
`a. subscriber loop
`b.
`feeder cable
`c.
`trunk line
`d. backbone system
`7. Time-division multiplexing of eight signals at 150 Mbit/s each produces
`a. eight optical channels each carrying 150 Mbit/s.
`b. one channel carrying 120 Mbit/s.
`c. one channel carrying 1.2 Gbit/s.
`d. eight signals at 150 MHz.
`
`MASIMO 2014
`PART 2
`Apple v. Masimo
`IPR2020-01526
`
`

`

`Fundamentals of Communications
`
`8. What are the “pipes” used to broadcast television signals from a station on the
`
`ground?
`a. air
`b. optical fibers
`c. coaxial cables
`d. twisted pair
`9. The carrier signal modulated to produce one optical channel in a fiber-optic
`system is
`a. a single wavelength of light generated in the transmitter.
`b. a radio-frequency signal supplied electronically to the transmitter.
`c. an acoustic vibration in the optical fiber.
`d. a combination of wavelengths generated by several light sources.
`1 0 . Who offers DSL and what service does it normally provide?
`a. Television broadcasters offer it for Internet access.
`b. Cable television carriers offer it for Internet access.
`c. Telephone carriers offer it for Internet access.
`d. Cable television carriers offer it for telephone service.
`e. Internet service providers offer it for telephone service.
`1 1 . What is the only important telecommunications system that uses fiber to
`transmit analog signals?
`a. local telephone service
`b. long-distance telephone systems
`c. Internet backbone systems
`d. cable T V systems
`e. none
`1 2 . What U.S. government agency regulates telecommunications?
`a. Federal regulations have been abolished.
`b. Department of Homeland Security
`c. Department of Commerce
`d. Federal Communications Commission
`e. International Telecommunications Union
`
`

`

`

`

`Types of
`Optical Fibers
`
`About This Chapter
`
`Not all optical fibers are alike. Several different types, made for different applications,
`guide light in different ways. This chapter describes the basic concepts behind standard
`fibers, concentrating on fiber design and light guiding. It is closely linked to the chapters
`that follow. Chapter 5 describes the important properties of optical fibers. Chapter 6
`covers fiber materials, structures, and manufacturing, which play a vital role in deter-
`mining fiber properties. Chapter 7 covers specialty fibers used in amplifiers, wavelength
`selection, and applications other than merely guiding light.
`
`Light Guiding
`
`Chapter 2 showed how the total internal reflection of light rays can guide light along
`optical fibers. This simple concept is a useful approximation of light guiding in many
`types of fiber, but it is not the whole story. The physics of light guiding is considerably
`more complex, because a fiber is really a waveguide and light is really an electromagnetic
`wave with frequency in the optical range.
`Like other waveguides, an optical fiber guides waves in distinct patterns called modes,
`which describe the distribution of light energy across the waveguide. The precise pat-
`terns depend on the wavelength of light transmitted and on the variation in refractive
`index that shapes the core, which can be much more complex than the simple, single cores
`described in Chapter 2. In essence, these variations in refractive index create boundary
`conditions that shape how electromagnetic waves travel through the waveguide, like the
`walls of a tunnel affect how sounds echo inside.
`
`

`

`Chapter
`
`Total internal
`reflection is only
`a rough
`approximation of
`light guiding in
`optical fibers.
`
`Core-cladding
`structure and
`material
`composition are
`key factors in
`determining fiber
`properties.
`
`It’s possible to calculate the nature of these transmission modes, but it takes a solid
`understanding of advanced calculus and differential equations, which is far beyond the
`scope of this book. Instead, we’ll look at the characteristics of transmission modes, which
`are important in fiber-optic systems. By far the most important is the number of modes the
`fiber transmits. Fibers with small cores can transmit light in only a single mode. It can be
`hard to get the light into the fiber, but once it’s inside, the light behaves very uniformly. It’s
`easier to get light into fibers with larger cores that can support many modes, but light does
`not behave the same way in all the modes, which can complicate light transmission, as you
`will learn later in this chapter.
`This chapter covers the many types of optical fibers that have been developed to meet a
`variety of functional requirements. Their designs differ in important ways. For example,
`bundles of fibers used for imaging need to collect as much light falling on their ends as pos-
`sible, so their claddings are made thin compared to their cores. Communications fibers
`have thicker claddings, both to keep light from leaking out over long distances and to sim-
`plify handling of single fibers. Various types of communications have their own require-
`ments. Fibers for short links inside cars or offices typically have large cores to collect as
`much light as possible. Long-distance fibers have small cores, which can transmit only a
`single mode, because this well-controlled light can carry signals at the highest speed.
`The two considerations that affect fiber properties most strongly are the core-cladding
`structure and the glass composition. The size of the core and cladding and the nature of
`the interface between them determine the fiber’s modal properties and how it transmits
`light at different wavelengths. The simple types of fiber discussed in Chapter 2 have a
`step-index structure, where the refractive index changes sharply at the abrupt boundary
`between a high-index core and a low-index cladding. Replacing that abrupt boundary with
`a gradual transition between core and cladding, or including a series of layers, changes fiber
`properties. Glass composition, covered in Chapter 6, strongly affects fiber attenuation, as
`well as influencing pulse spreading.
`Combined with other minor factors, these parameters determine important fiber character-
`istics, including
`
`^ Attenuation as a function of wavelength.
`• Collection of light into a fiber (coupling).
`• Transmission modes.
`• Pulse spreading and transmission capacity, as a function of wavelength.
`• Tolerances for splicing and connecting fibers.
`• Operating wavelengths.
`• Tolerance to high temperature and environmental abuse.
`• Strength and flexibility.
`
`Figure 4.1 shows selected types of single fibers (as distinct from bundled fibers), along
`with a plot of refractive index across the core and cladding, called the index profile. Only
`the core and cladding are shown for simplicity; actual fibers have an outer plastic coating
`to protect them from the environment. The coating’s thickness depends on fiber size. For
`
`

`

`Types of Optical Fibers
`
`FIGURE 4.1
`Common types o f
`optical fib er (to
`scale). IT U
`designations are
`standards o f the
`International
`Telecommunications
`Union.
`
`pm
`O
`
`W -
`
`80 pen
`
`-A-
`
`d. Nonzero
`Dispersion
`Shifted
`Single-Mode
`Fiber
`(ITU G.655)
`
`Index
`P rofile
`
`e. Reduced Core
`Step-lndex
`Single-Mode
`Fiber
`
`a. Step-lndex Multimode Fibers
`
`50/125
`
`5 0 p m
`
`62.5/125
`
`6 2? F pm
`
`-«— 125 p m — »■
`
`— 125 pm — * -
`
`Index
`(cid:1)-n
`J
`\ ______ P rofile
`
`
`
`( V
`
`b. Graded-lndex Fibers (50/125 is ITU G.651)
`
`_TL
`
`c. Step-lndex
`Single-Mode
`Fiber
`(ITU G.652)
`
`

`

`Chapter 4
`
`a typical communications fiber with 125-|xm cladding, the plastic coating is 250 |xm. I will
`start with the fiber type that is simplest to explain in terms of total internal reflection, called
`step-index multimode fiber, because it transmits many modes.
`
`Step-index Multimode Fiber
`
`As we saw in Chapter 2, bare, transparent filaments surrounded by air are the simplest type
`of optical fiber, but they don’t work well in practice. Cladding the fiber with a transparent
`material having lower refractive index protects the light-carrying core from surface
`scratches, fingerprints, and contact with other cores of the same material, so the light will
`not escape from the surface. This simple fiber consists of two layers of material, the core
`and cladding, which have different refractive indexes. If you drew a cross section of the fiber
`and plotted the refractive index, as in Figure 4.1(a), you would see a step at the core-
`cladding boundary, where the index changes abruptly.
`Light-Guiding Requirements
`As long as the core of a fiber has a diameter many times larger than the wavelength of light
`jt carries, we can calculate fiber properties using the simple model of light as rays. The fun-
`damental requirement for light guiding is that the core must have a higher refractive index
`t^an ^ d a tin g material. We saw in Chapter 2 that the critical angle for total internal
`reflection, 0cr;t, depends on the ratio or core and cladding retractive indexes.
`n
`.
`c
`c
`„
`.
`,
`,
`•
`■
`j^cladA
`
`j
`
`i
`
`© crit = arcsin
`
`j
`
`j
`
`-
`
`j
`
`For a typical fiber, the difference is small, about 1%, so the critical angle is arcsin (0.99),
`or about 82°. This means that light rays must be within 8° of the axis of the fiber to be con-
`fined in the core, as shown in Figure 4.2. This value is called the confinem ent angle,
`^confinement’ ar*d equals 90° — 0cr;t. The angle is not very sensitive to the refractive-index
`
`Only light falling in this
`angle is guided along the fiber.
`
`Critical Angle
`for Total Internal
`Reflection
`
`•
`To guide light, the
`fiber core must
`ave re rac ive
`index hiqher than
`the cladd'ng
`
`FIGURE 4.2
`Light guiding in a
`large-core step-
`index fiber. The
`confinement angle
`measures the angle
`between guided
`light rays and the
`fib er axis; the
`acceptance angle is
`measured in air.
`
`

`

`Types of Optical Fibers
`
`difference. If the difference is doubled to 2%, the confinement angle becomes 11.5°. You can
`directly calculate the confinement angle measured from the core-cladding boundary using the
`arc-cosine:
`
`® confinem ent
`
`1
`a r c C O s f
`y "core J
`
`The confinement angle gives the maximum angle at which guided light can strike the core-
`cladding boundary once it’s inside the glass. However, refraction occurs when the light
`enters the glass from air, bending light toward the axis of the fiber. To calculate the
`acceptance angle, measured in air, you must account for this refraction using the standard
`law of refraction. As long as the light enters from air, you can simplify this to
`sin Ohalf-acceptance
`^ co re ^
`^ co n fin em en t
`which gives the sine of the largest possible angle from the axis of the fiber, called the half-
`acceptance angle, Ohalf-acceptance- You can calculate the half-acceptance angle directly by jug-
`gling the trigonometry a bit more:
`
`O half-acceptance
`
`arcsin(/tcore X sin O confinem ent)
`Doubling the half-acceptance angle gives the full-acceptance angle. The confinement angle
`is small enough that you can roughly approximate the half-acceptance angle by multiply-
`ing the confinement angle by the refractive index of the core, nCOK.
`Imaging Fibers
`The first clad optical fibers developed for imaging were what we now call step-index mul-
`timode fibers. Developers tested a variety of cladding materials with low refractive indexes,
`including margarine, beeswax, and plastics. However, the key practical development was a
`way to apply a cladding of glass with lower refractive index than the core.
`As we will see in Chapter 6, glass comes in many different formulations with varied
`refractive indexes. The simplest way to make glass-clad fibers is to slip a rod of high-index glass
`into a tube with lower refractive index, heat the tube so the softened glass collapses onto the
`rod, let them fuse together, then heat the whole preform, and pull a fiber from the molten end.
`The cladding of imaging fibers generally is a thin layer surrounding a thicker core. The
`reason for this design is that imaging fibers are assembled in bundles, with light focused on
`one end of the bundle to emerge at the other. Light falling on the fiber cores is transmit-
`ted from one end to the other, but light falling on the cladding is lost. The thinner the
`cladding, the more light falls on the fiber cores and the higher the transmission efficiency.
`Reducing the size of individual fibers increases the resolution of images transmitted
`through a bundle, but very fine fibers are hard to handle and vulnerable to breakage.
`Typically, the smallest loose fibers used in imaging bundles are about 20 |xm (0.02 mm,
`or 0.0008 in.). Even at this size, they remain large relative to the wavelength of visible
`light (0.4 to 0.7 |xm in air), and you can get away with considering light guiding as
`determined by total internal reflection of light rays at the core-cladding boundary. (The
`highest-resolution fiber bundles are made by melting fibers together and stretching the
`whole solid block.)
`
`The confinement
`angle is the
`largest angle at
`which light rays
`confined to a
`fiber core strike
`the core-cladding
`boundary.
`
`Step-index
`multimode fibers
`were the first
`fibers developed
`for imaging.
`
`

`

`Illuminating and Beam-Delivery Fiber
`Single step-index fibers with large cores— typically 400 p,m to 1 mm— can be used to
`guide a laser beam from the laser to a target or industrial workpiece. The large diameter
`serves two purposes. First, it can collect power from the laser more efficiently than a
`smaller core fiber. In addition, it spreads the laser power over a larger area at the ends of
`the fiber and through a larger volume within the fiber. This is important because some
`laser power inevitably is lost at the surfaces and within the fiber. If the beam must be
`focused tightly to concentrate it in the fiber, the power density (power per unit area) may
`reach levels so high it can damage exposed ends of the fiber.
`The design of these large-core fibers is similar to those in Figure 4.1(a). The core diam-
`eters are proportionally larger, whereas cladding thicknesses do not increase as rapidly. As
`the fibers become thicker, they also become less flexible.
`Communications Fibers
`Step-index multimode fibers with cores not quite as large can be used for some types of
`communications. One smaller type, shown in Figure 4.1(a), has a 100-p.m core sur-
`rounded by a cladding 20 ptm thick, for total diameter of 140 p,m. It is typically called
`100/140 fiber, with the core diameter written before the overall diameter of the cladding.
`Typically an outer plastic coating covers the whole fiber, protecting it from mechanical
`damage and making it easier to handle. The large core is attractive for certain types of
`communications, because it can collect light efficiently from inexpensive light sources
`such as LEDs.
`If you think of light in terms of rays, you can see an important limitation of large-core
`step-index fibers for communication (see Figure 4.3). Light rays enter the fiber at a range
`of angles, and rays at different angles travel different paths through the same length of
`fiber. The larger the angle between the light ray and the axis, the longer the path. For
`example, a light ray that entered at 8° from the axis (the maximum confinement angle in
`the earlier example) of a perfectly straight 1-m length of fiber would travel a distance of
`1.0098 m (1 m/cos 8°) before it emerged from the other end. Thus light just inside the
`confinement angle would emerge from the fiber shortly after light that traveled down the
`middle. This pulse-dispersion effect becomes larger with distance and can limit data-
`transmission speed.
`In fact, the ray model gives a greatly simplified view of light transmission down opti-
`cal fibers. As I mentioned earlier, an optical fiber is a waveguide that transmits lightwaves
`
`■ Chapter 4
`
`Large-core step-
`index fibers are
`used to deliver
`laser power.
`
`Light pulses stretch
`out in length and
`time as they travel
`through large-core
`step-index fiber.
`
`FIGURE 4.3
`Light rays that
`enter multimode
`step-index fib er at
`different angles
`travel different
`distances through
`the fiber, causing
`pulse dispersion.
`
`

`

`Types of Optical Fibers
`
`•
`Small-core fibers
`carry arsing e
`
`^
`^ fiber is a
`ec rlc op ica
`°
`
`in one or more transmission modes. Stay tuned for the next section, and I’ll explain more
`about these modes. The larger the fiber core, the more modes it can transmit, so a step-
`index fiber with a core of 20 |xm or more is a multimode fiber. Light rays enter the fiber
`at different angles, and the various modes travel down the fiber at different speeds. What
`you have as a result is modal dispersion, which occurs in all fibers that carry multiple
`modes. It is largely irrelevant for imaging and guiding illuminating beams, but it is a
`serious drawback for communications. To understand why, we need to take a closer look
`at modes.
`
`Modes and Their Effects
`
`Modes are stable patterns that waves form as they pass through a waveguide. The number
`of modes that can travel along a waveguide depends on the wavelength of the wave and the
`size, shape, and nature of the waveguide. For an optical fiber, the dominant factor is the
`core diameter; the larger the core, the more modes the fiber can carry. This leads to a fun-
`damental trade-off between the higher signal quality possible with single-mode transmis-
`sion and the easier input coupling with larger-core fibers.
`Waveguide theory, which describes modes, originally was developed for microwaves, but
`can be applied to any guided electromagnetic waves— including light passing through the
`core of an optical fiber. You don’t want to worry about the mathematical details of wave-
`guide theory— and I certainly don’t— but it is important to learn some basic concepts
`about waveguides and modes.
`Electromagnetic waves are oscillating electric and magnetic fields, and how they oscillate
`in a waveguide depends on how they are confined. The best-known microwave waveguides
`are rectangular metal tubes, but flexible plastic rods called dielectric waveguides also can
`guide microwaves. (Dielectric means electrically insulating.) A dielectric microwave wave-
`guide is equivalent to a bare optical fiber, with the surface guiding the waves— so anything
`touching the surface causes losses.
`In a clad optical fiber, the guiding dielectric surface is the boundary between core and
`cladding, where the refractive index changes. In the ray model of light propagation, light
`guided in the fiber is totally reflected at this boundary. But waveguide theory reveals that
`a small fraction of the light actually extends beyond the core into the inner part of the
`cladding, which leads to some complications.
`As long as the fiber core is big enough to accept any light, it can carry light in the lowest-
`order mode, where the electric field intensity is highest at the center of the core and drops
`to the sides, as shown at left in Figure 4.4. As the core diameter increases beyond a certain
`point, called the cu toff wavelength, the fiber can support transmission in additional modes.
`The two curves at right in Figure 4.4 show the second and third lowest-order modes. Fiber
`cores support many modes simultaneously, with the number increasing very rapidly with
`the core diameter. The difference in refractive index between the core and cladding also
`influences the number of modes.
`An optical fiber is a cylindrical waveguide. It’s also possible to make planar optical wave-
`guides as stripes of high-index material on a substrate with lower refractive index. You will
`learn more about planar waveguides later.
`
`

`

`Chapter 4
`
`Single-mode fibers
`must have small
`
`Some light
`penetrates into
`the cladding.
`
`FIGURE 4.4
`Electric fields fo r
`the lowest-order
`mode in an
`optical fib er (left)
`and fo r the
`second-order and
`third-order modes
`(right). Higher-
`order modes are
`more complex.
`
`Single-Mode Waveguides
`Conventional microwave waveguides carry a single mode. Multimode microwave wave-
`guides don’t work well because interactions between the modes generate noise. Single-
`mode transmission is cleaner and simpler, and it’s also preferred for fiber-optic systems.
`The main limitation is that the core of the fiber must be small enough to restrict transmission
`to a single mode, yet large enough to collect most of the input optical signal.
`The balance is struck by adjusting the difference between core and cladding refractive
`index. The smaller the core-cladding difference, the larger the core can be. The refractive
`index difference is large for a bare glass fiber (with n — 1.5) in air (with n = 1.000293),
`so the core must be around 1 pm to transmit only a single mode at the usual transmission
`wavelengths. Standard single-mode telecommunications fibers have a cladding index only
`about 0.5% lower than the core index; this allows core diameters above 9 pm, which is sev-
`eral times the 1.5-pm wavelength used for long-haul transmission.
`Larger-core fibers carry multiple modes. In practice, transmission is much better when a
`fiber carries many modes than when it carries a few, so there is a large gap between single-
`mode fibers with core diameters below 10 pm and multimode fibers with core diameters
`50 pm or larger.
`
`Modal Properties
`Although the core-cladding boundary is nominally the surface of the waveguide in a clad
`optical fiber, the light energy does not really propagate along that boundary. Some light
`penetrates the boundary and goes a short distance into the cladding, while most of the
`light remains inside the core. This effect occurs in all types of clad fibers, but is most
`important in single-mode fibers, where it is characterized by the m ode-field diameter,
`which is slightly larger than the core diameter. Technically, the mode-field diameter is the
`point where light intensity drops to l/e2(0.135) of the mode’s peak intensity. Figure 4.4
`shows the distribution of light energy in modes, while Figure 4.5 shows the path of light
`in a single-mode fiber.
`
`M o d e -F ie ld D ia m e te r
`
`M ode
`
`M ode
`
`M ode
`
`

`

`C la d d in g
`
`Light penetrates slightly into cladding.
`
`Types of Optical Fibers
`
`FIGURE 4.5
`Light penetrates
`slightly into the
`cladding o f a
`single-mode step-
`index fiber.
`
`Mode-field diameter
`is slightly larger
`than core.
`
`In te n s ity P ro file of
`L ig h t in L o w e s t-O rd e r
`M ode
`
`Light leakage into the cladding makes cladding transmission important, although not as
`critical as for the core. Guided waves travel mostly in the core in single-mode fibers. In
`multimode fibers, some modes may spend more time in the cladding than in the core.
`Modes are sometimes characterized by numbers. Single-mode fibers carry only the
`lowest-order mode, assigned the number 0. Multimode fibers also carry higher-order
`modes. The number of modes that can propagate in a fiber depends on the fiber’s
`numerical aperture (or acceptance angle) as well as on its core diameter and the wave-
`length of the light. For a step-index multimode fiber, the number of such modes, N m,
`is approximated by
`
`Modes = 0.5
`
`core diameter X NA X ir
`wavelength
`
`N m = 0.5
`
`txD X NA
`
`where X is the wavelength and D is the core diameter. To plug in some representative num-
`bers, a 100-ptm core step-index fiber with NA = 0.29 (a typical value) would transmit
`thousands of modes at 850 nm. This formula is only an approximation and does not work
`for fibers carrying only a few modes.
`
`Leaky Modes
`Low-order modes are better guided than the higher-order modes in a multimode fiber.
`Modes that are just beyond the threshold for propagating in a multimode fiber can travel
`for short distances in the fiber cladding. In this case, the cladding itself acts as an unclad
`optical fiber to guide those cladding modes.
`
`Some modes can
`propagate short
`distances in the
`cladding of a
`multimode fiber.
`
`

`

`Chapter 4
`
`Because the difference between guided and unguided modes is small, slight changes in
`conditions may allow light in a normally guided mode to leak out of the core. Likewise,
`some light in a cladding mode may be recaptured. Slight bends of a multimode fiber are
`enough to allow escape of these leaky modes.
`Modal-Dispersion Effects
`Each mode has its own characteristic velocity through a step-index optical fiber, as if it were
`a light ray entering the fiber at a distinct angle. This causes pulses to spread out as they
`travel along the fiber in what is called m odal dispersion. The more modes the fiber trans-
`
`•
`Modal dispersion
`n multimode step-
`
`laT ester$ . T
`argest type o
`
` mitS’ the m ° re PU1S£S Spread 0Ut'
`Later we will see that there are other kinds of dispersion, but modal dispersion is the
`largest in multimode step-index fibers. Precise calculations of how many modes cause how
`much dispersion are rarely meaningful. However, you can make useful approximations by
`using the ray model (which works for multimode step-index fibers) to calculate the differ-
`ence between the travel times of light rays passing straight through a fiber and bouncing
`along at the confinement angle. For the typical confinement angle of 8° mentioned earlier,
`the difference in propagation time is about 1%. That means that an instantaneous pulse
`would stretch out to about 30 ns (30 billionths of a second) after passing through a kilo-
`meter of fiber.
`That doesn’t sound like much, but it becomes a serious restriction on transmission
`speed, because pulses that overlap can interfere with each other, making it impossible to
`receive the signal. Thus pulses in a 1-km fiber have to be separated by more than 30 ns.
`You can estimate the maximum data rate for a given pulse spreading from the equation
`
`Data rate =
`
`° J
`pulse spreading
`
`Plug in a pulse spreading of 30 ns, and you find the maximum data rate is about 23 Mbit/s.
`In practice, the maximum data rate also depends on other factors.
`Dispersion also depends on distance. The total modal dispersion is the product of the
`fibers characteristic modal dispersion per unit length, Dq, multiplied by the fiber length, L:
`D — D q X L
`Thus a pulse that spreads to 30 ns over 1 km will spread to 60 ns over 2 km and 300 ns
`over 10 km. (For very accurate calculations, you should replace L with Id , where 7 is a fac-
`tor normally close to 1, which depends on the fiber type.)
`Because total dispersion increases with transmission distance, the maximum transmis-
`sion speed decreases. If the maximum data rate for a 1 -km length of fiber is DR<), the maxi-
`mum data rate for L kilometers is roughly
`
`DRq
`DR = — -
`
`We will learn more about dispersion in Chapter 5. For now, the important thing to
`remember is that modal dispersion seriously limits transmission speed in step-index
`multimode fiber.
`
`

`

`Types of Optical Fibers
`
`Replacing the
`sharp boundary
`between core and
`cladding with a
`refractive-index
`gradient nearly
`eliminates modal
`dispersion.
`
`Graded-lndex Multimode Fiber
`
`As communications engineers began seriously investigating fiber optics in the early 1970s,
`they recognized modal dispersion limited the capacity of large-core step-index fiber. Single-
`mode fibers promised much more capacity, but many engineers doubted they could get
`enough light into the tiny cores. As an alternative, they developed multimode fiber in
`which the refractive index grades slowly from the center of the core to the inner edge of the
`cladding. Careful control of the refractive-index gradient nearly eliminates modal disper-
`sion in fibers with cores tens of micrometers in diameter, giving them much greater trans-
`mission capacity than step-index multimode fibers.
`Optically, graded-index fibers guide light by refraction instead of total internal reflec-
`tion. The fiber’s refractive index decreases gradually away from its center, finally dropping
`to the same value as the cladding at the edge of the core, as shown in Figure 4.6. The
`change refracts the light, bending rays back toward the axis as they pass through layers with
`lower refractive indexes, as shown in Figure 4.7. The refractive index does not change
`abruptly at the core-cladding boundary, so there is no total internal reflection. (Don’t be
`fooled by the change in slope at the edge of the core in Figure 4.6; it’s more like starting
`up a slow hill than hitting the cliff of a step-index transition.) Refraction bends guided
`light rays back into the center of the core before they reach the cladding boundary. (The
`refractive-index gradient cannot confine all light entering the fiber, only rays that fall
`within a limited confinement angle, as in step-index fiber. The refractive-index gradient
`determines that angle.)
`As in a step-index fiber, light rays follow different paths in a graded-index fiber.
`However, their speeds differ because the speed of light in the fiber core changes with its
`refractive index. Recall that the speed of light in a material, cmat, is the velocity of light in
`a vacuum, £Vacuum> divided by refractive index:
`
`_ ^vacuum
`Cmat ~ ~n'T T iat
`
`Thus the farther the light goes from the axis of the fiber, the faster its velocity. The differ-
`ence isn’t great, but it’s enough to compensate for the longer paths followed by the light
`
`FIGURE 4.6
`Refractive-index
`profile o f a
`
`with 62.5-fJim
`core.
`
`R a d iu s (|tm )
`
`

`

`Chapter 4
`
`FIGURE 4.7
`The refractive-
`index gradient in a
`graded-index fiber
`bends light rays
`back toward the
`center o f the fiber.
`
`Graded-index fiber bends
`light back into core as the
`refractive index decreases
`(darker shading indicates
`higher refractive index).
`
`C la d d in g
`
`Light goes faster in the
`low-index outer core, so
`it catches up with light in
`the higher-index center.
`
`rays that go farthest from the axis of the fiber. Careful adjustment of the refractive-index
`profile— the variation in refractive index with distance from the fiber axis— can greatly
`reduce modal dispersion by equalizing the transit times of different modes.
`Practical Graded-index Fiber
`Graded-index fibers were developed especially for communications. Standard types have
`core diameters of 50 or 62.5 pm and cladding diameters of 125 pm, although some have
`been made with 85-pm cores and 125-pm claddings. The 50-pm core fiber is covered by
`the International Telecommunications Union (ITU) G.651 standard. The core diameters
`are large enough to collect light efficiently from a variety of sources. The cladding must be
`at least 20 pm thick to keep light from leaking out.
`The graded-index fiber is a compromise, able to collect more light than small-core
`single-mode fiber and able to transmit higher-speed signals than step-index multimode fibers.
`It was used in telecommunications systems extending farther than a few kilometers until
`the mid-1980s, but gradually faded from use in telephone systems because single-mode
`fibers offered much higher bandwidth. Recent improvements have improved the modal dis-
`persion of graded-index fibers so they can carry higher-speed signals, but they remain limited
`to data communications and networks that carry signals no farther than a few kilometers.
`Limitations of Graded-index Fiber
`Graded-index fibers suffer some serious limitations that ultimately made them impractical
`for high-performance communications.
`Modal dispersion is not the only effect that spreads out pulses going through optical fibers.
`Other types of dispersion arise from the slight variation of refractive index with the wave-
`length of light. These are present in graded-index fibers and became increasingly important
`as transmission moved to higher speeds. Chapter 5 will describe these dispersion effects.
`Multimode transmission itself proved a serious problem. Different modes can interfere
`with each