This Page Intentionally Left Blank Standards C.1 C.1.1 C.1.2 International Telecommunications Union (ITU-T) These standards can be ordered through www.itu.ch. Fiber G.652. Characteristics of a single-mode optical fiber cable. G.653. Characteristics of a dispersion-shifted single-mode optical fiber cable. G.655. Characteristics of a nonzero-dispersion-shifted single-mode optical fiber cable. SDH (Synchronous Digital Hierarchy) G.691. Optical interfaces for single-channel STM-64, STM-256 systems, and other SDH systems with optical amplifiers. G.707. Network node interface for the synchronous digital hierarchy (SDH). G.708. Sub STM-0 network node interface for the synchronous digital hierarchy (SDH). G.774. Synchronous digital hierarchy (SDH) management information model for the network element view. Several addendums exist. G.780. Vocabulary of terms for synchronous digital hierarchy (SDH) networks and equipment. 721 722 STANDARDS C.1.3 C.1.4 G.781. Synchronization layer functions. G.783. Characteristics of synchronous digital hierarchy (SDH) equipment functional blocks. G.784. Synchronous digital hierarchy (SDH) management. G.803. Architecture of transport networks based on the synchronous digital hierar- chy (SDH). G.805. Generic functional architecture of transport networks. G.831. Management capabilities of transport networks based on the synchronous digital hierarchy (SDH). G.841. Types and characteristics of SDH network protection architectures. G.842. Interworking of SDH network protection architectures. G.957. Optical interfaces for equipments and systems relating to the synchronous digital hierarchy. Optical Networking G.692. Optical interfaces for multichannel systems with optical amplifiers. G.709. Interface for the optical ~ransport network (OTN). G.798. Characteristics for the OTN equipment functional blocks. G.871. Framework for recommendations. G.872. Architecture for optical transport networks (OTN). G.874. Management aspect of optical transport network elements. G.875. OTN management information model for the network element view. G.957. Optical interfaces for equipment and systems related to SDH. G.959. Optical networking physical layer interfaces. G.983. Broadband optical access systems based on passive optical networks (PON). G.astn. Automatic switched networks. G.vsr. Optical interfaces for intraoffice systems. Management M.3000. Overview of TMN recommendations. M.3010. Principles for a telecommunications management network. M.3100. Generic network information model. C.2 Telcordia 723 Q.822. Stage 1, stage 2, and stage 3 description for the Q3 interface~performance management. x.744. Information technologymopen systems interconnectionmsystems manage- ment: Software management function. C.2 C.2.1 C.2.2 Telcordia These standards can be ordered through www.telcordia.com. Physical and Environmental FR-2063. Network Equipment-Building System (NEBS) family of requirements (NEBSFR). SONET GR-253. Synchronous optical network (SONET) transport systems: Common generic criteria. GR-496. SONET add-drop multiplexer (SONET ADM) generic criteria. GR-1230. SONET Bi-directional line-switched ring equipment generic criteria. GR-1244. Clocks for the synchronized network: Common generic criteria. GR-1250. Generic requirements for synchronous optical network (SONET) file transfer. GR-1365. SONET private line service interface generic criteria for end users. GR-1374. SONET inter-carrier interface physical layer generic criteria for carriers. GR-1377. SONET OC-192 transport system generic criteria. GR-1400. SONET dual-fed unidirectional path switched ring (UPSR) equipment generic criteria. GR-2875. Generic requirements for digital interface systems. GR-2899. Generic criteria for SONET two-channel (1310/1550-nm) wavelength division multiplexed systems. GR-2900. SONET asymmetric multiplex functional criteria. GR-2950. Information model for SONET digital cross-connect systems (DCSs). GR-2954. Transport performance management based on the TMN architecture. 724 STANDARDS GR-2996. Generic criteria for SONET digital cross-connect systems. GR-3000. Generic requirements for SONET element management systems (EMSs). GR-3001. Generic requirements for SONET network management systems (NMSs). C.2.3 Optical Networking GR-1209. Generic requirements for fiber optic branching components. GR-1377. SONET OC-192 transport system generic criteria. GR-2918. DWDM network transport systems with digital tributaries for use in metropolitan area applications: Common generic criteria. GR-2979. Common generic requirements for optical add-drop multiplexers (OADMs) and optical terminal multiplexers (OTMs). GR-2998. Generic requirements for wavelength division multiplexing (WDM) element management systems (EMSs). GR-2999. Generic requirements for wavelength division multiplexing (WDM) network management systems (NMSs). GR-3009. Optical cross-connect generic requirements. C.3 American National Standards Institute (ANSI) These can be ordered from www.ansi.org. C.3.1 SONET T1.105. Telecommunications~synchronous optical network (SONET)~basic de- scription including multiplex structures, rates, and formats. T1.105.01. Telecommunications~synchronous optical network (SONET)~auto- matic protection switching. See also all the other T1.105.::" documents. C.3.2 ESCON and Fibre Channel X3.289. Information technology~Fibre Channel~fabric generic requirements (FC-FG). C.3 American National Standards Institute (ANSI) 725 X3.296. Information technologymsingle byte command code connection (SBCON) architecture. (This is the ANSI version of IBM's ESCON). X3.303. Fibre Channel physical and signaling interface-3 (FC-PH-3). This Page Intentionally Left Blank Wave Equations TrtE of electromagnetic waves is governed by the following PROPAGATION Maxwell s equations: V.D - p (D.1) V.B - 0 (D.2) 8B V • E = (D.3) 8t 8D V• - J+ (D.4) 8t Here, p is the charge density, and J is the current density. We assume that there are no free charges in the medium so that p = 0. For such a medium, J = erE, where cr is the conductivity of the medium. Since the conductivity of silica is extremely low (or ~ 0), we assume that J = 0; this amounts to assuming a lossless medium. In any medium, we also have, from (2.5) and (2.6), D - ~oE + P, where P is the electric polarization of the medium and B - #o(H + M), where M is the magnetic polarization of the medium. Since silica is a nonmagnetic material, we set M - 0. 727 728 WAVE EQUATIONS Using these relations, we can eliminate the flux densities from Maxwell's curl equations (D.3) and (D.4) and write them only in terms of the field vectors E and H, and the electric polarization P. For example, O2E 02p V x V x E = -#oEo-~7 Y - #o Ot y. (D.5) To solve this equation for E, we have to relate P to E. If we neglect nonlinear effects, we can assume the linear relation between P and E given by (2.7) and further, because of the homogeneity assumption, we can write X (t) for X (r, t). We relax this assumption when we discuss nonlinear effects in Section 2.4. We can solve (D.5) for E most conveniently by using Fourier transforms. The Fourier transform 1~ of E is defined by (2.4); P and I2I are defined similarly. It follows from the properties of Fourier transforms that 1 F l~(r, co) exp(-iwt) do). E(r,t)=~ oo By differentiating this equation with respect to t, we obtain the Fourier transform of OE/Ot as-ico]~. Taking the Fourier transform of (D.5), we get V • %7 • ~ __ /Z0~00)2]~ _+_ ~0o)2p. Using (2.8) to express P in terms of E, this reduces to V • %7 • E ~__./z060(_.02]~ +/z060(.02)~]~. We denote c - I/x/#060; c is the speed of light in a vacuum. When losses are neglected, as we have neglected them, ~ is real, and we can write n(co) = v/1 + )~ (oo), where n is the refractive index. Note that this is the same as (2.9), which we used as the definition for the refractive index. With this notation, ~ o)21/2 VxVxE= c2 1~. (D.6) By using the identity, V X V X E' V(V.E)-V2E, (D.6) can be rewritten as m2n 2 V2E -'}- c2 ~ - V(V. E). (D.7) WAVE EQUATIONS '/29 Because of our assumption of a homogeneous medium (;( independent of r) and using (D.1) and (2.9), we get 0 V. fi = 60V. (1 + )~)E - 60n2V 9 E. (D.8) This enables us to simplify (D.7) and obtain the wave equation (2.10) for 1~. Following similar steps, the wave equation (2.11) can be derived for I2I. . of a single-mode optical fiber cable. G.653. Characteristics of a dispersion-shifted single-mode optical fiber cable. G.655. Characteristics of a nonzero-dispersion-shifted single-mode optical. Channel physical and signaling interface-3 (FC-PH-3). This Page Intentionally Left Blank Wave Equations TrtE of electromagnetic waves is governed by the following PROPAGATION Maxwell s equations:. digital tributaries for use in metropolitan area applications: Common generic criteria. GR-2979. Common generic requirements for optical add-drop multiplexers (OADMs) and optical terminal multiplexers