The University of Adelaide, School of Computer Science 19 September 2018 Optical Networks: A Practical Perspective, 3rd Edition Chapter 2 Propagation of Signals in Optical Fiber Copyright © 2010, Elsevier Inc. All rights Reserved Chapter 2 — Instructions: Language of the Computer

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.1 Chapter 2 Figure 2.1 Attenuation loss in silica as a function of wavelength. (After [Agr97].) Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.2 Chapter 2 Figure 2.2 The three bands, S-band, C-band, and L-band, based on amplifier availability, within the low-loss region around 1.55 μm in silica fiber. (After [Kan99].) Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.3 Chapter 2 Figure 2.3 Cross section and longitudinal section of an optical fiber showing the core and cladding regions. a denotes the radius of the fiber core. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.4 Chapter 2 Figure 2.4 Reflection and refraction of light rays at the interface between two media. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.5 Chapter 2 Figure 2.5 Propagation of light rays in optical fiber by total internal reflection. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.6 Chapter 2 Figure 2.6 Limit on the bit rate–distance product due to intermodal dispersion in a step-index and a graded-index fiber. In both cases, = 0.01 and n1 = 1.5. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.7 Chapter 2 Figure 2.7 Illustration of pulse spreading due to PMD. The energy of the pulse is assumed to be split between the two orthogonally polarized modes, shown by horizontal and vertical pulses, in (a). Due to the fiber birefringence, one of these components travels slower than the other. Assuming the horizontal polarization component travels slower than the vertical one, the resulting relative positions of the horizontal and vertical pulses are shown in (b). The pulse has been broadened due to PMD since its energy is now spread over a larger time period. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.8 Chapter 2 Figure 2.8 A (negatively) chirpedGaussian pulse.Here, and in all such figures, we show the shape of the pulse as a function of time. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.9 Chapter 2 Figure 2.9 Illustration of the pulse-broadening effect of chromatic dispersion on unchirped and chirped Gaussian pulses (for β2 < 0). (a) An unchirped Gaussian pulse at z = 0. (b) The pulse in (a) at z = 2LD. (c) A chirped Gaussian pulse with κ = −3 at z = 0. (d) The pulse in (c) at z = 0.4LD. For systems operating over standard single-mode fiber at 1.55 μm, LD ≈ 1800 km at 2.5 Gb/s, whereas LD ≈ 115 km at 10 Gb/s. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.10 Chapter 2 Figure 2.10 Illustration of the pulse compression effect of chromatic dispersion when κβ2 < 0. (a) A chirped Gaussian pulse with κ = −3 at z = 0. (b) The pulse in (a) at z = 0.4LD. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.11 Chapter 2 Figure 2.11 Evolution of pulse width as a function of distance (z/LD) for chirped and unchirped pulses in the presence of chromatic dispersion. We assume β2 < 0, which is the case for 1.55 μm systems operating over standard single-mode fiber. Note that for positive chirp the pulse width initially decreases but subsequently broadens more rapidly. For systems operating over standard single-mode fiber at 1.55 μm, LD ≈ 1800 km at 2.5 Gb/s, whereas LD ≈ 115 km at 10 Gb/s. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.12 Chapter 2 Figure 2.12 Material, waveguide, and total dispersion in standard single-mode optical fiber. Recall that chromatic dispersion is measured in units of ps/nm-km since it expresses the temporal spread (ps) per unit propagation distance (km), per unit pulse spectral width (nm). (After [Agr97].) Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.13 Chapter 2 Figure 2.13 Typical refractive index profile of (a) step-index fiber, (b) dispersion-shifted fiber, and (c) dispersion-compensating fiber. (After [KK97, Chapter 4].) Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.14 Chapter 2 Figure 2.14 Effective transmission length calculation. (a) A typical distribution of the power along the length L of a link. The peak power is Po. (b) A hypothetical uniform distribution of the power along a link up to the effective length Le. This length Le is chosen such that the area under the curve in (a) is equal to the area of the rectangle in (b). Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.15 Chapter 2 Figure 2.15 Effective cross-sectional area. (a) A typical distribution of the signal intensity along the radius of optical fiber. (b) A hypothetical intensity distribution, equivalent to that in (a) for many purposes, showing an intensity distribution that is nonzero only for an area Ae around the center of the fiber. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.16 Chapter 2 Figure 2.16 The effect of SRS. Power from lower-wavelength channels is transferred to the higher-wavelength channels. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.17 Chapter 2 Figure 2.17 SRS gain coefficient as a function of channel separation. (After [Agr97].) Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.18 Chapter 2 Figure 2.18 Illustration of the SPM-induced chirp. (a) An unchirped Gaussian pulse. (b) The pulse in (a) after it has propagated a distance L = 5LNL under the effect of SPM. (Dispersion has been neglected.) Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.19 Chapter 2 Figure 2.19 The phase (a), instantaneous frequency (b), and chirp (c) of an initially unchirped Gaussian pulse after it has propagated a distance L = LNL. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.20 Chapter 2 Figure 2.20 Dispersion profiles (slopes) of TrueWave fiber, TrueWave RS fiber, and LEAF. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.21 Chapter 2 Figure 2.21 Refractive index profile of (a) normal NZ-DSF and (b) LEAF. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.22 Chapter 2 Figure 2.22 Distribution of power in the cores of DSF and LEAF. Note that the power in the case of LEAF is distributed over a larger area. (After [Liu98].) Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.23 Chapter 2 Figure 2.23 Typical chromatic dispersion profiles of fibers with positive and negative chromatic dispersion in the 1.55 μm band. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.24 Chapter 2 Figure 2.24 Chromatic dispersion in the C-band, and the chromatic dispersion slope, for various fiber types. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.25 Chapter 2 Figure 2.25 (a) A fundamental soliton pulse and (b) its envelope. Copyright © 2010, Elsevier Inc. All rights Reserved

Copyright © 2010, Elsevier Inc. All rights Reserved Figure 2.26 Chapter 2 Figure 2.26 Two examples of the crosssection of holey fibers. Copyright © 2010, Elsevier Inc. All rights Reserved