IPO Working Group Dimitri Papadimitriou Category: Informational Draft Jean-Paul Faure Expiration Date: May 2002 Olivier Audouin Alcatel Roy Appelman Civcom November 2001 Non-linear Routing Impairments in Wavelength Switched Optical Networks draft-papadimitriou-ipo-non-linear-routing-impairm-01.txt Status of this Memo This document is an Internet-Draft and is in full conformance with all provisions of Section 10 of RFC2026 [1]. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet- Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet- Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at http://www.ietf.org/ietf/1id-abstracts.txt The list of Internet-Draft Shadow Directories can be accessed at http://www.ietf.org/shadow.html. 1. Abstract Today, in transparent optical networks, the increasing bit-rate (10 Gbit/s and up to 40 Gbit/s in the future), combined with the increasing number of wavelengths (16 and higher up to 320) and a narrowing of the channels spacing, enhance the impact of non-linear effects on optical signal quality. Thus, non-linear effects like Self-Phase Modulation (SPM), Cross- Phase Modulation (XPM), Four-Wave Mixing (FWM) as well as Stimulated Raman Scattering (SRS) and Brillouin scattering have to be examined in order to evaluate their impacts on the transmission quality. If these effects appear to be significant, they have to be taken into account in the routing of a wavelength throughout a transparent optical network. D.Papadimitriou et al. û Expires May 2002 1 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 The aim of this draft is to extend the previous works dedicated to routing impairments ([IPO-IMP] and [IPO-ORI]) in order to determine which are the non-linear effects that must be considered and which kind of engineering rules may be used to take these effects into account in constraint-based optical routing. Moreover, we propose to introduce IGP routing protocol extensions to transport information related to non-linear impairments relevant for wavelength routing decisions. 2. Conventions used in this document The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC-2119 [2]. 3. Introduction Non-linear effects are due to the fact that the optical properties of the medium (refractive index, loss, etc.) become dependent of the signal power of the optical channels present in this medium. As a consequence, this power dependency tends to modify the propagation of the optical waves and also lead to interactions between these waves. Non-linear interactions depend on the transmission length (distance between the transmitter and the receiver), the type of fiber, the cross-sectional area of the fiber, the wavelength and the power level. Basically, these effects become more intensive when the optical power or the transmission length increase or when the channel spacing becomes narrower (the different wavelengths tend to interact more each other). As a consequence, non-linearities can impose significant limitations on high bit-rates (10 Gbit/s and higher), Long Haul (LH) and Ultra-Long Haul (ULH) systems, or high capacity DWDM systems. Linear impairments are extensively addressed in [IPO-IMP] and corresponding IGP routing protocol extensions in [IPO-ORI]. In these previous works, the approach for non-linear impairments was to consider that: ôOne could assume that non-linear impairments are bounded and increase the required OSNR level by X dB, where X for performance reasons would be limited to 1 or 2 dB, consequently setting a limit on the maximum number of spans. For the approach described here to be useful, it is desirable for this span limit to be longer than that imposed by the constraints which can be treated explicitly.ö However, this approximation may lead to both an over or an under estimation of the real impact of non-linear effects. If the actual impact is less than 2 dB on the OSNR, then, the margin taken will forbid some feasible path(s) (as it limits the maximum number of spans). On the contrary, if the real impact is over 2 dB, the corresponding route(s) may be chosen despite they are not feasible from the optical transmission point of view. D.Papadimitriou et al. û Expires May 2002 2 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 Therefore, the objective of this document is first to determine which kind of non-linear effects must be taken into account, and to give some simple engineering rules to determine their maximum tolerable value, second, to propose IGP routing protocol extensions in order to cover non-linear optical routing impairments. Additional complexity may arise from the fact that for instance when minimizing degradations through Self Phase Modulation (SPM) after setting a distinct Lambda LSP (L-LSP) or optical channel in the network, this L-LSP will suffer a changing degradation by Cross- Phase Modulation (XPM) through the changing number of concurrent optical channels on the fiber links. Thus, as we will point out, cross channels effects should be minimized at the system design in order to be compatible with SPM and other impairments. 4. Non-Linear Impairments Non-linear optical impairments can be classified into two categories. The first category consists of effects occurring due to the dependence of the refractive index on the optical signal power (generally called Kerr effect). This category includes Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM) and Four-Wave Mixing (FWM). The second category of effects consists of inelastic scattering effects in the fiber medium and are due to the interaction of the light waves with the optical phonons of the fiber medium leading to Stimulated Raman Scattering (SRS) or with the acoustic phonons (sound waves) of the medium leading to Stimulated Brillouin Scattering (SBS). SPM and XPM essentially affect the phase of the signals and cause its spectral broadening which lead to temporal distorsions because of dispersion. FWM lead to energy exchange between signals that induces in-band crosstalk, whereas SBS and SRS provide gain or loss to the light waves. Nevertheless, the actual impact of these non- linear effects on transmission quality depends strongly on dispersion management. 4.1 Refractive Index The general equation for the refractive index of the core in an optical fiber is given by: n = n(0) + [n(2) x P / A(eff)] where: - n(0) = the refractive index of the fiber core at low optical power level (no unit) - n(2) = the non-linear refractive index coefficient (for instance, 2.35 x 10^(-20) m^2/W for silica) - P = optical signal power in Watts (W) - A(eff) = the effective area of the core in square meters (m^2) Clearly, this equation indicates that two strategies for minimizing D.Papadimitriou et al. û Expires May 2002 3 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 non-linearities due to refractive index power dependence are to minimize the launched optical power P and/or to maximize the effective area of the fiber A(eff). Minimizing P is limited by the fact that during network design, there is a strong trade-off between non-linear effects and optical signal to noise ratio (decreasing P will decrease non-linear effects but also the OSNR). On the other hand, augmenting A(eff) is being targeted by some fiber vendors while keeping other non-linear effects unchanged. This optical power dependence of the refractive index introduces the following non-linear effects: SPM, XPM, FWM, SBS and SRS as explained here below. 4.1.1 Self-Phase Modulation (SPM) Self-Phase Modulation (SPM) arises from the power dependency of the refractive index of the fiber core. Fluctuations in the optical signal power cause changes in the phase of the signal referred to as a non-linear phase shift. This induces an additional frequency chirp on the spectrum of the optical pulse which interacts with the fiberÆs dispersion to broaden the pulse and lead to intensity fluctuations. Therefore, this effect leads to higher penalties due to Inter-Symbol Interference (ISI). This chirping effect affects each channel independently of the other and is proportional to the optical channel power. Therefore SPM effects are more pronounced in systems using higher transmitted signal power. Moreover because the SPM effect leads to extra ISI, higher bit-rate systems will be more affected. It is important to point out that in a DWDM transmission system at 10 Gbit/s with 100 GHz channel spacing, SPM is generally considered as a significant non-linear effect (except may be when low dispersion fibers are used). 4.1.2 Cross-Phase Modulation (XPM) For a given optical signal, Cross-Phase Modulation (XPM) is a consequence of a modification of the refractive index of the medium due to the optical power of the closest neighboring channels present in the fiber. As for SMP, the induced phase shift lead to intensity fluctuations after interaction with dispersion. XPM increases when optical channel spacing becomes narrower as long as the adjacent channels are closer in the spectral domain, so that they travel roughly at the same velocity and interact over a longer time period. As XPM effect depends on channel spacing, it can be a significant problem for high capacity DWDM system with channel spacing of 50 GHz or lower. On the other hand, when the bit rate increases (from 10 Gbit/s to 40 Gbit/s), the impact of XPM decrease as long as the time during which the interacting channels temporally overlap is considerably D.Papadimitriou et al. û Expires May 2002 4 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 reduced. For moderate bit rate systems (10 Gbit/s), XPM effect generally becomes significant compared to SPM when channel spacing is lower than 100 GHz, and when the local dispersion is low. This means that XPM should be taken into account for 50 GHz spacing DWDM systems. Here, we want to point out that solutions demonstrated in laboratory environments may be implemented to decrease the effect of XPM by introducing a phase-mismatch between optical channels at the link input by using interleaved polarization or using a suitable dispersion management. 4.1.3 Four-Wave Mixing (FWM) In a (high capacity) DWDM system, based on different optical channels at different wavelengths (i.e. frequencies), the power dependence of the refractive index of the fiber core also gives rise to the generation of new frequencies (i.e. new optical signal). Practically, there is an interaction between the different channels, leading to energy transfer between these channels. This effect is called Four-Wave Mixing (FWM) because if three optical channels with frequencies f1, f2 and f3 propagates simultaneously within the same fiber, a fourth optical channel is generated and frequency f4 which is related to the other frequencies by the following relation: f4 = f1 (+ or -) f2 (+ or -) f3. In theory, several frequencies corresponding to different combinations are possible. However, in practice only the frequency combinations of the form f4 = f1 + f2 û f3 are the most troublesome for (high capacity) DWDM systems. These fourth optical channels can become even nearly phase-matched when optical channel wavelengths are close to the zero-dispersion point. As a consequence, significant optical power can be transferred between neighboring optical channels through the FWM effect. Though, in contrast to SPM and XPM, which are bit-rate dependent, the FWM effect is not really dependent of the bit-rate. Nevertheless, like XPM, it depends strongly on the optical channels spacing and the fiber dispersion. Clearly, FWM becomes significant only at narrow channel spacing (50 GHz or lower) or when the local dispersion is low. As a consequence, significant optical power can be transferred between neighboring optical channels through the FWM effect. Though, in contrast to SPM and XPM, which are bit-rate dependent, the FWM effect is not really dependent of the bit-rate. Nevertheless, like XPM, it depends strongly on the optical channels spacing and the fiber dispersion. Clearly, FWM becomes significant and should be taken into account for DWDM systems with narrow channel spacing (50 GHz or lower) or when the local dispersion is low. 4.2 Scattering Effects Scattering effects, the second set of mechanisms generating non- D.Papadimitriou et al. û Expires May 2002 5 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 linearities give rise to SRS and SBS. 4.2.1 Stimulated Raman Scattering (SRS) In DWDM systems, the fiber acts as a Raman amplifier such that the longer wavelengths channel are amplified by the shorter wavelengths channels as long as the wavelength difference is within the Raman Gain spectrum. Therefore, if two or more signals at different wavelengths are injected into a fiber, the SRS effect causes optical signal power to be transferred from the lower wavelength optical channels to the higher wavelength optical channels. The gain coefficient increases with increasing channel spacing up to 125 nm. This amplification leads to increase power fluctuations, which add to receiver and degrade receiver performance. This phenomenon known as Raman inter- channel crosstalk can be avoided if channel powers are made so small that Raman amplification is negligible over the fiber length. However, the coupling between wavelengths occurs only if both optical channels are launched simultaneously so that the impact of the SRS is reduced by the dispersion introduced by the silica medium. Basically, SRS induces a gain tilt over the whole bandwidth of the fiber, which is proportional to the total power of all channels present in the fiber. Moreover, periodic amplification of the DWDM signal in ULH fiber links can also increase the impact of the SRS-induced degradation. This phenomenon occurs because in-line amplifiers add noise which experiences less Raman loss than the signal itself, resulting in degradation of the SNR. In brief, the total capacity of DWDM systems is then limited to below 100 Gbps for a transmission distance of 5000 km or more. As a matter of fact, SRS should not be considered for impairment based optical routing, as long as its induced Raman tilt will be managed link by link during the network design. 4.2.2 Stimulated Brillouin Scattering (SBS) Scattering effects in the optical fiber occur due to the interaction of the optical channels with the sound waves (acoustic phonons) present in the silica medium. In SBS, the scattering process is stimulated by photons with a wavelength higher than the wavelength of the incident signal. This interaction takes place over a very narrow band of 20 MHz at 1550nm. The scattered waves and the incident optical light waves propagate in opposite directions. Thus, SBS produces an additional loss in the propagating signal but does not induce any interaction between different optical channels. In practical implemented systems, the Brillouin inter-channel crosstalk phenomenon can be easily avoided by always keeping the SBS threshold power higher than the optical signal power. Moreover, the D.Papadimitriou et al. û Expires May 2002 6 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 probability for SRS to occur is much higher than that for SBS because the gain bandwidth for SRS is ~5 THz, while the gain bandwidth for SBS is ~0.05 GHz. Consequently, the losses induced by the SBS effect are not a real problem when considering impairment- based optical routing. 5. Fiber and Optical Amplifiers In the course of moving from pure optical centrally managed transmission to flexible wavelength switched networks many problems have to be solved. One of these problems is the fiber diversity among the different links, and the impact of non-linear effects inside the different transmission fibers. 5.1 Influence of the fiber medium An optical transparent network is composed of many nodes (optical LSR) connected by links (a link is a transmission system between two nodes). Each link is composed of transmission spans of identical fiber, whereas in the most general case, different types of fibers may be deployed among the different links. The main types of fibers that are generally deployed in today optical networks are mainly based on G.652 as well as G.655 and G.653 ITU-T Recommendations. Also and Dispersion Compensating Fibers (DCF) used to compensate the dispersion is present inside the network element. The intensity of non-linear effects is also dependent on the intrinsic optical properties of each fiber, thus, fiber diversity in optical networks must be taken into account when regarding the non- linear impairments. In particular, non-linear effects arise not only in the transmission fiber but also inside the Dispersion Compensating Fiber (DCF) present in the network elements. An additional important point is that in today optical networks, the dispersion of the transmission fiber is compensated for each link by a specific dispersion map. The residual dispersion after cascading a certain number of links must be compatible with the cumulated impact of non-linear effect such as SPM or XPM. In most common optical networks, of moderate bit-rate (10 Gbit/s) and channel spacing (100 GHz), Self-phase modulation (SPM) is the strongest non-linear degradation effect. Changing the path length in the network will then increase the SPM contribution when it increases the total path length, or when the optical path crosses highly non-linear fiber links. Only for highly dense DWDM systems (channel spacing of 50 GHz or less), XPM at its turn will take more and more importance, as well as FWM (even if this latter effect can be reduced with specific design in the link). In that case, after setting a distinct path in the network, this path may suffer a changing degradation by XPM and eventually FWM through the changing number of concurrent channels on a same fiber link. Thus, XPM and FWM must be minimized at system D.Papadimitriou et al. û Expires May 2002 7 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 design but even then their impact must be taken into account for impairment-based optical routing. 5.2 Optical Amplifiers Potentially, non-linear effects may also occur in the fiber amplifiers, but they can be considerably reduced provided a specific design will be done. Then, it is not worth to take them into account, as long as they are kept under control at system design. 6. Non-linear Phase The intensity of the SPM, XPM and FWM non-linear effects can be quantified through the Non-Linear Phase shift NLP (see [AGR-FOCS]) induced in the fiber by the Kerr effect. As a matter of fact, the NLP was shown to be a robust empiric parameter able to evaluate the impact of non-linear effects as described in [OFC00-NLP] and [OFC02- NLP] while related considerations can be found in [ELEC-ODS]. In this section we propose to use the Non-Linear Phase (NLP) as an empiric criterion to correlate the cumulated effects of SPM, XPM and FWM with a given penalty. This penalty corresponds to an upper bound value of the NLP (NLPmax) which depends on the bit-rate, the channel spacing and the fiber type. Since the NLP is additive along an optical path (including several links and spans), the cumulated NLP value (NLPcum) can be compared to the maximum tolerated value of the NLP (NLPmax). Consequently, this method ensures that an optical channel is not affected by non- linear effects when NLPcum < NLPmax. 6.1 Definition The Non-Linear Phase (NLP) for a given transmission span NLP(span) is given by the following formula (see [AGR-NFO]): NLP(span) = P(in) x F(span) where: - P(in) = optical power in Watts (W) at the span input - F(span) = function assumed to be constant for a given span. The F(span) function is directly proportional to: F(span) ~ [n(2) x L(eff)] / [w x A(eff)] where: - n(2) = non-linear refractive index coefficient (m^2/W) - L(eff) = effective interaction length (m) - w = wavelength of the optical channel (m) - A(eff) = effective area of the fiber core in square meters (m^2) While the effective interaction length L(eff) is defined as: D.Papadimitriou et al. û Expires May 2002 8 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 L(eff) = [1 û exp(-aL)] / a where: - a = linear absorption coefficient of the fiber (m^-1) - L = fiber length (m) It is important to point out that the function F is defined as an integral of a rational function, which can be easily calculated and leads to an analytical formula. Then, for each span, the NLP can be easily computed using the above coefficients: w, n(2), A(eff) and L(eff). For a transmission span, one must take into account the NLP due to the transmission fiber and Dispersion Compensating Fiber (DCF). Therefore, the total NLP for a whole span (NLP(span)) is then given by the following formula: NLP(span) = NLP(fiber) + NLP(DCF) = P(in) x F(span) where: - P(in) = optical power at the span input - F(span) = global function containing the parameters of the span including transmission fiber and inline DCF Notice that the only varying parameter in the formula described in this section is the optical power at the span input P(in). 6.1.1 Calculation of the NLP for a link A link between two optical LSR is constituted by N transmission spans. Then, the cumulated NLP for a given link (NLP(link)) is equal to the sum of the different NLP due to each span and is given by: NLP(link) = Sum(NLP[i]) = Sum(P[i] x F[i]) where: - NLP[i] = NLP due to span ôiö - P[i] = power at the input of span ôiö - F[i] = F function of span ôiö This formula allows the calculation of the cumulated NLP for any link, provided one knows the optical power at each span input, and the F function for each span. An interesting case is when the N spans (including the same fiber type) can be considered as roughly identical, so that we can simplify the above formula to: NLP(link) = N x NLP(span) = N x P x F(span) where: - NLP(span) = NLP of the spans D.Papadimitriou et al. û Expires May 2002 9 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 - P = power at the input of the link - F(span) = F function of the spans It is important to note that the NLP(link) is a static information which characterizes the link, and is calculated locally. Therefore, it is the only required parameter to be flooded by IGP protocols. 6.1.2 Calculation of the NLP for an optical path Considering the establishment of an optical path within a network, this path will be a succession of ôjö different links, each link being composed of a specific fiber type. For instance, consider an optical path going from ingress node S to egress node D, via node A and B where the link between S and A is includes SMF fiber, the link between A and B, E-Leaf fiber and the link between B and D, True- Wave Fiber. Then, the total cumulated NLP over the whole optical path NLP(path) is given by: NLP(path) = Sum(NLP(link)[j]) where NLP(link)[j] is the NLP due to link ôjö. With this simple formula, it is possible to calculate the total cumulated NLP (referred to as NLPcum) for any optical path, using the previously calculated NLP of the different links. 6.2 NLP Constraint For a given optical path, the total cumulated NLP due to SPM, XPM and FWM non-linear effects can be computed according to the previous formula. In Section 6.1, we have demonstrated that the NLP is an additive variable along an optical path (including several links and spans) which depends on the bit-rate, the channel spacing and the fiber type. Therefore, the cumulated NLP value (NLP(path)) for a given optical path can be compared to the maximum tolerated value of the NLP (NLPmax). The latter is used as empiric criterion to correlate the SPM, XPM and FWM non-linear effects leading to the NLPmax upper bound value of the NLP. Consequently, the non-linear optical routing cumulative constraint including the SPM, XPM and FWM effects can be expressed as follow: for a given residual dispersion after crossing an optical path, the total cumulated dispersion NLP(path) must be lower than NLP(max), the maximum tolerable value for the NLP: NLP(path) < NLPmax D.Papadimitriou et al. û Expires May 2002 10 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 When the NLP(path) fulfills this constraint, the corresponding optical channel is not limited by the SPM, XPM and FWM non-linear effects do not limit a given optical system. For example, simulations have shown that the non-linear constraint NLPmax can be expressed as follows (assuming an accurate dispersion compensation management): - NLPmax < 0.45 pi at 10Gbit/s - NLPmax < 0.3 pi at 40Gbit/s It is important to point out that we assume in this approach that the dispersion is managed at the link level using available technology being developed, so that for each link, the residual dispersion is compatible with the NLP of the link. Moreover, in a high density DWDM system, the NLP shift per span for a given optical channel does not only depend on the optical power of that channel and the fiber type. The NLP depends also on the power of the closest neighboring optical channels typically (8 in practical applications), as well as on the channel spacing. This implies that one have to consider the NLPmax constraint with respect to the channel spacing. Consequently, the NLP value per link (NLP(link)) must be flooded by the IGP routing protocol to take the channel spacing effect into account. 7. Traffic-Engineering Routing Protocol Extension As mentioned here above, the NLP parameter must be flooded per optical channel spacing (i.e. 100 GHz, 50 GHz and 25 GHz) using a dedicated extension to the IGP TE-Routing protocol. In OSPF, these NLP parameters are included in a common sub-TLV of the Link TLV in the Traffic Engineering LSA. The Type value of this sub-TLV is to be attributed (TBA). The length of this sub-TLV is 12 octets and the corresponding value specifies the NLP value (in IEEE floating point format) per channel spacing. The format of the NLP sub-TLV is as shown: 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | Type = TBA | Length = 12 | +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | NLP at 100GHz | +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | NLP at 50GHz | +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | NLP at 25GHz | +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ D.Papadimitriou et al. û Expires May 2002 11 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 In IS-IS, we propose to enhance the sub-TLVs for the extended IS-IS reachability TLV. The length of the NLP sub-TLV is 12 octets and specifies the NLP value (in IEEE floating point format) per channel spacing (in IEEE floating point format). Specifically, we add the following sub-TLV: - Sub-TLV type: TBA - Length(in bytes): 12 - Name: NLP 8. Security Considerations There are no additional security considerations than the ones already covered in OSPF and IS-IS. 9. Reference 1. Bradner, S., "The Internet Standards Process -- Revision 3", BCP 9, RFC 2026, October 1996. 2. Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997 3. [AGR-NFO] Govind P. Agrawal, ôNonlinear Fiber Opticsö, (section 2.6.2: ôNonlinear refractionö), Academic Press, 1995. 4. [AGR-FOCS] Govind P. Agrawal, ôFiber-Optic Communication Systemsö, Second Edition, Wiley Series in Microwave and Optical Engineering, March 1997. 5. [ELEC-ODS] A. F„rbet et al., ôOptimised dispersion scheme for long-haul optical communication systemsö, Electronic Letters 14, October 1999, Vol.35, No.21. 6. [GYS-XT] T. Gyselings, ôInvestigation and Reduction of CrossTalk in Wavelength Division Multiplexed All-Optical Cross-Connectsö, PhD Thesis, INTEC, Universiteit Gent. 7. [IPO-IMP] A. Chiu et al., ôImpairments And Other Constraints On Optical Layer Routingö, Internet Draft, Work in progress, draft- ietf-ipo-impairments-00.txt, May 2001. 8. [IPO-ORI] A. Banerjee et al., ôImpairment Constraints for Routing in All-Optical Networksö, Internet Draft, Work in progress, draft-banerjee-routing-impairments-00.txt, May 2001. 9. [OFC02-NLP] J.-C. Antona et al. ôNonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systemsö, Technical paper submitted to OFCÆ02. 10. [OFC00-NLP] Y. Frignac and S. Bigo, ôNumerical optimization of residual dispersion in dispersion-managed systems at 40 Gbit/sö, Paper TuD3, OFCÆ00, Baltimore. D.Papadimitriou et al. û Expires May 2002 12 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 10. Acknowledgments The authors would like to thank B. Sales, E. Desmet, J.C. Antona, S. Bigo and A. Jourdan for their constructive comments and inputs. 11. Author's Addresses Dimitri Papadimitriou Alcatel Francis Wellesplein 1, B-2018 Antwerpen, Belgium Phone: +32 3 240-8491 Email: dimitri.papadimitriou@alcatel.be Jean-Paul Faure Alcatel Route de Nozay 91461 Marcoussis Cedex, France Phone: +33 1 6963-1307 Email: jean-paul.faure@ms.alcatel.fr Olivier Audouin Alcatel Route de Nozay 91461 Marcoussis Cedex, France Phone: +33 1 6963-2365 Email: olivier.audouin@ms.alcatel.fr Roy Appelman Civcom Phone: +1 972 3 922-9229 Email: roy.a@civcom.com D.Papadimitriou et al. û Expires May 2002 13 draft-papadimitriou-ipo-non-linear-routing-impairm-01 November 2001 Full Copyright Statement "Copyright (C) The Internet Society (date). All Rights Reserved. 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