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2 Wavelength Multiplexing: WWDM, CWDM, and DWDM

2 Wavelength Multiplexing: WWDM, CWDM, and DWDM

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128 CHAPTER 5 Wavelength Division Multiplexing

1530 is “S-Band”; 1530 through 1565, including the lowest attenuation wavelengths
and most currently used close-spaced wavelengths, is “C-Band”; and 1565 through
1625 is “L-Band.”
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.
Various abbreviations 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 at 1550 nm. The
wavelengths are 1470, 1490, . . . 1610 nm and include all of the S-, C-, and L-Bands.
Generally, this scheme is referred to as coarse 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 as discussed in Chapter 4. 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, 100-GHz,
or 50-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

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.

5.2 Wavelength Multiplexing: WWDM, CWDM, and DWDM 129


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 and cross-phase modulation are both maximum
when the signals travel at nearly the same velocity. 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 wavelength
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.

Min loss


Water peak

Relationship of wavelength bands.






λ (nm)

Figure 5.1 shows the relationship of bands, CWDM channels, and DWDM channels.
Cable systems using linear DWDM technology generally use 200-GHz-spaced channels from among the set of 20 listed in Table 5.1, though a few vendors offer 100GHz spacing. For network designs that use fewer than 20 of the listed wavelengths,
various vendors have chosen to offer different subsets. Most offer C21 through C35

130 CHAPTER 5 Wavelength Division Multiplexing

Table 5.1 Commonly Used DWDM Channels

ITU channel designation









































as the first eight, but one vendor offers C39 through C53 as the second eight,
another offers C45 through C59, and a third has chosen to offer C37 through
C51. This is obviously inconvenient for operators who wish to have multiple
sources for optical transmitters and DWDM multiplexers.

Constructing WDM systems requires the use of some components not required
for single-wavelength links and tighter control over the specifications of other

5.3 Components for WDM Systems 131

5.3.1 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 (e.g., 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 to 1.5 dB higher, whereas a 2-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 to 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 wavelengthspecific multiplexers.
At the receiving end, however, there is no alternative to using wavelengthspecific 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.2 Table 5.2 shows typical performance specs for 16- or 20-wavelength, 200-GHz channel-spacing filters.
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.

Table 5.2 Performance Specifications
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

132 CHAPTER 5 Wavelength Division Multiplexing

5.3.2 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 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 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 À6 dBm to þ6 dBm. Typical
devices offer a maximum total power output of up to 20 dBm, gain of 17 to 26 dB,
and a noise figure of 5 to 5.5 dB.3
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’s modulated linewidth (the usual case), the result will be CSO degradation in the demodulated RF signals. 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 and multiplexer=demultiplexer 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.

Figure 5.2 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,

5.4 WDM-Specific Design Factors 133

RF input 1

RF input n

RF input 1
RF spectra)
RF input n

multiplexer or
Optical amplifier



RF output 1


RF output n

multiplexer or
Optical amplifier


RF output


Separate transmitters and receivers (a) versus separate transmitters and a shared receiver (b) in
WDM applications.

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
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
(e.g., 50 to 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 10.
In the first application, the following performance parameters must be considered, in addition to those discussed in Chapter 4:

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 4, 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

134 CHAPTER 5 Wavelength Division Multiplexing

optical Kerr effect, or OKE). In multiple-wavelength systems, these variations lead
to various inter-wavelength 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 exhibit incremental gain
or loss to other signals through a process known as stimulated Raman scattering

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 among signals at other wavelengths and RF frequencies that fall in the
RF spectrum of the first link.


The final balancing of RF levels among those transmitted on each link will be a
combination of the optical modulation index (OMI) and the relative optical
received levels, and thus cannot be adjusted at the receiving site. When WWDM
is used in a split-band downstream transmission, the difference in attenuation at
1310 versus 1550 nm will make level balancing dependent on the length of the
fiber, and thus prevent two links of different lengths fed by a common transmitter
from both being properly balanced.

Each of these will be considered in detail later.

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 optical network
segment that may include multiplexers, fiber, amplifiers, and=or demultiplexers.4
Some of the calculations discussed later are rather complex or, at the least, contain so many terms that they require careful manipulation. To make it easier, the
Excel workbook entitled Optical Crosstalk-Individual Mechanisms.xls, available
for download at www.elsevierdirect.com/companions/9780123744012, provides

5.5 Crosstalk Mechanisms 135

easy-to-use, parameterized calculations of major crosstalk mechanisms affecting
the performance of a multi-wavelength link. These degradations can be added to
the single-wavelength calculations discussed in the previous chapter (most of which
are in the spreadsheet entitled Single-Wavelength Performance Calculator.xls) to
determine total link performance.

5.5.1 Imperfect Demultiplexer Wavelength Isolation
Imperfect multiplexer isolation affects the amount of light from each source that
shows up at the wrong output port(s), but otherwise it has no effect on link operation.
Imperfect demultiplexer isolation, however, allows some light from undesired wavelengths to impinge on the detector along with light at the desired wavelength. This is
not a cross-modulation effect, but does contribute to total crosstalk performance.
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 modulated RF signals carried on 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 noise-like 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
C=IISOLATION ¼ À10 log 2 Â 10ÀA=5 þ ðn À 3Þ Â 10ÀB=5
For the highest and lowest wavelengths, there is only one adjacent wavelength,
so the equation becomes
C=IISOLATION ¼ À10 log 10ÀA=5 þ ðn À 2Þ Â 10ÀB=5
C=IISOLATION ¼ the ratio of the desired to the total undesired RF signal power in the
demodulated spectrum of the victim optical carrier in dB
A ¼ the adjacent optical channel isolation of the WDM demultiplexer in dB
B ¼ the nonadjacent optical channel isolation of the WDM demultiplexer in dB
n ¼ the number of optical carriers

136 CHAPTER 5 Wavelength Division Multiplexing

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.

5.5.2 Cross-Phase Modulation Combined with Fiber Dispersion
Recall from Chapter 4 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

B 4pn2 bO2 P20 rXPM C
C À 10 log 1 þ eÀ2az À 2eÀaz ð1 À az Þ
C=IXPMÀD ðdBÞ ¼ À20 logB
l2 A a2 þ ðd12 OÞ2

2Ã 2
cosðd12 Oz Þ À 2z½a þ d12 Oe
sinðd12 Oz ފ þ a þ ðd12 OÞ z
where all variables are in a consistent set of units. In meter-kilogram-second (MKS)
C=IXPM ¼ the ratio, in dB, of desired to undesired RF signal powers in the
demodulated spectrum of the victim optical carrier (assuming equal
optical modulation indices of both optical signals)
n2 ¼ the nonlinear refractive index of the fiber, typically 2.6 Â 10À20 m2=W
b ¼ À(l22D)=(2pc)
l1 ¼ the wavelength of the victim optical carrier, generally between
1.53 Â 10À6 and 1.56 Â 10À6 m
l2 ¼ the wavelength of the interfering modulated optical carrier, in meters
D ¼ the dispersion coefficient of the fiber in sec=m2 (For standard fiber
near 1550 nm, this is typically 17 ps=nm-km ¼ 17 Â 10À6 sec=m2.)

5.5 Crosstalk Mechanisms 137

e ¼ the speed of light in a vacuum ¼ 3 Â 108 m=sec
O ¼ the frequency of the modulating RF signal in radians ¼ 2pfI, where fI is
the modulating frequency in Hz
P20 ¼ the power level of the modulated interfering optical signal, in watts
rXPM ¼ the effective polarization overlap between the interfering and the victim
optical carriers (This varies from 1 for copolarized signals to 1=3 for crosspolarized signals. At 45 it is 2=3.)
A ¼ the effective mode cross-sectional area of the fiber core, about
80 Â 10À12 m2 for non-dispersion-shifted fibers and 50 Â 10À12 m2 for
dispersion-shifted fibers
a ¼ the fractional power attenuation of the fiber per meter of length
¼ 1 À 10À(a0=10,000), where a0 is the attenuation in dB=km (A typical
value of a0 for standard fiber at 1550 nm is 0.21 dB=km, for which
a ¼ 4.835 Â 10À5 per meter.)
z ¼ the length of the shared fiber, in meters
d12 ¼ the group velocity mismatch between the interfering and victim optical
carriers % D(l1 À l2)
Converting this to more common engineering units and assuming operation near
1550 nm, we get

À 10 log 1 þ eÀ2X À 2eÀX
C=IXPMÀD ðdBÞ ¼ 459:5 À 2PI À 20 log
A½ X þ Y Š
ð1 À X Þ cosðY Þ À 2X À 2YeÀX sinðY Þ þ X 2 þ Y 2 Þ


PI ¼ the launch power of the interfering optical carrier in dBm
fRF ¼ the modulation frequency in MHz
D ¼ the fiber dispersion in ps=nm-km (For non-dispersion-shifted fiber near
1550 nm this is typically 17.)
L ¼ the length of the fiber in km
rXPM ¼ 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 ¼ the effective cross-sectional area of the fiber core. For non-dispersionshifted fiber this is typically 80 Â 10À12 m2
a ¼ the fractional power attenuation of the fiber per km ¼ 1À10À(a0=10),
where a0 is the attenuation in dB=km (A typical value of a0 for standard
fiber at 1550 nm is 0.21 dB=km, for which a ¼ 0.047.)
Dl ¼ the difference in wavelength between the interfering and victim optical
carriers in nm
X ¼ the “loss parameter” aL (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 ¼ the “walk-off parameter” D Dl(2pfRF)L (For fiber with a dispersion of
17 ps=nm-km, this is 1.068 Â 10À4 Dl fRF L.)

138 CHAPTER 5 Wavelength Division Multiplexing

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 1dB 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 copolarized 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 5.3 shows the maximum and minimum expected crosstalk from this
mechanism for a single copolarized interfering carrier whose launch power is
þ7 dBm and whose optical carrier is 1.5 nm away from the victim carrier, with both
transmitted through 30 km of standard fiber.







50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
Frequency (MHz)

C=I due to cross-phase modulation interacting with fiber dispersion.