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 298 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. OBARA: BIDIRECTIONAL WDM TRANSMISSION TECHNIQUE UTILIZING TWO IDENTICAL SETS OF WAVELENGTHS 299 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 300 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007 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) OBARA: BIDIRECTIONAL WDM TRANSMISSION TECHNIQUE UTILIZING TWO IDENTICAL SETS OF WAVELENGTHS 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 302 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007 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. 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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.