Chapter 13 Wavelength-Division Multiplexing
13.1 Introduction
Chapter 12 covered the basics of linear fiber-optic signal transportation. These are applicable to situations in which just a single optical signal is sent through each fiber. Fibers, however, are capable of carrying multiple independent optical signals on different wavelengths simultaneously with a minimum of mutual interaction. The general term for such shared use of fiber is wavelength-division multiplexing (WDM). A network design may choose to use WDM as an economical alternative to installing more fibers or as a means for combining signals that will be detected simultaneously by a common receiver. Both techniques have applications in cable systems.
This chapter will deal with the technology and performance issues encountered in various WDM applications, including component performance, mutual interaction in fibers, and link design trade-offs. You should first be familiar with the material covered in Chapter 12 because only the incremental information related to multiwavelength use of fibers will be covered here.
13.2 Wavelength Multiplexing: WWDM, CWDM, and DWDM
Wavelength multiplexing refers to any application in which multiple optical signals on different wavelengths share the use of common fibers. Within that general definition, however, there is a considerable range of applications and wavelength usage plans. Different acronyms are applied, somewhat inconsistently, to these plans to distinguish them. For our purposes, we will distinguish among three wavelength plans.
1310/1550 dual-wavelength plans – WWDM: The earliest WDM plan involved just two wavelengths: one in the 1310-nm window and one in the 1550-nm window. A typical cable application might involve transporting two signals over a shared link where they would be separated at the far end, or sending two signals modulated with nonoverlapping RF spectra to a common detector where they would be detected and combined in a single operation. Although WDM generally refers to any level of multiplexing, the term is sometimes applied to 1310/1550 multiplexing, as distinguished from the more dense plans discussed later. ITU draft standard ITU-T G.671 considers any channel spacing greater than 50 nm to be wide wavelength-division multiplexing (WWDM); we will use that designation here.
20-nm-spaced plans — CWDM: An optical industry interim standard uses up to eight wavelengths, spaced 20 nm apart and centered approximately in the “third window” of optical fiber, also known as the “C band” (see Figure 12.6) at 1550 nm. The wavelengths are: 1470, 1490, 1610 nm. Generally, this scheme is referred to as course wavelength-division multiplexing (CWDM), in accordance with ITU-T G.671 (any channel spacing between 8 and 50 nm). ITU-T Recommendation G694-2, approved in June 2002, extends this down to 1270 nm (18 wavelengths), anticipating the ready commercial availability of fiber with no “water peak” of loss between the 1310-nm and 1550-nm transmission windows,1, 2 as discussed in Chapter 12. Such an extended-wavelength plan is, of course, applicable only to nonamplified systems, until such time as optical amplifiers with similarly extended bandwidths are developed.
Subnanometer-spaced plans—DWDM: The International Telecommunications Union (ITU) has defined a usage plan that can scale to as many as 45 wavelengths in the third window and whose spacings have been further split in some systems to yield twice that number. The defined channel designations are for channels spaced 100 GHz apart (about 0.8 nm). Regardless of whether 200-GHz or 100-GHz spacings are used, the usage plan is referred to as dense wavelength-division multiplexing (DWDM).
A few properties are common to all the plans, each with obvious parallels in RF technology.
• The closer the wavelengths are spaced, the harder (and more expensive) it is to separate them in the demultiplexers and simultaneously achieve adequate adjacent channel isolation, minimal in-channel flatness variation, and low insertion loss.
• The closer the wavelengths are spaced, the more frequency stability is required of the transmitters.
• The closer the wavelengths are spaced, the better the signal transmission velocities will match. Four-wave mixing is maximum when the signals are closely phase matched, whereas cross-phase modulation is maximum when group velocities are closely matched. The degree of matching is, of course, also dependent on fiber dispersion, with standard fiber having high dispersion at 1550 nm but low dispersion at 1310 nm. By contrast, close wave-length spacing leads to reduced crosstalk from stimulated Raman scattering. These mechanisms are discussed later.
• The more wavelengths that share a fiber, the lower must be the power per wavelength for a given amount of mutual interaction due to nonlinear glass properties.
Cable systems using DWDM technology generally use 200-GHz-spaced channels from among the set of 20 listed in Table 13.1 For network designs that use fewer than 20 of these wavelengths, various vendors have chosen to offer different subsets of them. Most offer C21 through C35 as the first eight, but one vendor offers C39–C53 as the second eight, another offers C45–C59, and a third has chosen to offer C37–C51. This is obviously inconvenient to operators who wish to have multiple sources for optical transmitters and DWDM multiplexers.
Table 13.1 Commonly Used DWDM Channels
| Wavelength (nm) | ITU channel designation |
|---|---|
| 1560.61 | C21 |
| 1558.98 | C23 |
| 1557.36 | C25 |
| 1555.75 | C27 |
| 1554.13 | C29 |
| 1552.52 | C31 |
| 1550.92 | C33 |
| 1549.32 | C35 |
| 1547.72 | C37 |
| 1546.12 | C39 |
| 1544.72 | C41 |
| 1542.94 | C43 |
| 1541.35 | C45 |
| 1539.77 | C47 |
| 1538.19 | C49 |
| 1536.61 | C51 |
| 1535.04 | C53 |
| 1533.47 | C55 |
| 1531.90 | C57 |
| 1530.33 | C59 |
13.3 Components for WDM Systems
Constructing WDM systems requires the use of some components not required for single-wavelength links and tighter control over the specifications of other components.
13.3.1 Wavelength Multiplexers
Essential to shared use of fibers is a means by which to combine incoming signals at the transmit end and to separate them at the receiving end. It is possible to use simple wideband splitter/combiners or directional couplers to combine optical signals at the transmit end, and some applications do just that. The trade-off is that a broadband optical combiner, such as an RF combiner, has a minimal theoretical insertion loss of about 3 dB per two-way splitting level, with practical devices having losses 0.5-1.5 dB higher, whereas a two-wavelength multiplexer may have a loss of under 2 dB, and a 20-wavelength multiplexer a loss of under 4 dB.
At the current state of technology, the retail cost of a broadband combiner is about 10–15% of the cost of a 200-GHz-spaced WDWM multiplexer with an equivalent number of ports. Thus, the decision as to whether to use wavelength-specific or broadband combining at the transmit end of a WDM link must be driven by consideration of the overall link design, including the passive loss and the relative cost of obtaining higher-power transmitters as compared to the cost of wavelength-specific multiplexers.
At the receiving end, however, there is no alternative to using wavelength-specific demultiplexers if the signals are to be detected separately, because detectors are generally insensitive to minor changes in wavelength, with the result that all of the RF spectra modulated onto all of the received optical signals, along with beats among the optical spectra, will otherwise appear at the detector output port.
The technology used to build WDM filters is developing rapidly, with corresponding improvements in both performance and price.3 Typical 16- or 20-wavelength, 200-GHz channel-spacing filters available in 2002 had the following characteristics in devices costing about $500 per wavelength:
| Adjacent channel isolation | 27–30 dB |
| Nonadjacent channel isolation | 30–40 dB |
| Total insertion loss, including connectors | 3.8–4.0 dB |
| Differential insertion loss | 1.0 dB |
| In-channel loss variation | 0.5 dB |
| Polarization-dependent loss variation | 0.5 dB |
Not generally specified is the maximum in-channel transmission slope, which is crucial to calculating how various phase modulation mechanisms convert to noise and second-order distortion.
Both the price and performance parameters have significantly improved recently, and they are expected to continue to improve.
13.3.2 Gain-Flattened Optical Amplifiers
Not only fibers, but optical amplifiers, are capable of handling multiple optical signals on separate wavelengths. In single-wavelength applications, they are almost always operated in a saturated mode and thus have a constant output power regardless of drive level (over a defined range, of course). Thus, any variation of gain with wavelength is not an important consideration. When operated in saturated mode while amplifying multiple wavelengths, however, the total output power will be divided among all the signals, so if one input level changes or a signal is removed or added, the level of all the other signals will also change, which is obviously unacceptable in analog optical links where the RF output power of a detector is a function of both modulation level and optical power level.
Manufacturers avoid this problem by offering products that can optionally be operated in constant-gain-per-wavelength mode. As with coaxial amplifiers, however, the uniformity of gain with (optical) frequency is an essential factor. In general, amplifiers designed to handle a single wavelength do not exhibit a sufficiently flat response. Not only that, but their optical frequency response varies as a function of input level. Thus, a class of amplifiers known as gain-flattened amplifiers has been developed for DWDM applications. These devices are designed to operate in a fixed-gain mode of operation and offer a much flatter frequency response. Typical specifications for such a device include gain flatness within 1 dB peak-to-peak from 1530 to 1565 nm and over a composite power input range of −6 dBm to +6 dBm. Typical devices offer a maximum composite power output of up to 20 dBm per-wavelength gain of 17–26 dB, and a noise figure of 5–5.5 dB.4
The imperfect frequency response of the optical channel (the total of multiplexer, demultiplexer, and amplifier variation) interacts with each source’s incidental wavelength modulation (chirp) to produce distortion products. To the extent that the response variation is approximately linear across the transmitter modulated linewidth (the usual case), the result will be a degradation in CSO in the demodulated signal. If the response variation is noticeably nonlinear, third-order products will be produced as well.
Second, the imperfect in-channel frequency response will interact with any cross-phase modulation occurring before the device to produce cross-amplitude modulation, as discussed later.
Finally, the broader response variation (the total of wideband variation in amplifier response, multiplexer and demodulator channel-to-channel insertion loss variations) will also make the various optical signals arrive at their detectors at different levels, resulting in a less-than-optimum balance between noise and distortion for some of the wavelengths.
13.4 WDM-Specific Design Factors
Figure 13.1 illustrates the two generic applications of WDM. In the first application, optical signals on multiple wavelengths are generated by independent transmitters, multiplexed together, transmitted through a shared fiber, optionally amplified, demultiplexed at the receiving end, and detected by independent receivers. In the second application, the signals are not demultiplexed, but rather fed to a common receiver.
A typical example of the first application would be the transmission of multiple node-specific digital programming from a headend to a hub, where the signals destined for each node would be separated before detection. The second application is frequently used for combining common RF spectra modulated on one wavelength (for instance, 50–550 MHz modulating a 1310-nm transmitter) with node-specific programming (using some portion of the spectrum above 550 MHz modulating a 1550-nm transmitter) and then detecting both at the node using a common detector. Sometimes these applications are cascaded, as will be discussed in Chapter 18.
In the first application, the following performance parameters must be considered, in addition to those discussed in Chapter 12:
• Detectors are largely wavelength independent. Thus, to the extent that light from other wavelengths is not perfectly excluded from the desired wavelength output of the demultiplexer, the recovered RF spectrum will also contain some level of the signals modulated on other wavelengths.
• As discussed in Chapter 12, optical signals parametrically modulate the properties of the glass through which they pass. More specifically, the refractive index varies slightly in proportion to the instantaneous optical power level (known as the optical Kerr effect, or OKE). In multiple-wavelength systems, these variations lead to various interwavelength effects: cross-phase modulation (XPM), four-wave mixing (FWM), and cross-polarization modulation. These, in turn, interact with the properties of both the fiber and the discrete devices along the transmission path to produce noise and cross modulation in the detected RF signals. Additionally, the presence of each signal can cause the fiber to have incremental gain or loss through a process known as stimulated Raman scattering (SRS).
• To the extent that the optical frequency response of each channel (including the multiplexer, any amplifiers, and the demultiplexer) is not flat, that will combine with any transmitter chirp to generate in-band second-order distortion products in the recovered RF spectrum.
When a common detector is fed more than a single wavelength, some additional parameters must be considered.
• Since there is no way to filter the RF output spectra before combining, each portion of the final spectrum will be degraded by broadband noise from both optical links.
• Similarly, each portion of the spectrum will be degraded by distortion components arising from the other links that fall in the RF spectrum of the first link.
• The final balancing of RF levels between those transmitted on each link will be a combination of the optical modulation index (OMI) and relative optical received levels and thus cannot be adjusted at the receiving site.
13.5 Crosstalk Mechanisms5
The first set of factors to be considered are those that lead to crosstalk — defined as the level of postdetection products and wideband noise relative to desired signals that are caused by the presence of modulated optical signals other than the one whose performance is being considered and that share use of a common network segment that may include multiplexers, fiber, amplifiers, and/or demultiplexers.
13.5.1 Imperfect Demultiplexer Wavelength Isolation
Imperfect multiplexer isolation affects the amount of light from each source that shows up at the output of other sources, but otherwise it has no effect on link operation. Imperfect demultiplexer isolation, however, makes some light from undesired wavelengths impinge on the detector along with the light at the desired wavelength.
In the detector, each of the incoming optical signals will be detected, resulting in a composite RF spectrum that contains elements of the modulating spectra of all the signals. Since the detector is a square-law device, the contributions from undesired signals will be lower than the desired RF output by twice the difference in optical levels at the detector input, assuming similar received optical power levels and modulation indices (the assumption throughout this chapter, unless stated otherwise).
Thus, if the adjacent channel isolation in a DWDM demux is 30 dB and OMIs are similar, then the modulating signal from each of the adjacent wavelengths will appear about 60 dB below the desired signal after detection. If the modulation is analog video and the same nominal channel frequencies are used for each link, then the undesired video carriers will appear close to the desired carriers and have the same effect as ingressing signals. If the modulation on both desired and adjacent signals is digital, then the undesired RF output will appear noiselike and the two adjacent signals together will generate a contribution to the total link C/N of 57 dB.
More generally, if the link were carrying a total of n wavelengths, each modulated with a similar spectrum of signals, the adjacent channel isolation were A dB, and the nonadjacent isolation were B dB, then the total link C/I contribution (for all but the shortest and longest wavelengths) due to imperfect demultiplexer isolation would be
(13.1)For the highest and lowest wavelengths, there is only one adjacent wavelength, so the equation becomes
(13.2)where
C/IISOLATION = the ratio of the desired to the undesired RF signal powers in the demodulated spectrum of the victim optical carrier, in dB
A = the adjacent optical channel isolation of the WDM demultiplexer in dB
B = the nonadjacent optical channel isolation of the WDM demultiplexer in dB
Assuming an environment where all optical signals are at the same nominal level and optical modulation index (the usual case), the level of postdetection crosstalk interference will be independent of the average optical levels and modulation frequency; thus, this is considered a linear degradation factor.
13.5.2 Cross-Phase Modulation Combined with Fiber Dispersion (XPM-D)
Recall from Chapter 12 that self-phase modulation (SPM) results from the fact that the refractive index of optical fiber changes slightly in the presence of high electrical fields. Thus, a sufficiently high amplitude signal will cause the index of refraction to vary as the square of its own instantaneous electrical field strength, resulting in incidental phase modulation, because the velocity of propagation varies inversely with the index of refraction.
When two or more optical signals share a fiber, whatever modulation of the index of refraction takes place affects all of the signals. Thus, the amplitude variations of each of the individual signals result in some degree of phase modulation of the other signals. In a perfect transmission path and with a perfect broadband detector, this phase modulation would have no effect on performance. The cross-phase modulated signal, however, travels through fiber that exhibits chromatic dispersion to create cross-intensity modulation in the optical signal and, thus, cross-amplitude modulation in the detected RF signals.
Assuming equal optical modulation indices, crosstalk from each interfering modulated optical carrier due to the interaction of cross-phase modulation with fiber dispersion is given by
(13.3)where all variables are in a consistent set of units. In meter-kilogram-second (MKS) units:
C/IXPM = the ratio, in dB, of desired to undesired RF signal powers in the demodulated spectrum of the victim optical carrier, in dB (assuming equal optical modulation indices of both optical signals)
n2 = the nonlinear refractive index of the fiber, typically 2.6 × 10−20 m2/W
λ1 = the wavelength of the victim optical carrier, generally between 1.530 × 10−6 and 1.560 × 10−6m
λ2 = the wavelength of the interfering modulated optical carrier, in meters
D = the dispersion coefficient of the fiber in sec/m2. For standard fiber near 1550 nm, this is typically 17 ps/nm-km = 17 × 10−6 sec/m2
c = the speed of light in a vacuum = 3 × 108 m/sec
Ω = the frequency of the modulating RF signal in radians = 2πfI, where fI is the modulating frequency in Hz
P20 = the power level of the modulated interfering optical signal, in watts
QXPM = the effective polarization overlap between the interfering and the victim optical carriers. This varies from 1 for copolarized signals to 1/3 for cross-polarized signals. At 45° it is 2/3
A = the effective mode cross-sectional area of the fiber core, about 80 × 10−12 m2 for non-dispersion-shifted fibers and 50 × 10−12 m2 for dispersion-shifted fibers
α= the fractional power attenuation of the fiber per meter of length
= 1 − 10−(α0/10,000), where α0 is the attenuation in dB/km. A typical value of α0 for standard fiber at 1550 nm is 0.21 dB/km, for which α= 4.835 × 10−5 per meter
z = the length of the shared fiber, in meters
d12 = the group velocity mismatch between the interfering and victim optical carriers ≈ D(λ1 − λ2)
Converting this to more common engineering units and assuming operation near 1550 nm, we get
(13.4)where
PI = the launch power of the interfering optical carrier in dBm
fRF = the modulation frequency in MHz
D = the fiber dispersion in ps/nm-km. For non-dispersion-shifted fiber near 1550 nm this is typically 17
L = the length of the fiber in km
QXPM = the effective polarization overlap between the interfering and victim optical carriers. This varies from 1 for copolarized signals to 1/3 for cross-polarized signals and is 2/3 for 45° relative polarization
A = the effective cross-sectional area of the fiber core. For non-dispersion-shifted fiber this is typically 80 × 10−12 m2
α= the fractional power attenuation of the fiber per km
= 1 − 10−(α0/10), where α0 is the attenuation in dB/km. A typical value of α0 for standard fiber at 1550 nm is 0.21 dB/km, for which α= 0.047
Δλ = the difference in wavelength between the interfering and victim optical carriers in nm
X = the “loss parameter” αh. For fiber with a loss of 0.21 dB/km, this is 0.047L, where L is the length of the fiber in km
Y = the “walkoff parameter” D Δλ (2πfRF) L. For fiber with a dispersion of 17 ps/nm-km, this is 1.068 × 10−4Δλ fRFL.
The amount of optical cross-phase modulation, and thus intensity modulation after interaction with the dispersion, varies linearly with the level of the interfering optical signal. Thus, after detection, this degradation factor will vary 2 dB for every 1-dB change in the level of the interfering optical signal.
The amount of optical cross-phase modulation also varies according to the polarization match between the interfering and victim optical signals in the fiber. For cross-polarized signals, the cross modulation is one-third that for polarization-aligned signals.
Due to dispersion in the fiber, the interfering and victim optical signals will travel at slightly different velocities. This property, also known as walk-off, reduces the peak cross-phase modulation because the peak amplitude of the interfering signal “slides” along the victim signal rather than synchronously acting on the same spot in time. The greater the wavelength difference, the faster the walk-off occurs, resulting in less peak cross-phase modulation.
The effects of cross-phase modulation are greatest at higher RF frequencies. One reason is that a constant level of phase deviation versus frequency results in an optical frequency deviation that linearly increases with modulating frequency, and it is the frequency change that interacts with dispersion to create the crosstalk.
Figure 13.2 shows the maximum and minimum expected crosstalk from this mechanism for a single copolarized interfering carrier whose launch power is +7 dBm and whose optical carrier is 1.5 nm away from the victim carrier, with both transmitted through 30 km of standard fiber.
13.5.3 Stimulated Raman Scattering (SRS)
At a sufficiently high optical signal level, one optical signal can act as a “pump” so as to provide gain (either positive or negative) to other signals sharing the fiber. If the pump signal has a wavelength that is shorter than the victim signal, then the gain will be positive, whereas if the pump signal is longer, the gain will be negative (in other words, loss). The gain is maximum for WDM channels with optical frequencies separated by about 13 THz and is proportionately lower for narrower separations. Another way of looking at this phenomenon is that power is transferred from the shorter-wavelength optical carrier to the longer-wavelength carrier as they travel through the shared fiber; but since they are both modulated, the SRS gain follows the instantaneous carrier levels and results in mutual cross-amplitude modulation.
Assuming equal optical modulation indices, crosstalk from each interfering modulated optical carrier due to stimulated Raman scattering is given by
(13.5)where the units are the same as for Equation (13.3), with the following additions:
C/ISRS= the ratio of desired to undesired RF signal powers in the demodulated spectrum of the victim optical carrier, in dB (assuming equal optical modulation indices of both optical signals)
ρSRS = the effective polarization overlap between the interfering and victim signals. This equals 1 for copolarized signals and less than 0.1 for cross-polarized signals
g12 = the Raman gain coefficient, which is positive if the interfering signal is of shorter wavelength than the victim signal and negative if the interfering signals is of longer wavelength = gSRSc(λ2 – λ1)/(λ2λ1), where gSRS = the Raman gain slope for the fiber, typically 5 × 10−27 m/W-Hz.
Converting this to more convenient engineering units, we get
(13.6)where the units are the same as for Equation (13.4), with the following additions:
C/ISRS = the ratio of desired to undesired RF signal powers in the demodulated spectrum of the victim optical carrier, in dB (assuming equal optical modulation indices of both optical signals)
QSRS = the effective polarization overlap between the interfering and the victim optical carriers. This varies from 1 for copolarized signals to less than 1/10 for cross-polarized signals. At 45° relative polarization, it has a value of 0.5.
As with XPM crosstalk, SRS varies 2 dB for every 1-dB increase in optical carrier level; however, the degree of SRS “coupling” between the signals is more highly dependent on the polarization match between them and drops to less than a tenth for cross-polarized signals, meaning that the RF crosstalk can vary more than 20 dB.
Crosstalk due to SRS is maximum at low modulation frequencies but decreases in a nonlinear way, with a periodic variation superimposed on the general decrease as a function of frequency due to the walkoff between the interfering and victim channels. The variation exhibits more cycles across the modulation frequency spectrum when the optical channels are more widely separated, since the velocity mismatch is then greater.
Figure 13.3 shows the maximum and minimum expected crosstalk from SRS for a single copolarized interfering carrier whose launch power is +7 dBm and whose optical carrier is 24 nm away from the victim carrier, with both transmitted through 30 km of standard fiber.
SRS crosstalk is typically the most serious of the crosstalk mechanisms at far wavelength spacings and low modulation frequencies, with the crosstalk at 50 MHz being worse than for any other mechanism at any other frequency. One researcher has suggested reducing the effect of SRS by transmitting pairs of closely spaced optical carriers, modulated 180° out of phase, so that the SRS crosstalk on a third carrier from one would approximately cancel the crosstalk from the other. Experimental data confirms a reduction of about 30 dB at 50 MHz and 15 dB at 800 MHz for 1-nm-spaced interfering carriers, with 4- to 5-nm spacing to the victim carrier. Whether this will be a cost-effective solution to the problem has yet to be determined.6
13.5.4 Cross-Phase Modulation Combined with Transmission Slope (XPM-TS)
Aside from the conversion from XPM to intensity modulation that takes place in the fiber itself, the phase-modulated victim signal also reacts with any device whose transmission slope is not flat with frequency (transmission slope, or TS). Generally, the least flat component is the wavelength demultiplexer. This gives rise to a slope-detection conversion from phase to amplitude modulation. Assuming equal modulation of the two carriers, the crosstalk is given by this equation:
(13.7)where all variables have the same units and meanings as in Equation (13.3), with the following additions:
T0 = the linear transmission coefficient of the component in question (i.e., the ratio of output power to input power)
∂T/∂f = the differential of the linear transmission coefficient at the wavelength being used with respect to frequency (i.e., the change in the ratio of output power to input power divided by the change in optical frequency)
The product of these, in MKS units, can be calculated using
(13.8)where S is the transmission slope of the demultiplexer or other component in dB/GHz.
In more common engineering units, this reduces to
(13.9)where the units are the same as for Equation (13.4), with the following additions:
Unfortunately, the in-band transmission slope of wavelength demultiplexers is seldom specified. One researcher has found typical devices to have a slope that averaged 0.02 dB/GHz but were as high as 0.11 dB/GHz.7
As with crosstalk, due to the interaction between cross-phase modulation and fiber dispersion, XPM-TS is greater at higher modulating frequencies and higher optical powers but is reduced at wider optical channel spacing and higher fiber dispersion. Figure 13.4 shows the variation with frequency for two copolarized signals spaced by 1.5 nm and launched at 7 dBm. Curves are plotted for 0.02 dB/GHz and 0.1 dB/GHz, which represent the typical range of measured values for commercially available DWDM demultiplexers.
XPM-TS can add either in phase or out of phase with XPM-D, depending on the slope of the filter loss.
13.5.5 Optical Kerr Effect Combined with Polarization-Dependent Loss (OKE-PDL)
As seen already, both XPM and SRS are maximum when the polarizations of the interfering signals are aligned with the target signal and minimum when they are cross polarized. When they are at some other relative polarization, however, the polarization, as well as the gain and phase of the target signal are modulated.
This can be understood if the target signal is viewed as the vector addition of two signals, one polarization aligned with the interfering signal and one cross polarized to it. The one that is polarization aligned undergoes much greater cross-amplitude and cross-phase modulation than the one that is cross polarized, with the result that the vector sum of the two has a net polarization that varies.
As with XPM, in a perfect network followed by a perfect detector, the OKE would have no effect on the detected signals. When either the fiber or a discrete device has a polarization-dependent loss (PDL), however, it is converted to amplitude modulation. One researcher found a typical WDM demultiplexer to have a PDL of 0.03-0.17 dB8; however, as noted earlier, typical specifications for production devices are of the order of 0.5 dB.
Assuming equal optical modulation indices, crosstalk from each interfering modulated optical carrier due to the interaction of the optical Kerr effect with polarization-dependent loss in a terminating component is given by the following general equation:
(13.10)where the units are the same as for Equation (13.3), with the following additions:
C/IOKE-PDL = the ratio of desired to undesired RF signal powers in the demodulated spectrum of the victim optical carrier, in dB, for a single interfering carrier
ΔT = the transmission difference through the terminating device as a percentage of the maximum transmission as a function of polarity
= 1 – 10−PDL/10, where PDL is the polarity-dependent loss through the device in dB
Q3 = the effective polarization overlap factor for this mechanism. This varies from 0.75 at 45° relative polarization to zero for signals that are either copolarized or orthogonally polarized
t2, t3 = transmission parameters that can vary over the range from +1 to − 1. Crosstalk is maximum for t3 = 1 and t2 = −1.
Converting this to more common engineering units and calculating the maximum possible crosstalk, we get
(13.11)where the units are the same as for Equation (13.4), except that ΔT and ρ3 are as in Equation (13.9).
Although the maximum possible OKE-PDL effect can be calculated, the level in practical applications can vary widely, due to two factors. First, the degree of cross-polarization modulation varies with the relative polarizations between the interfering and victim signals. Second, the conversion from polarization modulation to amplitude modulation depends on the polarization of the victim signal relative to the maximum slope of loss versus polarization in the demultiplexer. One researcher found that the experimental C/I from this effect was 6 dB better than the minimum predicted and that the median C/I was 9 dB better.9
With good-quality WDM demultiplexers, the total crosstalk between optical channels is dominated by SRS effects at low modulation frequencies and by XPM effects at high modulation frequencies. In the region where those effects would be expected to cancel through vector addition, however, the OKE-PDL effect becomes dominant. Generally this occurs when optical channels are closely spaced, when the interfering optical carrier is at a shorter wavelength than the victim carrier (so that the phase of the SRS effect is opposite that of the XPM effect), and at the low end of the RF spectrum. Above 0.1 dB of PDL, OKE-PDL can be the dominant crosstalk mechanism at 50 MHz, above 0.4 dB it can dominate across most of the typical CATV spectrum if the polarizations between interfering and target signals happen to be at or close to 45° polarization difference and the output is oriented to the maximum PDL slope of the terminating device. Unlike the other crosstalk mechanisms, OKE-PDL effects typically vary with time and temperature because the polarization in field-installed single mode fiber is essentially uncontrolled and, thus, the polarization of the received signal will vary with respect to the slope of the PMD of the terminating filter. In field testing, OKE-PDL varied over as much as 30 dB, approximating the theoretical maximum at times.10 Finally, as with XPM-TS, OKE-PDL will tend to add either constructively or destructively with the XPM-D and SRS, depending on the slope of the PDL effect, which is not predictable in practical situations.
Figure 13.5 plots the maximum possible OKE-PDL for two optical signals spaced 10 nm apart, polarized 45° relative to each other, and launched through 30 km of fiber at 7 dBm.
13.5.6 Four-Wave Mixing
The fact that the refractive index responds to the total optical power level means that the transmission system is nonlinear. As with nonlinearity in an RF amplifier, this leads to the creation of new optical signals whose frequencies are sums and differences of the primary signal frequencies. The third-order products (equivalent to CTB products at RF) can fall in the wavelength range of interest and, given the equal spacing of channels in both CWDM and DWDM systems, can fall nominally on top of desired signals. These are at frequencies A + B – C and 2A – B, where A, B, and C are optical frequencies of the primary signals. As expected, the buildup of products is exactly the same as for CTB products in RF systems. In optical systems, these are known as four-wave mixing (FWM) products, because three wavelengths (A, B, and C) combine to produce a fourth wavelength.
Four-wave mixing products can have two types of effects. If the products fall within the bandwidth of the wavelength demultiplexer channel, then they will pass through the same demultiplexer port and be demodulated along with the desired signals, with the resultant RF products being suppressed below the desired RF spectra by twice the difference in optical levels. Should the difference in the optical frequencies between the desired signal and a third-order product be less than the highest modulating RF frequency, however, then a high-level beat product will be generated in the demodulated RF spectrum. This is obviously of greater concern when the transmitters are externally modulated units whose optical frequencies are very stable. It is less of a concern with directly modulated DFB transmitters, due to chirp.
Four-wave mixing is greatest when the signals giving rise to a product interact cohesively over an extended length of fiber. When the signals travel at different velocities, the interaction is reduced. Therefore, it is of greatest concern when dispersion-shifted fiber is used and when the optical channels are closely spaced. For baseband digital systems utilizing channels spaced as closely as 50 GHz and dispersion-shifted fiber, it can be the dominant distortion mechanism. The efficiency of the process drops dramatically, however, when the interfering signal moves by as little as 100–200 GHz from the zero-dispersion wavelength, falling off as the square of the dispersion and as the fourth power of the difference in wavelengths of the interfering and victim signals.11, 12 This effect is negligible for the most common cable television use of DWDM, which utilizes 200-GHz-spaced channels transmitted through standard optical fiber.
13.5.7 Summary of Cross-Modulation Effects in WDM systems
All of the cross-modulation mechanisms described here are coherent for a given pair of wavelengths, and thus the effects add vectorially. When the interfering signal is at a longer wavelength than the victim signal, XPM-D and SRS effects are at nominally opposite phases and the net crosstalk is less than the larger of the two. When the interfering signal is at a shorter wavelength, they add to produce crosstalk greater than either mechanism alone. On the other hand, SRS crosstalk increases, while XPM decreases, as the difference in wavelengths increases, resulting generally in a broad minimum as the wavelength spacing approaches zero, whereas OKE-PDL has a broad maximum at small wavelength spacings and prevents XPM and SRS effects from cancelling completely at any spacing.
XPM-TS, like OKE-PDL, can add constructively or destructively with the net of XPM and SRS, depending on the slope of the response of the device, which is generally not predictable. Finally, crosstalk due to imperfect demultiplexer isolation will add constructively with XPM-D crosstalk.
Thus, the most conservative calculation of optical cross modulation in a two-wavelength system would require adding the worst-case demultiplexer isolation and XPM-D magnitudes, then adding or subtracting (depending on relative wavelengths) the SRS magnitude, and then adding the XPM-TS and OKE-PDL magnitudes to the absolute value of the previous calculation. More formally:
(13.12)where the plus sign is used where the interfering carrier is at a shorter wavelength than the victim carrier and the minus sign otherwise and
C/ICROSSTALK = the net crosstalk occurring between two optical carriers similarly modulated
I = the isolation of the WDM demultiplexer at the wavelength of the interfering carrier, in dB
C/IXPM-D = the crosstalk due to cross-phase modulation interacting with fiber dispersion, in dB
C/ISRS = the crosstalk due to stimulated Raman scattering, in dB
C/IOKE-PDL = the crosstalk due to the optical-Kerr-effect-caused cross-polarization modulation interacting with polarization-dependent loss in the WDM demultiplexer, in dB
C/IXPM-TS = the crosstalk due to cross-phase modulation interacting with imperfect channel flatness in the WDM demultiplexer, in dB
Such a calculation will overstate the total cross modulation if worst-case levels are assumed for all mechanisms, because the OKE-PDL magnitude cannot be maximum at the same input-signal relative polarization that maximizes SRS and XPM. To be safe, the calculation can be run with relative polarizations of 0° (where OKE-PDL is zero) and also at 45° (where OKE-PDL is maximum) to see which results in the worst-case crosstalk.
In practical headend and field installations, relative polarizations will not be known or controlled and can be assumed to vary randomly. Since XPM crosstalk varies by about 10 dB with polarization and SRS varies by 20 dB or more, at best, an approximation of the total likely cross modulation will be possible.
In systems of more than two wavelengths, the calculated cross modulations between various pairs of optical carriers will vary due to different channel spacings, different numbers of lower and higher interfering channels relative to each victim channel, different qualities of optical demultiplexer channels (combined with transmitter wavelength tolerance relative to nominal channel center wavelength), and random polarization combinations. In addition, it is not uncommon in CATV systems for at least part of the spectrum to be common to multiple transmitters driving a common fiber. This means that, potentially, multiple interfering carriers could be modulated synchronously over at least part of the RF spectrum and therefore that the cross-modulation effects could add vectorially rather than randomly. One researcher has found that ignoring possible synchronous effects (that is, by adding the calculated distortion from each interfering carrier on a power, rather than voltage, basis) agreed with experimental results within 7 dB at all frequencies and within 3 dB above 500-MHz modulation in an eight-wavelength system.13
Using this approach, Figure 13.6 shows the maximum possible contributions of each crosstalk mechanism and the net crosstalk affecting the longest and shortest wavelengths for a 16-wavelength, 30-km-long optical circuit, with each optical carrier launched at a power of +7 dBm. The optical carriers were assumed to occupy odd-numbered ITU channels C21 through C51 and to be copolarized. Fiber was assumed to be standard unshifted fiber with a dispersion of 17 ps/nm-km and a loss of 0.21 dB/km. The wavelength demultiplexer was assumed to have a transmission slope of 0.05 dB/GHz, a PDL of 0.25 dB, an adjacent channel isolation of 27 dB, and a nonadjacent channel isolation of 32 dB. The optical carriers were assumed to be modulated to similar levels, with crosstalk evaluated over a range extending from 50 to 1000 MHz.
The composite crosstalk is seen to be dominated by factors related to the quality of the demultiplexer, except for frequencies below 500 MHz, where SRS effects are largest. As would be expected, the shortest-wavelength signal (C51) has better performance, due to the out-of-phase combining of SRS with the sum of isolation and XPM-D. Since the signals are copolarized, OKE-PDL does not contribute to the composite crosstalk level.
Figure 13.7 is the same, except evaluated for one of the two center optical channels (C35). The performance is better at low modulation frequencies because there are fewer widely spaced channels and therefore less SRS. At the high end of the spectrum, the cross modulation is slightly worse because of a larger contribution from the demultiplexer isolation due to the presence of two adjacent channels, rather than one as in the previous graph.
Figure 13.8 is the same as the first graph, but it shows the change if we assume that the signals are polarized at 45°, where OKE-PDL is maximized, but that XPM and SRS are both reduced. In this case, the crosstalk is dominated by OKE-PDL and demux isolation, and the composite C/I is degraded by 2–3 dB across most of the spectrum.
In summary, in every case modeled, the performance is dominated over at least the top half of the spectrum by some performance limitation of the demultiplexer: isolation, PDL, or transmission slope. While typical production devices may perform better, the values used in this model are typical of, or superior to, specified performance in 2002.
The relationship of actual system performance to the worst case predicted is difficult to guess. If signals in some fibers are cross polarized or close to it, all of the mechanisms with the exception of demultiplexer isolation will be greatly reduced. This suggests that the best performance may be close to the 48 to 50-dB limit imposed by the demux isolation, with typical C/I probably falling somewhere in the 42- to 45-dB range for the conditions specified. Whatever the case, it is clear that the various combined cross-modulation effects combine to make such multiwavelength networks inadequate to carry analog video channels.
13.6 CSO Due to Transmitter Chirp Combined with Imperfect Channel Flatness
Directly modulated DFB transmitters exhibit an incidental wavelength modulation, known as chirp. Additionally, due to the Kerr effect, each optical carrier generates self-phase modulation (SPM), which adds an additional component of wavelength variation. When transmitted through fiber with appreciable dispersion, these cause second-order distortion in the demodulated signals because the transmission rate through the fiber then varies as a function of the modulation level. Both of these phenomena are covered in Sections 12.6.3 and 12.4.7.
In DWDM systems, however, another factor arises due to the variations in channel amplitude response as a function of optical frequency. Various components may contribute to this, including the optical multiplexer, optical amplifiers, and the demultiplexer. Transmitter chirp interacts with this imperfect channel response to add another stage of optical modulation. Since each modulation is proportional to the modulating current and the modulation stages are effectively in series, the current at the output of the detector will have a component that is proportional to the square of the input current, thus, there will be a second-order distortion mechanism (chirp + transmission slope, or CHIRP-TS). For systems carrying analog video channels exclusively, the calculation is relatively simple.
First, given a change in modulating current ΔiM, the optical power will vary by ΔPOPT = k1 Δ iM, where k1 is the modulation slope of the laser diode. The frequency of the optical carrier will also vary by ΔfOPT = k2 ΔiM, where k2 is the chirp slope of the laser diode in Ghz/mA. The changing optical frequency interacts with the transmission slope of the channel, TS, in dB/GHz, to produce a change in optical power of ΔfOPTTS = k2 ΔiMTS dB.
In order to calculate the total effective modulation on the signal as received at the detector, it is necessary to convert this second stage of modulation back into a scaler quantity and to multiply it by the normal laser modulation. When we do that we get
(13.13)ΔPR = the change in optical received power resulting from a change in modulating current
k1 = the modulation slope of the transmitter diode in mW/mA
ΔiM = the change in modulating current in mA
Multiplying the change in power by the responsivity of the detector gives us the change in output current as a function of the change in input current and, thus, the equation for the transfer function of the system:
(13.14)where
This can be simplified by converting the power of 10 to a power of e and then taking the first two terms of the Taylor expansion of ex = 1 + x + x2/2! + x3/3! … This is equivalent to assuming that, over small changes in wavelength, the multiplication of the chirp slope and the transmission slope results in linear modulation as a function of input current. With that simplification, the transfer function becomes
(13.15)Referring to the derivation of CSO in Chapter 10, this is in the form of Equation (10.20), but expressed in terms of current rather than voltage, where iO = AiM + Bi2M, with A = Rk1 and B = 0.23026Rk1k2Ts.. From the analysis in Section 10.3.3, we know that the amplitude of the fundamental is AiM and that the amplitude of the individual second-order products is Bi2M and therefore that the ratio of amplitudes of the fundamental and second-order products is A/B, or 1/(0.23026k2TsIM), where IM is the peak input modulating current. Since power is proportional to the square of current and the composite second-order product will be determined by the power sum of products, we can write an equation for composite second-order distortion from this mechanism:
(13.16)C/CSOCHIRP-TS = the ratio of the desired carrier on the channel being evaluated to the composite power in the second-order products resulting from the interaction of transmitter chirp and the flatness of the transmission channel
k2 = the chirp slope of the transmitter diode in Ghz/mA
TS = the transmission slope of the demultiplexer channel in dB/GHz
IM = the peak per-channel modulating current in mA
N = the number of second-order beats falling in a cluster affecting the channel being evaluated (from Equation (10.25)).
As was shown in Chapter 12, CSO resulting from the use of directly modulated 1550-nm DFB transmitters combined with transmission through standard fiber resulted in CSO products that made this combination unusable for analog video transmission when the spectrum is greater than an octave. The same is true for transmitter chirp when combined with typical WDM filter transmission slope. For example, a transmission slope of 0.05 dB/GHz (a very moderate assumption because it is typical of just the DWDM demux alone) combined with the typical DFB chirp of 0.25 GHz/mA and 2-mA/channel modulating current results in second-order products that are 44.8 dB below the desired signal. The power addition of the 31 upper-side products affecting the highest channel in a 550-MHz system would result in a C/CSO of only 29.8 dB.
When the RF modulation consists wholly or partially of QAM modulated signals, however, the second-order products are no longer narrow. The low-side product of a QAM channel mixing with an analog video channel exhibits a flat, noiselike spectrum 6 MHz wide centered 1.75 MHz above the lower channel boundary, since the analog carrier is 1.25 MHz above the lower channel boundary and the QAM channel is 3 MHz above the lower channel boundary. The second-order products resulting from the mixture of two QAM channels will be noiselike, centered on the boundary between two channels, but 12 MHz wide (assuming the mixing channels were each 6 MHz wide) with a triangular spectral shape. When a continuous spectrum of adjacent QAM channels is carried, these products will overlap, leading to a relatively flat composite intermodulation noise (CIN) floor whose level can be approximated using the earlier formula, even though the level arises from products each of whose average noiselike density is spread over two channels. For the case of 45 QAM channels extending from 600 to 870 MHz, each modulated at 2 mA/channel, the magnitude of the second-order intermodulation noise per 6 MHz of bandwidth falling near channel 2 would be 29.2 dB below the level of the digital signals. This is 20 dB worse at channel 2 than the CSO, due to chirp interacting with just fiber dispersion (Equation (12.12)) and shows that the degradation due to discrete components often is the limiting factor in system performance. The import of this severe level of CSO will be discussed later when composite transmission systems are considered.
While this mechanism has been described in the context of the composite optical channel response, it has been investigated by others considering only the response of an optical amplifier, with results that are consistent with the preceding analysis. One experimenter found C/CSO levels as poor as 40 dB for wavelengths between 1535 and 1565 nm but rising to worse than 30 dB at 1525 nm.14
13.7 Degradation in Shared-Detector, Multiwavelength Systems
13.7.1 Postdetection White Noise and CIN Addition
When optical signals modulated with nonoverlapping RF spectra are combined and then fed to a common detector, each portion of the detected spectrum will be affected by broadband noise from both transmitters. In the general case, the optical modulation levels of the two transmitters will be different and the relative optical levels and modulation indices will be adjusted at the transmit end so that the levels of the detected signals are in the proper proportion.
As an example, suppose that the signals consist of a spectrum of analog video channels covering the spectrum from 50 to 550 MHz modulating one transmitter and a spectrum of 45 QAM digital signals covering the spectrum from 600 to 870 MHz modulating a second transmitter. It is desired that, after detection, the rms levels of the QAM signal levels be 6 dB below the sync peak levels of the analog video signals.
It is common to set the optical modulation index (OMI) of an externally modulated analog transmitter carrying 78 signals to approximately 3%. This represents a typical compromise among C/N, C/CTB, C/CSO, and clipping probability in the link. It is similarly desired to set the OMI of the QAM transmitter as high as possible, consistent with low clipping probability, to maximize C/N in that portion of the spectrum. When a spectrum consists of many noncoherent signals, the overall peak-to-rms current ratio tends to be independent of the number of signals.15 Therefore, the probability of clipping remains relatively constant if the total RF drive power remains constant. Since the optical modulation index varies as the drive current, an approximation of the maximum usable per-channel OMI of a transmitter is related to the number of carried channels by
(13.17)where
mi = the maximum per-channel optical modulation index percentage
N = the number of equal-power RF channels in the modulating spectrum
The constant represents the commonly achievable performance as of the writing of this book. With improved linearization techniques and advanced techniques such as phase control of the modulating carriers and timing control of modulation, it is possible to increase the optical modulation per channel. Given this relationship, the maximum acceptable OMI for the 45 QAM channels in the example is approximately 3.95%.
After detection, each of the recovered RF carriers will be at a level proportional to the square of the OMI, so if the optical carrier levels were the same at the input to the detector, the QAM channels would exceed the analog video channels by 20 log (5.3/3.0) = 2.37 dB. Since we want those carriers to be lower than the analog carriers by 6 dB, we need to reduce the relative level of the optical signal carrying the QAM channels by about 4.2 dB [(2.37 + 6)/2]. It is typical to design analog optical links with a received power of 0 dBm, so the QAM carrier level for proper postdetection level matching would be −4.2 dBm. With the optical system levels now determined, we can calculate the effective C/N for each portion of the spectrum.
In Section 12.10.1 we calculated the C/N of a single optical carrier link. Of the four factors considered, however, only transmitter RIN and IIN are related to each optical signal as received at the detector. The other two, shot noise and postamplifier noise, are related to the detector and the arriving light and so don’t add when a common detector and postamp are used.
Thus, the first step is to calculate, independently, just the RIN plus IIN contributions to C/N for the analog (C/NA1) and digital (C/ND1) links. Second, the full link, single-carrier C/N for the analog (C/NA2) and digital (C/ND2 — about 2.5 dB better than the analog due to higher OMI, but reduced because of 4.2-dB-lower optical receiver power) should be calculated using Equation (12.21). Third, the C/CIN for the QAM channels due to chirp, combined with fiber dispersion and demultiplexer transmission slope, should be calculated as discussed earlier (C/CIN). Given those, and knowing that the digital signals will be 6 dB below the analog signals after detection, we can calculate the effective carrier-to-thermal noise on the analog link as follows:
(13.18)where
C/NANALOG = the ratio of analog signal level to thermal noise and noiselike intermodulation noise from the QAM channels
C/CIN = the C/CIN as calculated earlier for channel 2 (the most affected analog channel)
Similarly, the effective carrier-to-thermal noise on the digital link will be
(13.19)A typical CATV downstream network might consist of a broadcast spectrum (50–550 MHz) of analog channels externally modulated (to avoid chirp) and then amplified and split to feed several nodes. The 45 node-specific QAM channels (600–870 MHz) would then each be directly modulated on ITU-grid DFB transmitters and combined in a multiplexer for transmission to a hub. At the hub, they would be demultiplexed; then each would be combined with broadcast programming to be fed to a node. The network designer needs to know the total link C/N for both analog and QAM channels.
If, for example, the fiber cable length is 30 km and the in-channel slope of the demultiplexer is 0.05 dB/GHz, then typical values for the parameters required might be as follows: C/NA1 = 60 dB, C/ND1 = 65 dB, C/NA2 = 53 dB, C/ND2 = 50.5 dB, C/CINCHIRP-DISPERSION = 49.2, C/CINCHIRP-TS = 29.4 (using the assumptions in the earlier example). Using these assumptions, it is not important whether the two C/CIN effects add constructively or destructively, because the CHIRP-TS effect dominates. Plugging these values into Equations (13.18) and (13.19) we get C/NANALOG = 35.3 dB and C/NQAM = 48.9 dB. Thus, the degradation from white noise affecting the QAM channels is about 1.6 dB, but it results in a net C/N that is still well above typical end-of-line specifications for this service. On the other hand, clearly this is unacceptable analog performance.
An alternate configuration uses a shared detector at the node but does not use WDM in the QAM circuit before the optical signals carrying the analog and QAM signals are combined. In that case, the noise contribution in the analog spectrum due to second-order intermod products (C/CIN) would be restricted to that associated with fiber dispersion, and net analog C/N would improve to 50.9 dB, which might be acceptable under some circumstances. Given that C/CIN degrades as the square of the length of the path, the performance would likely be acceptable for the relatively short paths between hubs and nodes in headend-hub-node architectures if the combining happened at the hub.
Here are some possible remedies for circumstances where the performance is unacceptable.
• Restrict the QAM spectrum to less than 54 MHz (so that all the second-order products fall below channel 2).
• Give up using a common detector: Use separate detectors at the node, and place a high-pass filter following the QAM detector and a low-pass filter following the analog detector before combining the RF spectra. In the example analyzed, the filter must suppress the second-order intermodulation products at 270 MHz and below by at least 30 dB to avoid significant contribution to total C/N.
• Avoid the use of WDM to transmit multiple QAM spectra ahead of the analog/QAM optical combining.
• Purchase DWDM demultiplexers with flatter response.
• Use externally modulated transmitters for the QAM signals, to eliminate chirp.
13.7.2 Postdetection Discrete Distortion Product Addition
In the usual common-detector configuration, a common spectrum of signals, primarily analog video, uses the lower part of the spectrum and some combination of QAM signals uses the upper part of the spectrum, as discussed earlier. The analog link, considered alone, will include both second-order (CSO) and third-order (CTB) discrete product clusters, which will extend above the analog spectrum. When using a common detector, there is no opportunity to low-pass filter the analog spectrum, with the result that those components will show up as interfering carriers in the QAM spectrum.
Here are the analog components that must be considered:
• Those due to nonlinearity in the optical transmitter/receiver combination
• CSO due to self-phase modulation interacting with fiber chromatic dispersion (discussed in Section 12.4.7)
• If relevant, CSO due to directly modulated DFB transmitter chirp interacting with fiber chromatic dispersion (discussed in Section 12.6.3)
• Clipping distortion products (discussed in Section 12.10.3)
• If relevant, CSO due to directly modulated DFB transmitter chirp interacting with WDM demux in-channel response slope (discussed in Section 13.4.5)
In estimating the probable link performance, it is necessary to consider how the effects add. There is no obvious correlation between residual transmitter/receiver nonlinearities and other effects. The three CSO effects, on the other hand, will either be in phase or directly opposite in phase (depending on the direction of the response slope of the WDM demux). While the probability that clipping will occur is fairly predictable, the magnitude and polarity of individual clipping distortion products are very difficult to predict. The most conservative approach is to assume in-phase addition of all calculable products and thus a “20 log” combination.
Having estimated the worst-channel CTB and CSO products among the analog carriers, Section 10.3.3 discussed the number of products falling in each channel. In the case of CSO products, Equation (10.25) can be used to calculate the number of products in each channel, including above the analog spectrum, and it can be assumed that the number of third-order products will be greatest near the middle of the analog spectrum and that the greatest magnitude of CTB distortion will fall higher in the spectrum. Knowing the worst-case distortion and the number of distortion products as a function of frequency, the magnitude of C/CTB and C/CSO distortion in any channel can be calculated by assuming that the distortion magnitude will vary as “10 log n,” where n is the number of products in that channel. Finally, the ratio of digital carrier to analog C/CSO or C/CTB products will be lower (worse) than the foregoing, by the ratio of analog signal levels to QAM signal levels in the combined RF spectrum (typically 6 dB).
Only the upper-side CSO products (2.5 MHz above the lower channel boundary) need be considered because only those products extend above the analog spectrum and because the lower-side products fall between standard channel boundaries. CTB products will fall 1.25 MHz above the lower channel boundary.
If we look at the previous example of a 30-km optical link and assume that the analog signals, occupying 50–550 MHz, modulate an externally modulated transmitter operating in the 1550-nm range with a launch power of +17 dBm, we get the following contributions to distortion:
• The transmitter/receiver pair will typically generate upper-side C/CSO and C/CTB of 65 dB on the most affected channels.
• Self-phase modulation will interact with the fiber to produce C/CSO at a level of about 70 dB.
At worst, the CSO effects will add on a voltage basis to produce a total C/CSO of 61 dB at the highest analog channel. Assuming the digital spectrum occupies 600–870 MHz, the level at the lowest digital channel will be 3.7 dB lower relative to the analog carriers (from Equation (10.25) and assuming that CSO varies as 10 log(n), where n is the number of high-side products) but will be higher relative to the QAM signals that are run at 6-dB-lower levels than analog, giving a net C/CSO in the lowest QAM channel of 58.7 dB.
The analog CTB will be highest somewhere above the center of the analog spectrum and fall off by approximately 2 dB at the upper edge of the analog spectrum and by about 3 dB at the lowest QAM channel. As with CSO, however, we need to account for the 6-dB difference in levels between analog and QAM signals, giving us a net C/CTB for the lowest QAM channel of about 62 dB.
Given a typical end-of-line C/(N + I) spec of 40 dB, the levels of CTB and CSO products resulting from use of a common detector are seldom a problem, provided externally modulated analog transmitters are used.
13.8 Summary of WDM Link Performance
Wavelength-division multiplexing has become standard in the engineering of cable television and similar networks because it facilitates the delivery of switched services to small groups of customers. It does this by allowing the transport of many independent signals over shared fibers and through shared optical amplifiers.
Unfortunately, optical signals on separate wavelengths interact as they travel through the fiber, and those interactions, sometimes in conjunction with discrete optical components in the circuit, generate various levels of crosstalk. Depending on the parameters of a given link, these mechanisms can have a serious effect on recovered RF signal quality. As our analysis shows, the quality of discrete components in general, and of the wavelength demultiplexer in particular, is typically the limiting factor in achieving acceptable low levels of crosstalk interference.
The analysis also shows that the achievable quality for 16-wavelength DWDM circuits with lengths approaching 30 km will not be acceptable for analog video but will be adequate for at least 256 QAM modulated signals with adequate component quality.
1. Bernard Eichenbaum, Coarse WDM Applications, Architectures, and Scalability for HFC and FTTH Digital Broadband Access, Proceedings Manual and Collected Technical Papers, Cable-Tec 2002 Expo, SCTE, Exton, PA, June 2002, pp. 19–38.
2. New Global Standard Set for Metro Networks, IEEE Spectrum, August 2002, pp. 21, 24.
3. For a brief, nonmathematical summary comparing wavelength multiplexer technologies, see Schlomo Ovadia, Broadband Cable TV Access Technologies. Prentice-Hall, Upper Saddle River, NJ, 2001, Sec. 6.1.1.
4. Based on data sheets for current products from Scientific Atlanta and Arris. (both located in Atlanta, Georgia).
5. Much of the material in this section related to XPM, OKE-PDL, and SRS is based on the excellent and clearly explained work of M. R. Phillips (sometimes copublished with D. M. Ott), various of whose papers covering optical cross modulation are referenced in subsequent endnotes.
6. K. Y. Wong et al., Nonlinear Crosstalk Suppression in a WDM Analog Fiber System by Complementary Modulation of Twin Carriers, OFC2001 conference, Optical Society of America, 2000, pp. WV5-1 – WV5-3.
7. M. R. Phillips and D. M. Ott, Crosstalk Caused by Nonideal Output Filters in WDM Lightwave Systems. IEEE Photonics Technology Letters, Vol. 12, No. 8, August 2000.
8. Mary R. Phillips and Daniel M. Ott, Crosstalk Due to Optical Fiber Nonlinearities in WDM CATV Lightwave Systems. Journal of Lightwave Technology, Vol. 17, No. 10, October 1999.
9. Ibid, p. 1788.
10. Ibid, p. 1790.
11. Kyo Inoue, Four-Wave Mixing in an Optical Fiber in the Zero-Dispersion Wavelength Region. Journal of Lightwave Technology, Vol. 10, No. 11, IEEE, November 1992, pp. 1553–1561.
12. James J. Refi, Optical Fibers for Optical Networking, Bell Labs Technical Journal, January-March 1999, pp. 246–261.
13. M. R. Phillips, Crosstalk in an Eight-Wavelength WDM Analog Lightwave System: Measurement and Analysis. Optical Fiber Communication Conference and Exhibit, 2001, OFC 2001, Vol. 3, pp. WCC1, 1–3.
14. C. Y. Kuo and E. E. Bergmann, Erbium-Doped Fiber Amplifier Second-Order Distortion in Analog Links and Electronic Compensation, IEEE Photonics Technology Letters, Vol. 3, No. 9, September 1991, pp. 829–831.
15. Section 17.3 of the Recommended Practices for Measurements on Cable Television Systems, NCTA, 2002, contains an excellent tutorial on this subject. It shows that the probability of exceeding a given peak-to-rms voltage ratio is essentially unchanged as the number of summed signals increases beyond 10.