Optical Networks: A Practical Perspective - Part 34 pptx

Let P denote the average received signal power and 6 P the average received crosstalk power from a single other crosstalk channel.. Here, dst = {0, 1}, depending on whether a 0 or 1 is

Figure 5.9 Sources of intrachannel crosstalk (a) A cascaded wavelength demultiplexer and a mul- tiplexer, and (b) an optical switch

The crosstalk penalty is highest when the state of polarization (SOP) of the crosstalk signal is the same as the SOP of the desired signal In practice, the SOPs vary slowly with time in a system using standard single-mode fiber (nonpolarization preserving) Similarly, the crosstalk penalty is highest when the crosstalk signal is exactly out of phase with the desired signal The phase relationship between the two signals can vary over time due to several factors, including temperature variations

We must, however, design the system to work even if the two SOPs happen to match and the signals are exactly out of phase Thus, for the calculations in this section, we will assume that the SOPs are the same and compute the penalty when the signals are out of phase, which is the worst-case scenario

The power penalty due to intrachannel crosstalk can be determined as follows Let P denote the average received signal power and 6 P the average received crosstalk power from a single other crosstalk channel Assume that the signal and crosstalk are at the same optical wavelength The electric field at the receiver can be written as

E(t) = ~/2Pds(t) cos[2rCfct + ~bs(t)] + ~2 ~Pdx(t) cos[2rrfct + ~bx(t)]

Here, ds(t) = {0, 1}, depending on whether a 0 or 1 is being sent in the desired channel; dx(t) = {0, 1}, depending on whether a 0 or 1 is being sent in the crosstalk channel; fc is the frequency of the optical carrier; and 4~,(t) and Ckx(t) are the ran- dom phases of the signal and crosstalk channels, respectively It is assumed that all channels have an ideal extinction ratio of oo

5.6 Crosstalk 3 0 1

5 6 2

The photodetector produces a current that is proportional to the received power within its receiver bandwidth This received power is given by

P~ = Pds(t) + ~Pdx(t) + 2x/~Pds(t)dx(t)cos[cks(t) -4~x(t)] (5.10) Assuming ~ << 1, we can neglect the ~ term compared to the x/F term Also the worst case above is when the cos(.) = - 1 Using this, we get the received power during a

1 bit as

Pr(1) = P(1 - 2v/~)

and the power during a 0 bit as

Pr (0) = o

First consider the case where the detection is limited by receiver thermal noise, which

is independent of the received power Using (5.3), the power penalty for this case is PPsig-indep - 10 log(1 - 2x/~-) (5.11)

In amplified systems, or in systems with APD receivers, the dominant noise compo- nent is signal dependent (see Section 5.2) For this case, or1 (x x/P and or0 << Crl Using (5.4), the power penalty in this case becomes

PPsig-dep 5 log(1 2,ff-~-) (5.12)

If there are N interfering channels, each with average received power ~i P, then

in (5.11) and (5.12) is given by x/ff Z i = I ~ N (see Problem 5.12)

Figure 5.10 shows the crosstalk penalties plotted against the crosstalk level for intrachannel and interchannel crosstalk, which we will consider next If we allow

a 1 dB penalty with signal-independent noise, then the intrachannel crosstalk level should be 20 dB below the desired signal

Interchannel Crosstalk

Interchannel crosstalk can arise from a variety of sources A simple example is

an optical filter or demultiplexer that selects one channel and imperfectly rejects the others, as shown in Figure 5.11 (a) Another example is in an optical switch, switching different wavelengths (shown in Figure 5.11(b)), where the crosstalk arises because

of imperfect isolation between the switch ports

Estimating the power penalty due to interchannel crosstalk is fairly straightfor- ward If the wavelength spacing between the desired signal and the crosstalk signal

is large compared to the receiver bandwidth, (5.10) can be written as

Pr = Pds (t) + ~ Pdx (t)

Figure 5.10 Thermal noise limited intrachannel and interchannel crosstalk power penalties as a function of crosstalk level, -10log 6 Signal-spontaneous noise limited penalties would be reduced by half the values shown in the figure

Figure 5.11 Sources of interchannel crosstalk (a) An optical demultiplexer, and (b) an optical switch with inputs at different wavelengths

Therefore, in the worst case, we have

Pr(1)= P,

5.6 Crosstalk 303

5.6.3

5.6.4

and

Pr(O) = { P

Using (5.3), the power penalty for the thermal noise limited case is given by

For systems dominated by signal-dependent noise, the penalty is obtained from (5.4)

a s

If there are N interfering channels, each with average received power {i P, then ~ in (5.13) and (5.14) is given by ~ - ~/N_ 1 ~i (see Problem 5.12)

Consider an unamplified WDM system with a filter receiving the desired channel and rejecting the others The main crosstalk component usually comes from the two adjacent channels, and the crosstalk from the other channels is usually negligible Assuming a 0.5 dB crosstalk penalty requirement, the adjacent channel suppression must be greater than 12.6 dB

Crosstalk in Networks

Crosstalk suppression becomes particularly important in networks, where a signal propagates through many nodes and accumulates crosstalk from different elements at each node Examples of such elements are muxes/demuxes and switches In order to obtain an approximate idea of the crosstalk requirements, suppose that a signal accu- mulates crosstalk from N sources, each with crosstalk level ~s This neglects the fact that some interfering channels may have higher powers than the desired channel Net- works are very likely to contain amplifiers and to be limited by signal-spontaneous beat noise Figure 5.12 plots the power penalties calculated from (5.12) and (5.14) For example, if we have 10 interfering equal-power crosstalk elements, each produc- ing intrachannel crosstalk, then we must have a crosstalk suppression of below 35

dB in each element, in order to have an overall penalty of less than I dB

Bidirectional Systems

In a bidirectional transmission system, data is transmitted in both directions over a single fiber, as shown in Figure 5.13 Additional crosstalk mechanisms arise in these systems Although the laws of physics do not prevent the same wavelength from being used for both directions of transmissions, this is not a good idea in practice because of reflections A back-reflection from a point close to the transmitter at one

Figure 5.12 Signal-spontaneous noise limited intrachannel and interchannel crosstalk penalties as a function of crosstalk level -10 log 6s in a network The parameter N denotes the number of crosstalk elements, all assumed to produce crosstalk at equal powers

Figure 5.13 A bidirectional transmission system

end, say, end A, will send a lot of power back into A's receiver, creating a large amount of crosstalk In fact, the reflected power into A may be larger than the signal power received from the other end B Reflections within the end equipment can

be carefully controlled, but it is more difficult to restrict reflections from the fiber link itself For this reason, bidirectional systems typically use different wavelengths

in different directions The two directions can be separated at the ends either by using an optical circulator or a W D M mux/demux, as in Figure 5.14 (If the same wavelength must be used in both directions, one alternative that is sometimes used

in short-distance access networks is to use time division multiplexing where only one end transmits at a time.)

If a W D M mux/demux is used to handle both directions of transmission, crosstalk can also arise because a signal at a transmitted wavelength is reflected within the mux

5.6 Crosstalk 30~

Figure 5.14 Separating the two directions in a bidirectional system: (a) using a wave- length multiplexer/demultiplexer, and (b) using an optical circulator Both methods can introduce crosstalk, as shown by dashed lines in the figure

into a port that is used to receive a signal from the other end, as in Figure 5.14(a) The mux/demux used should have adequate crosstalk suppression to ensure that this

is not a problem Likewise, if an optical circulator is used, crosstalk can arise because

of imperfect isolation in the circulator, as shown in Figure 5.14(b) We have to be careful about these effects when designing bidirectional optical amplifiers as well

5.6.5 Crosstalk Reduction

The simplest (and preferred) approach toward crosstalk reduction is to improve the crosstalk suppression at the device level; in other words, let the device designer worry about it The network designer calculates and specifies the crosstalk suppression required for each device based on the number of such cascaded devices in the network and the allowable penalty due to crosstalk However, there are a few architectural approaches toward reducing specific forms of crosstalk, particularly crosstalk arising

in optical switches

The first approach is to use spatial dilation, which is illustrated in Figure 5.15 Figure 5.15(a) shows a 2 x 2 optical switch with crosstalk 6 To improve the crosstalk suppression, we can dilate the switch, as shown in Figure 5.15(b), by adding some unused ports to it N o w the crosstalk is reduced to 62 The drawbacks of dilation are that it cannot be achieved without a significant increase in the number of switches Usually, the number of switches is doubled

Another approach to reduce switch crosstalk in a W D M network is to use wave- length dilation in the switches This is particularly useful if a single switch is to handle

Figure 5.15 Using spatial dilation to reduce switch crosstalk (a) A simple 2 x 2 switch (b) A dilated version of a 2 x 2 switch

Figure 5.16 Using wavelength dilation to reduce switch crosstalk MZI denotes a Mach-Zehnder interferometer that separates the channels into two groups or combines them

multiple wavelengths, such as the acousto-optic tunable filter of Section 3.3.9 To reduce the interchannel crosstalk, you can use two switches instead of one, as shown

in Figure 5.16 The first switch handles the odd-numbered channels, and the second the even-numbered channels This effectively doubles the channel spacing as far as crosstalk is concerned Again the cost is that twice as many switches are required

In the extreme case of wavelength dilation, we can have a separate switch for each wavelength

The previous methods have dealt mainly with switch crosstalk A simple method

to reduce crosstalk in the mux/demux of Figure 5.9 is to add an additional filter

5.6 Crosstalk 3 0 7

Figure 5.17 Bandwidth narrowing due to cascading of two filters

Mux 1

Mux 2

Figure 5.18 Wavelength misalignment between two mux/demuxes

for each wavelength between the demux and mux stages The extra filter stage pro- duces an additional level of isolation and improves the overall crosstalk performance dramatically, but of course adds to the cost of the unit

5.6.6 Cascaded Filters

Networks are likely to have several mux/demuxes or filters cascaded When two mux/demuxes or filters are cascaded, the overall passband is much smaller than the passbands of the individual filters Figure 5.17 shows this effect The required

wavelength stability and accuracy in these systems therefore goes up with the number

of cascaded stages

A related problem arises from the accuracy of wavelength registration in these mux/demuxes If the center wavelengths of two units in a cascade are not identical (see Figure 5.18), the overall loss through the cascade for the desired signal will

be higher, and the crosstalk from the adjacent channels could also be higher If we are concerned only with one channel, we could align the center wavelengths exactly

by temperature-tuning the individual mux/demuxes However, other channels could become even more misaligned in the process (tuning one channel tunes the others

as well) In addition, the lasers themselves will have a tolerance regarding their center wavelength In a cascaded system, wavelength inaccuracies cause additional power penalties due to added signal loss and crosstalk (see Problems 5.18 and 5.19)

Dispersion is the name given to any effect wherein different components of the transmitted signal travel at different velocities in the fiber, arriving at different times

at the receiver A signal pulse launched into a fiber arrives smeared at the other end

as a consequence of this effect This smearing causes intersymbol interference, which

in turn leads to power penalties Dispersion is a cumulative effect: the longer the link, the greater the amount of dispersion

Several forms of dispersion arise in optical communication systems The impor- tant ones are intermodal dispersion, polarization-mode dispersion, and chromatic dispersion Of these, we have already studied intermodal dispersion and chromatic dispersion in Chapter 2 and quantified the limitations that they impose on the link length and/or bit rate

Intermodal dispersion arises only in multimode fiber, where the different modes travel with different velocities Intermodal dispersion was discussed in Section 2.1 The link length in a multimode system is usually limited by intermodal dispersion and not by the loss Clearly intermodal dispersion is not a problem with single-mode fiber

Polarization-mode dispersion (PMD) arises because the fiber core is not perfectly circular, particularly in older installations Thus different polarizations of the signal travel with different group velocities PMD is proving to be a serious impediment in very high-speed systems operating at 10 Gb/s bit rates and beyond We discuss PMD

in Section 5.7.4

5.7 Dispersion 309

5.7.1

The main form of dispersion that we are concerned with is chromatic dispersion,

which has a profound impact in the design of single-mode transmission systems (so much so that we often use the term "dispersion" to mean "chromatic dispersion") Chromatic dispersion arises because different frequency components of a pulse (and also signals at different wavelengths) travel with different group velocities in the fiber, and thus arrive at different times at the other end We discussed the origin

of chromatic dispersion in Section 2.3 Chromatic dispersion is a characteristic of the fiber, and different fibers have different chromatic dispersion profiles We dis- cussed the chromatic dispersion profiles of many different fibers in Section 2.4.9 As with other kinds of dispersion, the accumulated chromatic dispersion increases with the link length Chromatic dispersion and the system limitations imposed by it are discussed in detail in the next two sections

Chromatic Dispersion Limits" NRZ Modulation

In this section, we discuss the chromatic dispersion penalty for NRZ modulated signals We will consider RZ modulated signals in Section 5.7.2

The transmission limitations imposed by chromatic dispersion can be modeled

by assuming that the pulse spreading due to chromatic dispersion should be less than

a fraction 6 of the bit period, for a given chromatic dispersion penalty This fraction has been specified by both ITU (G.957) and Telcordia (GR-253) For a penalty of

1 dB, ~ = 0.306, and for a penalty of 2 dB, ~ = 0.491 If D is the fiber chromatic dispersion at the operating wavelength, B the bit rate, Ak the spectral width of the transmitted signal, and L the length of the link, this limitation can be expressed as

D is usually specified in units of ps/nm-km Here, the ps refers to the time spread

of the pulse, the nm is the spectral width of the pulse, and km corresponds to the link length For standard single-mode fiber, the typical value of D in the C-band

is 17 ps/nm-km For this value of D, ~ 1.55 #m, and 6 0.491 (2 dB penalty), (5.15) yields the condition BL < 29 (Gb/s)-km This limit is plotted in Figure 5.19 Thus even at a bit rate of 1 Gb/s, the link length is limited to < 30 km, which is a severe limitation This illustrates the importance of (1) using nearly monochromatic sources, for example, DFB lasers, for high-speed optical communication systems, and (2) devising methods of overcoming chromatic dispersion

Narrow Source Spectral Width

We now consider the case of using sources with narrow spectral widths Even for such a source, the spectral width of the transmitted signal depends on whether it is