## Info

Figure 7.3 (a) Refractive-index profiles of two DCFs designed with two concentric cores, (b) Dispersion parameter as a function of wavelength for the same two designs. (After Ref. 7 1996 IEEE.) with the outer core (A0 ss 0.3 ), but the core sizes are chosen such that each core supports a single mode. The three size parameters a, b, and c and the three refractive indices hi, 2, and 3 can be optimized to design DCFs with desired dispersion characteristics. The solid curve in Figure 7.3(b) shows...

## References

Jopson, in Optical Fiber Telecommunications, Vol. 3 A, I. P. Kaminow and T. L. Koch, Eds., Academic Press, San Diego, CA, 1997, Chap. 7. 2 J. Zyskind, R. Barry, G. Pendock, M. Cahill, and J. Ranka, in Optical Fiber Telecommunications, Vol. 4B, I. P. Kaminow and T. Li, Eds., Academic Press, San Diego, CA, 2002, Chap. 7. 3 A. E. Willner and B. Hoanca, in Optical Fiber Telecommunications IV, Vol. 4B, I. P. Kaminow and T. Li, Eds., Academic Press, San Diego, CA, 2002, Chap. 14....

## Specific Analytic Solutions

As a simple application of the moment or variational method, consider first the case of a low-energy pulse propagating in a constant-dispersion fiber with negligible nonlinear effects. Recalling that (1 +C2) T2 is related to the spectral width of the pulse that does not change in a linear medium, we can replace this quantity with its initial value (1 +Cq) Tq, where 7o and Co are input values at z 0. Since the second term is negligible in Eq. (4.6.7), it can be integrated easily and provides the...

## Switching Technologies for Cross Connects

All OXCs need a switching fabric capable of interconnecting a large number of input and output ports in an arbitrary fashion with suitable electronic control signals. As discussed in Section 9.1 of LT1, several technologies can be employed for this purpose. Examples include electro-optic switches based on LiNbC> 3 waveguides, thermo-optic switches based on silica waveguides and fabricated with silica-on-silicon technology, microscopic mirrors built with micro-electro-mechanical system (MEMS)...

## Jul

Figure 2.2 Schematic illustration of the external-modulation scheme. A DFB laser is biased at a constant current while the time-dependent electrical signal is applied to the modulator. fiber. For this reason, direct modulation of the laser output becomes impractical as the bit rate of a lightwave system is increased beyond 2.5 Gb s. The effects of frequency chirp on pulse broadening are considered in Section 3.2 where we discuss the impact of fiber dispersion. The chirping problem can be solved...

## Linear Degradation Mechanisms

The most important issue in designing WDM lightwave systems is the extent of interchannel crosstalk. The system performance degrades whenever crosstalk leads to transfer of power from one channel to another. Such a transfer can occur because of the nonlinear effects in optical fibers, a phenomenon referred to as nonlinear crosstalk as it depends on the nonlinear nature of the communication channel. However, some crosstalk occurs even in a perfectly linear channel because of the imperfect nature...

## High Speed Lightwave Systems

So far we have focused on a single channel operating at most at a bit rate of 40 Gb s. If intrachannel nonlinear effects can be controlled, it is possible to increase the bit rate beyond 40 Gb s. Such optical signals cannot be generated electrically because of the limitations imposed by high-speed electronics. However, as mentioned in Section 1.4.1, the TDM technique can be employed in the optical domain to create bit streams at data rates higher than 100 Gb s. Experimentally, optical TDM...

## Cd 0 Tj

33 ji 2 AP-RZ 67 RZ-DPSK 33 RZ-DPSK 33 CSRZ 33 RZ-Duobinary 33 RZ-AMI 33 CSRZ 33 RZ-Duobinary 33 RZ-AMI 33 ji 2 AP-RZ 67 RZ-DPSK 33 RZ-DPSK Figure 2.9 Experimentally recorded optical spectra for nine different modulation formats for a 42.7-Gb s optical bit stream. (After Ref. 22 2004 IEEE.) Figure 2.9 Experimentally recorded optical spectra for nine different modulation formats for a 42.7-Gb s optical bit stream. (After Ref. 22 2004 IEEE.) The CSRZ scheme can be implemented in practice using...

## Ofc 2003

Eral experiments that realized a capacity of 1 Tb s. By 2001, the capacity of WDM systems exceeded 10 Tb s in several laboratory experiments. In one experiment, 273 channels, spaced 0.4 nm apart and each operating at 40 Gb s, were transmitted over 117 km using three in-line amplifiers, resulting in a total capacity of 11 Tb s and a NBL product of 1.28 (Pb s)-km 12 . Table 9.1 lists several WDM experiments in which the NBL product exceeded 1 Pb s. In this table, OFC and ECOC stand, respectively,...

## Intensity Noise of Lasers

In practice, light emitted by any laser exhibits power fluctuations. Such fluctuations, called intensity noise, have been discussed in Section 5.3.4 of LT1 in the context of semiconductor lasers. An optical receiver converts power fluctuations into current fluctuations, which add to those resulting from shot and thermal noises. As a result, the receiver SNR is degraded and is lower than that given in Eq. (5.2.10). An exact analysis is complicated as it involves the calculation of photocurrent...

## Sensitivity Degradation

The discussion of receiver sensitivity in Section 5.3 includes thermal noise but is still overly simplified in many respects. In particular, the analysis assumes that the optical signal incident on the receiver consists of an ideal bit stream such that 1 bits consist of an optical pulse of constant energy, while no energy is contained in 0 bits. In practice, an optical signal deviates from this ideal situation even at the transmitter end. Moreover, it can be degraded during its transmission...

## JfJYJ

Figure 2.12 (a) The NRZ data (b) its differentially encoded version (c) original (solid) and delayed (dashed) phase profiles at the output coupler (d) final RZ bit stream and (e) phase variations across it. (After Ref. 31 2001 IEEE.) passive optical delay-line (MZ) interferometer to produce the RZ output from a phase-modulated optical signal. Figure 2.12 shows how such a device functions. The differential encoder takes the NRZ data in part (a) and converts it into another electrical bit stream...

## Receiver Sensitivity

Receiver sensitivity is an important parameter for any lightwave system. Among a group of optical receivers, a receiver is said to be more sensitive if it achieves the same performance with less optical power incident on it. The performance criterion for digital receivers is governed by the BER, defined as the probability of incorrect identification of a bit by the decision circuit of the receiver. For example, a BER of 2 x 10 9 corresponds to 2 errors per billion bits, on average. Modern...

## Problems

8.1 Solve the NLS equation (8.1.2) numerically using the same dispersion map employed for Figure 8.1. Consider a 40-Gb s system designed using RZ pulses of Gaussian shape with a 6.25-ps width (FWHM). Use a 128-bit pseudo-random bit pattern to construct curves similar to those shown in Figure 8.1(a), assuming that the maximum distance corresponds to a 1 -dB penalty in the eye opening. Is this system design better than the 50 duty cycle used for Figure 8.1 Justify your answer in physical terms....

## Interscience

A JOHN WILEY & SONS, INC., PUBLICATION Copyright 2005 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without...

## Mh

Figure B.l Main window of OptSim simulation software showing various components interconnected to solve a specific problem. It contains two toolbars on the top and to the left of the window in addition to the standard menu bar at the top and a status line at the bottom. book. For example, the subfolder marked chapter4 contains four problems related to Chapter 4. These four examples illustrate the impact of different nonlinear effects on the performance of lightwave systems. All examples are...

## Wdm Ocmux

Figure 10.23 Schematic of the Lambdanet with N nodes. Each node consists of one transmitter and N receivers. After Ref. 96 1990 IEEE. the Lambdanet, and its architecture was developed in the late 1980s 96 , Each node in the Lambdanet is equipped with one transmitter emitting at a unique wavelength and N receivers operating at N distinct wavelengths, where N is the number of nodes. The output of all transmitters is combined in a passive star and distributed to all receivers equally. Each node...

## Numerical Approach

The preceding estimate is crude since it does not include the impact of nonlinear effects discussed in Chapter 4. Even though power levels are kept relatively modest for each channel, the nonlinear effects can become quite important because of their accumulation over long distances. For single-channel systems, the most dominant nonlinear phenomenon that limits the system performance is SPM. An estimate of power limitation imposed by the SPM can be obtained from Eq. 4.1.17 . If we use a 0.2 dB...

## Describe The Evolution Of Light Wave Systems

Lightwave systems represent a natural extension of microwave communication systems inasmuch as information is transmitted over an electromagnetic carrier in both types of systems. The major difference from a conceptual standpoint is that, whereas carrier frequency is typically 1 GHz for microwave systems, it increases by five orders of magnitude and is typically 100 THz in the case of lightwave systems. This increase in carrier frequency translates into a corresponding increase in the system...

## Control of XPM Interaction

Since XPM affects the performance of all WDM systems, a lightwave system must be designed to control its impact so that it can operate reliably. In practice, the dominant contribution to XPM affecting the performance of a specific channel comes from the two channels that are its nearest neighbors in the spectral domain. The XPM interaction between neighboring channels can always be reduced by increasing the channel spacing. A larger channel spacing increases the mismatch between the group...

## Effects of Group Velocity Mismatch

The preceding analysis overestimates the XPM-induced phase shift because it neglects the time-dependent nature of the optical signal. In practice, each channel carries an optical bit stream in which the location of pulses representing 1 bits is data-dependent or pseudo-random . Moreover, pulses belonging to different channels travel at different speeds and walk through each other at a rate that depends on their wavelength difference. Since XPM can occur only when pulses overlap in the time...

## Dispersive Pulse Broadening

Dispersion-induced pulse broadening affects the receiver performance in two ways. First, a part of the pulse energy spreads beyond the allocated bit slot and leads to intersymbol interference. Second, the pulse energy within the bit slot is reduced when the optical pulse broadens. Such a decrease in pulse energy reduces the SNR at the decision circuit. As the SNR should remain constant to maintain the system performance, the receiver requires more average power. This is the origin of...

## EDFA Noise

EDFAs makes use of a rare-earth element erbium that is doped into the fiber core during the manufacturing process l - 3 . When erbium is incorporated into the amorphous silica-glass matrix, it is ionized triply. Figure 6.1 a shows a few energy levels of Er3 ions. The amorphous nature of silica broadens all energy levels into bands. The energy separation between the two lowest bands corresponds to a wavelength range from 1.46 to 1.62 fim that happens to coincide with the low-loss region of...

## Receivers with a pin Photodiode

In the case of a p-i-n photodiode, we use Eq. 5.1.11 in Eq. 5.2.1 together with I R iPm- The SNR is related to the incident optical power as where Rd r q hvo is the responsivity of the p-i-n photodiode for photons of energy hvo and r is its quantum efficiency. Figure 5.1 shows the dependence of SNR on received power Pm for three values of Oj for a receiver with Rd 1 AAV, I, 0, and a bandwidth of 30 GHz. Thermal noise dominates for aj 5 fiA but it is almost negligible, and shot noise dominates...

## Worked Problems In Light Wave Distribution Networks

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

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...

## Bit Error Rate

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...

## 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...

## Four Wave 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 Cross Connects

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...