Info Gyy
Figure 3.15 Measured DGD as a function of wavelength for a link containing a single fiber with large PDL sandwiched between two fibers with 5.65-ps DGD. The principal axes of the PDL fiber are either aligned with the other two fibers solid curve or rotated by 45 dashed curve . The dotted lines show the theoretical prediction. After Ref. 60 2000 IEEE. These two equations can be solved analytically to find various moments of Si and A if one assumes that the vectors a and b are parallel to each...
Problems Fcs
10.1 A distribution network uses an optical bus to distribute the signal to 10 users. Each optical tap couples 10 of the power to the user and has a 1-dB insertion loss. Assuming that 1 mW of power is launched into the optical bus, calculate the power received by the stations 8, 9, and 10. 10.2 A cable-television operator uses an optical bus to distribute video channels to its subscribers. Each receiver needs a minimum of 100 nW to operate satisfactorily. Optical taps couple 5 of the power to...
Www.cdmsystems.ev
As discussed in the preceding chapter, the first step in any lightwave system is to generate a digital bit stream at the optical transmitter in the form of a coded train of optical pulses such that it contains all the information available in the corresponding electrical signal. It turns out that the conversion of a bit stream from electrical to optical domain can be carried out in several different formats. The choice of an appropriate modulation format depends on a large number of factors and...
Electrical SNR
Optical SNR, although useful for design purposes, is not what governs the BER at the receiver. In this section, we focus on the electrical SNR of the current generated when an ASE-degraded optical signal is incident on a photodetector. For simplicity of discussion, we use the configuration shown in Figure 6.5 and assume that a single optical amplifier is used before the receiver to amplify a low-power signal before it is detected. This configuration is sometimes used to improve the receiver...
Pseudolinear Lightwave Systems
Pseudo-linear lightwave systems operate in the regime in which the local dispersion length is much shorter than the nonlinear length in all fiber sections of a dispersion-managed link. This approach is most suitable for systems operating at bit rates of 40 Gb s or more and employing relatively short optical pulses that spread over multiple bits quickly as they propagate along the link. This spreading reduces the peak power and lowers the impact of SPM on each pulse. There are several ways one...
D
Figure 5.5 Variation of BER with Id jh for three values of I c . by thermal noise 07 crs and is independent of the average current. In contrast, shot noise is larger for 1 bits as cr2 varies linearly with the average current. In the case of APD receivers, the BER should be minimized by setting the decision threshold in accordance with Eq. 5.3.9 . The BER with the optimum setting of the decision threshold is obtained by using Eqs. 5.3.6 and 5.3.8 and depends only on the Q factor as 1 , f Q exp...
WDM Systems
Chapter 8 focused on single-channel systems operating at 40 Gb s or more through electrical and optical TDM. As discussed in Chapter 1, channels can also be multiplexed in the spectral domain through frequency-division multiplexing FDM . Indeed, this technique is routinely used for radio waves and microwaves. Its extension to optical domain permits, in principle, the capacity of lightwave systems to exceed 10 Tb s because of a large frequency associated with the optical carrier. Since the...
Plc
Figure 10.16 Design of an optical switch used to add or drop the packets depending on CDM-encoded labels. After Ref. 71 2004 IEEE. For example, if the carrier is modulated sinusoidally at 10 GHz, two sidebands separated by 20 GHz can be generated by this technique. The packet and the label are transmitted through the network on these two distinct sidebands. Experimental results show that 10-Gb s packets with 2.5-Gb s labels can be routed through a DWDM network designed with standard 50-GHz...
APD Receivers
Optical receivers that employ an APD generally provide a higher SNR for the same incident optical power. The improvement is due to the internal gain see Section 7.3 of LT1 that increases the photocurrent by a multiplication factor M so that where apd MRj is the APD responsivity, enhanced by a factor of M compared with that of p-i-n photodiodes. The SNR would improve by a factor of M2 if the receiver noise were unaffected by the internal gain mechanism of APDs. Unfortunately, this is not the...
Dfbld Mmi Soa
Figure 2.21 Schematic view of a wavelength-selective transmitter designed with a WSL chip left inset in which the output of multiple DFB lasers is coupled into a single SOA through a MMI coupler. The right inset shows photograph of the butterfly package housing the transmitter. After Ref. 78 2002 IEEE. Figure 2.21 Schematic view of a wavelength-selective transmitter designed with a WSL chip left inset in which the output of multiple DFB lasers is coupled into a single SOA through a MMI coupler....
Brillouin Threshold
At low pump powers lt 1 mW or so , not much power is reflected by spontaneous Brillouin scattering in the form of a Stokes wave. However, the situation changes when the power level exceeds a threshold value. The power of the Stokes wave grows exponentially beyond the SBS threshold. In fact, the fiber appears to act as a mirror far above this threshold because most of the pump power is reflected backward. The SBS process in optical fibers is governed by a set of two coupled nonlinear equations...
Problems 1
5.1 Consider a 0.8-jUm receiver with a silicon p-i-n photodiode. Assume 20 MHz bandwidth, 65 quantum efficiency, 1 nA dark current, 8 pF junction capacitance, and 3 dB amplifier noise figure. The receiver is illuminated with 5 juW of optical power. Determine the noise currents due to shot noise, thermal noise, and amplifier noise. Also calculate the signal-to-noise ratio. 5.2 The receiver of Problem 5.1 is used in a digital communication system that requires a signal-to-noise ratio of at least...
BitError Rate 1
The calculation of BER for lightwave systems employing optical amplifiers follows the approach outlined in Section 5.3.1. More specifically, BER is given by Eq. 5.3.2 . However, the conditional probabilities ' O 1 and P 1 require knowledge of the probability density function PDF for the current I corresponding to symbols 0 and 1. Strictly speaking, the PDF does not remain Gaussian when optical amplifiers are used, and one should employ a more complicated form of the PDF for calculating the BER...
References 1
1 S. D. Personick, Bell Syst. Tech. J. 52, 843 1973 52, 875 1973 . 2 T. P. Lee and T. Li, in Optical Fiber Telecommunications I, S. E. Miller and A. G. Chynoweth, Eds., Academic Press, San Diego, CA, 1979, Chap. 18. 3 R. G. Smith and S. D. Personick, in Semiconductor Devices for Optical Communications, H. Kressel, Ed., Springer, New York, 1980. 4 B. L. Kasper, in Optical Fiber Telecommunications II, S. E. Miller and I. P. Kaminow, Eds., Academic Press, San Diego, CA, 1988, Chap. 18. 5 S. B....
Frequency Chirping
The preceding discussion of dispersion-induced power penalty assumed that the input pulses were unchirped. An initial chirp on optical pulses is known to limit the performance of 1.55-jUm lightwave systems when directly modulated semiconductor lasers are used to generate the digital bit stream 19 - 32 . As discussed in Section 3.3, frequency chirping can enhance the dispersion-induced broadening of optical pulses and thus may degrade the performance of a long-haul lightwave system more than...
FourWave Mixing
Four-wave mixing FWM becomes a major source of interchannel crosstalk whenever more than two channels are transmitted simultaneously over the same fiber, and it has been studied extensively in the context of WDM lightwave systems 54 - 67 . On a fundamental level, FWM can be viewed as a scattering process in which two photons of energies h 0 and ho gt i are destroyed, and their energy appears in the form of two new photons of energies h Oi and fta gt 4 such that the total energy is conserved....
Fiber Bragg Gratings
The optical filters discussed in Section 7.3 are often fabricated using planar silica waveguides. Although such devices are compact, they suffer from high insertion losses, resulting from an inefficient coupling of light between an optical fiber and a planar waveguide. Insertion losses can be reduced by using a fiber-based optical filter. As discussed in Section 2.2 of LT1, a fiber Bragg grating acts as an optical filter because of the existence of a stop band a spectral region over which most...
Manakov Equation
Equation 4.7.6 is the vector NLS equation governing pulse propagation in a realistic fiber in which residual birefringence varies randomly along the fiber length. It includes not only the dispersive and nonlinear effects but also the PMD effects. It must be solved numerically in general. Even a numerical solution is not easy to obtain because of different length scales associated with the PMD, GVD, and SPM phenomena. Birefringence in a typical optical fiber varies on a length scale of 10 to 100...
Architecture of Optical CrossConnects
As seen in Figures 10.7 and 10.8, wavelength-routing networks employ OXCs at each node within the core network. The architecture of OXCs depends on several factors Figure 10.9 a An OXC with electronic switching b an OXC with wavelength conversion at each node c an OXC with shared conversion d an OXC with partial conversion e a wavelength-selective OXC with no conversion. After Ref. 35 2003 IEEE. Figure 10.9 a An OXC with electronic switching b an OXC with wavelength conversion at each node c an...
Lumped Amplification
In a chain of cascaded lumped amplifiers see Figure 3.1 , ASE accumulates from amplifier to amplifier and can build up to high levels 2 . The ASE power added by any amplifier is attenuated in succeeding fiber sections, but it is also amplified by all following amplifiers. The net effect is that one can simply add the ASE powers of all amplifiers at the end of a fiber link. Assuming that all amplifiers are spaced apart by the same distance I.a and are operated with the same gain G expf , the...
Optimization of Dispersion Maps
As discussed in Chapters 7 and 8, the performance of a single-channel lightwave system depends on details of the dispersion map because of the nonlinear effects and can be improved by optimizing the dispersion map. This is also the situation for WDM systems 97 106 . The parameters that can be adjusted are amount of precompensation, lengths and dispersions of each fiber section used to form the dispersion map, residual dispersion per map period, and the amount of postcompensation. It has been...
Quantum Limit of Photodetection
A question one may ask is related to the quantum limit of the photodetection process. Assuming that a perfect optical signal is incident on an ideal receiver only limited by shot noise, how many photons per bit are needed for recovering the signal reliably In this subsection we address this question. We assume that zero bits carry no power, and thus o 0. In the absence of thermal noise, do 0 since shot noise also vanishes for the 0 bit if the dark-current contribution is neglected for an ideal...
References
1 A. R. Chraplyvy, J. Lightwave Technol. 8, 1548 1990 . 2 F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, in Optical Fiber Telecommunications, Vol. 3A, I. P. Kaminow and T. L. Koch, Eds., Academic Press, San Diego, CA, 1997, Chap. 8. 3 E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks, Wiley, New York, 1998. 4 G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed., Academic Press, San Diego, CA, 2001. 5 G. P. Agrawal, Fiber-Optic Communication Systems, 3rd...
Problems
in the limit of zero dispersion fc. 0 and derive an expression for the SPM-induced nonlinear phase shift for pulses of arbitrary shape. How is this shift affected by fiber losses 4.2 Apply the result of Problem 4.1 to input pulses with A 0,i v sech i 7o and plot the frequency chirp as a function of time at the output of a 25-km-long fiber. Assume a 0.2 dB km, y 2 W_1 km, and 5-ps pulses FWHM with 20-mW peak power. 4.3 A 1.55- tm continuous-wave signal with 6-dBm power is launched into a fiber...
BitError Rate
To calculate the BER, we consider the electrical bit stream generated at the receiver in the form of a time-varying current f that has been corrupted by noise. Figure 5.4 a shows schematically the fluctuating signal received by the decision circuit of the receiver. A clock-recovery circuit provides information about the duration of each bit slot. Depending on the design, the receiver may integrate the signal over the bit slot, or sample it periodically at the decision instant to set at the...