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
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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.
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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.
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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
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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
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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-
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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
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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
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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:
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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
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- 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
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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 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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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. Frbet 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.
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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
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D.Papadimitriou et al. û Expires May 2002 14