b You have another transmitter that operates at a wavelength of 1.3/zm, has a spectral width of 2 nm, and an output power of i mW.. Compute the dispersion-limited transmission distance f
Trang 15.3
5.4
5.5
(a) You have a transmitter that operates at a wavelength of 1.55/~m, has a spec- tral width of I nm, and an output power of 0.5 mW The receiver requires
- 3 0 dBm of input power in order to achieve the desired bit error rate What
is the length of the longest link that you can build?
(b) You have another transmitter that operates at a wavelength of 1.3/zm, has
a spectral width of 2 nm, and an output power of i mW Assume the same receiver as before What is the length of the longest link that you can build? (c) You have the same 1.3 # m transmitter as before, and you must achieve an SNR of 30 dB using an APD receiver with a responsivity of 8 A/W, a gain of
10, an excess noise factor of 5 dB, negligible dark current, a load resistance of
50 f2, and an amplifier noise figure of 3 dB Assume that a receiver bandwidth
of B/2 Hz is sufficient to support a bit rate of B b/s What is the length of the longest link you can build?
(d) Using the same 1.3/~m transmitter as before, you must achieve an SNR of
20 dB using a pin receiver with a responsivity of 0.8 A/W, a load resistance
of 300 f2, and an amplifier noise figure of 5 dB Assume that a receiver bandwidth of B/2 Hz is sufficient to support a bit rate of B b/s What is the length of the longest link you can build?
Compute the dispersion-limited transmission distance for links with standard single-mode fiber at 1550 nm as a function of the bit rate (100 Mb/s, 1 Gb/s, and
10 Gb/s) for the following transmitters: (a) a Fabry-Perot laser with a spectral width
of 10 nm, (b) a directly modulated DFB laser with a spectral width of 0.1 nm, and (c)
an externally modulated DFB laser with a spectral width of 0.01 nm Assume that the modulation bandwidth equals the bit rate and the dispersion penalty is 2 dB Assume that N R Z modulation is used
Repeat Problem 5.3 for NZ-DSF assuming a dispersion parameter of 5 ps/nm-km Consider a length L of step-index multimode fiber having a core diameter of 5 0 / z m and a cladding diameter of 200/zm The refractive indices of the core and cladding are 1.50 and 1.49, respectively A fixed-wavelength, 1310 nm DFB laser (operating
at 0 dBm) is used at one end of the fiber to serve as a 155.52 Mb/s transmitter source
At the far end, a photodetector is used as a receiver Assume that N R Z modulation
is used
(a) Draw and label a diagram that illustrates the above configuration
(b) What would be the corrugation period of the DFB laser at this wavelength? (c) Compute the numerical aperture for this fiber
(d) What would be the maximum acceptable fiber length when operating at this bit rate?
(e) Assuming an attenuation of 0.40 dB/km, what would be the output power (in dBm) at the receive end of the fiber?
Trang 2Problems 3 51
5.6
5.7
5.8
(f) Assuming a perfectly efficient photodetector, what would be the resulting photocurrent?
(g) If we instead used single-mode fiber for this application, what would be the new requirement on its core diameter?
Note that this problem requires you to understand the material in Chapters 2, 3, and
4 as well
Consider a passive W D M link of length L, consisting of single-mode fiber into which five wavelengths are launched through an optical combiner such that the aggregate launch power at its output is 5 mW These five wavelengths are centered on the 193.1 THz ITU grid, with uniform 100 GHz interchannel spacing The transmitters all use directly modulated DFB lasers with a spectral width of 0.1 nm Each channel is transporting a SONET OC-48 (2.5 Gb/s) signal At the end of this link, the channels are optically demultiplexed and are each received by a direct detection pin receiver For this problem, neglect all losses and crosstalk associated with the W D M mux and demux Assume that N R Z modulation is used
(a) Draw and label a diagram illustrating this configuration
(b) Calculate the wavelengths (in nm, to two decimal places) associated with these five channels
(c) Calculate the average launch power per channel at the output of the W D M combiner
(d) Assuming O t d B - - 0.25 dB/km, D - 17 ps/nm-km, and D p M D - - 0.5 ps/k~/-k-mm, calculate the worst-case dispersion, PMD, and loss limits for this link (e) What is the maximum value of L meeting all of these requirements?
Consider a point-to-point link connecting two nodes separated by 60 km This link was constructed with standard single-mode fiber, and a 2.5 Gb/s system is deployed over the link The transmitter uses a directly modulated 1310 nm DFB laser The receiver uses perfectly efficient pin photodiodes, and we will assume, for this problem, that they can be modeled as ideal receivers The bit error rate requirement for this system is 10 -12 Assume l Y d B - - 0.4 dB/km and that N R Z modulation is used
(a) Draw and label a diagram illustrating this configuration
(b) Is this system loss limited or dispersion limited? Briefly explain your rea- soning
(c) What is the required receiver sensitivity (in mW and dBm)?
(d) What would be the resulting photocurrent?
(e) What would be the required launch power (in dBm)?
The link of Problem 5.7 is at full capacity, and we must design a solution that will enable capacity expansion and accommodate further growth After consid- ering the options, we determine that the most cost-effective solution is to add a
1550 nm point-to-point system over the existing set of fibers, thereby realizing a
Trang 35.9
5.10
5.11
5.12
5.13
5 1 4
two-wavelength (1310 nm/1550 nm) passive WDM configuration Assume that 3 dB couplers are used to combine the two signals just after the transmitters and separate the two signals just before the receivers The next step is to determine what bit rate can be supported by this 1550 nm system Assume that the 1550 nm transmitter uses
a directly modulated DFB laser (with spectral width of 0.1 nm) At 1550 nm, assume
(a) Draw and label a diagram illustrating this new configuration
(b) What is the launch power now required for the original 2.5 Gb/s 1310 nm system to maintain the same level of receiver performance?
(c) If we assume an ideal receiver with the s a m e 1 0 - 1 2 bit error rate performance for the 1550 nm system, determine the associated receiver sensitivities for both 2.5 Gb/s and 10 Gb/s signals
(d) Calculate bit rate limits based on loss, dispersion, and PMD for the new system
(e) Can 10 Gb/s be suitably transported by this new system? Briefly explain your reasoning
(f) For the 2.5 Gb/s and 10 Gb/s (if it is possible) line rates, calculate the required launch power to successfully transport the signal
Derive equation (5.4)
Show that the extinction ratio penalty in amplified systems limited by signal- spontaneous beat noise and spontaneous-spontaneous beat noise is
( ~ - 1 ~/r + 1)
PP = - 10 log
+ 1 , / 7 + 1 Assume that other noise terms are negligible
Consider the amplifier chain discussed in Section 5.5.3 Using equations (5.6) and (5.7), compute the steady-state values of Pout and G in a long chain of amplifiers Assume Gmax 35 dB, l - 120 km, c~ = 0.25 dB/km, nsp 2, psat 10 mW, and
B o - 50 GHz How do these values compare against the unsaturated gain Gmax and the output saturation power of the amplifier iDsat) 9 out" Plot the evolution of the signal power and optical signal-to-noise ratio as a function of distance along the link Derive equations (5.11), (5.12), (5.13), and (5.14) when there are N interfering signals rather than just one
Why is equation (5.24) an approximation? Derive a precise form of this equation Consider the WDM link shown in Figure 5.1 Each multiplexer and demultiplexer in- troduces crosstalk from adjacent channels that is C dB below the desired channel
Trang 4Problems 353
Figure 5.36 A node in a WDM network for Problems 5.16-5.19
5.15
5.16
5.17
(a) Compute the crosstalk at the output when N such stages are cascaded (b) What must C be so that the overall crosstalk penalty after five stages is less than 1 dB?
Consider a WDM system with W channels, each with average power P and extinction ratio P1/P0 = r Derive the interchannel crosstalk power penalty in (5.13) for this system compared to a system with ideal extinction and no crosstalk What should the crosstalk level be for a maximum 1 dB penalty if the extinction ratio is 10 dB? Consider the WDM network node shown in Figure 5.36 Assume the node has two inputs and two outputs The multiplexers/demultiplexers are ideal (no crosstalk), but each switch has a crosstalk level C dB below the desired channel Assume that
in the worst case, crosstalk in each stage adds coherently to the signal
(a) Compute the crosstalk level after N nodes
(b) What must C be so that the overall crosstalk penalty after five nodes is less than 1 dB?
Consider the WDM network node shown in Figure 5.36 Assume the node has two inputs and two outputs The mux/demuxes have adjacent channel crosstalk suppressions o f - 2 5 dB, and crosstalk from other channels is negligible The switches have a crosstalk specification o f - 4 0 dB How many nodes can be cascaded in a network without incurring more than a 1 dB penalty due to crosstalk? Consider only intrachannel crosstalk from the switches and the multiplexers/demultiplexers
Trang 55.18
5.19
5.20
5.21
5.22
Consider a W D M system with N nodes, each node being the one shown in Fig- ure 5.36 The center wavelength )~" for each channel in a mux/demux has an ac- curacy of +A~ nm around the nominal center wavelength )~c Assume a Gaussian passband shape for each channel in a mux; that is, the ratio of output power to input power, called the transmittance, is given by
(~_~.~)2 TR()~) - e 2,2
where cr is a measure of the channel bandwidth and U c is the center wavelength This passband shape is typical for an arrayed waveguide grating
(a) Plot the worst-case and best-case peak transmittance in decibels as a function
of the number of nodes N for cr = 0.2 nm, A~ = 0.05 nm Assume that the laser is centered exactly at )~c
(b) What should A)~ be if we must have a worst-case transmittance of 3 dB after
10 nodes?
Consider a system with the same parameters as in Problem 5.18 Suppose the W D M channels are spaced 0.8 nm apart Consider only crosstalk from the two adjacent channels Compute the interchannel crosstalk power relative to the signal power in decibels, as a function of N, assuming all channels are at equal power and exactly centered Compute the crosstalk also for the case where the desired channel is exactly centered at )vi, but the adjacent channels are centered at ~-i-1 q- A~, and ~.i+1 A)v Consider the simple add/drop element shown in Figure 3.14(b) Suppose we use another circulator instead of the coupler shown in the figure to add the wavelength This eliminates the loss due to the coupler Let the input power on the wavelength
to be dropped be - 3 0 dBm and the transmitted power on the added wavelength
be 0 dBm Suppose the grating has a reflectivity of 99% Compute the intrachannel crosstalk power arising from (a) leakage of the added wavelength into the dropped wavelength, and (b) leakage of the dropped wavelength into the added wavelength Assume that each circulator has a loss of I dB Will the element work?
Show that the optimum choice of the pulse width of an unchirped Gaussian pulse (with narrow spectral width) that minimizes the pulse-broadening effects of chro- matic dispersion over a fiber of length L is
To~ p t - v//~2L
If 0 <_ E < 1 is the power-splitting ratio between the two polarization components, the random power penalty in decibels due to PMD is related to the random differential
Trang 6Problems 355
5.23
5.24
5.25
5.26
time delay as
Ar 2 PP(dB) - o t - ~ ~ ( 1 - ~ ) , where T is the bit period and c~ is a constant depending on the pulse shape and takes values in the range 12-25 f.qr commonly studied pulse shapes [KK97a, Chapter 6] Note that we have already taken logarithms in the above equation Thus the random variable PP is a function of the random variables Ar and ~ Assuming a Maxwellian distribution for Ar with mean (At) and a uniform distribution for 6, show that
PP has an exponential distribution What is the mean value of PP? What is the probability that PP > 1 dB?
Neglecting the depletion of the pump wave, solve (2.14) and (2.15) to obtain the evolution of the SBS pump and Stokes waves
Compute the SBS threshold power for the following systems" (a) a single-channel system using a Fabry-Perot laser with 10 lines, each line having a modulated line width of 1 GHz, (b) a multichannel system with a DFB laser having a modulated line width of 1 GHz, and (c) same as (b) except that the line width is 10 GHz
Consider (5.27) as expressing TL, the pulse width after a distance L, in terms of the initial pulse width To
(a) As in the case of chromatic dispersion, there is an optimum initial pulse width (for a given link length L) Find an expression for this optimum initial pulse width
(b) Assuming a pulse with this optimum width is used, find the maximum link length for a power penalty of 1 dB Note that this power penalty is due to both SPM and chromatic dispersion
(c) Assume that a pulse of the same initial width is used but that the link has no SPM but only chromatic dispersion Using (2.13), calculate the pulse width
at the end of the link and hence the penalty due to chromatic dispersion The remainder of the 1 dB penalty is due to SPM Note that the SPM penalty can
be negative for some combinations of link, dispersion, and nonlinear lengths This occurs when the initial pulse compression due to the chirping caused by SPM results
in a narrower pulse at the end of the link, compared to the case when SPM is absent and only chromatic dispersion is present
You are required to design a four-wavelength transmission system operating over dispersion-shifted fiber The four wavelengths are to be placed in a band from 193.1 THz to 194.1 THz The possible slots are spaced 100 GHz apart in this band Pick the four wavelengths carefully so that no four-wave mixing component falls on any of the chosen wavelengths
Trang 75.27
5.28
5.29
5.30
Compute and plot the four-wave mixing limit on the transmit power per channel for a WDM system operating over NZ-DSF Assume that the channels are equally spaced and transmitted with equal power, and the maximum allowable penalty due
to FWM is 1 dB For the fiber, assume the dispersion parameter D = 3 ps/nm-km in the middle of the transmitted band of channels, and the slope of the dispersion curve
is dD/dk = 0.055 ps/nm-km 2 Consider the same three cases as in Figure 5.30: (a) 8 channels spaced 100 GHz apart, (b) 32 channels spaced 100 GHz apart, and (c) 32 channels spaced 50 GHz apart
Why do second-order nonlinearities typically not affect a lightwave system?
In discussing the chromatic dispersion penalty, the Telcordia standard for SONET systems [Tel99] specifies the spectral width of a pulse, for single-longitudinal mode
(SLM) lasers, as its 20 dB spectral width divided by 6.07 We studed these lasers in Section 3.5.1 Show that for SLM lasers whose spectra have a Gaussian profile, this
is equivalent to the rms spectral width
For a narrow but chirped Gaussian pulse with chirp factor K = - 6 , calculate the chromatic dispersion limit at a bit rate of i Gb/s, in the 1.55/zm band, for a penalty
of 2 dB Compare this with the chromatic dispersion limit for unchirped pulses plotted in Figure 5.19
References
[Agr95] G.P Agrawal Nonlinear Fiber Optics, 2nd edition Academic Press, San Diego,
CA, 1995
[BA94] E Bruy4re and O Audouin Assessment of system penalties induced by polarization
mode dispersion in a 5 Gb/s optically amplified transoceanic link IEEE Photonics Technology Letters, 6(3):443-445, March 1994
[Bak01] B Bakhshi et al 1 Tb/s (101 x 10 Gb/s) transmission over transpacific distance
using 28 nm C-band EDFAs In OFC 2001 Technical Digest, pages PD21/1-3,
2001
[Big01] S Bigo et al 10.2 Tb/s (256 x 42.7 Gbit/s PDM/WDM) transmission over 100 km
TeraLight fiber with 1.28bit/s/Hz spectral efficiency In OFC 2001 Technical Digest, pages PD25/1-3, 2001
[BOS99] E C Becker, N A Olsson, and J R Simpson Erbium-Doped Fiber Amplifiers:
Fundamentals and Technology Academic Press, San Diego, CA, 1999
[Bre01] J E Brennan III et al Dispersion and dispersion-slope correction with a fiber Bragg
grating over the full C-band In OFC 2001 Technical Digest, pages PD 12/1-3,
2001
Trang 8References 357
[Buc95] J.A Buck Fundamentals of Optical Fibers John Wiley, New York, 1995
[Cai01] J.-X Cai et al 2.4 Tb/s (120 x 20 Gb/s) transmission over transoceanic distance
with optimum FEC overhead and 48% spectral efficiency In OFC 2001 Technical Digest, pages PD20/1-3, 2001
CDdM90] E Curti, B Daino, G de Marchis, and E Matera Statistical treatment of the
evolution of the principal states of polarization in single-mode fibers IEEE/OSA Journal on Lightwave Technology, 8(8):1162-1166, Aug 1990
[Chr84] A.R Chraplyvy Optical power limits in multichannel wavelength-division-
multiplexed systems due to stimulated Raman scattering Electronics Letters,
20:58, 1984
[Chr90] A.R Chraplyvy Limitations on lightwave communications imposed by
optical-fiber nonlinearities IEEE/OSA Journal on Lightwave Technology,
8(10):1548-1557, Oct 1990
IDes94] E Desurvire Erbium-Doped Fiber Amplifiers: Principles and Applications John
Wiley, New York, 1994
[FTC95] E Forghieri, R W Tkach, and A R Chraplyvy WDM systems with unequally
spaced channels IEEE/OSA Journal on Lightwave Technology, 13(5):889-897, May 1995
[FTCV96] E Forghieri, R W Tkach, A R Chraplyvy, and A M Vengsarkar Dispersion
compensating fiber: Is there merit in the figure of merit? In 0FC'96 Technical Digest, pages 255-257, 1996
[Fuk01] K Fukuchi et al 10.92 Tb/s (273 x 40 Gb/s) triple-band/ultra-dense WDM
optical-repeatered transmission experiment In OFC 2001 Technical Digest, pages PD24/1-3, 2001
[GEE94] E.L Goldstein, L Eskildsen, and A E Elrefaie Performance implications of
component crosstalk in transparent lightwave networks IEEE Photonics
Technology Letters, 6(5):657-670, May 1994
[Gol00] E.A Golovchenko et al Modeling of transoceanic fiber-optic WDM
communication systems IEEE Journal of Selected Topics in Quantum Electronics,
6:337-347, 2000
[HH90] P.A Humblet and W M Hamdy Crosstalk analysis and filter optimization of
single- and double-cavity Fabry-Perot filters IEEE Journal of Selected Areas in Communications, 8(6):1095-1107, Aug 1990
[Jac96] J.L Jackel et al Acousto-optic tunable filters (AOTFs) for multiwavelength optical
cross-connects: Crosstalk considerations IEEE/OSA JLT/JSA C Special Issue on Multiwavelength Optical Technology and Networks, 14(6):1056-1066, June 1996
Trang 9[Kar01] M Karlsson et al Higher order polarization mode dispersion compensator with
Academic Press, San Diego, CA, 1997
Academic Press, San Diego, CA, 1997
[LZNA98] G Luo, J L Zyskind, J A Nagel, and M A Ali Experimental and theoretical
analysis of relaxation-oscillations and spectral hole burning effects in all-optical
Technology, 16:527-533, 1998
Journal on Lightwave Technology, 16:745-756, 1998
[Nak00] M Nakazawa et al Ultrahigh-speed long-distance TDM and WDM soliton
Electronics, 6:363-396, 2000
Technical Digest, pages ThF1/1-3, 2001
Lightwave Technology, 7(7):1071-1082, July 1989
[OSYZ95] M.J O'Mahony, D Simeonidou, A Yu, and J Zhou The design of a European
May 1995
[PAP86] M.J Potasek, G P Agrawal, and S C Pinault Analytic and numerical study of
of America B, 3(2):205-211, Feb 1986
Digest, pages TuP1/1-3, 2001
[PN87] K Padmanabhan and A N Netravali Dilated networks for photonic switching
IEEE Transactions on Communications, 35:1357-1365, 1987
[PTCF91] C D Poole, R W Tkach, A R Chraplyvy, and D A Fishman Fading in
Technology Letters, 3(1):68-70, Jan 1991
[RL93] R Ramaswami and K Liu Analysis of effective power budget in optical bus and
Lightwave Technology, 11(11):1863-1871, Nov 1993
Trang 10References 359
[SBW87] N Shibata, R P Braun, and R G Waarts Phase-mismatch dependence of
efficiency of wave generation through four-wave mixing in a single-mode optical fiber IEEE Journal of Quantum Electronics, 23:1205-1210, 1987
[SKA00] H Sunnerud, M Karlsson, and P A Andrekson Analytical theory for
PMD-compensation IEEE Photonics Technology Letters, 12:50-52, 2000
[SKA01] H Sunnerud, M Karlsson, and P A Andrekson A comparison between NRZ and
RZ data formats with respect to PMD-induced system degradation IEEE
Photonics Technology Letters, 13:448-450, 2001
[Smi72] R.G Smith Optical power handling capacity of low loss optical fibers as
determined by stimulated Raman and Brillouin scattering Applied Optics,
11(11):2489-2160, Nov 1972
[SNIA90] N Shibata, K Nosu, K Iwashita, and Y Azuma Transmission limitations due to
fiber nonlinearities in optical FDM systems IEEE Journal of Selected Areas in Communications, 8(6):1068-1077, Aug 1990
[TCF+95] R.W Tkach, A R Chraplyvy, E Forghieri, A H Gnauck, and R M Derosier
Four-photon mixing and high-speed WDM systems IEEE/OSA Journal on
Lightwave Technology, 13(5):841-849, May 1995
[Tel99] Telcordia Technologies SONET Transport Systems: Common Generic Criteria,
1999 GR-253-CORE Issue 2, Revision 2
[TOT96] H Takahashi, K Oda, and H Toba Impact of crosstalk in an arrayed-waveguide
multiplexer on n • n optical interconnection IEEE/OSA JLT/JSA C Special Issue on Multiwavelength Optical Technology and Networks, 14(6):1097-1105, June 1996 [VPM01] G Vareille, E Pitel, and J E Marcerou 3 Tb/s (300 • 11.6 Gbit/s) transmission
over 7380 km using 28 nm C+L-band with 25 GHz channel spacing and NRZ format In OFC 2001 Technical Digest, pages PD22/1-3, 2001
[WK92] J.H Winters and S Kasturia Adaptive nonlinear cancellation for high-speed
fiber-optic systems IEEE/OSA Journal on Lightwave Technology, 10:971-977,
1992
[ZCC+96] J Zhou, R Cadeddu, E Casaccia, C Cavazzoni, and M J O'Mahony Crosstalk
in multiwavelength optical cross-connect networks IEEE/OSA JLT/JSA C Special Issue on Multiwavelength Optical Technology and Networks, 14(6):1423-1435, June 1996
[Zhu01] B Zhu et al 3.08 Tb/s (77 x 42.7 Gb/s) transmission over 1200 km of non-zero
dispersion-shifted fiber with 100-km spans using C- L-band distributed Raman amplification In OFC 2001 Technical Digest, pages PD23/1-3, 2001
[Zir91] M Zirngibl Gain control in erbium-doped fiber amplifiers by an all-optical
feedback loop Electronics Letters, 27:560, 1991