JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007
297
Bidirectional WDM Transmission Technique
Utilizing Two Identical Sets of Wavelengths
for Both Directions Over a Single Fiber
Hitoshi Obara, Member, IEEE
Abstract—In-band crosstalk due to Rayleigh backscattering
(RB) can be avoided in bidirectional wavelength-division multiplexed (WDM) transmission systems when using two identical
sets of wavelengths in opposite directions over a single fiber.
We describe this by using such sets in a disjoint manner and
eliminating the RB crosstalk with the help of simple optical edge
filters instead of the WDM comb filters previously employed
in interleaved bidirectional systems. We also provide a practical application example and describe the power penalty due
to the interferometric RB crosstalk, taking into account recent
polarized optical noise research because RB light is partially
polarized. Numerical results for externally modulated intensitymodulation/direct-detection (IM/DD) optical systems show that
the power penalty can be kept less than 0.5 dB with moderate
edge filters, even for more than several tens of optically amplified
repeater segments.
Index Terms—Bidirectional transmission, bit error rate (BER),
crosstalk, optical fiber communication, optical filters, optical
noise, power penalty, Rayleigh scattering, wavelength-division
multiplexed (WDM).
I. I NTRODUCTION
IDIRECTIONAL
wavelength-division
multiplexed
(WDM) transmission techniques on a single fiber
have been a research focus in optical fiber communication
systems primarily because of their cost reduction and capacity
enhancement. For example, bidirectional coarse-WDM techniques are already developed for fiber-to-the-home (FTTH)
access networks [1] where two wavelength signals separated
by several tens or hundreds of nanometers are provided for
simultaneous uplink and downlink in a single fiber. One of two
bidirectional fibers normally necessary for either link is saved
at the cost of inexpensive coarse-WDM filters provided at
both fiber ends for signal coupling and separation. Interleaving
techniques are also known for dense-WDM core networks (e.g.,
[2]–[4]). They can double wavelength efficiency compared to
unidirectional systems because a nominal wavelength spacing
of 100 GHz for each direction is kept unchanged, while the
total number of channels in a given bandwidth is doubled.
Wider channel spacing assures less susceptibility to nonlinear
B
Manuscript received May 25, 2006; revised September 21, 2006. This work
was supported in part by JSPS under Grants 15560315 and 17560327.
The author is with the Electrical and Electronic Engineering (EEE) Department, Akita University, Akita 010-8502, Japan (e-mail: obara@ee.akitau.ac.jp).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2006.887180
effects such as four-wave mixing and XPM [5]. Bidirectional
WDM signals are easily merged and separated with optical
circulators provided at both fiber ends.
Optical fiber, however, is diffractive in nature. In fact,
Rayleigh scattering is a dominant factor of fiber attenuation [6].
Most scattered light traverses backward for standard telecommunication fibers, which is called Rayleigh backscattering
(RB). RB is useful for some applications such as optical time
domain reflectometers (e.g., [33]) and remote sensing (e.g.,
[34]). In interleaved bidirectional WDM systems, on the other
hand, RB gives rise to crosstalk noise, which is interweaved
with the counter-propagating signals. Note that RB crosstalk
power grows with the fiber length to saturation at a specific
value of the launched signal power multiplied by the RB
coefficient. Also, the spacing between signals and crosstalk
components is reduced to half the nominal channel spacing. The
implication of these observations is twofold. First, if a WDM
demultiplexer at the receiving end has a poor attenuation at the
center of two adjacent channels, the optical signal to noise ratio
(SNR) will degrade due to the spurious RB crosstalk within
the receiving optical bandwidth. Second, it will degrade for
long fibers because the receiving signal power of the counterpropagating signals will go down due to fiber attenuation, while
RB crosstalk power will‘ remain constant.
In optically amplified linear repeater systems, the regeneration and accumulation of RB noise gives rise to serious design
issues. Optical preamplifiers (OAs) compensate the receiving
signal loss. They regenerate RB crosstalk noise as well. In
cascaded optically amplified fiber segments, every segment
gives birth to a new RB crosstalk component which is regenerated at every segment; thus, its total power at the receiving end
will accumulate in proportion to the number of fiber segments.
In order to suppress the RB noise accumulation, WDM comb
filters are necessary in every segment [7]. Note that every
peak and valley of the comb filter must match up with the
halved signal grid. Consequently, with regard to crosstalk noise,
interleaved WDM transmission systems are not different from
unidirectional WDM systems with reduced channel spacing,
which makes bidirectional design difficult.
As the two sets of wavelengths used for both directions
become more identical, the spacing between the signal and
crosstalk becomes zero. RB noise having the same wavelength
as the receiving signal cannot be eliminated at all with the
WDM filters, but is also amplified by the associated signal like
a coherent detection system [8], [9]. We call it the in-band RB
0733-8724/$25.00 © 2007 IEEE
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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007
Fig. 1. Linear network using the proposed bidirectional technique.
noise, as published most recently in [10]. It is also sometimes
referred to as optical beat interference (e.g., [11]), interferometric (e.g., [12]), or coherent (e.g., [13]) noise. The basic
properties of RB noise in optical fiber communications and its
impacts on transmission performance under a variety of system
configurations and analytical assumptions have been shown in
a number of papers through theory and experiment. The introduction sections of recently published papers [7], [14]–[18]
give a concise collection of references on the effects of RB
crosstalk noise on transmission performance. The conclusion
from them is that its negative effects are so severe that it is a
“blue rose” for bidirectional WDM transmission systems to use
two identical sets of wavelengths for opposite directions over a
single fiber.
We address the previously unanswered question of how
such bidirectional WDM transmission systems can be put into
practical use in spite of the in-band RB noise. Our motivations
for using two identical sets of wavelengths are that it enables the
sharing of a single light source by a couple of transmitters for
both directions from a node and it keeps channel spacing maximum to relax WDM filter requirements. Our solution is to use
them in a disjoint manner and eliminate the RB crosstalk with
the help of optical edge filters instead of conventional comb
filters. An outline of the proposed technique is introduced in
Section II, where we will briefly refer to application examples
of the technique. In Section III, a detailed theoretical analysis of
power penalty due to the RB crosstalk is presented. We focus
on a single RB, taking into account the latest research results
of polarization effects on optical noise [19], [20] because RB
light is partially polarized. We believe that such an approach
has never been undertaken in previous studies. Double RB
has been analyzed [16], [21] and is beyond the scope of this
paper. Numerical results and discussion are given in Section IV.
Section V concludes the paper.
II. O UTLINE OF THE P ROPOSED B IDIRECTIONAL WDM
T RANSMISSION T ECHNIQUE
A. Principle
Consider a linear network as shown in Fig. 1 [22], [23].
In this example, there are two end nodes (ENs) and three
intermediate nodes (INs). The WDM level is three (or λ1 , λ2 ,
and λ3 ). The INs launch a couple of identical wavelengths (or,
in general, a number of contiguous wavelengths in a waveband)
in opposite directions. The dashed line, which is shown only
at λ1 for simplicity, denotes the RB signal. The ENs receive
the wavelengths from the INs along with the RB signals and
demultiplex them for termination. As a result, the wavelengths
Fig. 2.
Functional block diagram of INs.
Fig. 3.
Wavelength assignment and EF transmission curves.
provide a star connection for uplinks between the ENs and the
INs. A downlink star can also be provided in a similar manner,
but it is omitted in Fig. 1 for the sake of simplicity.
In Fig. 1, a couple of identical wavelengths are set in a
disjoint manner, and thus, RB crosstalk can be eliminated at
the INs by using optical filters. Fig. 2 shows a brief functional diagram of the INs. Bidirectional signals are divided
and merged by optical circulators (CC) with two branches;
each of which corresponds to each direction and has a similar
configuration. Edge filters (EF1 and EF2) eliminate RB
crosstalk. OAs compensate the loss of fiber and other optical
components. Launched signals from the ith IN couple with
passing signals through couplers (CPLs). We assume that there
are N INs and the ith IN inserts a couple of identical wavelengths in both directions. Note that wavelength channels are
ordered from λ1 to λN on the wavelength axes, as shown in
Fig. 3. Under these assumptions, EF1 in the ith IN eliminates
(λ1 , λ2 , . . . , λi ) and passes (λi+1 , λi+2 , . . . , λN ), while EF2
eliminates (λi , λi+1 , . . . , λN ) and passes (λ1 , λ2 , . . . , λi−1 ),
because RB crosstalk is included in their stopbands. Fig. 3
also shows the transmission curve of EF1 used in Fig. 1. As
described above, EF1 stops (λ2 , λ3 ) because there are RB
crosstalk components that are generated at the left-hand side
of IN2, while it passes λ1 , which goes from IN1 to EN2.
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Fig. 4(a), the number of fibers increases with the number of
nodes. Note, however, that several destination nodes can share
a fiber [25]. In other words, the fiber line in Fig. 4(a) can be
regarded as a waveband in a fiber.
In Fig. 4(b), we can see that wavelength efficiency degrades
compared to conventional WDM add/drop systems because
wavelengths are not reused at all as they are in those systems.
However, if we substitute Fig. 1 for Fig. 4(b), we have a bidirectional design shown in Fig. 4(c), where wavelength efficiency
turns out to be nearly twice as high (or two unidirectional fibers
a and b are merged into a single bidirectional fiber). Note that
reconfigurability is still preserved [26].
III. P ERFORMANCE A NALYSIS
Our main concern in this paper is to estimate the effect of
RB noise through numerical analysis over multiple amplified
segments in the bidirectional WDM systems and to show the
effect of the EFs, taking polarization effects into account. Let
us begin with an analysis of RB noise in a single segment.
Although we borrow it from [21] for most part, it gives a basis
for the following analysis of multiple segments.
Fig. 4. Simple example of MWENs. (a) Ring-type network configuration of
MWEN. (b) Unidirectional design. (c) Bidirectional design (proposed).
The advantage of this idea is that RB noise can be suppressed
repeatedly by the EFs. For instance, the λ3 signal emitted from
IN3 in the left direction will give birth to RB noise at every
fiber section between IN3 and EN1. The RB noise, on the other
hand, can be attenuated by every EF1 in IN1, IN2, and IN3. As
a consequence, RB noise can be suppressed with EFs having
modest rejection performance.
B. Application Example
The bidirectional transmission technique can be applied to
emerging multifiber WDM express networks (MWENs) [24]
as well as conventional WDM networks. Fig. 4(a) shows an
example of a ring-type MWEN. In this example, there are four
nodes (n1 , n2 , n3 , and n4 ) and four unidirectional fibers (a,
b, c, and d). A fiber is dedicated to its designated node. It
originates from a node adjacent to the destination node, where
it is terminated. Nodes other than the destination node add
wavelengths to the fiber. As a result, the arrangement shown
in Fig. 4(a) provides a full-mesh connection among the nodes.
Thus, the MWEN architecture offers a high capacity through
space-division multiplexing in addition to WDM. It is also
practical because it is composed of existing simple devices.
The network is symmetric and can be decomposed into four
identical unidirectional subsystems, one of which is shown in
Fig. 4(b). We see that a full-mesh connection can be decomposed into multiple stars. Add/drop operation in Fig. 4(b) is
as follows: n2 , n3 , and n4 launch wavelengths onto fiber b,
which are destined to n1 . Note that any combination of the
idle wavelengths can be inserted at the nodes, thus enhancing
reconfigurability. These inserted wavelengths pass through INs
with minimal processing and are finally demultiplexed at the
destination node n1 . Wavelengths couple to the fiber through
passive optical combiners, which are omitted for simplicity. In
A. Basic Properties of RB Noise
We consider a linearly polarized electrical source field e(t)
(1)
e(t) = ℜ εs (t)ejωt
with optical frequency ω and complex amplitude εs (t), where
ℜ[·] denotes the real part. We assume that εs (t) is given by
εs (t) = m(t)ejφ(t)
(2)
where m(t) and φ(t) denote the variation of electric field
amplitude and phase due to modulation. The source intensity
Is (t) coupled into the fiber can be expressed as follows:
Is (t) = |e(t)|2 = m(t).
(3)
For example, m(t) for the IM-DD systems with a nonreturn
to zero (NRZ) pulse shape is given by
Im for “1”
m(t) =
0
for “0”
Ia = m(t) = Im /2
(4)
where the overline of m(t) denotes time-average.
For now, we assume that the RB light is completely polarized
and its state is preserved during backscattering. By assuming
that the source is at z = 0, the complex amplitude of the
traveling field at location z is then given by
z − (α/2+jβ)z
e
(5)
ε(t, z) = εs t −
ν
where ν, α, and β are group velocity, fiber attenuation coefficient, and propagation constant, respectively. Since we are
mainly interested in a high-speed transmission of gigabytes
per second or more, the slowly changing phase noise of the
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optical carrier is not considered here. The single Rayleigh
backscattered field from a small section of the fiber at location z
is given by [31]
z − (α/2+jβ)z
e
∆ρ(z).
(6)
∆εRB (t, z) = εs t −
ν
Comparing (11) with the result of a previous study [32]
yields
The spatial reflection coefficient ∆ρ(z) describes the fraction
of the backscattered field with respect to the forward signal
field. It has been proved that the polarization state of RB in low
birefringent fiber is the same as that of the forward traveling
field [19]. We do not have to consider the change of the polarization state at the reflection point. A differential RB coefficient
has been defined as
where αs is the intensity attenuation coefficient due to scattering and S is the fiber recapture factor, which indicates the
fraction of the scattered power that is recaptured and guided
backwards in the fiber (0 ≤ S ≤ 1). As a result, we have a
relation between the time-averaged source intensity and the RB
intensity with the RB coefficient Rb .
ρ(z) = lim
∆z→0
∆ρ(z)
.
∆z
εRB (t) =
εs
0
2z
t−
ν
− (α+j2β)z
e
ρ(z)dz.
(8)
The RB signal generated at z has already undergone the propagation length of z from the source. Since it further traverses
from z to the source and mixes with the counter-propagating
signal, the total propagation length becomes 2z in (8). As a
result, the RB intensity at the source is given by
IRB (t) = εRB (t) · ε∗RB (t)
=
L L
0
0
2z1
εs t −
ν
× e−j2β
(z2 −z1 )
2z2
ε∗s t −
ν
ρ(z1 )ρ∗ (z2 )dz1 dz2
e−α
(z1 +z2 )
(9)
where ∗ denotes the complex conjugate.
To calculate the time-average of IRB (t), we assume that
ρ(z) can be modeled as delta-correlated zero-mean circularcomplex-Gaussian random variable [17], i.e.,
ρ(z1 )ρ∗ (z2 ) = 2σ 2 δ(z1 − z2 )
(10)
where < x > denotes the expected value (or ensemble average)
of x. This assumption has been justified by the fact that the
variation of the electric fields due to the polarization state
change, phase noise, and fiber attenuation is extremely coarse
compared with the correlation distance of the refractive index
fluctuations. Note that ρ(z) is a complex function and σ 2 is the
variance of both the real and imaginary parts of ρ(z). By using
(10), (9) simplifies to
2
IRB (t) = 2σ Is (t)
L
and
Rb =
αs S
(1 − e−2αL ).
2α
(13)
For example, Rb for the standard single-mode fibers is in the
range of −33 to −31 dB at 1.55 µm when L → ∞ [19].
B. Interference of RB Noise and Reverse Transmission Signal
While the time-averaged RB intensity is given by (13), there
is another field emitted in the reverse direction from the source
in our model, as shown in Fig. 1. We assume that the reverse
transmission signal has identical signal properties to the original forward signal. This is a worst case scenario corresponding
to a design where light from a shared source is split into two
halves, followed by independent external modulators for both
directions. The total intensity I(t) for the reverse direction at
the source becomes
I(t) = |ε(t, 0)|2 +|εRB (t)|2 +[ε(t, 0)ε∗RB (t)+ε∗ (t, 0)εRB (t)] .
(14)
The first term in (14) is the counter-propagating signal, the
second term is the intensity due to RB, and the third term is their
beat noise. The second term is negligible because |ε(t, 0)| ≫
|εRB (t)| holds. Now, we have the RB-signal beat noise intensity
IRB-S (t) as follows:
IRB-S (t) = 2ℜ [ε(t, 0) · ε∗RB (t)] .
(15)
To find the RB beat noise power spectrum density (PSD), we
introduce the time-averaged autocorrelation function (ACF) of
the IRB-S (t) after [27]. Namely, we have
e−2αz dz
0
2
=
(12)
IRB (t) = Rb Ia
(7)
The RB field at the source is given by integrating (6) over the
total fiber length L.
L
αs S = 2σ 2
σ Ia
(1 − e−2αL ).
α
(11)
1
T →∞ T
RRB-S (τ ) = lim
T
0
IRB-S (t) · IRB-S (t + τ ) dt
(16)
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301
where < · · · > denotes ensemble averaging. By substituting
(15) into (16), we have
1
RRB-S (τ ) = lim
T →∞ T
T
0
[ε(t, 0) · ε∗RB (t) + ε∗ (t, 0) · εRB (t)]
× [ε(t + τ, 0) · ε∗RB (t + τ )
Fig. 5. Cascade model of bidirectional MWENs.
+ ε∗ (t + τ, 0) · εRB (t + τ )] dt
1
= lim
T →∞ T
T
0
[ε(t, 0)ε(t +
τ, 0)ε∗RB (t)ε∗RB (t
+ τ)
By using the same process as in (16) and (17) and taking the
DOP of the RB noise into consideration [18], the PSD of the
RB noise SRB (f ) is given by
+ ε(t, 0)ε∗ (t + τ, 0)ε∗RB (t)
SRB (f ) = (1 + DOP2 )Rb2 ℑ
× εRB (t + τ ) + ε∗ (t, 0)ε(t + τ, 0)
×
εRB (t)ε∗RB (t
=
∗
+ τ ) + ε (t, 0)
× ε∗ (t + τ, 0)εRB (t)εRB (t + τ )] dt.
|Rs (τ )|2
10 2
Rb F
|Rs (τ )|2
9
(22)
2
is given by
and thus, σRB
(17)
2
σRB
Again, by substituting (8) in (17) and taking (10) into consideration, we obtain
2
RRB-S (τ ) ∼
= 2Rb |Rs (τ )| (1 − e−2αL )
(18)
=
∞
−∞
|H(f )|2 SRB (f )df − Ib2
where
Ib = IRB (t) = Rb Is (t) = Rb Ia .
where Rs (τ ) denotes the ACF of ε(t, 0). Thus, RRB-S (τ ) is
simply related to the ACF of the electrical field of the input
optical signal [6].
To remove the restrictive assumption made earlier on the
preservation of the state of polarization (SOP) of the electric
field, it has been shown that, in a standard single-mode fiber, the
RB signal has the same SOP as the input signal field and that its
degree of polarization (DOP) is near 1/3 [19]. This means that
(1 + 1/3)/2 = 2/3 of the RB field mixes with the input signal
field [20], [28]. As a consequence, we have a simple expression
of RRB-s (τ ) as follows:
RRB-S (τ ) =
4
Rb |Rs (τ )|2 (1 − e−2αL ).
3
(19)
The PSD of the RB beat noise can be obtained by taking the
Fourier transform of (19), yielding
SRB-S (f ) =
4
Rb (1 − e−2αL )ℑ |Rs (τ )|2
3
(20)
where ℑ{·} denotes the Fourier transform. The total meansquare RB beat noise is given by integrating (20) over the
frequency
2
σRB
-S
=
∞
−∞
|H(f )|2 SRB-S (f )df
(21)
where H(f ) is the detector frequency response, for which we
assume a rectangular transfer curve.
(23)
(24)
Since we assume digital IM/DD optical systems using external
NRZ modulation with a roll-off characteristic, the optical spectrum of the light source cannot spread beyond the modulation
rate. Then, the RB noise power will fall within the receiver
bandwidth. In this case, the integration ℑ{|Rs (τ )|2 } depends
on the following identity (Parseval’s equation):
∞
−∞
ℑ
|Rs (τ )|2
df = |Rs (0)|2 =
2
Im
.
4
(25)
C. RB Beat Noise in Optically Amplified Repeater Systems
Actually, RB noise is generated in every fiber segment, and
the total RB noise power at the origination node grows with the
number of fiber segments. Fig. 5 shows an open cascade model
for describing how the RB noise accumulates over optically
amplified multiple fiber segments. We assume that there are
N segments of RB noise generation and amplification before
coupling at the origination node, OAs gain of G compensates
the total loss of a single segment, and EFs rejection of RB noise
is D, which is defined by the ratio of passband gain to stopband
gain. Eventually, the RB noise is amplified and attenuated by
OAs and EFs. The net gain of RB noise in a segment appears
as η = G/D. The total power of RB noise and RB-signal beat
2
2
and σBN
are then given by
noise at the origination node σN
2
2
σN
= M (η, N )σRB
2
2
σBN
= M (η, N )σRB
-S
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where M (η, N ) is defined as a function of η and N as follows:
M (η, N ) =
(1 − η N )η
.
1−η
(26)
M (η, N ) denotes an overall gain of the RB noise and is a
dominant design factor for the proposed bidirectional system.
D. Power Penalty Due to RB Beat Noise
We discuss the effect of the RB noise in terms of the bit
error probability. By the Gaussian approximation of the RB
noise, which gives a slight overestimation [35], the bit error
probability is given in a simple form represented by
1
Pe = √
2π
∞
2
t
exp −
dt
2
Fig. 6. M (η, N ) versus N .
(27)
Q
with
Q=
S1 − S 0
σ1 + σ0
(28)
where S1 and S0 and σ1 and σ0 are signal level in mark and
space and rms noise level in mark and space, respectively [29].
When the RB noise exists in the transmission model shown
in Fig. 5, the mean-square noise currents for a space and a mark
at the receiver are given by
2
2
= σ02 + σN
σRB,0
2
σRB,1
= σ12
+
2
σBN
Im
2
σBN
+
σ02
2
2 +σ
+ σs−sp
+ σsh
0
When there is no RB noise, the receiving signal level Im0
required to maintain the same error probability is given by
Im0 =
(29)
2
2
2
2
2
where σ02 = σsp−sp
+ σth
and σ12 = σsp−sp
+ σs−sp
+ σsh
+
2
2
2
2
2
σth . Note that σs−sp , σsp−sp , σsh , and σth are signalspontaneous emission beat noise, spontaneous–spontaneous
beat noise, shot noise, and thermal noise, respectively. Since
we are interested in a standard WDM system with 100-GHz
spacing and multigigabytes per second high-speed modulation,
2
holds. By taking S1 = Im and S0 = 0 into account,
σ02 ≫ σN
we have
Q0 =
Fig. 7. M (η, N ) versus η.
.
(30)
σeq +
1
Q20
2σ0
Q0
.
(33)
Finally, the ratio of (32) and (33) gives the power penalty (PP)
as follows:
Im
2
PP = 10 log
(34)
= −10 log 1 − Q20 · σBNo
Im0
where Q0 is the Q-factor corresponding to a required bit error
probability (e.g., Q0 ∼
= 6 for BER = 10−9 ). We note that the
sensitivity of the optical receiver is assumed to be one throughout the analysis because it is eventually canceled out and has no
effect on the PP.
IV. N UMERICAL R ESULTS
2
2
Recall that both σs−sp
and σsh
depend on Im [30]. Similarly,
2
2
2
σBN (i.e., σRB-S ) depends on Im
from (25). Thus, we substitute
them as follows:
2
2 ∼
+ σsh
σs−sp
= Im · σeq
2
2
2
σBN
= Im
· σBNo
.
(31)
lim M (η, N ) = N.
From (30) and (31), we have the following relation:
Im =
2σ0
Q0
.
2
σBNo
σeq +
1
Q20
−
For numerical analysis, we assumed a set of parameters
for a typical IM/DD system using a standard SMF, i.e., α =
0.25 dB/km (or 0.058 Np/km), L = 40 or 80 km, Rb =
−30 dB, and Q0 = 6. From (26), we can easily see that the
RB noise will increase with N when η > 1, while it saturates at
a certain power as N → ∞ when η < 1. Note that
η→1
(32)
(35)
As a result, M (η, N ) increases with N when η = 1, although
its increasing rate is rather moderate. Figs. 6 and 7, which show
M (η, N ) against N and η, support these observations. In Fig. 6,
OBARA: BIDIRECTIONAL WDM TRANSMISSION TECHNIQUE UTILIZING TWO IDENTICAL SETS OF WAVELENGTHS
Fig. 8.
Power penalty versus η.
303
η is a normalized parameter independent from the fiber loss.
Fiber length L has a limited effect on the PP, as shown in (20).
In summary, the rejection of the EFs should be greater than
the gain of the OAs. If one hopes to make the power penalty
less than 0.5 dB, the EFs rejection should be greater than the
OAs gain by only 0.5 dB (or η = 0.9). For a design example, an
OA gain of 13 dB (23 dB) is enough to compensate the loss of
a 40-km (80-km) fiber and an optical circulator, as functionally
shown in Fig. 2. The corresponding 13.5-dB (23.5-dB) rejection
of the EFs is a moderate requirement. Recent advances in
thin-film multilayer optical filter technology have enabled the
realization of very sophisticated spectral profiles [36].
V. C ONCLUSION
Fig. 9.
Power penalty versus N .
We have described a new bidirectional WDM transmission
technique using two identical sets of wavelengths on a single
fiber, which has long been thought to be impractical, owing
to the interferometric RB noise. We pointed out that if we
reuse a wavelength in the opposite directions in different fiber
segments, ordinary optical edge filters can avoid in-band RB
noise, even in cascaded optical amplifiers. We derived a simple
expression for power penalty, taking into account the polarization effect of the RB noise. A detailed numerical analysis of
power penalty for externally modulated IM/DD optical systems
indicated that 13.5-dB (23.5-dB) rejection edge filters used
on 40 km (80 km) of fiber can keep the power penalty less
than 0.5 dB under a worst-case scenario of in-phase signal
polarization. We note that the bidirectional design not only
improves wavelength efficiency but also enhances reconfigurability. Our modeling method will require a substantial amount
of experimental verification before we can say that we have
created our “blue rose,” but it will be the subject of future study.
ACKNOWLEDGMENT
Fig. 10. Nmax versus η.
M (η, N ) grows with N when η ≥ 1, while it saturates when
η = 0.9. We can also see in Fig. 7 that M (η, N ) is less than
10 dB even if N → ∞. Consequently, η is a critical factor that
limits the performance of the proposed bidirectional system.
Therefore, first we show in Fig. 8 a family of the PP versus η
curves, with N as a parameter. As expected, the PP diverges
in the region of η ≥ 1, while it converges elsewhere even if
N → ∞. This result means the EFs rejection should balance
the OAs gain, at least. Recall the definition of η = G/D. In
other words, the accumulation of the RB noise severely degrades the SNR. It should also be stressed that, for η = 0.9, the
PP becomes as small as less than 0.5 dB, regardless of N . Fig. 9
shows how the PP depends on N under a set of given η. For
η ≥ 1, PP curves rise steeply when N has a small value,
whereas it saturates at 0.44 dB as N → ∞ for η = 0.9. Fig. 10
shows the maximum of N or Nmax under the constraint that the
PP is less than 1 dB for 40- and 80-km fibers. We can see that
Nmax steeply falls down to one in the range of η ≥ 1. The dependence of Nmax on the fiber length is negligible. Recall that
The author would like to thank K. Aida and H. Masuda for
the helpful discussion at the early stages of this paper.
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Hitoshi Obara (M’89) received the B.E. and M.E. degrees in telecommunications engineering and the Ph.D. degree in information science from Tohoku
University, Sendai, Japan, in 1978, 1980, and 2001, respectively.
He worked with the NTT Labs as a Senior Research Engineer in 1985–2001.
He engaged in the development of a fiber-optic HDTV transmission system. He
led research of input-queueing ATM switches and invented several advanced
scheduling algorithms based on the VOQ scheme. He was involved in the ATM
crossconnect system project under the joint research with Bell Labs in 1992
and contributed to realizing a growable high-capacity ATM switch fabric. In his
later years at NTT, he created a number of evolutionary architectures for WDM
networks and WDM crossconnect systems (e.g., the multifiber WDM express
network, the virtually crosstalk-free multistage wavelength router, the hybrid
WDM add/drop ring network, and the helical WDM ring network). He was a
Visiting Researcher with the Vienna University of Technology, Vienna, Austria,
in 2003. He is currently an Associate Professor with the EEE Department, Akita
University, Akita, Japan. His primary research area has been optical networks,
switching/crossconnect systems, and communication protocols, where he is the
author or coauthor of more than 40 refereed journal papers and holds 30 patents.
Dr. Obara is a member of the IEICE and SICE.