Chapter 12 Linear Fiber-Optic Signal Transportation
12.1 Introduction
Although coaxial cable is used for the “last mile” delivery of broadband services to subscribers, other technologies are frequently used to cover most of the physical distance between headend and tap. One reason for this is that the interrelationship between bandwidth, signal levels, number of cascaded devices, noise, and distortion (discussed in Chapter 11) limits the size of purely coaxial systems. Second, large coaxial systems are best suited to delivery of a common spectrum of signals to all parts of the network, whereas many services, such as data communications and telephony, require a bidirectional bandwidth allocation to every customer. In order to provide this capacity in a network of attainable bandwidth, the network must be segmented, and this requires the use of small coaxial sections, each connected by separate communications links to the headend.
In modern networks, these links almost always use linear fiber optics for at least the segment that interfaces with the coaxial network (though Chapter 14 will discuss the microwave alternative). Fiber strands have a loss that, at the optical wavelengths used by cable television systems, is approximately two orders of magnitude lower than the best coaxial cables. Furthermore, the noise and distortion added by a typical 5- to 15-mile-long fiber-optic link is less than that generated in a comparable-length coaxial trunk line section.
This chapter will begin with a brief introduction to some principals of optics that are important to fiber transmission of light. Then optical fibers will be examined in detail, particularly the interaction between the fiber and the signals passing through it. Passive optical devices, comparable with their coaxial counterparts, will be treated next. Active devices will include transmitters, amplifiers, and receivers. Finally, the total performance of optical links will be examined with end-to-end performance calculations of noise and distortion. The unique characteristics of multiwavelength systems will be covered in Chapter 13.
12.2 Optical Basics
Light “waves” are just much higher-frequency RF waves – about 300,000 times the highest frequency used in coaxial cable systems and 20,000 times the microwave frequencies sometimes used to relay cable television signals. Optical wavelengths are very short (remember that λ= c/f in a vacuum). For instance, visible yellow light has a frequency of about 5.5 × 1014 Hz, and thus a wavelength of only 0.00000055 m, more easily expressed as 550 nm (one nanometer is one billionth of a meter), considerably less than 1/10,000 of an inch.
At these frequencies, electromagnetic waves behave in ways that are sometimes counterintuitive. For one thing, physicists have long understood that the flow of energy is not continuous, but rather travels in “bundles” called quanta. In the case of light (and, for that matter, any radio waves), the carriers of the energy are massless subatomic particles called photons that travel, not surprisingly, at the speed of light (about 3 × 108 meters/second or, if you prefer, about 11.7 inches per nanosecond in a vacuum). The energy carried by each photon is directly proportional to the frequency of the signal, so photons at light frequencies are much more energetic than those at VHF radio frequencies. As a result, the “granularity” of VHF power transmission is extremely fine, whereas it is sufficiently coarse at optical frequencies to add measurable noise to optical transmission links.
So, is light energy carried by electromagnetic radio waves or by particles called photons? Fortunately, we do not have to answer that question. In fact, they are both convenient mathematical models that explain the behavior of light under various conditions. Physicists use whichever model is most convenient to the situation at hand, and so will we.
Also, fortunately, we need to know but little of the broad subject called optics to understand the use of light as a carrier of signals through glass fibers. We do, however, need to understand the fundamentals of the interaction between light and materials.
12.2.1 Velocity of Propagation and Wavelength
RF signals propagate more slowly through coaxial cables than in a vacuum. Specifically (Equation (10.8)), the ratio of cable propagation velocity to that in free space is 
, where εis the relative dielectric constant of the cable dielectric.
Given that light waves are simply higher-frequency radio waves, we would expect a similar phenomenon to occur in optical transmission lines, and it does. The difference is that the dielectric constant, at optical wavelengths, varies with frequency. At RF frequencies and below, the dielectric constant is dominated by molecular and atomic effects. At frequencies above the natural resonances of the molecular structures, they have less effect. The result is that the effective dielectric constant is both lower and wavelength dependent.
Rather than speak in terms of dielectric constant, the term index of refraction is used. The index of refraction of a material is numerically equal to the square root of the effective dielectric constant at the optical frequency being considered.
The speed of propagation through a material can be expressed as
(12.1)where
v = the velocity of the propagated signal in meters/second
The slowing of the light waves through materials is the result of a phenomenon known as forward scattering. When light signals travel through material, it interacts with the individual atoms. The wave model of what happens is that individual electrons get “excited” into a higher energy state and then give up that energy by generating a wave of their own. The particle model is that once in a while a photon slams into an electron, exciting it to a higher energy state. After a while, the electron returns to its former energy level, emitting a photon of equal energy in the process.
Whatever the model, the result is the same: Energy from the transmitted wave is temporarily transferred to the material and then released in the form of new waves at the same frequencies. In the uniform-density, almost-pure glass used for optical fibers, most of the new waves are transmitted in the same direction as the original wave, but delayed by the time period between excitation and reemission (when waves are retransmitted in different directions or with varying delays, the total transmitted energy in the main wave is reduced, as will be discussed later). The new waves vectorially combine with the original wave to form a composite transmitted wave that is slightly delayed from the original. This new wave then interacts with material further along its path, adding further delay. Since this delay is proportional to the distance the wave is transmitted through the material, the result is a uniformly slower transmission speed. The index of refraction is how we express the resultant velocity relative to that in a vacuum.
The wavelength of the signal is related to the frequency, the velocity of propagation, and the index of refraction by
(12.2)12.2.2 Reflection and Refraction
When light strikes a smooth, nonopaque surface, we know from common experience that some may be reflected and some may be transmitted into the material. We also observe that when light strikes a piece of glass or a still water surface at a very low angle, it is nearly all reflected, and the material resembles a mirror. At greater angles, only a small portion is reflected, and the material appears “transparent.” These effects are due to the difference in index of refraction between glass and air.
Specifically, if we draw a general diagram (Figure 12.1) showing light propagating from a material on the left with diffraction index n1 and hitting a perfectly smooth, flat interface with the material on the right (diffraction index n2) at an angle from normal, we can express the equations governing the reflected and transmitted waves as follows:
(12.3)Thus, if n2 > n1 (as in the figure), the transmitted wave will be closer to normal relative to the interface plane, whereas if n2 < n1, it will be more parallel to the interface. This relationship is known as Snell’s law.
In particular, if sin θ> n2/n1, there is no transmitted wave, and all the energy is reflected (this is strictly true only if the n2 material is thick). This is a crucial condition for some types of fiber transmission, as will be seen. Since the value of the sine function cannot exceed 1, total reflection is possible only when n1 > n2 (the opposite situation from that shown in Figure 12.1). The angle where total reflection occurs (the “critical angle”) = sin−1 (n2/n1).
• The reflected wave will leave the surface at an angle exactly opposite that of the incident wave, that is, an at angle -θ from normal (we will see later that this effect is used to advantage in certain types of optical fiber connectors).
The division of power between the reflected and refracted (transmitted) waves is a function of the refractive indices, the angle of incidence, and the direction of the electric fields of the incident signal. In the special case where the signal is normal to the interface, the ratio of reflected to incident power is
(12.4)and the ratio of transmitted to incident power is relative transmitted power
(12.5)or in decibel terms more useful for transmission analysis:
(12.6)
(12.7)Thus, perfect power transmission and zero reflected power require that n1 = n2.
As an example of less-than-perfect transmission, air has an index of approximately 1 (actually about 1.003) and common glass an index of about 1.5 at visible light frequencies, so about 96% of light striking window glass at a right angle is transmitted and 4% is reflected, a transmission loss of about 0.18 dB. These relationships are important to the design of optical connectors.
12.2.3 Light Absorption
As with coaxial cables, some of the energy in a light signal propagating through materials is converted into heat. Though an exact understanding of the mechanisms is not essential, the effect is that an optical transmission path of uniform characteristics has a loss that, as with coaxial cables, is linear (in decibels) as a function of distance.
Absorption, if it is due to atomic resonance effects, is very wavelength dependent. At the wavelengths used for signal transmission through fibers, resonances effectively prevent the use of some of the optical spectra, whereas the effects of the resonances cause transmission characteristics at other wavelengths to be enhanced.
12.2.4 Scattering Loss and Rayleigh Scattering
Although on-axis (forward) scattering is what happens most of the time, photons may sometimes be emitted in different directions or with varying delays, leading to signal loss in the principal transmitted wave. Many mechanisms lead to this scattering, including impurities in the material, nonuniform densities, and nonlinearities due to extreme power levels. One such scattering phenomenon is known as Rayleigh scattering, after Lord Rayleigh, who is credited with first demonstrating that the sun’s light is scattered by nitrogen and oxygen molecules in the air. Rayleigh scattering is very wavelength dependent, varying approximately as the inverse fourth power of wavelength, which is why the blue (short wavelength) end of the solar spectrum is scattered much more than the red end so that we see a sharp-edged red-yellow sun surrounded by a diffuse blue sky.
The loss of energy in light waves transmitted through standard optical fibers is due primarily to scattering loss and secondarily to absorption and several additional minor effects.
12.2.5 Wavelength Dispersion
Except for wavelengths close to the natural atomic resonance frequencies of the material, n varies with wavelength approximately as
(12.8)where A, B, and C are constants related to a particular material. This wavelength dependence is known as material dispersion. Near atomic resonances, n varies wildly, and a significant amount of absorption also takes place. Such a resonance happens to occur near the wavelengths used for optical signal transmission.
A common example of dispersion in the visible spectrum is the common glass prism (see Figure 12.2). When white light strikes a piece of glass at an angle, signals at the various colors bend toward the normal (right angle to the surface) at different angles, due to the difference in n across the visible light spectrum (whose wavelengths range from about 400 to 650 nm). If the glass is a flat sheet, such as a window, the reverse bending takes place on the far side, and all signal wavelengths end up restored to their original angles, and we don’t notice anything. If the sides are not parallel, however, then when the light impinges upon the second interface, the angular deviation is made even greater as each wavelength bends away from the normal by varying amounts depending on the difference in n as a function of wavelength, and we observe the separated spectrum.
Dispersion is a major concern in optical communication cables, not primarily because of the bending effect, but because of the differing transmission speeds associated with changing n. If the components of a signal are, for some reason, generated over a range of wavelengths and transmitted through a cable whose index of refraction varies, then the components will not arrive simultaneously at the receiver. Depending on the signal format, this can lead to various kinds of distortion. The affect of dispersion is, in fact, just optical group delay (see Chapter 15) and has the same types of effect.
In addition to the foregoing, the interaction of light with very small glass fibers produces some unique interactions that will be discussed in the next section.
12.3 Multimode Optical Fibers
If we construct a long, smooth, narrow (but large compared with the wavelength of the light), circular-cross-section bar of glass and shine light into one end, some of the light will travel along the length of the bar and exit the far end. That will be true even if the bar isn’t perfectly straight. The reason can be seen in Figure 12.3.
Since the refractive index of glass is greater than that of air, light entering the bar at a sufficiently shallow angle will be completely reflected at the glass-to-air interface and will stay in the bar, simply bouncing along from side to side and eventually exiting the far end. Light entering at a greater angle will lose some of its energy at each reflection and will quickly be dissipated. The maximum angle where all of the energy is internally reflected defines the circular cone of acceptance for the bar.
If the bar is curved slowly (again, relative to the wavelength of the light), the light will still be totally reflected and will follow the curvature. If it is curved too tightly, however, some of the light will strike the outer surface at angles above the critical angle, and a percentage of the energy will be diffracted out of the bar.
The performance of this simple transmission line can be improved (though the cone of acceptance will be much smaller) if we coat the outside with a second layer of glass that has a slightly lower index of refraction than the core. So long as this coating is sufficiently thick, we can now handle the rod or place it next to other objects without interfering with its light transmission properties.
If the entering light is imperfectly collimated (that is, it enters at more than one angle), it can readily be appreciated that the light traveling straight down the core will go less distance than light that is near the critical angle and bounces frequently. The difference in transmission path length will depend on the length of the bar and causes another form of dispersion (known as modal dispersion) that is extremely important to signal transmission.
If we modify the index of refraction so that it decreases radially from the center, light that travels at a small angle with respect to the axis will slowly be bent back toward the core as it travels farther from the center. It will, however, have traveled more quickly than light transmitted straight down the core, because it will have spent a percentage of its travel time in a medium with a lesser n and therefore greater velocity. Thus, by varying the index of refraction properly, the variation in transmission time with respect to angle can be reduced.
Now imagine that the “bar” of glass is round, with a core whose index of refraction is 1.49, whose diameter is only 50 × 10−6 or 62.5 × 10−6 meters (50 or 62.5 μm, or “microns“) and whose length is up to thousands of feet, and you have a typical “multimode” optical fiber. The preceding analysis, with a few exceptions, explains how signals are transmitted in such cable. Fibers made with just a single coating are known as step index fibers, whereas those with a graduated index of refraction are known as graded index fibers.
Where the simplified analysis breaks down is that when the core of a fiber is not very large compared with the optical wavelength, only certain transmission paths are supported, whereas under the simplified analysis, light introduced at any angle within the cone of acceptance would be transmitted. The most common wavelengths transmitted through multimode fiber are 850 and 1310 nm. In glass with n = 1.49, these wavelengths shorten to 537 and 879 nm, respectively. Thus the diameter of a 62.5-μm fiber core is 116 or 71 wavelengths: large but not infinite.
Little or no multimode fiber is used for cable television long-distance signal transmission because of the angle-dependent dispersion effect discussed earlier. This form of dispersion is caused by the difference in axial transmission speeds of light traveling along different transmission paths or modes and is known as modal dispersion. How dispersion affects signals is illustrated by Figure 12.4. If a short burst of imperfectly collimated monochomatic (all one frequency) light is introduced into multimode fiber at time T0, the signal will be introduced into the fiber at a range of angles (relative to the fiber axis) and, thus, travel different total distances. If the pulse is examined after it has passed through a length of fiber, we will “see” first a little light from the signal traveling parallel to the core, then from the next fastest modes, and so on, until we finally receive light from the highest angles. Similarly, at the end of the pulse, the light from the fastest modes will disappear first, and then gradually all the light will disappear. The effect is to shorten the top of the pulse and broaden the bottom (T1). If the pulse is sufficiently short, or the fiber sufficiently long, the top will disappear entirely (T2). For still longer fibers, the leading and trailing edges of the pulse will
overlap, and we will see a longer, lower-amplitude pulse (T3). If we transmit a series of pulses (representing, for instance, a digitally encoded signal), then the maximum pulse rate will be determined by when the residual effects from one pulse interfere with the onset of the next pulse. One way of expressing this maximum is the bandwidth of the fiber. If we drive the fiber with light that has been amplitude modulated at varying rates, the bandwidth is the point where the amplitude of the demodulated signal drops by 3 dB relative to its value at low modulation frequencies. Alternatively, the bandwidth is approximately equal to 0.35/tr, where tr is the apparent rise time of the detected pulse when the input pulse has zero rise time.
Multimode fibers are rated according to the amount of this length-dependent bandwidth. Typical fibers with a 62.5-micron core diameter exhibit a bandwidth-length product of 300 MHz-km at 1310 nm and 160 MHz-km at 850 nm. Fibers with a smaller, 50-micron core can reach 400 MHz-km. What this means is that a 50-micron core fiber that is 1 km long will have a bandwidth of 400 MHz, whereas one that is 10 km long will have a bandwidth of only 40 MHz.
Clearly, such fibers are not suitable for transporting 870 MHz of cable television spectrum over the long distances required in modern networks.
12.4 Single Mode Optical Fibers
If the core diameter is reduced sufficiently, fibers will support only light traveling collinearly with the axis (known as the LP01 mode), thereby eliminating modal dispersion. Such fibers, known as single mode, are almost universally used for long-distance, high-bandwidth applications.
12.4.1 Structure
The most common single mode fiber construction consists of an 8.3-micron-diameter core, surrounded by cladding glass with a uniform, lower index of refraction and extending out to about 125 microns. This, in turn, is surrounded by a protective layer (the coating) extending out to 250 microns. This outer layer is generally colored to enable easy fiber identification in bundles. This construction is known as matched-clad, nondispersion-shifted fiber.
The necessary condition for suppression of higher-order modes is
(12.9)where
V = the V parameter, or normalized frequency
a = the core diameter in micrometers
n1 = the core refractive index
n2 = the cladding refractive index
λ = the free-space wavelength in micrometers1
As can be seen, this requires very small core diameters and a very small difference in the refraction coefficients for the core and the cladding.
A variant on the preceding construction is to use two layers of cladding: a lower-n inner cladding followed by an outer layer with an intermediate n. This is known as depressed clad, nondispersion-shifted fiber and is otherwise the same in construction as matched clad fiber. With few exceptions, its performance as a transmission medium is very similar as well. Figures 12.5(a) and (b) show the refraction index profile and layers of construction of both types.
Figure 12.5 Cladding profiles for various fiber types. (a) Nondispersion-shifted matched clad fiber doping profile. (b) Nondispersion-shifted depressed clad fiber doping profile. (c) Dispersion-shifted fiber — one of several possible doping profiles.
With either type, the light travels mostly in the core but also partially in the cladding. The effective index of refraction is about 1.467 for either type at either of the common wavelengths used: 1310 nm or 1550 nm.
12.4.2 Attenuation
The total loss due to absorption and scattering is amazingly low. At 1310 nm, typical guaranteed losses for cables sold to the CATV market are only 0.35 dB/km, whereas at 1550 nm, they drop to 0.25 dB/km. Otherwise stated, at 1550 nm, only half the light energy is lost through a strand of glass 12 km (about 8 miles) long.
The curve of attenuation-versus-free-space wavelength is shown in Figure 12.6 (also from Ron Cotton). The local minima around 1310 and 1550 nm are known as the second and third windows of transmission (the first is at 850 nm). The high absorption peak around 1380 nm, known as the water peak, is due to absorption by hydroxyl ions. The water peak height has decreased as fiber production techniques have improved, and at least one manufacturer now offers fiber entirely free from this effect, as shown in Figure 12.7.2
12.4.3 Chromatic (Wavelength) Dispersion
With the large modal dispersion eliminated, more subtle dispersion mechanisms become the limiting factors. Chromatic dispersion is a measure of the degree to which the effective propagation velocity changes as a function of wavelength. It is the sum of two factors: material dispersion, which is a measure of the change in refraction index of the glass with wavelength, and waveguide dispersion. In optical fibers, the signal travels partially in the core and partially in the cladding, and the total mode field diameter changes with wavelength. Since the refraction index is different in the core than in the cladding, a change in mode field diameter also results in a change in average dispersion index and, therefore, signal velocity. The ratio of wavelength change to velocity change due to this effect is known as waveguide dispersion.
As with modal dispersion, chromatic dispersion is a linear function of transmission system length. The units of chromatic dispersion are picoseconds per nanometer-kilometer; that is, for a 1-nm free-space wavelength change, this gives the number of picoseconds of delay change per kilometer of fiber length.
Standard fiber exhibits zero chromatic dispersion near 1310 nm (because the slopes of waveguide and material dispersion components are equal in magnitude and opposite in direction at that wavelength). In cases where it is important to have low dispersion at 1550 nm, the null point can be shifted upward by altering the fiber doping profile and/or using several layers of cladding. Figure 12.5(c) gives one example of a doping profile for dispersion-shifted fiber.3 Figure 12.8 shows a typical chromatic dispersion curve for both non-dispersion-shifted and dispersion-shifted single mode fibers.
Typical commercial specifications for chromatic dispersion are 2.8-3.2 ps/nm-km from 1285- to 1330-nm wavelength and 17-18 ps/nm-km at 1550 nm for nonshifted fibers.4
Dispersion is very important in communications circuits because the optical sources used do not transmit on a single wavelength. The interaction between various source wavelengths and network performance will be discussed later in this chapter.
12.4.4 Polarization Mode Dispersion
Light transmitted through single mode fiber may be thought of as two separate signals (polarization modes) with their electric fields 90° apart relative to the axis of the fiber. So long as the fiber looks exactly the same to both signals, they will have the same transmission time and will arrive in phase at the detector.
Two conditions, however, can detract from equal transmission velocity: dimensional irregularities and nonequal index of refraction.
• As discussed, waveguide dispersion is a function of the mode field diameter, because the signal travels partially in the core and partially in the cladding. Should the fiber core not be completely round, the ratio of core to cladding utilized for one polarity will be different from that for the other.
• More subtly, the glass may have a dimensional preference in its atomic structure that causes n to be greater in one direction than the other. This preference is typically nonuniform along the fiber and also modified by local stresses and temperature variations.
The situation is made more complicated because energy is exchanged between the polarization modes due to imperfections in the fiber, connectors, splices, and so on.
The net effect of all these mechanisms is called polarization mode dispersion (PMD). PMD is typically wavelength dependent and interacts with optical transmitter wavelength changes to cause system distortion. A typical commercial specification for PMD is ≤0.5 ps/
at 1310 nm in non-dispersion-shifted cable,5 though typical values are 0.1-0.2 ps/
. At these values, PMD does not add materially to total system distortion in most cable networks.
12.4.5 Attenuation in Bent Fibers
As with the waveguides utilized for microwave signal transmission lines, single mode fibers may not be sharply bent without causing signal loss. Two classifications of bends are normally considered. Microbends are microscopic imperfections, often introduced in the manufacturing process, such as irregularities in the core material or in the interface between core and cladding. Losses due to microbending are included in manufacturers’ specifications for cable performance.
Macrobends are bending of the completed fibers. If the radius of a macrobend is sufficiently small, significant amounts of the light will be transmitted out through the cladding and be lost. For that reason, manufacturers specify cable and individual fiber-bending radii that must be respected.
The fact that light is not constrained to remain within the fiber when bent has been exploited by manufacturers of light insertion and detection (LID) fusion splicers. They bend the incoming fiber sufficiently to insert light on one side of the splice location (light can “leak” into, as well as out of, fiber when it is bent) and then bend it on the other side and detect the leaked light. By manipulating the position of the fibers at the joint for maximum transmission before fusing, splice loss can be minimized. One ambitious manufacturer even reached the field trial stage with a fiber-to-the-curb (FTTC) telephone and cable television distribution system that used bent-fiber couplers to extract and insert light at every node.6 Their first version utilized multimode fiber, but later versions utilized single mode fiber.
A typical commercial fiber-bending specification is 0.05-dB maximum loss @ 1310 nm and 0.10 dB @ 1550 nm for 100 turns of fiber wound around a 75-mm- (2.95-inch-) diameter mandrel. The specified loss for a single turn around a 32-mm- (1.26-inch-) diameter mandrel is 0.5 dB @ 1550 nm.7 In general, bending losses are higher at 1550 nm than at 1310 nm.
12.4.6 Stimulated Brillouin Scattering
When the power level of monochomatic light transmitted into a long fiber strand is increased, the output power increases proportionately until a threshold is hit. Beyond that level, the received power stays relatively constant, and energy reflected toward the source increases dramatically. The signal-to-noise and signal-to-distortion ratios of the received signals both degrade. This phenomenon is known as stimulated Brillouin scattering (SBS).
SBS occurs because glass is electrostrictive – that is, an electrical field causes a mechanical stress on the material. When the field associated with the light signal reaches a certain amplitude, only some of the energy from excited electrons is returned as forward-transmitted waves. The remainder is translated into an acoustic wave that propagates through the material. This acoustic wave, in turn, modulates the index of refraction due to the sensitivity of the index of refraction in glass to pressure. The varying index of refraction then causes the main light wave to alternately slow down and speed up, causing the detected signal to have increased distortion. A portion of the reflected light is re-reflected at acoustic wavefronts due to the change in index of refraction, and the random phase relationship between the original and double-reflected signal, as received at the detector, causes increased noise.
SBS is a function of fiber geometry, loss, and length, as well as transmitted power. It is also a wavelength-specific process, in that energy at light frequencies separated by as little as 20–100 MHz behave independently, so when light is transmitted at several wavelengths each experiences about the same Brillouin threshold.
The basic equation for the single-wavelength SBS threshold is
(12.10)where
PSBS = the threshold power of SBS scattering in mW
A = the cross-sectional area of the fiber core (approximately 80 × 10−12 m2 for non-dispersion-shifted fibers and 50 × 10−12 m2 for dispersion-shifted fibers)
γ = the Brillouin gain coefficient (2-2.3 × 10−14 meters/mW, depending on the degree of polarization randomness in the signal)
α = the fiber’s attenuation in dB/km × 2.3 × 10−4 (numerically equal to twice the attenuation in nepers/m)
L = the fiber’s length in meters8
Figure 12.9 shows typical SBS threshold values for standard (Std) fibers at both 1310 and 1550 nm and for dispersion-shifted (DS) fibers at 1550 nm.
Figure 12.9 Brillouin scattering limit for monochromatic light as a function of fiber length, type, and operating wavelength.
Power higher than the monochromatic SBS threshold can be transmitted if divided among optical carriers whose frequencies differ by more than the SBS linewidth. Some vendors use spectrum-spreading techniques to allow transmitted powers as high as +17 dBm (50 mW) at 1550 nm in standard fiber without significant distortion. Clearly SBS extension becomes a balance between widening the spectrum sufficiently to avoid the Brillouin limit while keeping it sufficiently narrow to avoid significant chromatic dispersion. One method commonly used is to phase modulate the source with a sufficiently high amplitude and frequency to adequately spread the spectral power while creating added modulation sidebands that fall above the highest RF signal carried by the system.9
12.4.7 Self-Phase Modulation Interacting with Dispersion
Another power-related effect that occurs in optical fibers is known as self-phase modulation (SPM). This is caused by the fact that the index of refraction, n, is slightly modulated by variations in the instantaneous intensity of the transmitted light. This causes a different propagation velocity (as the instantaneous power varies) and thus an effective envelope distortion, resulting in phase modulation as seen at the detector. The nature of the distortion will be affected by whether the wavelength is centered on the fiber’s dispersion null or on one side of the null.
In general, the effect of SPM will be an increase in the level of composite second-order (CSO) distortion through the link. Although the analysis is not straightforward, the C/CSO will be degraded when
• The chromatic dispersion is higher.
• The RF carrier frequency is higher.
• The wavelength of the light is longer.
• The average light level is higher.
• The optical modulation index (OMI, the intensity variation due to the modulating waveform) per carrier is higher.
Figure 12.10 shows the measured and calculated C/CSO degradation due to SPM as a function of average optical power level under the following conditions:10
• 527Length = 50 km of non-dispersion-shifted fiber with a power coefficient of diffraction. index equal to 2 × 10−20 m2/W, attenuation of 0.0576 nepers/km, and chromatic dispersion at 1553 nm of 17 ps/nm-km.
• Channel loading = 77 RF carriers, with OMI/carrier approximately 2.5% (top curve) and 3.4% (lower curve).
• C/CSO measured on top channel (547.25 MHz).
• The transmitter is an externally modulated DFB laser at 1553 nm (optical transmitter characteristics are discussed later in this chapter).
In Figure 12.10, the solid lines are the calculated results, and the discrete points are measured data. The referenced paper offers no explanation for the deviation between calculated and measured data at higher OMI values.
Figure 12.11 shows the variation as a function of length for a fixed +18-dBm optical power level. For lengths greater than 50 km, the signal was amplified after the first 50 km and transmitted through the additional fiber length. The solid line is the calculated performance, while the × marks are measured data.
As can be seen in these graphs, at higher optical levels, the degradation in C/CSO is significant. In some cases, this may be a compelling argument for the use of dispersion-shifted fiber for long 1550-nm analog links.
In systems containing components other than fiber, SPM also interacts with any response variation to produce additional distortion components. This is covered in more detail in Chapter 13, since wavelength division multiplexers are often the primary contributors to this additional CSO source. Because self-phase modulation effects the transmission properties of a link, it is one of the mechanisms that limits performance when more than one optical signal (on different wavelengths) shares a fiber, a phenomenon known as cross-phase modulation, which is discussed in Chapter 13.
12.5 Network Passives
In coaxialdistributionsystems, passive devices are used for various signal-splitting and -combining functions. Optical equivalents exist for many of the same functions, with the obvious exception of multiplexing of 60-Hz power with signals. Discussed next are the essential passive components used in linear optical links.
12.5.1 Connectors
Methods for joining fibers fall into three general classes: fusion splices, mechanical splices, and connectors. Fusion splicing consists of carefully preparing the end of each of the fibers to be joined and then bringing the ends together carefully and literally melting them. Automated and semiautomated fusion splicers have evolved that consistently produce splices with less than 0.1 dB of loss.
Mechanical splices generally involve similar fiber-end preparation. The difference is that the fibers are brought into proximity and embedded in a gel-like material whose index of refraction closely matches that of glass. A mechanical sleeve holds the fibers in position. Though the loss at such splices is higher than at fusion splices (typically 0.1-0.2 dB), they are quick to manufacture and are favored for rapid field repair tasks in cases where a fusion splice crew can later replace the temporary fix.
A wide variety of connector families have been developed by various vendors. These are used for interfacing between active equipment and fiber lines and for patch panels that allow test points and reconfiguring of systems. Typical connector losses are higher than mechanical splices (about 0.25-0.5 dB) and are variable with remating.
The difficulty in improving connectors lies in their imperfect fiber-to-fiber interface. As discussed at the beginning of this chapter, signals lose approximately 0.18 dB at each fiber-air interface. Unless the fiber ends are in intimate contact, a mated connector pair will have two such interfaces and a loss of 0.36 dB due to the two fiber-air interfaces alone. Worse, the return loss from each interface could be as bad as 14 dB.
A number of different connector families have been used over the years, and more will likely be developed in the future. The SC series is currently popular in North America. This is a small push-on-pull-off connector that is capable of low insertion loss and good return loss if the fiber ends are properly polished. A zirconia ceramic ferrule is used to align the two fibers. It has a central capillary hole into which the fiber is cemented, following which the end is polished. Connectors may be attached in the field or supplied preattached to fiber pigtails that can be fusion spliced in the field.
Ultra-Polished and Angle-Polished Connectors
SC connectors, as well as some other series, either come with flat, highly polished tips or have angle-polished tips. The flat (SC/UPC) version allows for somewhat better insertion loss when cleaned properly but has typically 5-dB worse return loss than the angled (SC/APC) version.
The reason for the lower reflections from the APC version is shown in Figure 12.12. Whatever light is reflected at the fiber end (due to alignment errors between the fibers, air gaps, imperfect polishing, or differences in the index of refraction) is returned at an angle equal to twice the end angle of the fiber, which is 8° to 12°. The reflected light is outside the cone of acceptance of the fiber and so is not transmitted toward the source.
By contrast, the UPC connector requires a higher degree of polishing, which results in lower insertion loss, but with the disadvantage that whatever light is reflected will propagate back toward the source. Because of this difference, the return loss of an imperfectly cleaned UPC connector degrades more quickly than that of an APC connector.
The preoccupation with return loss levels in optical circuits, which are much lower than the 16 dB typical for coaxial components (as discussed in Chapter 10), is because directly modulated laser diode transmitters are very sensitive to reflections, as discussed in Section 12.6. Generally, optical return loss values must be significantly better than 40 dB to avoid problems.
Connector Cleaning Issues
Proper cleaning of optical connectors is mandatory for good performance. Many problems in optical links are caused by dirty connectors. Proper installation and maintenance practices call for careful cleaning and inspection of all connectors before mating or remating, preferably using inspection microscopes made for that purpose. Recent experiments have shown that, even when connectors on new equipment were carefully cleaned and capped for protection, they were unacceptably dirty when uncovered for use after undergoing a simulated shipping environment.11
If dirty connectors are mated, it is possible that the foreign material, if abrasive, can damage the polish of the fiber-end faces, permanently degrading the performance. In that case, the only remedy is to install a new connector.
Two methods of cleaning are currently accepted. In the first, a slightly abrasive tape is wiped across the connector end face. The tape is contained within a cartridge and is advanced after a set number of cleanings. This method has been found effective with SC/UPC connectors; however, its use on SC/APC connectors is questionable since excessive use can damage the angle polish.
The second method uses at least 91% pure isopropyl alcohol applied with a lint-free swab, followed by a dry swab and then blowing it dry using canned air. This method seems to be adequate for any type of connector. Standard “rubbing alcohol” is not acceptable because of impurity levels that may leave a residue.
12.5.2 Signal Splitters
Signal splitters can be made with virtually any splitting ratio. Excess losses (that is, the difference between input light power and the sum of the powers appearing at all output ports) are generally under 1 dB. Often, multiple splitters are packaged to create multiple port splitters with 10 or more legs.
12.5.3 Wavelength Division Multiplexers
WDM couplers are the optical equivalent of RF diplex filters. They are used to route light to the correct port on the basis of the optical wavelength. The simplest versions divide 1310-nm light from that at 1550 nm. More complex WDM couplers can separate multiple wavelengths in the 1550-nm range that differ in wavelength by as little as 0.8 nm. Such systems are known as dense WDM. Wavelength division multiplexers are discussed in greater depth in Chapter 13.
12.6 Linear Optical Transmitters
Transmitters generate optical carriers and intensity modulate those carriers with wideband RF spectra. In addition to linearity and noise requirements that are analogous to those placed on RF amplifiers, optical transmitters must exhibit optical characteristics that are compatible with the interconnecting fiber strands.
12.6.1 General Characteristics
In general, optical transmitters use an electrical signal to modulate the power of a light source. The most common application is simple on-off modulation used to convert high-speed binary signals to light pulses. At the receiving end, detectors need only detect the presence or absence of light to accurately reproduce the original digital stream. Digital modulation is a conceptually simple and robust format, and relatively high noise levels can be tolerated. At the present state of the art, speeds in excess of 10 gigabits per second (Gb/s) are commercially deployed, whereas optical losses of 30 dB can be tolerated between transmitters and receivers.
Figure 12.13 shows theoretical bit error rate as a function of signal-to-noise ratio for a baseband, binary transmission system.12 Quite moderate S/N ratios (compared with those required for modulated analog NTSC signals) yield very good bit error rates. Baseband digital modulation is frequently employed in fiber-deep architecture (fiber-to-the-curb or fiber-to-the-home) due to the lower cost of the transmitters relative to those commonly used in HFC systems. Chapter 19 discusses fiber-deep architecture in detail.
Figure 12.13 Bit error as a function of signal-to-noise ratio for a binary digital transmission system.
By contrast, transmission of an FDM analog signal is much more complex. In the usual cable television application, the composite headend output waveform (with spectral components extending from 50 to 750 MHz or more) is used to control the light intensity in a proportional manner. The modulation must be highly linear or, more correctly, must complement exactly the demodulation characteristic so that the total link is highly linear. Not only that, but the end-to-end C/N of each multiplexed RF signal must be compatible with signal-quality requirements. Typically, the fiber-optic link is required to provide a C/N of 50 dB or greater for each analog video carrier with composite distribution products 60–65 dB down. Since stimulated Brillouin scattering and other nonlinear fiber effects limit the maximum transmitted power to +10 to +17 dBm, and receiver power levels of about 0 dBm are required to sufficiently overcome “shot noise” (see Section 12.8) at the receiver, this limits practical optical budgets for typical 80-channel fiber-optic links. These relationships will be further explored later in this chapter.
In fact, optical transmitters and receivers are not linear devices but “square law” devices; that is, the instantaneous light output power of a transmitter is proportional to the input current and thus to the square root of the input signal power. At the other end of the circuit, the RF output power from the detector is proportional to the square of the optical power received, so the total link is nominally linear (predistortion is often used to overcome residual nonlinearities). As will be seen, however, the square law transfer function has an effect on noise and distortion addition. In particular, because of the square law detector transfer function, a change of 1 dB in optical loss will result in a 2-dB change in detected RF power, leading to the commonly stated, but incorrect, statement that “optical decibels are twice as big as RF decibels.”
From a system standpoint, and regardless of the technology used to generate the signals, transmitters can be characterized by their wavelength, spectral purity, and stability and by their bandwidth, linearity, and noise levels. These interact with the fiber and detector characteristics to determine the total link quality.
12.6.2 Directly Modulated Fabry-Perot Laser Diodes
Although a number of technologies can produce the roughly monochromatic light required for optical transmitters, few meet the dual requirements of sufficient power output along with a linear relationship between input voltage or current and light output power.
One that does is the Fabry-Perot semiconductor laser, named for the French scientists Charles Fabry and Alfred Perot. In a Fabry-Perot (F-P) laser, light is reflected and re-reflected between two “mirrors” at either end of a semiconductor material that has been biased electrically. The material and two mirrors form a resonant cavity that roughly determines the wavelength of the light produced. One of the mirrors is only partly reflective, allowing some portion of the light to “leak” out into an external fiber, whereas most is internally reflected. This is directly analogous to a “high-Q” resonant L-C tuned circuit where the circulating energy is much higher than that coupled into a load.
Physical processing limitations dictate that the spacings between the mirrors form a resonant chamber long enough that oscillation can take place at any of several frequencies (longitudinal modes) for which the cavity length is an integer number of half wavelengths. Though the total output power of F-P diodes is relatively constant (for a given bias current), that power fluctuates randomly among several modes, each with a slightly different wavelength. For typical 1310-nm F-P diodes, the spectral lines are spaced about 1 nm, and the energy is spread among several such lines. When this signal is transmitted through a fiber, light at each of these frequencies transmits at a slightly different speed due to chromatic dispersion. At the detector, the randomly varying transmission times translate into noise.
In addition to this mode partition noise, F-P diodes exhibit a certain amount of instability in their total optical power, known as relative intensity noise (RIN), and typically deviate slightly from an ideal square law transfer curve. For all these reasons, F-P diodes are not generally used for wideband downstream transmission, although their moderate cost makes them attractive for upstream use, where, typically, a single analog video channel or a limited number of digitally modulated signals are carried.
12.6.3 Directly Modulated Distributed Feedback (DFB) Laser Diodes
A modification of the basic F-P laser uses a diffraction grating (which serves as an optical tuned circuit) along the length of the cavity to restrict oscillation to a single mode. Known as a distributed feedback (DFB) laser, this is the most common light source used in downstream optical transmitters. High-grade DFB lasers may have linewidths (the width of the optical spectrum in the absence of modulation) as narrow as 1 MHz. As will be seen, source linewidth is an important factor for certain noise-generating mechanisms.
The key characteristics of F-P and DFB lasers are covered next. Although this discussion applies generally to either type, the typical values given will be applicable to DFB units optimized for direct modulation, unless otherwise specified.
Linearity as a Directly Modulated Source!
The typical transfer curve showing the relationship between driving current and light output power for a DFB is shown in Figure 12.14. In modern diodes that are designed for analog modulation, a C/CSO of 60 dB or better and a C/CTB of 65 dB or better are common for a signal loading of 80 unmodulated carriers and for signals that stay within the linear portion of the curve. The sharp discontinuity at low currents, however, causes abrupt clipping of applied waveforms that are too large. This is discussed later in this chapter.
Relative Intensity Noise (RIN)
The light from laser diodes has some random amplitude fluctuation. This is generally expressed in terms of the noise power in a 1-Hz bandwidth compared with the average optical power level. Typical values for quality DFBs are approximately −160 dB/Hz, provided there is no reflected light. Any light reflected from the load, however, will degrade this quickly. For that reason, high-performance DFB sources are connected to fibers through optical isolators that serve to prevent reflected light from reaching the source.
In order to assess the effect of source RIN on link C/N, we need to compare it to the modulation of the light source by each carrier. The optical modulation index (OMI) is defined as the peak optical power variation from the unmodulated level divided by the the difference between the unmodulated level and the threshold level (A/B in Figure 12.14). Since the device is highly linear, OMI can also be defined as the peak deviation from the bias current level relative to the difference between bias and threshold current levels.
We can speak of the total modulation of the transmitter by the sum of all the RF carriers or of the modulation by some individual carrier. Though it is important that the total modulation not exceed 100%, to keep the signal from being clipped, we are also frequently interested in the performance of individual channels. The peak modulation of the optical carrier by an individual carrier is abbreviated mi, which will be an important factor in calculating the per-channel noise performance of an optical link.
The RIN contribution to total link C/N as a function of source RIN, mi, and channel bandwidth is expressed by the formula
(12.11)where
C/NRIN = the contribution of the source noise to the C/N of a signal, expressed in dB
RIN = the source noise level (relative to the unmodulated light power), expressed in dB/Hz
BW = the receiver noise bandwidth, in Hz, for the communications channel being evaluated
As an example, if a source has an RIN of −160 dB/Hz and is modulated 3% (typical for a 77-channel system) by an NTSC video channel whose noise is measured in a 4-MHz bandwidth, the C/N will be approximately 60.5 dB. This puts a length-independent ceiling on the performance of a fiber-optic link (which will be further degraded by detector and postamplifier noise, as discussed later.)
Incidental Wavelength Modulation (Chirp)
When the current through a directly modulated laser diode changes as a result of modulation, there is also a small effect on the instantaneous wavelength of the produced light. This incidental FM is known as chirp. In typical laser diodes, the rate of frequency shift can vary over a range from approximately 50 to 500 MHz/mA with a total shift of ±1.5 to ±15 GHz, with DFBs exhibiting lower shifts than F-Ps and 1550-nm lasers exhibiting higher shifts than 1310-nm lasers.13
Chirp has several important effects on link performance. First, it spreads the energy over a range of wavelengths, which increases the effective Brillouin scattering threshold and thus allows higher optical power levels to be transmitted. On the other hand, it interacts with chromatic dispersion to cause a decrease in C/CSO. Finally, it interacts with reflected light to degrade effective source RIN.
Because the energy of a directly modulated DFB source is spread over a wider spectrum, it is possible to transmit higher power levels without reaching the Brillouin scattering threshold. Experience has shown that launch powers in excess of 25 mW into standard 1310-nm fiber are possible without a discernable increase in noise or distortion.
CSO Caused by Chirp Interacting with Dispersion
Over the relatively small wavelength shifts associated with chirp, the fiber’s index of refraction will shift in an approximately linear manner. Thus, as the instantaneous modulating signal swings in one direction, the light will shift to a wavelength that travels slightly faster, whereas at the other polarity the generated light will travel slightly slower. Because the variance is approximately linear with modulation, the resultant distortion in the detected signal will affect one peak of the RF waveform exactly opposite of its effect on the other peak. As was discussed in Chapter 10, distortion with this characteristic causes only even-order products, of which the dominant is C/CSO. The relationship between chirp, RF frequency, fiber dispersion, and link length is given by the following formula:
(12.12)where
C/CSOCHIRP-D = the ratio of the level of the visual carrier in question to the level of the CSO products falling in that channel
D = the fiber chromatic dispersion, in ps/nm-km, at the optical frequency used
L = the length of the fiber in km
Δλ = the laser chirp per channel, in nm, as a result of modulation
fRF = the frequency of the CSO product being analyzed, in MHz
N2 = the number of second-order products in the composite beat that falls in the channel being analyzed (see Equation (10.25))14
The CSO affects channels differently because (1) a given amount of time shift represents more degrees of phase shift at higher frequencies, and (2) the number of second-order products falling into channels varies.
If the laser chirp per channel is known in terms of optical frequency rather than wavelength, it can be converted to wavelength chirp using
(12.13)For example, typical 1310-nm DFBs exhibit about 100 MHz/mA incidental frequency modulation. If such a laser were modulated at 2 mA/channel and the signal transmitted through 20 km of standard fiber with a chromatic dispersion of 3 ps/nm-km, the chirp-related C/CSO at 550 MHz (31 upper-side second-order products) would be 60.6 dB.
Directly modulated 1550-nm DFBs tend to have higher chirp values – typically 250 MHz/mA. If such a source were modulated at the same 2 mA/channel and the light transmitted through the nonshifted 20-km fiber described earlier, the C/CSO would decrease to 35.8 dB due primarily due to the 18-ps/nm-km chromatic dispersion at that frequency. Thus, directly modulated DFB transmitters are only suitable for multichannel FDM video transmission when operated near the zero-dispersion wavelengths of fibers or when modulated by an RF spectrum of less than an octave so that the second-order products fall out of band.
Effects of Reflected Light
When light is reflected back into a DFB (or F-P) laser from a connector, passive component, receiver, or the fiber itself due to Raleigh backscattering, it can have a significant effect on RIN. Because the wavelength of the laser changes with modulation, it is almost certain that its wavelength will be different from that of the reflected signal due to the round-trip transmission time from transmitter to point of reflection.
If the laser wavelength is close to that of the reflected signal, it will try to lock its present oscillation to the frequency of the returned light. However, this is not the frequency the laser “should” be on, based on the modulating signal. The result is similar to that of an electronic oscillator that is receiving energy at a frequency close to, but not exactly on, its own frequency. The oscillator “pulls” toward the incoming frequency, resulting in a noisy output. The same thing happens with a laser and results in spurious emissions and an overall degradation in effective RIN. Some protection is afforded where optical isolators (components that exhibit low forward loss but typically greater than 30 dB of isolation in the reverse direction) are installed in laser diode output fibers, but attention to reflections from the driven optical circuits is also required. The jumps in frequency also add a degree of uncertainty to the calculation of interferometric intensity noise (see Section 12.9.1).
Temperature Effects
The current-versus-light transfer function for diodes shown in Figure 12.13 is stable at any one temperature. As the temperature changes, the curve shifts horizontally and may also change slope. Since this could result in a shift of the operating point from the optimum value, lasers used for wideband, downstream transmission are almost always connected to thermoelectric coolers (TECs) that act to maintain a constant chip temperature.
While the use of TECs would be desirable in all linear modulation applications, the cost and power consumption have resulted in the use of noncooled transmitters in many lower-performance upstream transmitters.
12.6.4 Externally Modulated Continuous Wave Sources
Externally modulated transmitters consist of a continuous wave light source whose intensity is varied through the use of an external device that is driven by the FDM waveform. This configuration offers several advantages, including:
• Freedom from the incidental wavelength modulation (chirp) associated with direct modulation of laser diodes (though modulators have some residual shift of their own)
• Improved isolation of the source from reflections in the transmission system, thereby decreasing effective source RIN
• The ability to use a variety of optical sources without regard to their ability to vary light output in proportion to an electrical modulating signal
The most common external modulator is a Mach-Zehnder (M-Z) device constructed on a lithium niobate (LiNbO3) substrate. In an M-Z modulator, the incoming light is divided proportionately between two outputs in response to an electrical stimulus. The transfer function to each output is very nearly sinusoidal, as illustrated in Figure 12.15. When used as a linear transmitter for cable television distribution, the predictable symmetric curvature of the transfer function (which causes large odd-order distortion products) is compensated for by predistortion in the driver circuit.
The transfer function of M-Z modulators provides one important additional advantage over directly modulated sources: The distortion is symmetrical about the inflection point of the transfer function, offering significantly improved second-order distortion products (see Chapter 10, dealing with distortion in coaxial systems).
Externally modulated transmitters can be constructed at either 1310 or 1550 nm. At 1310 nm, the usual source is a relatively high-powered (80-mW typical) YAG oscillator. This device, whose wavelength is actually 1319 nm, exhibits a low RIN and optical linewidth.
At 1550 nm, it is more common to use a DFB diode for the light source and then to amplify to the desired power level using optical amplifiers. Because an unmodulated DFB has a spectral width of less than 100 MHz, this makes Brillouin scattering a concern.
Regardless of the light source, when an FDM spectrum extending up to between 500 MHz and 1.0 GHz is used to amplitude modulate the light, the optical spectrum will have sidebands extending to the maximum modulating frequency on each side of the unmodulated optical center frequency. It might be expected that this would effectively raise the Brillouin limit. An analysis, however, has shown that 99% of the energy is still concentrated at the unmodulated wavelength, and actual measurements have demonstrated a negligible increase in scattering limit.15
High launch powers are possible, however, if the total optical power is spread more evenly over a range of wavelengths. Two methods are commonly used: phase modulation in the same external modulator used for AM modulation and, in the case of DFB sources, intentional chirp generated by modulating the DFB’s operating point with a constant frequency. In either case, the wavelength spreading must be sufficient that the beats between the optical frequencies fall above the highest modulating frequency. Manufacturers who employ SBS extension techniques commonly claim the ability to launch +16 to +17 dBm into long single mode non-dispersion-shifted fibers with acceptably low levels of CSO degradation at either 1310 or 1550 nm.
12.7 Optical Amplifiers
Optical amplifiers boost the level of amplitude modulated light without requiring the optical-to-electrical conversion, RF amplification, and remodulating otherwise required in a repeating location in a network. Understanding the process requires a knowledge of atomic physics that is beyond the scope of this book, but a broad explanation of the principles follows.
The most common form of amplifier is the 1550-nm erbium-doped fiber amplifier (EDFA). In an EDFA, the incoming signals are combined, in a WDM coupler, with a high-power unmodulated signal at 980 nm* from one or more “pump” sources. The two signals are then sent through a special length of fiber that is “doped” with erbium (that is, a carefully controlled amount of erbium is added). The pump signal causes electrons in the erbium atoms to jump to a higher energy band. When they return to their normal state, the difference in energy boosts the signals at 1550 nm. Figure 12.16 shows one of several possible basic schematics of a dual-pump EDFA.
The magic of EDFAs is that they have completely different characteristics than coaxial amplifiers with respect to noise and distortion. Even though they operate in a saturated mode (where a normal coaxial amplifier would produce pulses with a high harmonic and IM content), EDFAs add no measurable distortion to the modulated signal. Not only that, but they can be overdriven, if desired, so that their input noise level is small compared with the signal to be amplified. The C/N contribution from an EDFA is given by
(12.14)where
C/NEDFA = the carrier-to-noise per channel (measured in a 4-MHz bandwidth) in dB
Pi = the optical input power to the EDFA in dBm
The noise Figure of a standard EDFA depends somewhat on input power. Figure 12.17 shows typical variations in NF based on several manufacturers’ specifications.
Commercial amplifiers are available with saturated power output levels in excess of 100 mW. The highest-powered units utilize two or more pump sources, injecting light into ends of the doped fiber (actually, four pumps are possible, two at each end, if they are cross polarized), while multiple-stage devices are also common. Increasing pump power increases the available output power since more energy is stored in excited electrons that can be tapped to produce optical emissions. A modified technology uses erbium and ytterbium doping and an 800-nm pump wavelength and achieves even higher powers, potentially in the hundreds of milliwatts.16
Unfortunately, the efficiency and performance of an optical amplifier are accidents of the properties of specific atomic elements. Although 1550-nm amplifiers are a mature technology, it has proved much more difficult to produce commercially practical units at 1310 nm. Recently reported results, though, include a +20-dBm unit with a 22-dB small signal gain and 6-dB noise Figure. This unit uses praseodymium doping.17
12.8 Optical Receivers
Unlike transmitters, optical detectors are relatively standardized. The incoming light impinges on the active area of a photodiode that has a very precise square law transfer curve (that is, the output current is proportional to input optical power). Typical responsivity (the slope of the received optical power versus output current transfer function) is 0.8-1.0 mA/mW.
The noise performance of an optical receiver is limited by the noise current of the diode (shot noise due to the statistical variation in arriving photon distribution) and by the noise of the following coaxial amplifier. Since the inherent impedance of the detector diode is not 75 ohms, either an impedance-matching transformer or an active circuit is required to match it to the gain stages. Sometimes a transimpedance amplifier is used. Though these amplifiers have an excellent noise figure, they have limited dynamic range, with the result that the light level reaching a receiver must typically be controlled within a few decibels of 0 dBm for the best balance between noise and distortion for AM modulated links. It is common for manufacturers of analog broadband fiber-optic terminal equipment to specify link performance at or near 0-dBm received power. The formula for the C/N contribution due to shot noise is
(12.15)where
C/NSHOT = the C/N of an individual carrier due to shot noise in the detector, expressed in dB
Pr = the received optical power level in dBm
mi = the peak modulation of the light source by the carrier
R = the responsivity of the receiving diode in amperes per watt (or mA/mW)
BW = the noise susceptibility bandwidth of the channel in Hz
For example, if the OMI per carrier is 3%, the diode response is 0.9 A/W, the received optical power is 0 dBm, and the video bandwidth is 4 MHz, then the noise contribution due to shot noise will be approximately 55 dB.
Added to that must be the contribution from the postdetector amplification system. If a transimpedance amplifier is used, its C/N contribution can be calculated using
(12.16)where
C/NPOSTAMPLIFIER = the C/N of a signal due to thermal noise generated within the postamplifier, expressed in dB
Note that the C/N varies 2:1 with received optical power (the factor 2Pr) because of the square law nature of the detector, as opposed to C/NSHOT, which varies 1:1 with optical power because it occurs in the optical domain (before detection).
If, in the previous example, the detector diode is attached to a postamplifier having a 3-dB noise figure and 1200-ohm transimpedance, the noise contribution due to postamplifier noise will be 65.3 dB. Transimpedance amplifiers, however, have very limited dynamic range. In commercial optical receivers optimized for cable television applications, a variety of means are used to couple photodiodes to postamplifiers, including both direct and impedance-matching transformers. A more general way to calculate postamplifier noise uses the total postamplifier equivalent thermal noise (which includes both the irreducible noise due to the impedance and the excess noise generated within the amplifier).
If Equation (12.16) is reconfigured to use equivalent amplifier thermal noise input current, the postamplifier C/N contribution can be calculated using18
(12.17)where
C/NPOSTAMPLIFIER = the C/N of a signal due to thermal noise generated within the postamplifier, expressed in dB
Pr = the received optical power level in dBm
mi = the peak modulation of the light source by the signal being evaluated
R = the responsivity of the photodiode in amperes/watt (or mA/mW)
Ir = the postamplifier equivalent input noise current density in pA/
180 = a factor that results from converting the input power to milliwatts from watts and the amplifier noise to picoamperes from amperes
For example, if we use the same parameters as in the last example but assume instead that the amplifier input noise current density is 7 pA/
(typical values will be 6–8), we can calculate that the postamplifier C/N for an analog video channel will be 62.7 dB.
12.9 Interactions Among Transmitters, Fibers, and Receivers
In addition to the noise and distortion that take place within transmitters and receivers, additional signal degradation takes place because of the interaction of fiber characteristics with the characteristics of the optical transmitter and receiver. These additional effects can have a significant effect on link performance, which is why it is important that fiber-optic equipment be specified and tested through actual fiber links, not just attenuators.
12.9.1 Double Rayleigh Backscattering: Interferometric Intensity Noise
Some portion of light that is scattered backward through the fiber due to Rayleigh scattering will be rescattered in the forward direction and will combine with the normally transmitted light. Since the sum of the double-scattered light from various lengths will not be coherent with the normal light, the effect when both reach the optical detector is that they mix to produce products at the differences in optical frequencies (and multiples thereof) and will show up as an effective increase in link noise. This interferometric intensity noise (IIN) is spread across a spectrum that is about twice the total effective linewidth of the transmitter (including the effect of chirp, if present). The effective link IIN is given by
(12.18)where
IIN = the level of double-scattering-caused noise relative to the unmodulated light level, in dB/Hz
L = the length of the fiber in km
α0 = the loss of the fiber in dB/km
ΔfRMS = the total rms effective linewidth (in the case of directly modulated transmitters, this is the total wavelength spread, chirp, of the source as a result of modulation; in the case of externally modulated transmitters, this is the linewidth of the unmodulated source if not dithered or phase modulated)19
For affected frequencies, IIN can be related to in-channel C/N in the same way as transmitter RIN:
(12.19)where
C/NIIN = the contribution of the IIN effects to the C/N of a signal, expressed in dB
IIN = the interferometric noise level (relative to the unmodulated light power), as calculated in Equation 12.18 and expressed in dB/Hz
BW = the receiver noise bandwidth, in Hz, for the communications channel being evaluated
Figure 12.18 shows an example of the effect of IIN on video C/N as a function of fiber length for several optical linewidths at 1310 nm. The assumed OMI per carrier was 3%.
For externally modulated sources, absent SBS suppression techniques that cause considerable line spreading, the linewidth is so narrow that IIN noise density is very high and is concentrated at very low frequencies. In order to avoid severe IIN degradation to television channel 2, which starts at 54 MHz, the linewidth must be either less than a few megahertz or artificially spread to levels at least comparable with those found with directly modulated lasers. Since a wider spectral line may be required as part of SBS suppression techniques, the latter approach is generally taken.
Finally, IIN may affect long upstream DFB links in a different way. The unmodulated linewidth of a typical DFB is approximately 10 MHz. Since an upstream link may not be used continuously, when it is idle there may be a significant level of IIN extending up to about 20 MHz much of the time. A possible answer is to apply a “dithering” modulation to the laser continuously to ensure a wider chirped linewidth.20
12.9.2 Phase Noise Contribution to Link Performance
Even though DFB diodes oscillate in only a single longitudinal mode, they still exhibit some residual frequency instability. As in F-P diodes, this variance interacts with dispersion to create link noise.
The relationship between source phase noise and link C/N is given by the formula21
(12.20)where
C/NPM-AM = the contribution to channel C/N (in dB) due to the phase noise in the optical source being converted to amplitude noise in the detector
Δv = the source linewidth in MHz
BWRF = the noise susceptibility bandwidth of the channel in Hz
D = the fiber dispersion constant in ps/nm-km
λ = the operating free-space optical wavelength in nm
The 398.55 factor is the result of converting all other values to common engineering units.
As can be seen, the noise affects the RF channels unequally, increasing as the square of the RF channel frequency. It also increases as the square of the fiber length.
Phase-related amplitude noise is generally not of concern in 1310-nm links using nonshifted fiber but may be significant in cases of long fiber links using non-dispersion-shifted fiber at 1550 nm. As an example, assume a 750-MHz analog video channel used to externally modulate (OMI/ch = 3%) an amplified 1550-nm DFB whose optical linewidth is 1 MHz. The signal is then transmitted through a 60-km fiber whose chromatic dispersion is 17 ps/nm-km. The detected signal will exhibit a C/N due to PM-AM conversion of 53.8 dB.
12.10 End-to-End Fiber-Optic Link Performance
The characteristics of the transmitter, interconnecting fiber, receiver, and, optionally, any amplifiers work together to determine the link performance. In particular, the interaction between the signals and the transmission media is much more complex in optical than in coaxial links.
12.10.1 Noise Performance
The total link C/N will have contributions due to transmitter RIN, detector shot noise, and postamplifier noise Figure as well as due to the IIN interaction among laser linewidth, double scattering, and detector mixing. These noise effects are noncorrelated and so will add on a power basis:
(12.21)where
C/NLINK = the net per-channel C/N
C/NRIN = the per-channel transmitter relative intensity noise (Equation (12.11))
C/NIIN = the per-channel interferometric intensity noise (Equation (12.19))
C/NSHOT = the per-channel shot noise at the detector input (Equation (12.15))
C/NPOSTAMPLIFIER = the per-channel postamplifier noise contribution (Equation (12.16) or (12.17))
If the end-to-end C/N of a simple DFB link is plotted as a function of optical loss, the curve will typically have three asymptotes, as shown in Figure 12.19 (the effects of IIN are not readily plotted on the same chart because they vary not with received optical power but with line length).
For high received power levels, the transmitter RIN will dominate, and the C/N will be independent of path loss; at lower received levels, the shot noise will begin to dominate, and the link C/N will change 1 dB for every decibel of reduction in received power level. At some point, the postamplifier noise will begin to dominate, and the link will begin to degrade 2 dB for every decibel of loss, due to the square law receiver response. The range of receiver power over which each of these effects dominates depends, of course, on the quality of the individual components. For typical links, the slope of C/N versus level near 0-dBm received power is about 1:1.
In addition to the factors shown in Equation (12.21), other elements and interactions may affect the end-to-end C/N. For instance, if an EDFA is used, its C/N must be included within the parentheses as an additional factor. In long 1550-nm links, residual phase noise may be a factor.
12.10.2 Small-Signal Distortions
Directly modulated DFB transmitters behave similarly to single-ended RF amplifiers, generating both second- and third-order distortion whose amplitudes, as a function of RF drive level, increase roughly 1 dB/dB (in the case of second-order products) and 2 dB/dB (in the case of third-order products). As with their coaxial counterparts, CSO products tend to be the limiting distortion. As discussed earlier, typical specifications for such transmitters are 60–62 dB for C/CSO and 65 dB for C/CTB under normal operating conditions with a loading of 77 unmodulated carriers. These distortions arise from the combination of small transfer function nonlinearities and large signal clipping.
Externally modulated transmitters exhibit symmetrical distortion and are thus similar to conventional push-pull coaxial amplifiers in that regard. That, combined with the predictability of the nonlinearities, allows C/CSO and C/CTB values of 65 or better with channel loadings of 77 unmodulated carriers.
Distortion occurring in the optical receiver must be added to that generated in the transmitter. Like the transmitter, the detector-postamplifier combination behaves like a single-ended amplifier, with dominant second-order distortion. Often manufacturers specify link performance with a given received power, rather than individually specifying transmitter and receiver.
When the link loss includes fiber, the CSO degradations due to both chirp-induced dispersion and SPM must be included in the calculation of end-to-end performance. Since the CSO distortion mechanisms are synchronized primarily with the modulating waveform (with the exception of the small-signal DFB nonlinearities), the various CSO contributions could be expected to add on a voltage (20 log) basis rather than on a power basis. Though this is true, the chirp and SPM effects may, in fact, be of opposite polarity and tend to cancel each other, rather than add. Nevertheless, an assumption of voltage addition is the most conservative approach to link design.
One technique for reducing the effects of chirp, SPM, and receiver-generated CSO is to transmit both outputs of a Mach-Zehnder type modulator through parallel networks to the receiver. If the two signals are separately detected and then combined out of phase at RF, these second-order effects will tend to cancel, just as they do in push-pull RF amplifiers. C/CSO values of greater than 70 dB have been reported using this technique, known commercially as a Harmonic Link Extender®. As an added benefit, when the signals are combined, the noise will be largely uncorrelated (except for the contribution from transmitter RIN) and so will add on a power basis, whereas the signals will add on a voltage basis, resulting in a net 3-dB increase in C/N in the link. Link performance of 55-dB C/N over 50-km links at 1550 nm has been reported.22
12.10.3 Clipping Distortion
The ratio of peak-to-average absolute voltage in a simple unmodulated carrier is about 1.6:1. When two equal-amplitude nonrelated carriers are summed, however, the relationship is not as simple. Figure 12.20 shows three possible waveforms resulting from the simple addition of two sine waves when one is exactly twice the frequency of the other. Depending on their relative phases, the peak voltages can vary by nearly a factor of 2.
The case when many signals are summed is much more complex. When many summed signals are randomly distributed in both frequency and phase, the peak-to-average level seldom exceeds 14 dB, as discussed in Chapter 15 (though with occasional higher peaks). The downstream spectrum of cable systems is not random, however. The most extreme case occurs when a large number of carriers are harmonics of a common root frequency (as in the ANSI/EIA-542 HRC channelization plan) and all the carrier phases are aligned. In that case, the time domain waveform can resemble a string of impulses spaced by a time interval equal to the period of the common root frequency. This is not a surprising result since the Fourier transform of an infinite string of zero-width pulses is an infinite string of carriers.23
In the more commonly used EIA-542 Standard frequency plan, most of the visual carriers are offset by approximately 1.25 MHz from harmonics of 6 MHz and are neither frequency nor phase related. Despite this, the composite waveform has characteristics that are close to harmonically related carriers if the carrier phases do happen to align at some time. Figure 12.21 shows the resultant instantaneous voltage of the standard channels between 54 and 550 MHz, with each assigned a frequency at random within its tolerance range but with the signal phases aligned at t = 30 ns on the horizontal scale. The peak-to-average voltage is approximately 34:1. If we look at the same waveform later in time, however, the phases slowly move out of coincidence, and the peak voltage decreases. Figure 12.22 shows the condition at t = 15 μs. By 20–30 μs, the pulses are no longer distinguishable. Figure 12.23 shows a typical situation with truly random phase relationships.
Figure 12.21 Instantaneous voltage from addition of 77 FDM carriers with standard frequency assignments and tolerances with phases aligned at t = 30 ns.
Observations of actual headends carrying NTSC modulated carriers have confirmed that peak-to-average ratios generally vary from about 3.5:1 to greater than 7:1. When some subset of carriers happen to phase align, the result is voltage peaks spaced approximately 167 ns apart (the inverse of the 6-MHz channel spacing), which build up to a peak over a few tens of microseconds and then decrease again as the carriers move out of phase coincidence.
The importance of this occasionally occurring peak voltage condition is that, depending on the OMI, the optical transmitter may be driven into hard limiting (clipping) when a sufficient number of carriers are in phase alignment. This is particularly true in the case of directly modulated laser diodes, where a sharp knee occurs in the transfer function below which the light output is extinguished. When that occurs, intermodulation products are generated. As Figure 12.24 shows, both even- and odd-order distortion products are generated when one polarity of a sine wave is clipped off (though second-order products are always the largest). Thus, both CTB and CSO will show an increase when clipping happens with sufficient frequency to be statistically significant. Since clipping produces a string of pulses with the characteristic 167-ns spacing, the largest components produced will fall at harmonics of 6 MHz (which is at the position of the lower CSO beat when the EIA Standard or IRC channel allocation scheme is used and at the video carrier frequency when the EIA HRC channel scheme is used). With highly linear diodes, clipping may, in fact, be the principal contributor to IM products.
In the case of Mach-Zehnder external modulators, the nonlinearities are symmetrical, and the limiting is “softer,” resulting in less clipping and primarily odd-order resultant distortion.24
The visible effect on analog video channels is that, as OMI is increased, “dashes” resembling electrical interference begin to appear on the displayed picture. These visible effects are due to the integrated effect of a group of pulses (whose spacing is closer than the television can resolve).
In the case of high-order digitally modulated carriers sharing a linear link with a comb of analog television carriers, the result of clipping is an increase in bit error rate (BER). Data taken by one of the authors found that the BER through a fiber link loaded with 80 normally modulated video channels and one 64-QAM data channel (whose signal level was 10 dB below the video channels) was approximately 1.3 × 10−10. As the OMI was increased, the BER did not change until a critical threshold was reached, whereupon the BER increased to 7.6 × 10−8, a 600:1 degradation, with an OMI increase of less than 1 dB. This confirms findings of other researchers in this field. The observations of researchers using normal NTSC video signals were that the BER increased to unacceptably high values before any degradation was visible in displayed analog pictures.25
The crucial question is how often clipping occurs. This has been explored by a number of authors. David Grubb has suggested that if OMI per channel is held to 0.348/
(where N is the number of channels), the voltage will exceed the clipping threshold about 2.5 × 10−5 of the time.26 That analysis, however, is based on unmodulated, randomly phased carriers. He noted, however, that optimal phasing of harmonically related carriers can reduce the theoretical peak voltage. The ratio of theoretical maximum voltage with phases aligned to the maximum achievable by optimum phasing is 
/1.5. If the signals feeding an optical transmitter were so related, the modulation index could be increased to 0.67/
or about 5.7 dB higher. This would translate directly to an achievable C/N increase in the link (whose exact amount is related to the relative contribution of transmitter, shot, and postamplifier noise, as discussed earlier in this chapter).
Another factor is video modulation. Since NTSC signals are at maximum carrier level only a small percentage of the time (during synchronizing peaks), the sum of the instantaneous voltages of a number of randomly timed video channels is almost always lower than unmodulated carriers. As with carrier phasing, however, the key word is almost since it is possible that the synchronizing pulses will occasionally drift into alignment. Stuart Wagner has measured clipping noise and its effect on the BER of a digital signal carried along with 40 randomly timed analog video channels in a fiber link. What he found was that the peak OMI per analog carrier could be increased by approximately half the average difference in power level (in decibels) between the unmodulated and modulated carriers with no increase in noise or BER.27 As discussed in Chapter 10, the usual assumption is that average power levels are about 6 dB below peak levels. In particular, the black level of a video signal is about 2.5 dB below sync, so with random video timing it should be possible, on average, to raise peak OMI per channel by about 3 dB compared with the unmodulated carrier case.
On the other hand, with optimum video timing it should be possible to keep the total carrier power close to the average power by minimizing instances where carriers are simultaneously at peak levels. In that case, it should be possible to increase OMI by the difference between peak and average power, 6 dB, without increasing clipping distortion.28 That increase will lead to a similar increase in link C/N.
12.11 Summary
Linear fiber-optic links are capable of transporting the full spectrum of cable television services over distances exceeding 20 miles without amplification. Amplification, readily available at 1550-nm wavelength, can extend the attainable distance severalfold, with only a minor impact on end-to-end performance.
The basic C/N performance of optical links is limited by transmitter intensity noise, optical shot noise, the interaction between transmitter linewidth and doubly scattered light in the fiber, and receiver postamplifier noise. The interaction between transmitter residual phase noise and the fiber can further reduce the noise under some conditions.
Distortion is fundamentally limited by both small-signal nonlinearities in the transmitter and clipping caused by large-signal peaks. Additionally, interaction between incidental transmitter FM and fiber dispersion can cause second-order distortion, as can interaction between peak power levels and the glass material itself.
Increasing the optical modulation index per carrier in an optical link will improve C/N at the expense of distortion, just as increasing operating levels in a coaxial network will have the same effect. Similarly, decreasing the number of carriers will allow higher C/N and lower distortion per channel, as in a coaxial network.
Chapter 13 will discuss multiwavelength transmission through shared fibers. Chapter 15 will discuss the total end-to-end performance of cascaded fiber-optic and coaxial broadband distribution networks, Chapter 18 will discuss various HFC architectures, Chapter 19 will discuss fiber-deep achitecture, and Chapter 20 will discuss the reliability of various HFC architectures.
* 980 nm is the most commonly used pump wavelength. Older devices used 1480-nm pumps, and other wavelengths, such as 850 nm, are possible.
1. Ronald C. Cotten, Lightwave Transmission Applications. CableLabs, Louisville, CO, September, 1993, pp. 80–84.
2. Data provided by CommScope, Inc., Hickory, NC.
3. AT&T Generic Specification: Fiber-Optic Outside Plant Cable, Issue 11, December, 1995. AT&T Network Cable Systems, Norcross, GA.
4. CommScope Fiber Optic Cable Catalog, September, 1995. CommScope, Inc., Hickory, NC.
5. AT&T, op. cit.
6. Claude Romans and David Large, Optical Bus Architecture for Co-Deployment of Telephone and CATV Services in the FRG, Conference Record, Globecom ‘89. IEEE Communications Society, November 1989, pp. 37.5.1-37.5.9.
7. AT&T, op. cit.
8. David Grubb III and Yudhi Trisno, AM Fiber Optic Trunks — A Noise and Distortion Analysis, 1989 NCTA Technical Papers, NCTA, Washington, DC, May 1989.
9. F. W. Willems, W. Muys, and J. S. Leong, Simultaneous Suppression of Stimulated Brillouin Scattering and Interferometric Noise in Externally Modulated Lightwave AM-SCM Systems, IEEE Photonics Technology Letters. Vol. 6, No. 12, December 1994. See also S. W. Merritt, G. J. McBrien, and E. R. Yates, Integrated Optic Modulators for 1-GHz HFC Systems, CED, February 1996.
10. Dogan A. Atlas, Fiber-Induced Distortion and Phase Noise to Intensity Noise Conversion in Externally Modulated CATV Systems, 1996 NCTA Technical Papers, NCTA, Washington, DC.
11. AT&T Corporation, LGX Broadband Fiber Management System Application Guide, AT&T Network Systems, Norcross, GA, 1995.
12. Dan Harris, Primer on Baseband Digital Transmission on Single-Mode. Communications Technology, August 1996, pp. 92–98.
13. Ronald C. Cotten, op. cit., p. 148.
14. Henry A. Blauvelt et al., Optimum Laser Chirp Range for AM Video Transmission, 1992 NCTA Technical Papers. NCTA, Washington, DC, pp. 79–85.
15. X. P. Mao et al., Brillouin Scattering in Lightwave AM-VSB CATV Transmission Systems. Paper presented at OFC ‘92 Conference, San Jose, CA, February 1992. Digested paper in Technical Digest—Optical Fiber Communication Conference. Published by Optical Society of America, Washington, DC, 1992.
16. Roger Brown, Wave of New Products Set to Break. CED, September 1996, pp. 26–30.
17. Vincent Morin and Edouard Taufflieb, Improved Optical Fiber Amplifier for 1.3-μm AM-VSB CATV Systems. Scheduled for presentation at the 1998 NCTA National Conference and publication in the 1998 NCTA Technical Papers. NCTA, Washington, DC.
18. This equation is identical to that used by Ronald Cotten in the previously referenced paper (his Equation 16, page 171), but with the input variables converted to more common engineering units and with the bandwidth kept as a separate factor to allow the formula to be applied to various bandwidth services.
19. Henry A. Blauvelt, op. cit.
20. Donald Raskin and Dean Stoneback, Return Systems for Hybrid Fiber/Coax Cable TV Networks. Upper Saddle River, NJ: Prentice-Hall, 1998, pp. 152–154.
21. Dogan A. Atlas, op. cit. Modified after consultation with Dr. Dan Harris of Corning Fiber to give the result per channel and to convert the units to engineering units more familiar to cable engineers.
22. Patrick Harshman, Applying Push-Pull Technology to Optical Networks. CED, September 1996, pp. 56–61.
23. Athanasios Papoulis, Circuits and Systems: A Modern Approach. New York: Holt, Rinehart & Winston, 1980, pp. 331–389. Fourier transforms are used to convert between time domain waveforms and their equivalent frequency content.
24. D. Raskin et al., Don’t Get Clipped on the Information Highway, 1996 NCTA Technical Papers. NCTA, Washington, DC.
25. David Large and Rex Bullinger, Downstream Laser Clipping: Field Measurements and Operational Recommendations, Proceedings Manual, 1997 Conference on Emerging Technologies. SCTE, Washington, DC, January 1997.
26. David Grubb III and Yudhi Trisno. AM Fiber-Optic Trunks — A Noise and Distortion Analysis, 1989 NCTA Technical Papers. NCTA, Washington, DC, 1989.
27. Stuart S. Wagner, Thomas E. Chapuran, and Ronald C. Menendez, The Effect of Analog Video Modulation on Laser Clipping Noise in Optical Video-Distribution Networks, IEEE Photonics Technology Letters. Vol. 8, No. 2, February 1996, pp. 275–277.
28. David Large, Reducing Distortions Using Video Timing Techniques. CED, June 1989, pp. 114–119.