Note: Descriptions are shown in the official language in which they were submitted.
CA 02589851 2007-05-23
Motorola Docket No. BCSO4300
METHOD AND APPARATUS FOR REDUCING CROSSTALK AND
NONLINEAR DISTORTIONS INDUCED BY RAMAN INTERACTIONS IN A
WAVELENGTH DIVISION MULTIPLEXED (WDM) OPTICAL
COMMUNICATION SYSTEM
Field of the Invention
[0001] The invention relates generally to the transmission of wavelength
division
multiplexed (WDM) optical signals, and more particularly to a method and
apparatus for
reducing crosstalk and nonlinear signal distortions induced by Raman
interactions
between the optical channels.
Background of the Invention
[0002] In recent years wavelength division multiplexed (WDM) optical
transmission
systems have been increasingly deployed in optical networks. These include
coarse
wavelength division multiplexed (CWDM) and dense wavelength division
multiplexed
(DWDM) systems. Whether a system is considered to be CWDM or DWDM simply
depends upon the optical frequency spacing of the channels utilized in the
system.
Although WDM optical transmission systems have increased the speed and
capacity of
optical networks, the performance of such systems is limited by various
factors such as
chromatic dispersion and the fiber nonlinearity, which can cause pulse shape
change in
the case of baseband digital signals and distortions in case of analog
signals. These
impairments degrade the quality of the optically transmitted information.
Fiber
nonlinearities, for example, can give rise to crosstalk between optical
signals operating at
different wavelengths. When crosstalk occurs, modulation components of one
signal are
superimposed on another signal at a different wavelength. If the level of
crosstalk is
sufficiently large it will corrupt the information being transmitted by the
optical signals
impacted by this impairment.
[0003] One common cause of crosstalk, in an optical fiber communication system
with
multiple wavelengths, is Raman scattering. This type of crosstalk is caused by
stimulated
Raman scattering (SRS) in silica fibers (and other materials) when a pump wave
co-
propagates with a signal wave through it. Stimulated Raman scattering is an
inelastic
scattering process in which an incident pump photon loses its energy to create
another
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photon of reduced energy at a lower frequency. The remaining energy is
absorbed by the
fiber medium in the form of molecular vibrations (i.e. optical phonons) FIG.
(1) is a
schematic diagram of the stimulated Raman scattering process. The picture
depicts a
pump photon scattering in the Raman media. As a result of the scattering event
the pump
photon is annihilated and a new signal photon at the Stokes frequency is
created along
with an optical phonon at the Stokes shift frequency. Both energy and momentum
are
conserved:
hcopump = hcosignal + hcoOp phonon and hk pump = hksignal + hkOp phonon 5
where w, is the frequency of x and kX is the associated wavevector of x and h
is Planck's
constant divided by 27E.
[0004] The difference between the optical frequency of the pumping wave (the
higher
frequency) and the wave being amplified is referred to as the Stokes shift.
The Raman
gain window of a typical silica fiber is about 25 THz (terahertz) wide. The
Stokes shift
for the maximum Raman power transfer, in a typical silica fiber, is
approximately 13
THz. The Raman gain between two optical signals increases from zero as the
frequency
separation between the two signal increases until the peak gain is reached at
a 13 THz
separation. It then decreases back to zero as the separation increases beyond
25 THz. As a
result of SRS, energy from the pump wavelength can amplify a signal at a
longer
wavelength (lower optical frequency) so long as the optical frequency
separation between
the two signals falls within the Raman gain window of the fiber. The pumping
wave loses
energy (pump photon annihilation) to the signal wavelength (Stokes shifted
photon
creation) and also to the fiber (optical phonon creation). Thus, due to SRS,
the pump
amplitude decreases as its photon population depletes while the signal
wavelength is
amplified as its photon population increases.
[0005] SRS amplification is a benign process if the pump wave is not modulated
with any
type of information that would cause its amplitude to change with time. In
this case the
Raman amplification is fixed at a constant level over time. This simply serves
to boost the
amplitude of the Stokes shifted signal but does not disturb the information
that it might be
carrying. Problems arise, however, when both the pump and signal wavelengths
are
modulated. In this case the amplitude of the pumping wavelength is changing
over time
and, hence, the SRS amplification level varies in concert with the pump
modulation. This
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process imparts a scaled replica of the pump modulation onto the signal
wavelength
which is referred to as crosstalk. The crosstalk can interfere with and
degrade the quality
of the original information being transmitted by the signal wavelength. The
level of the
crosstalk modulation depends upon the Raman gain value, which, in turn,
depends upon
the optical frequency separation of the transmitted waves, amongst other
parameters.
Furthermore, the crosstalk process is a shared experience between the pump and
signal
wavelengths when they are both modulated. It is more probable that a pump
photon will
scatter and be annihilated in an SRS event when there are more signal photons
available
to facilitate the process. Therefore, at points in time-space where the signal
wavelength is
peaked, due to the modulation it carries, the pump will more easily lose
photons during
SRS. The reverse is true, as well, at points in time-space where the signal
wavelength is
smaller due to the time varying modulation it carries the pump is less likely
to lose a
photon in an SRS event. Hence the pump loses photons in concert with the
signal
wavelength's modulation. The result is that an inverted scaled replica of the
signal
wavelength's modulation is imparted upon the pump wavelength. This crosstalk
can
interfere with and degrade the quality of the original information being
transmitted by the
pump wavelength.
[0006] FIG. 2 shows how this transfer of energy gives rise to crosstalk. FIG.
2 is a
simplified illustration that is useful in facilitating an understanding of
Raman crosstalk
between two optical channels or signals S; and Sj, where Sj is at a longer
wavelength than
Si. FIG. 2A shows the signal Si and FIG. 2B shows the signal Sj. For
simplicity of
illustration Sj is shown as a signal with constant amplitude (i.e. a
continuous string of
zeros or ones). As indicated in FIG. 2C, the pattern of signal S; (dashed
line) is impressed
on the signal Sj by the process of Raman amplification. In other words, signal
Sj now
includes as one of its components the pattern of signal S;. Likewise, since
signal S; is
pumping the signal Sj, the pattern of signal Sj (had it been modulated) would
be
impressed upon the pump S; by the process of pump depletion. In a multiple
wavelength
system (three or more wavelengths) the crosstalk process is similar to what
has already
been described but the complexity grows since now there are multiple pumping
sources
and multiple signals generating crosstalk on each of the optical waves. The
Raman
crosstalk is a problem for both analog and digital modulation schemes.
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[0007] In addition to the generation of unwanted crosstalk the SRS process can
also lead
to the generation of Raman induced second order (CSO: composite second order)
and
third order (CTB: composite triple beat) distortions. These distortions occur
as result of
the nonlinear nature of the Raman amplification process which, in the
undepleted regime,
is exponential in form. Suppose there are two optical waves at wavelengths kS
(the signal
wavelength) and kp (the pump wavelength) propagating through a fiber of length
L with a
corresponding Raman gain coefficient GSp. If at the transmitter site the
instantaneous
optical power associated with kP is Pp(t) and the instantaneous optical power
associated
with kS is PS(t) then, in the undepleted power regime, the optical power at
the wavelength
kS at position L due to the Raman scattering is given by:
P,.(t,L)= P,.(t)e1G, P,. L,Pp(t) -aL] if ~p <ks (1a)
or
-Gs1, Pj. L~jf nnn'"p P, (t) - a L
.~' . ~
P~(t,L)=P,.(t)e if < kp (lb)
[00081 Here Leffis the effective length in the fiber at the pump wavelength, a
is the
power attenuation factor in the fiber at the signal wavelength, p, is the
running average
probability of finding the two signals in the same state of polarization, np
and nr are the
indices of refraction at the respective wavelengths. By defining a simple
function Hs,p 1 A,. > AP
H.t,r 1 npAp /1,. < AP (1 c)
n' A,.
Then (1 a) and (1 b) can be combined into a single equation:
[H.'P . G, p, Lff, e Pp (t) - a L] P.(t,L~= Ps.(t)e (ld)
This will come in handy when addressing a multi-wavelength optical
communication
system.
[0009] Expanding the exponential in (la) gives:
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P.(t, L) = P, .(t) 1+G L~1> ,.. PP (t) + 'GsP P' L,,)2 (PP (t))2 +... eaL
Sp Pr. 2
(2)
= P,. (t) + G IP Pc L'~t~ P, (t)Pr (t) + (G'P PL L,ff (t) (Pn (t)~ + . .. e- L
2
[00010] The second line of (2) provides the sought after explanation to the
Raman
induced crosstalk, CSO, and CTB distortions in the near zero dispersion
optical
communication system when the time dependent pump and signal wave powers are
represented by:
P, (t) = Po,. + Pm_, (t)
(3a)
= Po,. +Po,, m, f,(t)+CSOS +CTB,.
Pp(t)= Pop +Pmp(t)
(3b)
=Pop +Popmp fp (t)+CSOP +CTBP
[0011] Here Po, , PoF, are the average optical powers of the signal and pump
waves,
P,,,,. (t), P,,,P (t) represent the explicitly time dependent terms of the
optical powers, and ms,
mp are the respective optical modulation indices (OMI) for each laser. The
third and
fourth terms of the second lines in (3a) and (3b) represent the composite
second order
(CSOS, CSOp) and composite triple beat (CTBS, CTBp) distortions generated
within the
signal and pump optical transmitters themselves. The CSOs and CSOp distortions
are
native to the transmitters and are independent of the Raman interactions
taking place in
the fiber. The time dependent modulating functions fs (t) and fp(t)
represented the
information being carried on each optical wave. After substituting (3a) and
(3b) into (2)
and retaining only the most dominant terms one obtains:
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(4)
P(t,L)=
Po,[1+GsPPL1'e1,,PP] e aL+
P, ms. f.(t)[l+G" P" L"PPI e aL+G,nPr.Le frPo,(Popm, .f, (t)) e L+
CS0[1+Gr P,, L,rrP~~e aL +G" P~. L~~fPo.,CSO e-aL +G,p Pl. Lerr [P.~
msf,(t)][P,"zn fp(t)]e aL +
2 -aL
CT,q[1+G,, Pi, L~,,Pn]e aL +G"Pr LefrPo, CTB e -aL + G,, Pr 2 Le,~ [Ps
n?,fs(t)][Popmn fp(t)]
e
[0012] The second line of (4) contains the undistorted signal transmitter's RF
subcarrier
modulation multiplied by the Raman gain term (1 + Gsp P,, L~ff Pop) and an
additional first
order RF subcarrier term arising from the modulated pump laser. This
additional first
order term is RF subcarrier crosstalk, a direct transfer of the pump laser's
RF subcarrier
modulation ( Ponmp fn (t)) to the signal carrier scaled by the Raman factor
Grp P,, L~f~ Po,. =
When the RF subcarrier crosstalk is exactly in phase the signals
constructively add (plus
sign) while if they are exactly out of phase they destructively interfere
(minus sign), all
other phasing possibilities fall between these two extremes. The first terms
of the third
and fourth lines are the signal laser's generated CSOS and CTBS terms each
multiplied by
the same Raman gain term as the signal laser's RF subcarrier modulation. The
second
terms of the third and fourth lines are respectively the direct transfer of
the pump laser's
CSOp and CTBp distortions (distortion crosstalk) to the signal wave scaled by
the same
Raman factor as the RF subcarrier crosstalk that is transferred from the pump
wave to the
signal wave. The third terms of the third and fourth lines are the new Raman
generated
CSOR and CTBR distortions resulting from the product of the signal and pump
lasers' RF
subcarrier modulations. Collectively, the RF subcarrier crosstalk term, along
with the
second and third terms of the third and fourth lines constitute degraded
performance of
the signal transmitter due to the Raman interactions between the modulated
pump and
signal lasers. These will be denoted collectively as the Raman induced
distortions. If the
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pump and signal lasers' modulations are not in phase with one another
interference can
also result between the various terms within each line of (4). It is the
purpose of this
invention to elucidate the methods and apparatus that can be utilized to
reduce the
deleterious effects of the Raman induced RF subcarrier crosstalk and CSO
distortion
terms. The Raman induced CTB is insignificant in magnitude and not treated
here. When
there are three or more lasers in the system (4) must be modified to account
for the
multiple pumps. For a system with n transmitters (4) becomes:
(5)
P(t,L) _
" l-aL
P. 1+L, t~IHs,PGt,PPL.,.PP~, le +
P=1 J
( n 1 n / ILYL
Posm, f,.(t)+L~(IjHs,PGs',V PL s,P PoP +PSL~KlHr,P PoVmP./Plt)Cs,p PI, s,V e
l P=1 P=1
[cs[i+L,.tljI~,,PCS,pPL,,PPP~+Po,LfflHs,pCs,pPi,s,YCSO,,+P,mff,(t)LKlH+,PC,,pPL
,,PPPmpf,(t) e aL
P=1 P=1 P=t ]
l ( 2 _
[cT[I+P J+P ~G CTB [tp P m,f (t) e (J' s,P s,P I, s,P ~P ~s' ~ s,P s,p r[.
=s,V P ~s' S' 2 S,P 1, r~P ~P 7 P
]21 V=~ V=~ Y=~
[0013] The summations in (5) are over the parameters of the "n" transmitters
in the
system. It is important to note that equations (1) through (5) are to be
interpreted as being
in the optical domain. Therefore the powers in these equations, including the
distortions
(CSOS, CSOp, CTBS, and CTBP) are optical powers and not electrical (or RF)
power
levels.
[0014] The Raman induced crosstalk and nonlinear distortions are more
pronounced
when the wavelengths are located near the zero dispersion wavelength of the
optical
transmission media through which the signals are co-propagating (i.e. the
optical fiber).
In the case of a near zero dispersion system the optical pump and signal waves
are
propagating at nearly identical group velocities through the media. The zero
dispersion
wavelength of a transmission media refers to the wavelength at which an
optical signal
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will have no change in (inverse) group velocity with respect to changes in its
optical
frequency. The zero dispersion wavelength differs for different transmission
media. In
this case, the relative positions of the waves with respect to one another
will remain
nearly fixed throughout the length of the transmission media. Thus, if the
signals Si and Sj
are at or near the zero dispersion wavelength, they will largely maintain
their relative
phase with respect to one another. Hence, with very little walk off occurring
between the
optical channels the Raman induced crosstalk and distortions can build up
along the fiber
in a constructive manner. The dispersion will generally increase as the
wavelength
difference between the optical signal and the zero dispersion wavelength
increases. If the
signals S; and Sj are located at wavelengths far displaced from the zero
dispersion
wavelength, their relative phases will change as they propagate down the
transmission
path. The levels of Raman induced crosstalk and distortions are much lower in
the
nonzero dispersion scenario because, as the signals walk away from one
another, it
becomes more difficult for the crosstalk and distortions to build up
constructively along
the fiber length.
[0015] Accordingly, it is desirable to have a method and apparatus for
reducing the levels
of Raman induced crosstalk and distortions that arises among the individual
channels
comprising a WDM optical system. This is particularly true in the case of a
system
utilizing optical channels that are located near the zero dispersion
wavelength of the
transmission medium.
Summary of the Invention
[0016] A method and apparatus is provided for transmitting a WDM optical
signal. The
method begins by modulating a plurality of optical channels that are each
located at a
different wavelength from one another with a respective one of a plurality of
information-
bearing broadcast signals that all embody the same broadcast information, at
least one of
the broadcast signals being out of phase with respect to remaining ones of the
plurality of
broadcast signals. Each of the modulated optical channels are multiplexed to
form a
WDM optical signal. The WDM optical signal is forwarded onto an optical
transmission
path.
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[0017] In accordance with one aspect of the invention, a phase shift of 180
degrees may
be applied to at least one of the plurality of broadcast signals relative to
the remaining
ones of the plurality of broadcast signals.
[0018] In accordance with another aspect of the invention, a phase shift may
be applied to
selected ones of the plurality of broadcast signals so that the optical
channels modulated
thereby have contributions to Raman crosstalk at a selected one of the optical
channels
that are diminished by contributions to Raman crosstalk from optical channels
modulated
by RF signals that do not undergo a phase shift.
[0019] In accordance with another aspect of the invention, a phase shift may
be applied to
selected ones of the plurality of broadcast signals so that first and second
broadcast
signals modulate optical channels at first and second optical wavelengths,
respectively,
such that Raman crosstalk and induced distortions are reduced at a third
optical channel.
[0020] In accordance with another aspect of the invention, a narrowcast signal
may be
combined with each broadcast signal prior to modulating.
[0021] In accordance with another aspect of the invention, a difference in
wavelength
between any of the optical channels may be less than the maximum power
transfer Stokes
shift in the optical transmission path.
[0022] In accordance with another aspect of the invention, the relative
amplitudes of the
first, second and third modulated optical channels may be adjusted to further
reduce the
Raman crosstalk.
[0023] In accordance with another aspect of the invention, the relative laser
polarization
of the first, second and third modulated optical channels may be adjusted to
further
reduce the Raman crosstalk.
[0024] In accordance with another aspect of the invention, the optical
transmission path
may be a HFC network.
[0025] In accordance with another aspect of the invention, the optical
transmission path
may be located in a CATV transmission network.
[0026] In accordance with another aspect of the invention, the optical
transmission path
may be located in a PON.
[0027] In accordance with another aspect of the invention, the optical
channels may be
located at wavelengths at or near a zero dispersion wavelength of the
transmission path.
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[0028] In accordance with another aspect of the invention, the optical
channels are
located at wavelengths remote from a zero dispersion wavelength of the
transmission path
but dispersion impact is not significant.
[0029] In accordance with another aspect of the invention, WDM optical
transmitters are
provided. Each transmitter may include ~~~~~e o 1' a plurality of optical
sources for generating
optical channels located at different wavelengths; a plurality of optical
modulators each
having an input for receiving a respective one of a plurality of information-
bearing
broadcast signals that all embody the same broadcast information, each optical
modulator
being associated with a respective one of the plurality of optical sources to
thereby
provide a plurality of modulated optical channels; a phase shifter for
adjusting a phase of
at least one of the plurality of broadcast signals so that it is out of phase
relative to
another of the plurality of broadcast signals; and a multiplexer coupled to
the plurality of
optical sources to receive and combine the modulated optical channels to
produce a
multiplexed optical signal.
Brief Description of the Drawings
[0030] FIG. 1 is a schematic diagram illustrating the stimulated Raman
scattering
process.
[0031] FIGs. 2A and 2B show signals S; and Sj, respectively, and FIG. 2C shows
signal
Si pumping signal Sj, for the purpose of facilitating an understanding of
Raman crosstalk.
[0032] FIG. 3 shows a simplified block diagram of a conventional WDM
transmission
arrangement.
[0033] FIG. 4 illustrates a WDM system for common broadcast and different
narrowcast
transmissions in CATV transmission systems.
10034) FIG. 5 shows WDM optical signals S1, S2, S3 and S4, with signals S2 and
S3
selected to be 180 degrees out of phase with respect to signal S 1 and S4.
[0035] FIG. 6 shows one example of a transmitter arrangement in accordance
with the
present invention.
[0036] FIG. 7 is a flowchart showing one example of the method performed by
the
transmitter arrangement depicted in FIG. 5.
[0037] FIG. 8 shows the architecture of a Broadband Passive Optical Network
(BPON) in
which the transmitter arrangement of FIG. 5 may be employed.
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Detailed Description
[00381 Equations (4) and (5) presented above are the starting points in the
discussion on
eliminating the undesired Raman induced crosstalk and distortions that occur
in a near
zero dispersion optical communication system. Suppose that a constant phase
shift can be
applied to the composite RF subcarrier modulation applied to each transmitter.
This can
be accomplished by means of a broadband phase shifter such as a transformer
based all
pass filter that has a constant phase shift across the RF band of the
subcarriers. The
composite modulation signal feeding each transmitter is run though such a
phase shifter
specifically tailored for each laser with a specified phase. For the two
wavelength system
if a phase shift of ~p5, is applied to the signal laser and phase shift of
~pF, is applied to the
pump laser equation (4) is then modified to the following in the frequency
domain:
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Po, [1+GspP1, Leff pop]e -aL +
po.s m,. elcPI3[.fs(t)J+ [1+G,PPI,L,t~Pople-aL +Gp P,. L~~fpo.~ popmp el~p
3[fp~t~t+ e-aL +
L', csoe~~~ + e i 2~s j~7E cs~" ~ ~ 2 K(sos~ (po s~ m,, )2 [l + G,p P~ LO ff
po ple - a L+
ocsoe# + e i 2(pp NEcsoe~ 2 Kc:sop (po p mP )2 G p Pr. Le, l'o., e- a L+
e (( ti vp ) Noc:sOe~ + el ~~s +~p ~NECSC~e~ - G.~~ Pr. L~~ 7'o.s m.spo pm pe-
a L+
2
ei2cps 3NocrHct +ei3(ps ~TECrs~f
r) KcTB,(~'o, m.)3 [1+GsP P1. L~~rpople-aL +
ei2(pp 3Noc1H~~ +ei3(ppNECraeff 4 Kcrxplpop mp) Gsp Pr, Leff pot e-aL +
3e l cP.~ ocTH~~~ + el '~' + 2~p ) NECTS~~ ~'Gsp P~ L~ff )2 po, m, (Po pm p)2
e- a L+ C.C.
4 2
(6)
[0041] Where C.C. means complex conjugate and s[f,.(t)r is the positive
frequency
portion of the Fourier transform of the RF subcarrier modulation signals. Also
the
parameters Kcsos, KCSOp, KcTSs, and KCTBp are given by:
2 K s0a - ~ e]ecrrrcal (7a)
ms pos Ncso~N resns
2 (7b)
K ( =sop = , e~ecrrica~
mp pop Ncsoefr resop
~
K('7'H., = ( 2 4 (
~ eleclrical
7~t
lms PO.s ) 'v C7'B eff r('TB.s 7c
(7d)
K '(, 7,Bp = 4
l2 r electrica!
\m p PO p )NCTB eJj 'TBp
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[0042] Where r,-'!s'or'c ' and r~sOpr"ar are the native CSO ratios of the
signal and pump
y electrACa! are the native CTB ratios of the
transmitters in electrical units. Also r e'eC"~ ' and TaP
r~sc
signal and pump transmitters in electrical units. N,'s~,~,, is the effective
beat count (after
taking into consideration the random phasing of the RF subcarriers) at a
specific CSO
frequency. N'., is the effective beat count (after taking into consideration
the random
phasing of the RF subcarriers) at a specific CSO frequency.
[0043] For a multi wavelength system if a phase shift of ~p, is applied to the
laser under
investigation and phase shifts of ~oP are applied to the other lasers equation
(5) is then
modified to the following in the frequency domain (ignoring the third order
CTB terms
which are insignificant):
(8)
P,.(f,L)=
Pos~e-aL 1+Left1H"P G"P Pi,S,P PoP +
P=j
" _ "
Pos ms ei~S ~~t~~+e-aL [1+Leff.P G,P Pz.,,P PoP +e-aLLer~Po. *(t)]+1H,P C,P
PI.S,P PoPmP e(pP +
P=1 P=1
[sott+ei2 ~s ~IEC:soc!fr~ 1+Lefl~H~,P C~,P Pi,.~~,P PoP 2 Kcso.,~~Pos ms~2e-aL
+
P=1
cG~~,P PLS,P (PoP mP )2 +NECSOe1>JKcsoPHs~,P C~,P Pz s,P (PoP mP )2 e~ ~~P
Pos~Let~ ~ e-aL +
~4C.'soejrjHs,P G,,P pL.s,P PoPmpe-Z(pP +~~C:4oeff~Hs,P GS,P PLs,P PoPmPel~P
Po.s m.SLfrel~. ~ e-aL +C.C.
P=j P=1
100441 There are n of these equations, one for each of the transmitted
wavelengths in the
system, so that (8) is actually a matrix equation for each of the impairments.
Note that the
Raman gain is zero when the optical frequency separation between the signals
goes to zero
we have then for the s = p terms of (8) (the diagonal elements of the matrix
equation:
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-aL +ei2rPN~~ ~ (P m)~e-aL
P(f L) -Po,e-aL+Po.~ m,es[.f(t)].e o
csoe E cco~ cso.o,
+ C.C.
(9)
[0045] This is just the original signal including the native CSOS term
uninfluenced by the
Raman interactions.
100461 To understand how to eliminate the impairments each particular
impairment must be
set equal to zero by extracting the appropriate terms from either (6) or (8).
[0047] For the crosstalk in the two wavelength system this leads to the
following equation:
_ i
G.~~n PL L,rrPos Po~ ei~P' +Gsp PL Le.ffPoSPopmP e(pp = 0 (10)
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[0048] Which leads to the following conclusions:
100491 The Raman induced crosstalk in a two wavelength, near zero dispersion
system,
can only be eliminated if the transmitters have identical OMI's (mp ms) and
the
modulations are out of phase by a radians or if the length averaged
polarization overlap
p, is zero. The polarization condition can only be approximately satisfied by
launching
the pump and signal transmitters in orthogonal polarization states. In this
case p,, would
start out at zero and gradually drift towards the value of'/2 as the signals
co-propagate
down the length of the fiber. The longer the fiber the closer the value of pL
will be to 1/2
at the end of the link. Therefore the polarization method alone is less
effective in longer
fiber links.
[0050] Considering the CSO terms in the two wavelength system, equation (6)
leads to
two equations one for the difference beats and one for the sum beats. Denoting
the total
power in the CSO due to the difference beats as Po,so,a,a, and the total CSO
power due to
the sum beats as then the CSO terms in (6) give:
Pocso1o1a1 = Nocsoeff ~ e a L~cso~(Pos m., )2 + Kcsos (Pos ms )2 Gsp PL L~>~Po
p+
KC'SOp (POp mp ~ Gsp pL Leff Pos +E' Ps (Pp ) Gp pL LefJPOs Y12, POpYl2 p + l
.l
(11)
P =N, fe_aL ~ ei2K(P m)2+e12K(P m)2GLfj P+
CSOto[al E COefj (-SOs 0 s s ( SOs 0 s p~ I, e 0 p
e~2 cp pKcsop (Pop m p Y C'sp Pi. L, Po, +e~ ((P, +(0p) Gsp Pc L~ffPos msPopmp
+ C.C.
(12)
[0051] These equations, when set equal to zero, lead to following the phasing
requirements in order to reduce the CSO levels in a two wavelength system:
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~p, = 2n)T and ~pl, =)r where n is an integer (13)
[0052] With these phase requirements satisfied (11) and (12) both reduce to
the same
equation. Solving for the optimal value of the product p, Po, gives:
1 1
Pj.Pon (14)
electrica/
G Sp Lerf mp ~CSOs 1 r electrical
1 + electrical ~ mpNCSOell rC:SOs
ms r('SOp
[0053] To summarize, in order to reduce the effects of CSO distortions on two
identically modulated lasers in a near zero dispersion system the modulation
applied
to the pump and signal transmitters should be out of phase by 7r radians, and
the
product of the length averaged polarization overlap probability p,, and the
pump
launch power Por should satisfy (14). If (14) indicates an optimal p, value of
0.5 ,
then this can be accomplished by launching one optical wave in a linear
polarization
state and the other in a circular polarization state. Equation (14) is only
valid if (13) is
also satisfied for the modulation phases applied to the transmitters. Notice
that the
phasing conditions for CSO reduction and crosstalk elimination are identical.
The
crosstalk elimination also imposes the requirement that mp mS.
[0054] Next examining the methods of eliminating or reducing the crosstalk in
a multi
wavelength system. Equation (8) leads to the following matrix equation for the
crosstalk on all wavelengths in the system:
n
x,. =Po., m., el('0, *(t)]+e-aLL'#lH,p Gl,p PL.,P PoP +
p=1
-aL ~( ~ i~Pp
e LetlPO S t)l+ H,,p C'',P Pz.,,p Pommp e
p=1
(15)
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[0053] In (15) xs is a placeholder to remind us that there are n such
crosstalk
equations that must be solved simultaneously (all of the xs are to be set
equal to zero
in order to cancel out the Raman crosstalk on each wavelength):
xt . = 0=ms . el~' I H.,P ~,G.P POP +I HS.,P Gs,p PI, s,P POPmP e l ~P (16)
~ PL.e, P
P=1 P=1
[0054] This further reduces to:
xs. = 0 (m, ei~P, + mp ei(,Op HS,P G,P PI ~,p Pop (17a)
P=1
which can be put into the form:
n
1+ m el ~Pp - ~P., H,,p Gs~,P PI.,P Pop (17b)
x,. = 0=I
,
m
[0055] This is easily expressed as a matrix equation:
0 0 71,2 71,3 Yl ,n POl
0 72,1 0 72,3 72 ,n P02
0= 73,1 73,2 0 ... 73,n P03 (18)
0 Yn,1 7,,2 Yn ,3 0 POn
where the elements of the n x n crosstalk interaction matrix are given by:
Ys,p = 1+ m ei(~p ~s)
Hs,p Gs,p PLs,p (19)
mS.
[0056] Notice that the transpose elements are related by
Y.S = + m el'~Pp ~P.' H G (20a)
p p : p P/.r,P
ms.
ms i(~s ~P
Yp s= 1+ m e Hp Gs,p P~..,,P (20b)
P
So that if mp ms and for kS>a,p then:
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i(~Pr ~P')
,r (20c)
Ys, r= l+ e G,r PiS
_ ns A., i(~P.S - ~Pr ) n.,.
A5. * yr'' ~ 1+e G~.,r Pr..s~,r = -Y
n .,~.r (20d)
r r nrAr
In most typical WDM optical communication systems the ratio of refractive
indices
and wavelengths is approximately equal to unity:
ns/i' , 1 (20e)
nr~r
[0057] The only way that (18) can be satisfied in a nontrivial way, under all
conditions, is if each of the matrix elements is zero. This can happen if:
yV r= 0 if ~pr - ~ps =)z and also mp = ms or pl,s r= 0 (21)
[0058] Because polarization is a two dimensional Hilbert space, for any agreed
upon
basis, there will be exactly two orthogonal polarization states. All other
polarization
sates can be expressed as a linear combination of the chosen basis states.
Furthermore,
once any one of the modulation phases is fixed the modulation phase of any
other
signal, in the same polarization state, must be displaced by 71 radians.
Therefore for
any two states with the same polarization there are only two phases that will
satisfy
the first line of (21) (~p, ~p+;c). Essentially, then, there are only two
orthogonal
polarization states and two phases to choose from, the direct product of
modulation-
phase states and polarization then forms an effective 2 x 2 vector space in
which there
are four orthogonal states. If the two orthogonal modulation phase states are
~o) and
I ~p +ir) and if the polarization basis states are denoted by //) and I 1) ,
then the basis
states of the newly formed 2 x 2 modulation-phase and polarization space are
given
by:
I (p,ll)U, 1 (p, 1)h~ (p +;r,1/) (p +7r,i), (22)
[0059] In other words, (18) can only be satisfied exactly for a system
consisting of at
most 4 independent optical transmitters (each with identical OMI values so
that (21)
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is satisfied). These basis states will make all of the matrix elements in the
4 x 4 crosstalk interaction matrix zero. In (22) the subscripts a,b,c,d were
added to
help in identifying each of the basis vectors.
[0060] Within any set of four basis vectors the matrix elements YS , are all
zero
because one of the following must be true:
Gs.n = 0 if s=p (23a)
(~p, ( 'OP ) = 0 if ~p, = ( '0 p + 7T (23b)
I~Pol' ( PolP)2= 0 if the two polarization states are orthogonal (23c)
[0061] Where Pols and Polp are just the polarization states of the st" and pt"
optical
waves. Here it is implied that (Pols I PolP)2 is averaged over the fiber
length so that
_
KPo1 ~. Pol P) 2 =PLs,n =
[0062] The crosstalk is zero within the group of four orthogonal states. This
method
completely eliminates the Raman induced crosstalk along with the static Raman
gain
imparted upon the signal term.
[0063] Now suppose a system exists with more than 4 transmitters, it is
impossible
using the above method to completely eliminate the Raman generated crosstalk
in the
system. However, by simplifying the approach so that we explicitly treat only
the
Raman induced crosstalk and not the Raman gain on the signal under
consideration
we may significantly reduce the level of the Raman crosstalk. Taking this
approach
we ignore the first term in (16) so that we now have the following matrix
elements:
P = mPei(~PP - ~P.~~ ~j ,n ~'.~,~ Pr,.,,P (24)
Y.~,
[0061] The transpose elements are related by
Y.,,v _ mn ei((Pp -~Ps H.,,n G.,,n pl.S,n (25a)
-
YP s- ms e~~~~ - (pp HP,S Gs,P A'S,p (26b)
So that for XSAp then:
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YS,,, = mp ei(~P, -~PJ G.,p P~.s~,r (27a)
nsAz. i(~Ps - ~Pp ) 'n.,~ n.~~~'s 27b
y~ ~_-ms. n~ e G,~,p PL.s~,p m n~ Ys~,n ( )
pn p n n
If we let
SS p = mp n_pAp (28)
ms nsAs
Then for .~ < A2 ... < An_1 < An under these simplifications (18) reduces to:
o 0 -~1 z 72,1 -~1,3 73,1 -~],n Yn,] Po1
0 72,1 0 - E2,3 732 -~2 n Y*z P02
)
0- 73,1 Y3>2 0 P03 (29)
Yn,3
O Yn,l Yn,2 7n,3 ... 0 P0n
If the system is further restricted to have an odd number of wavelengths (n
odd) then
each row of the n x n Raman crosstalk interaction matrix contains an even
number of
nonzero elements. We may arrange the system so that the terms in the last row
cancel
out in pairs by assigning alternating phases as follows to the n wavelengths
of the
system:
~P] = ~~ 1 (P2 = rP1 + ~1 (,03 = (10] ... (ton-1 = rP] + /71 ~Pn = rP] (30a)
The simplest scheme is to let rp, = 0 then the phases assigned to the n
wavelengths
alternate between 0 and 71 (1800) as:
01, 1802, 03, 1804, 05,1806,...,0õ (30b)
Where the subscripts refer to the wavelength assigned the particular phase in
the
alternating series. The phases assigned to the corresponding wavelengths must
alternate in this fashion in order to ensure maximum cancellation of the Raman
induced crosstalk signals. This can easily be deduced in the case where the
coefficients ss p are all set equal to unity ( s, & 1) and the optical launch
powers are
arranged so that every term in each line of (29) has the same magnitude. In
this case
the phases will alternate by 180 degrees and because there are an even number
of non
zero terms in each line total cancellation of the Raman crosstalk is achieved.
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In the actual case the coefficients s,p will not all be equal to unity but
they will be
very close to one. Hence we conclude that under these conditions the crosstalk
will
nevertheless be minimized if not totally eliminated.
[0074] Now moving on to treat the Raman induced CSO in the case of a multiple
wavelength system. The CSO terms are the last three lines of (8). We follow
the
procedure of the previous paragraphs and set the sum beat and difference beat
terms
equal to zero independently giving:
n
+
1'ocsoraaa~ = Noc.soeff 2 Posmse-aL +LeffJHs,p GS,P s,P Pop
PL etecr
rical
p-1 Ncsoe~ resos
, -aL n mp 2Pop
Nocsoeff-Posmse 1- Hs,P Gs,P PLs,p Leff +
2 [=i ms Ncsoeff resoprr~ar
n
NocsOeff 2 Pos mse-aL JHs,p Gs,p PLs,p Popmpe-l~p Leffe~s +C.C.
P=~
(31 a)
[0077] There are n of these equations, one for each of the transmitted
wavelengths in the system,
_ n
P~CSOtotak =el 2 ~s~ECSOe2 POs mse aL 1+Le..~ZHsp Gs,p PLs,p Pop 2 +
~~ T ~ y, electrica/
1 VCSCkff CSOs
*n ~n -aL n mp 2Pp i2~pP
CSOef~sme ~ms relectrica! HGLs,p e ]4ff +
1 VCSChff CSOp
_ [~Hsp ~EcsOe,~2 PS mse aL Gs,p PLs,p 1'optnpel~p Leff e1~Ps +C.C.
(31 b)
[0078] There are n of these equations, one for each of the transmitted
wavelengths in
the system. In (31 a) and (31 b), equations (7a) and (7b) were used to express
the Kcsos
and Kcsop constants in terms of the native CSO ratios of the signal and pump
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transmitters. Equations (31) are actually each n x n matrix equations. Setting
each of
these equations equal to zero gives:
n I P MP Z~ A - ~901
04s - electrica ~H 'n~'p~'~'p~r eteclrrcal electrica 2 e
~ .Ncs~at reso.~~ Ns~af reso,~ NNst~f resoP
(32a)
2 n _ 1 mp I Z2(C~P-~) mP l~P-~
0~ _ +IH,P q,P s,P PP t- e ~ e
electricat ~" etectrrcat electncal
L effN
CS(2f reso.,Pl ~sc2f resos ~sClf I c:sop
(32b)
[0080] Where Oo, and OE are simply placeholder to remind us that there are n
such
equations to address. Each of these equations can be expressed in matrix form
as:
0 V/1 0 171 2 17l 3 ... F1 n Pol
0 qj 2 r2 1 0 r2 3 ... F2 n P02
0= yr3 + 173,1 r3 2 0 ... r3 ,n P03 (33)
[0]
O jrn 1 rn 2 rn 3 ... 0
n
[0081] Where the various matrix elements are given by:
1
jV s , ete~trt~at (34)
Leff Ncsoeff ~csos
[0082] For the difference beat equation (32a) the matrix elements r, P are:
rs = HS Gs Pr,s 1 + mp 1 + mp el(~s -(PP ~
p p p p ~ electracal electrical
NCSOeff CSOs ms NcSOeff FrCSOP 2
(35a)
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[0083] While for the sum beat equation (131b) the matrix elements 17, p are:
mp 1 i2(~p-~s/ mp t\~p-~sl
Ts,P -Hs,p Gs,p PLs,p e +e
electrrcal yyls * tr y electrrcal 2
N'CSC~ff rCSOs LVCS(kff CSOp
(35b)
[0084] The column vector of yrS. elements arises from the native CSO's of each
transmitter in the system. The crosstalk equation (18) had no such column
vector because
there is not any "native crosstalk."
[0085] All of the purely real terms in (35a), (35b) as well as (34) are
positive valued. If
there is to be any possibility of canceling out the positive terms, in order
to satisfy (33),
the last term of (35a) and (35b) must be real and negative therefore we may
impose the
first constraint on the phase angles:
~pp -(0.,. =;z (36)
[0086] Similar to the case of crosstalk elimination, once any one of the
modulation
phases is fixed the modulation phase of any other signal must be displaced by
7r radians.
Therefore for any two states there are only two phases that will satisfy (36)
(~p, ~9 + /T).
Essentially, then, there are only two modulation-phases to choose from. This
can again be
likened to a two dimensional Hilbert space with modulation-phase states ~p)
and I ~p +;z)
Unlike the crosstalk case, here we do not want the length averaged
polarization overlap
probabilities to be zero in all cases otherwise the 1, matrix elements would
all be zero
and there would not be any chance of satisfying (33). Since we wish to
maintain those
terms which are out of phase with the sth state by 7 radians we do not require
orthogonal
polarization states in general. However, for those states assigned the same
modulation-
phase as the sth state all of the terms of the matrix element I',. n will be
positive and
therefore these states cannot satisfy (33). These states should be in
orthogonal
polarization states with respect to the sth state under consideration, so that
p,, , n;:t~ 0 and
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the matrix elements will be zero. If we then require that the states with
modulation-phase
that are offset by ir radians to be in parallel polarization states p, s p& 1
so that these
matrix elements dominate then we have once again defined a two dimensional
polarization basis. Just as in the crosstalk discussion the direct product of
modulation-
phase states and polarization states then forms an effective 2 x 2 vector
space in which
there are four orthogonal states. If the two orthogonal modulation phase
states are ~p)
and ~p +;z) and if the polarization basis states are denoted by //) and 1) ,
then the basis
states of the newly formed 2 x 2 modulation-phase and polarization space are
exactly the
same as (22).
[0087] Also note that for those states in which (36) is satisfied that (35a)
and (35b) both
reduce to the same equation:
7-~ _u ~+ 1 mp 1 _ mp
1 s, p 'L s, p vs, pPL s, p t electrical + electrical
Ncsoeff resOs ms Ncsoeff rCSOp 2
PL s,p
(37a)
[0088] For those states in which ~p, = ~pp (35a) and (35b) both reduce to the
same
equation:
1 mp 1 mp
Fs,p Hs,p Gs,p PL s,p t electrical + r electrical +
NCSO eff cSos ms NCSO eff ~rCSop 2 N 0
pLs,p
(37b)
[0089] We will require that pL p& 1(parallel polarizations) for (37a) and p,,
, p;Z- 0
(orthogonal polarizations) for (37b).
[0090] Since the Hilbert space is just 4 dimensional (2 x 2 vector space) we
can only
satisfy the phase and polarization conditions exactly for the four orthogonal
basis states
given by (22).
[0091] Suppose we have the four states:
/11 1 Po>1( '0,A21 Po21 (10,1),IA3,Po3,~P+)z,a,a,Poa,~p+7F,(38)
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[0092] Then (33) reduces to the following:
~Vl 0 0 I'i 3 0 pol
1 yrZ - 0 0 0 1: 2 4 Po2 ~3 r3 1 0 0 0 P03 (39)
Y 4 0 174,2 0 0 P04
[0093] The four equations are decoupled and can easily be solved. The
solutions are
identical to (14) with the polarization overlap probability set equal to one
(since we have
l 1
pop -- (40)
electrical
H'S p G'SpLer~ mp rcSO.e 1 r I electrica(
mpN~-SOeJJrcSOs
1 + electrical 2
ms r('SOp
[0094] In (14) there was some flexibility in adjusting the transmitted power
because the
value of p, could be adjusted to compensate. In the four wavelength case the
p, , p each
has a fixed value. Compared to the two wavelength case in which it was deemed
desirable
to set the polarization overlap probability equal to V2 here the non zero
terms of (39) all
have polarization overlap probabilities set equal to 1. Therefore, the launch
powers for the
four wavelength system will need to be half that of the two wavelength system
launch
power values for similar circumstances.
[0095] In (39) the diagonal terms are zero because Gp p= 0, the Raman gain is
zero
when the wavelengths are identical.
[0096] Evidently, it will be quite difficult to eliminate CSO distortions in
the case of five
or more wavelengths. For example, suppose there is an eight wavelength system
with the
following states:
~, ,Po" Cp,ll>, 1/~,P02,(jo,-1'), I/~31 P03,( YO +)C,1/)' I A41 P04I +z, 1>>
(36)
A51 P05~(p,1/), IA61 P06~(10,1), .i-i,Po" rP+Z,ll~, A8,P08,~P+z,l)
[0097] Then (28) becomes
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yil 0 0 T(-)1,3 0 I'(+)1,5 0 I'(-)1,7 0 PoI
yi2 0 0 0 17(-)2,4 0 h(+) 2,6 0 h(-)2,8 Po2
yr3 I'( )3,1 0 0 0 T( )3,5 0 F (+) 3,7 0 P03
~_ 1) yr4 _ 0 I-'() 4,2 0 0 0 I-'(-)4,6 0 I'(+)4,8 P04
1V5 F(+)5,1 F ( )5,3 0 0 T(-)5,7 0 P05
Vf 6 F(+)6,2 T( )6,4 0 0 0 T( )6,8 P06
V 7 I(-)7,1 I(+)7,3 I'(-)7,5 0 0 0 Po7
y/8 I-'(-)8,2 I'(+)8,4 0 I'(-)8,6 0 0 Po8
(37)
[0098] In (37) the superscripts (-) or (+) simply indicate whether the mp /2
term in the
matrix elements is negative or positive signed. Also notice that only even
subscripts are
paired together and only odd subscripts are paired together and that no even-
odd pairing
exists. Therefore (38) can be reduced to two 4 x 4 matrix equations:
Vl 0 I'(-)1,3 h(+)1,5 I'(-)17 Pol
V3 _ I'(-)3 1 0 h(-)3,5 h(+)3,7 P03 (38a)
-V5 I'(+)5,1 I'( )5,3 0 I'(-)5,7 P05
Y7 F(-)7,1 I'(+)7,3 I'(-)7,5 0 Po7
yi2 0 I7(-)2,4 t'(+)2,6 h(-)z 8 P02
l y/4 _ h(-)4,2 0 I7(-)4,6 17(+)4,8 P04 ~ y/6 I-'(+)6,2 I'(-)6,4 0 I-'(-)6 8
Po6 (38b)
Y8 I'(-)8,2 17(+)8,4 I'(-)s,6 0 P08
[0099] Therefore the require launch powers are given by:
-
Pol 0 T-(-)1,3 h(+)1,5 I'(-)1,7 1 Y/1
P03 1 T( )3,1 0 T( )3,5 F(+)3,7 Vf 3 (39a)
P05 F(+)5 I F (-)5,3 0 h(-)5,7 W5
P07 I'(-)7,1 I'(+)7,3 I'(-)7,5 0 W7
and
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p02 0 I'(-)2,4 I-(+)2,6 j'( )2,8 -1 y/2
P04 I'(-)4 2 0 0-)4,6 I'(+)4,8 1V4 (39b)
PO6 h(+)6 2 I'(-)6 4 0 I'( )6,8 y/6
PO8 I'(-)8,2 I'(+)8,4 I'(-)8,6 0 198
[0100] In (38) and (39), when calculating the matrix elements using (32a) or
(32b), all of
the polarization overlap probabilities p,,,. r are equal to one. Equations
(39a) and (39b)
can easily be solved using a computer based mathematical analysis program. The
algorithm can be incorporated into a system controller that continuously
adjusts the
modulation-phase and polarization states of the transmitted optical waves to
correct for
changing environmental conditions that might upset the delicate balance of the
parameters that are required to reduce or eliminate these impairments.
[0101] To summarize, it is possible to completely eliminate Raman induced
crosstalk and
CSO distortions for up to four identically modulated transmitters in a near
zero chromatic
dispersion optical communication system. For systems consisting of five or
more optical
channels neither impairment can be completely eliminated although the
impairments can
be reduced by judiciously assigning modulation-phase and polarization states
to the
transmitted waves. Now suppose a system exists with more than 4 transmitters,
it is
impossible using the above method to completely eliminate the Raman generated
crosstalk in the system.
[0102] However, by simplifying the approach so that we explicitly treat only
the Raman
induced CSO and not the native CSO or Raman distortion crosstalk terms on the
signal
under consideration we may significantly reduce the level of the Raman induced
CSO if
not completely eliminate it. This can be accomplished quite easily by simply
ignoring
those terms in (32a) and (32b) which contain the native CSO factors r ereC1Y"
l or r e'e"r" r
cso~ csoP
Taking this approach we now have the following matrix equations:
" l (Cp. - CpP)
Oos.-1
Hp~,~s.~,'n,e Pp (40a)
~s~~
0,,. =1H.,P ~~,P ~ ,,P mPei (p -n ( V40b)
PA
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The matrix equation (33) reduces to:
0 0 T l 2 Tl 3... TI n POl
0 F2,1 0 r2 3 ... F2,n PO2
0 = ~1 F3 2 0 . . . 1~3,n P03 (41)
0- -Fn 1 Fn 2 Fn 3 ... 0 -P0n
Where the matrix elements are, for the difference beat equation (40a):
rs pA -YYlp2l (~s ~P )Hs p Gs, p/OLs, p (42a)
And for the sum beat equations (40b):
Ts p -, mp2l ((PP ~0s ) Hs>P Gs,p /OLs, p (42b)
Notice that (41) for the Raman induced CSO has the exact same form as (18) for
the
Raman induced crosstalk. Furthermore, matrix elements (42a), for the
difference CSO
beat equation, are identical to the simplified Raman crosstalk matrix elements
(24). The
matrix elements for the sum beat equation are simply related to those of the
difference
beat equation by complex conjugation:
Isp=(hsp)* (43c)
Therefore, equations (41) and (18) are identical to one another when
considering only the
explicit Raman crosstalk or Raman induced CSO (the sum beat equation is simply
the
complex conjugate of the difference beat equation). Hence equations (24)
through (30b),
along with all of the discussions and conclusions surrounding them, apply
equally well to
the Raman induced CSO. In fact, we may simply replace the term "crosstalk"
with "CSO"
within those paragraphs. Thus the same criteria apply to effectively reducing
the Raman
induced CSO and Raman induced crosstalk. Namely by setting up the phasing
criteria
given by (30a) or (30b) and adjusting the OMI's and/or the powers to make each
term in
each line of (41) (and therefore (18)) have nearly equal magnitudes, then both
the Raman
induced CSO and Raman induced crosstalk impairments will be substantially
reduced.
How closely the magnitudes can be adjusted so that they are all equal to one
another
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largely depends upon how close the each of the coefficients s, given by (28)
comes to
unity.
[0103] FIG. 3 shows a simplified block diagram of a conventional WDM
transmission
arrangement 200 in which data or other information-bearing signals SI, S2, S3
and S4 are
respectively applied to the inputs of modulators 2101, 2102, 2103, and 2104.
The
modulators 2101, 2102, 2103, and 2104, in turn, drive lasers 2121, 2122, 2123,
and 2124,
respectively. The lasers 2121, 2122, 2123, and 2124 generate data modulated
optical
channels at wavelengths k1, kZ, k3 and a,4, respectively, where k4 >k3 >k2
>),1. A
wavelength division multiplexer (WDM) 214 receives the optical channels and
combines
them to form a WDM optical signal that is then forwarded onto a single optical
transmission path 240. While the WDM transmission arrangement shown in FIG. 3
multiplexes four optical channels onto a single path, those of ordinary skill
in the art will
recognize that any number of optical channels may be multiplexed in this
manner.
[0104] In the context of a CATV network, optical channels ),,, k2, k3 and k4
may be
broadcast signals that all contain the same video signals, plus narrowcast
signals that are
different for different optical channels of k1, 4 ),3 and 4 Narrowcast signals
that are RF
frequency multiplexed into broadcast channels are normally much lower in
amplitude
than broadcast video signals. The arrangement of sending the same broadcast
signal and
different narrowcast signals over multiple wavelengths (WDM) is a means of
providing
more segmentation in CATV networks. This is demonstrated in FIG.4, which shows
an
RF splitter 216 that splits the broadcast signal among the lasers 2121, 2122,
2123, and
2124. As shown, the lasers 212 each receive a different narrowcast signal. In
FIGs. 2 and
3, like reference numerals denote like elements.
[0105] As previously noted, Raman crosstalk may occur among the optical
channels Xi,
4 ?13 and k4. In the case of the CATV application scenarios as described the
above,
Raman crosstalk not only causes interference (crosstalk) between optical
channels but
signal distortions as well when the broadcast signals are sent over different
WDM optical
channels. Because the amplitude of broadcast video signals is much higher than
that of
narrowcast digital signal, Raman crosstalk has more impact on analog video
signals
between optical channels than on narrowcast channels. The present inventors
have
recognized that this problem can be overcome by adjusting the phase of the
broadcast
video channels in optical channels with respect to one another. Specifically,
Raman
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crosstalk and the induced signal distortions can be reduced by shifting the
phase of some
of the signals by 180 degrees with respect to others of the signals. The
particular channels
that undergo this phase shift and the manner in which the phase shift is
accomplished will
depend on a number of factors such as the optical wavelengths employed, the
channel
spacing and the like. The following guidelines and examples that are discussed
in
connection with wavelengths X, - a,4 shown above, are presented by way of
illustration
only and should not be construed as a limitation on the invention.
[0106] FIG. 5 shows an illustrative example where the signals S 1, S2, S3 and
S4, with
signals S2 and S3 selected to be 180 degrees out of phase with respect to
signal SI and S4.
In this example a digital signal is used to represent the broadcast analog
signal for
simplicity. It should be noted that since the individual broadcast signals are
identical,
their patterns will all be the same prior to the phase shift. As a result of
Raman
amplification, signal S, will generate crosstalk at signal S4. However, this
crosstalk can be
reduced or even canceled by the crosstalk generated by signals S2 and S3 at
S4. This can
be accomplished if the amplitude of the crosstalk generated by S, equals the
amplitude of
the crosstalk generated by both S2 and S3. The relative amplitudes of SI, S2,
and S3 can be
selected to ensure that this relationship among the three crosstalk components
generated
at S4 is satisfied. Realizing the fact that when optical wavelengths are close
to zero
dispersion wavelengths or when the optical wavelengths are very close to each
other, the
phase relationship between optical channels is maintained for a certain length
of
transmission link, and therefore Raman crosstalk reduction is achieved
effectively along
the transmission link.
[0107] In a WDM signal, the wavelength spacing between adjacent ones of the
channels
X], X2, X3 and X4 is generally much less than the maximum power transfer
Stokes shift.
Accordingly, in general, the greater the spacing between any two of the
channels, the
greater the Raman crosstalk between them. That is, the Raman crosstalk between
signals
S1 and S4 generally will be greater than the crosstalk between S2 and S4,
which in turn
generally will be greater than the crosstalk between S3 and S4. This explains
why in the
above example both signals S2 and S3 were selected to be 180 degrees out of
phase with
S 1: the two smaller components of the crosstalk at S4 generated by S2 and S3
more readily
cancel the larger component of the crosstalk generated by S, at S4, thus
requiring smaller
adjustments to their relative amplitudes. Of course, those of ordinary skill
in the art will
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recognize that the signals that are chosen to be out of phase from the other
signals can be
selected in any desired manner based on level of generated Raman crosstalk and
relative
dispersion relationship etc. For instance, in one example the signals may be
pairwise out
of phase (i.e., the even signals are in phase and the odd signals are out of
phase). In the
case of signals X1, X2, X3 and X4 shown above, for instance, signals S I and
S3 may be
selected to be out of phase with signals S2 and S4. Of course, if the
crosstalk is to be
largely eliminated, this selection will typically require a greater adjustment
to their
relative amplitudes than the selection depicted in FIG. 5. It should be noted
that reduction
of Raman crosstalk through the above described technique reduces Raman induced
signal
distortions as well simultaneously. It should also be noted that the technique
as explained
above can be use in both CWDM and DWDM and therefore generally in any WDW.
[0108] As previously mentioned, Raman crosstalk can be particularly acute when
the
channels are located at wavelengths near the zero dispersion wavelength of the
transmission path because the optical channels largely maintain their relative
phases at
these wavelengths. For the same reason, the aforementioned technique in which
some of
the channels are arranged to be out of phase with respect to other channels
will be most
effective when the channels are located near the zero dispersion wavelength of
the
transmission path. For instance, for channels operating in the 1310 nm window
(typically
defined as the waveband between about 1280 nm and 1330 nm), a commonly
employed
single mode optical fiber is the SMF-28TM fiber, available from Coming,
Incorporated.
The SMF-28 fiber has a zero dispersion wavelength at or near 1310 nm.
Accordingly, if
this transmission fiber is employed, Raman crosstalk can be most effectively
reduced for
optical channels having wavelengths in the vicinity of 1310 nm. Similarly, for
optical
wavelengths operating in the C-band (wavelengths between about 1525 to 1565
nm), a
commonly available optical fiber is Corning's LeafTM fiber, which has a zero
dispersion
wavelength near 1500 nm. For the LeafTM fiber, the Raman crosstalk can be more
effectively reduced for channels having wavelengths in the vicinity of 1500 nm
than for
channels in the vicinity of 1525 nm or 1565 nm. If, on the other hand, the
optical
wavelengths operate in the L-band (wavelengths between about 1565 to 1625 nm),
a
commonly available optical fiber is Coming's Leaf RTM fiber, which has a zero
dispersion
wavelength near 1590 nm. For the Leaf.RT"' fiber, the Raman crosstalk can be
more
effectively reduced for channels having wavelengths in the vicinity of 1590 nm
than for
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channels in the vicinity of 1565 nm or 1625 nm. In the case where optical
wavelengths in
a WDM system are remote from the zero dispersion wavelength, closer wavelength
spacing between WDM channels may be required or link length may be limited in
order
to maintain the relative phase between channels and therefore the
effectiveness of this
technique.
[0109] FIG. 6 shows one example of a transmitter arrangement in which select
individual
signals can be arranged to be out of phase with respect to other signals. In
FIGs. 3 and 5
like elements are denoted by like reference numerals. As shown, an RF signal
g(t) is
applied to the input of a splitter 220. Splitter 220 has one output for each
of the
wavelengths that are to be multiplexed together by the transmitter
arrangement. In the
example shown in FIG. 5, the splitter has four outputs 2221, 2222, 2223 and
2224. Each
output is directed to an input of one of the modulators. Specifically, output
222, is
directed to an input of modulator 2124, output 2222 is directed to an input of
modulator
2123, output 2223 is directed to an input of modulator 2122, and output 2224
is directed to
an input of modulator 2121. The modulators 2101, 2102, 2103, and 2104, in
turn, drive
lasers 2121, 2122, 2123, and 2124, respectively. The splitter 220 is
configured so that
select ones of its outputs shifts the phase of the input signal by 180
degrees. Such phase
shifting splitters are well known components and do not need to be discussed
in detail.
Phase shifting can also be achieved separately. If the particular modulator
pattern shown
in FIG. 5 is employed, the outputs 2222 and 2223 of splitter 220 shift the RF
signal g(t) by
180 degrees. An amplitude adjuster 230 may be provided for adjusting the
relative
amplitudes of the RF signals that modulate lasers, i.e. the modulation index,
or of the
optical signal output level generated by each of the lasers 2121, 2122, 2123,
and 2124.
Additionally, polarization adjusters 2131, 2132, 2133, and 2134 (under control
of
polarization controller 231) can be used to provide polarization control of
the optical
wavelengths can also be used to achieve a maximum reduction in crosstalk and
distortion
as depicted in FIG. 6. It should be noted that the data signals added to
modulator 2101,
2102, 2103, and 2104, generally (though not always) include different
narrowcast signals.
In addition, while FIG. 6 shows direct modulators being employed, the
techniques
described herein can be applied to external modulators as well.
101101 FIG. 7 is a flowchart showing one example of the method performed by
the
transmitter arrangement depicted in FIG. 6. The method begins in step 505 by
receiving
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multiple information-bearing electrical signals that all embody the same
broadcast
information. The electrical signals may, for example, embody audio and/or
video
broadcast programming. Next, in step 510, multiple optical channels that are
each located
at a different wavelength from one another are modulated with a respective one
of the
electrical signals. In addition, in step 515 each optical channel is modulated
with an RF
signal. The RF signals all have a common functional broadcast waveform. At
least one of
the RF signals is out of phase with respect to remaining ones of the plurality
of RF
signals. The modulated optical channels are multiplexed in step 520 to form a
WDM
optical signal. Finally, in step 525 the WDM optical signal is forwarded onto
an optical
transmission path.
[0111] In addition to reducing crosstalk that arises from Raman interactions,
the methods
and techniques described herein can also mitigate and even eliminate the
affects of
distortion that arise from Raman interactions, particularly second order
distortion, which
is known to be especially serious for analog signals. While analog channels
are most
vulnerable to such distortion, digital channels are also impacted and thus the
methods and
techniques described herein can reduce Raman distortion arising in both analog
and
digital signals.
[0112] The transmitter arrangement described above can be advantageously used
in any
optical network in which a broadcast signal is multiplexed onto multiple
optical
wavelengths or channels. Such networks include, without limitation, various
all-optical
networks, hybrid fiber-coax (HFC) networks and networks utilizing a passive
architecture, which are often referred to as Passive Optical Networks (PONs).
In typical
HFC architectures, broadcast signal is split at optical hubs and then sent to
different nodes
together with narrowcast signals. At the fiber node the optical signal is
converted into an
electronic signal, and carried over multiple coax buses for distribution
throughout a
neighborhood. On the other hand, in a PON architecture, fibers carry signals
from optical
line terminator (OLT) to optical splitters, and further to optical-network
units (ONUs),
where optical-to-electronic conversion takes place. In the case of PON
architectures,
broadcast and narrowcast signals are sent in a similar manner. Both HFC and
PONs
generally carry the same downstream signals to multiple customers. In both
networks
multiple paths are typically used beyond the first node. Use of WDM in a fiber
to a node
allows further and more node segmentations. A primary advantage of a PON is
its
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reliability, ease of maintenance and the fact that the field-deployed network
does not need
to be powered. Accordingly, PONs are often used as access networks by cable TV
and
telecommunications providers for the purpose of distributing their services
from their
facility to the customer premises (e.g., a home or business). One example of
PONs is
sometimes referred to as Broadband PON (BPON), which is a combination of a PON
with wavelength division multiplexing (WDM) for downstream and upstream
signals.
The WDM techniques can be used for downstream signals and allow different
optical
wavelengths to support broadcast and multiple narrowcast (dedicated for each
wavelength) transmissions on the fiber employed in the BPON. WDM can also be
applied
to different PON standards.
[0113] FIG. 8 shows the architecture of a BPON in its most generalized form.
The BPON
100 includes a hub 102, remote nodes 104 that are deployed in the field, and
network
interface units (NIUs) 106. The hub 102, remote nodes 104 and NIUs 106 are in
communication with one another over optical fiber links. If the BPON 100 is a
telecommunications network, hub 102 is a central office or called OLT. The
NIUs 106
may be terminal equipment located on the customer premises or they may serve
multiple
customers, in which case the NIUs 106 simply provide another level in the
network
hierarchy below the remote nodes.
[0114] A method and apparatus has been described for reducing Raman induced
crosstalk
and distortion that arises among individual channels of a WDM optical signal,
which are
particularly severe among channels that are located near the zero dispersion
wavelength
of the transmission medium. The method and apparatus is particularly suitable
when the
individual channels support broadcast signals carrying the same information,
which are
sometimes transmitted over a transmission network such as an HFC or PON
network.
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