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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 6996–7003
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Reduction of double Rayleigh scattering noise in distributed Raman amplifiers employing higher-order pumping

Gabriele Bolognini and Alberto Bononi  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 6996-7003 (2009)
http://dx.doi.org/10.1364/OE.17.006996


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Abstract

We present a theoretical study of the performance of distributed Raman amplifiers with higher order pumping schemes, focusing in particular on double Rayleigh scattering (DRS) noise. Results show an unexpected significant DRS noise reduction for pumping order higher than third, allowing for an overall performance improvement of carefully designed distributed amplifiers, ensuring a large optical signal-to-noise ratio improvement together with reduced DRS-induced penalties.

© 2009 Optical Society of America

1. Introduction

The main practical limitation to the use of HOP at high gains or for pumping order higher than third is given by the large required pump power (> 1 W). However, detrimental effects on optical transmission fibers due to large power can be avoided, even on a ten-year time-scale, with suitable checks of optical fiber loss, carried out for example through optical time domain reflectometry-based inspection, ensuring the absence of hot points generated by concentrated high-absorption regions, e.g. given by a bad fusion splice.

Actually, both theory and simulations indicate an achievable decrease of DRS noise for pumping orders higher than third, a behavior which was unknown until now, and which could lead to the implementation of optimized HOP schemes at high gain values without significant DRS-induced penalties, thus overcoming the present performance limitations in higher-order Raman pumping techniques.

2. Theory

In this work, three different approaches were used to characterize the DRS noise in HOP schemes. In the first approach, a simplified qualitative model assuming undepleted pump and transparency conditions helped pointing out the fundamentals of the physical mechanism underlying the predicted reduction of DRS for suitable signal profile conditions. In the second approach, a fast-computing, semi-analytical evaluation of DRS was obtained through the integration of the scattering contributions along the fiber, following the derivation in [4

4. M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997opex-17-09-6996-g004998 (1999). [CrossRef]

], which allowed us to provide a quantitative analysis of the behavior of DRS in HOP schemes. Finally, quantitative results were also obtained with a third full-numerical approach, which was used to cross-validate the results of the semi-analytical method. In the third approach, the complete propagation equations were numerically integrated in a WDM scenario, as detailed in [3

3. S. Faralli and F. Di Pasquale, “Impact of double Rayleigh scattering noise in distributed higher order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 804–806 (2003). [CrossRef]

], taking into account fiber absorption, signal Rayleigh scattering and Raman effect among pumps and signals.

2. 1 Full numerical model

The employed full numerical method allows the description of both co- and counter-propagating Raman pumps. It takes into account the effects of wavelength-dependent fiber absorption, pump and signal multiple-order Raman interactions as well as Rayleigh scattering. Amplified spontaneous emission (ASE) light is neglected in order to reduce computational effort, especially when higher-order pumps are spanning a wavelength range of several hundreds of nm, as, e.g., in 6th order pumping [5

5. S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Sixth-order cascaded Raman amplification,” in Optical Fiber Communication Conference, 2008 OSA Technical Digest, (Optical Society of America, 2008), paper OthF4.

].

The complete set of differential equations describing the power evolution for the i-th forward- or backward-propagating Raman pump P± P_i(z), the i-th forward-propagating WDM signal P+ S_i(z) and the corresponding backward-propagating single-Rayleigh-scattering P- S_i(z), as well as the corresponding double Rayleigh scattering P+ DRS_i(z), allows to obtain the power evolution along the fiber coordinate z. The equations describing the i-th signal (i=lN) or pump (i=lM) evolution can be written as:

dPS_i,p_i±(z)dz=αS_i,p_iPS_i,p_i±(z)±γiPS_i,p_i±±jiCijPS_i,p_ii±·[Pp_j++Pp_j+PS_j++PS_j_]
(1)
dPDRS_i+(z)dz=αS_iPDRS_i++jCjP¯P_j·PDRS_j++γiP¯SRS_i
(2)

where P S,P indicate the signal/pump power values, the superscripts +/- represent the co- and counter-propagating directions and αsi,pi the absorption coefficients at the i-th signal/pump wavelength, γi is the Rayleigh backscattering coefficient and Cij indicates the normalized Raman gain coefficient:

Cij=gijAeffforλi>λj,Cij=λjλigijAeffforλi<λj
(4)

where gij is the Raman gain coefficient, and Aeff is the fiber effective area. Integration of the differential equation set is achieved using 4th -order Runge-Kutta techniques in a recursive algorithm in order to provide an accurate estimate of the power evolution in a counter-propagating signal frame, similarly to what done for both space-time variables in [6

6. G. Bolognini, S. Sugliani, and F. Di Pasquale, “Double Rayleigh scattering noise in Raman amplifiers using pump time-division multiplexing schemes,” IEEE Photon. Technol. Lett., IEEE Press , 16, 1286–1288 (2004). [CrossRef]

].

2.2 Semi-analytical model

The signal double Rayleigh scattering noise can also be quantitatively evaluated more simply once the signal gain profile along the fiber length is known. Such a profile can be obtained either theoretically by solving a set of simplified differential equations similar to Eq.(1) for pump and signal power evolution without ASE, as commonly implemented in many commercially-available simulators, or experimentally through optical time-domain reflectometry (OTDR) [7

7. P. Kim, J. Park, H. Yoon, J. Park, and N. Park, “In situ design method for multichannel gain of a distributed Raman amplifier with multiwave OTDR,” IEEE Photon. Technol. Lett. 14, 1683–1685 (2002). [CrossRef]

].

Once the signal gain profile G(z) along z is known, the DRS noise power (PDRS) at the fiber end can be calculated as [4

4. M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997opex-17-09-6996-g004998 (1999). [CrossRef]

]:

PDRS=PS·γ20L0z[G(z)G(ς)]2dςdz
(3)

where PS is the signal power at fiber-end, γ is the Rayleigh backscattering coefficient, G(z) is the signal gain profile, and L the fiber length. The integrand represents the double-pass gain experienced between the two Rayleigh-scattering points of the signal at coordinates ς and z, with ς < z. From the expression of the integrand in Eq. (3), the major relative contributions to DRS are expected from those portions of the fiber in which ς is located in a low-power lossy section, while z is in a high-power gain-section, so that the gain ratio within the integrand is large: G(z)/ G(ς)≫l.

2.3 Simplified analytical model

In order to provide a clear insight in the physical mechanism underlying the DRS noise decrease, we may consider a simplified gain G(z) with a first lossy section, reproducing the input fiber section where no significant Raman gain from counter-propagating Raman pumps is experienced by the signal, followed by a constant-gain amplified section, starting at the coordinate L1 where the penetrating high pump power levels result in non-negligible Raman gain. Therefore the simplified gain profile along the fiber becomes:

G(z)={exp[αz]z[0,L1]exp[g(zL)]z[L1,L],
(4)

Fig. 1. (Left) Examples of simplified gain profiles versus fiber length. (Right) Signal to DRS ratio, normalized to fully distributed value, versus normalized coordinate of breakpoint between initial lossy section and final gain section.

Figure 1(left) reports an example of three possible profiles of the simplified gain in dB versus fiber length, for x=1 (dotted line, representing an ideal lossless fiber), for x=0 (dotted line, representing an ideal case with lumped amplification at fiber end), and for an arbitrary x∊(0,1) (solid line). Letting G1= eg d1 = eαLx the signal net gain within the amplified section, from Eqs. (3)–(4) we can find:

PDRSPS=γ2L22[(G12+2lnG11)x2+G12(1G12)2x(1x)+(G122lnG11)(1x)22(lnG1)2]
(5)

where the first term in the summation within the square brackets gives the contribution of both scatter points ς and z located in the lossy section, the second term gives the contribution for the case where the scatter point ς is located in the lossy section and the scatter point z in the gain section, and, finally, the third term gives the contribution for the case where both scatter points are located in the gain section. The term γ2L2/2 is the relative DRS power in Eq. (4) for the case of ideal fully distributed amplification, i.e., G(z)=1 for every z.

The effect of increasing pumping order on DRS noise can be qualitatively understood from Eq. (5) by decreasing x (i.e. by increasing ‘penetration depth’), representing the increasing distributed gain effect provided by higher-order pumping. The limiting value x=1 corresponds to the case where no gain is present throughout the fiber, and all gain is provided in a lumped amplifier stage at the fiber end; conversely, the limiting value x=0 corresponds to the ideal case (possibly approached by very high pumping orders) where the gain is fully distributed along the fiber, exactly compensating the fiber loss at every point, thus creating a transparent optical fiber condition at every fiber length.

Fig. 2. (Left) Scheme of simulated counter-propagating Raman amplification with increasing pumping orders. (Right) Power evolution for the 1450 nm pump under different pumping orders.

Figure 1 (right) shows the normalized optical signal to DRS crosstalk ratio (OSXR≡PS/PDRS), in a dB scale, versus normalized breakpoint location x. The OSXR parameter is normalized to its value OSXRD = (γ2L2/2)-1 achieved in the case of fully distributed amplification. We can note from Fig. 1(right) that, starting from a “flat” gain profile (x=0), as we increase x the OSXR exhibits a degradation. This can be explained, referring to Fig. 1(left), since the signal gain profile G along z becomes more and more deeply “V” shaped, and extended sections start to appear where the gain ratio in the integrand of Eq. (1) is large, i.e. G(z)/ G(ς)≫l; this, as noted earlier, gives rise to the well-known increase in DRS noise (thus worsening the OSXR), an effect which is commonly observed in present-day higher-order pumping schemes [3

3. S. Faralli and F. Di Pasquale, “Impact of double Rayleigh scattering noise in distributed higher order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 804–806 (2003). [CrossRef]

]. At the opposite extreme, x=1, we have the case of a lumped amplification at the fiber end, which is obtained when the breakpoint L1 coincides with the fiber end L. In such a case, i.e. G1 = eαL, the integrand G(z)/ G(ς) in Eq. (3) is always less than unity, and only the first term in Eq. (5) is present, so that we have:

OSXROSXRD=2(lnG1)2G12+2lnG11=2(αL)2e2αL+2αL1αL
(6)

where the approximation assumes αLl. This is the largest achievable OSXR, clearly larger than that in case of flat gain (x=0). Intuitively, since a physical quantity like the OSXR should be continuous over x, a value of x ≠ 0 must exist where the OSXR is minimum, as shown in Fig. 1(right). This simple model predicts the location of such a minimum at a penetration depth around d~0.5/α. Thus, from this simple formulation we can intuitively understand how, as we use Raman pumping of increasing order to provide a flatter gain, after exceeding the value of penetration depth where OSXR is minimum, the OSXR starts improving, i.e., the DRS noise starts decreasing for higher pumping orders.

3. Results for HOP Raman amplifiers

Table 1. Fiber parameters and pump conditions for the highest-order pump employed under different pumping order schemes

table-icon
View This Table
Fig. 3. Scheme of signal power evolution at 1550.1 nm under different higher-order schemes.

To provide a sensible comparison, the analysis has been carried out with common gain for the schemes from 1st to 5st order. The ON-OFF peak gain value (for the channel at 1550.1 nm) was GON-OFF = 26.7 dB, with a gain ripple smaller than 1 dB. This was achieved for different pumping orders by suitably varying the absolute input power of the lower-order seeds, also ensuring an optimal pump and signal power evolution. The resulting power evolution for the 1450 nm pump, which is directly pumping the WDM channels, is shown in Fig. 2(right) in case of different HOP schemes. From the figure we notice that in a 5th order scheme the 1450 nm pump exhibits the maximum power value at about 20 km from the fiber end, thus resulting in a signal amplification well inside the transmission fiber, with a consequent OSNR improvement, as it can be seen in Fig. 3, where the power profile for the 1550.1 nm channel (the one with highest gain and therefore the worst case for DRS noise assessment) is reported. Such power profiles are then employed in Eq. (1) in order to calculate the signal DRS noise at the fiber end for increasing pump order (see Sec. 2.2).

Fig. 4. OSXR vs pumping order calculated with full numerical and semi-analytical method.

The accuracy of this semi-analytical approach is also compared with the full numerical integration providing the DRS noise directly from resolution of the set of propagation equations (as explained in Sec. 2.1). The results are shown in Fig. 4 (left y-scale), reporting the signal-to-DRS noise ratio (OSXR) at the fiber end versus pumping order (from 1st- to 5th-order), obtained with both the semi-analytical approach (open symbols) and a full numerical integration (solid symbols). Both approaches are in good agreement, thus validating the accuracy of the semi-analytical approach in estimating DRS noise in HOP schemes. The behavior of OSXR in Fig. 4 is notable: for the used pump and signal input power conditions, we can observe a monotonic decrease in OSXR up to 3rd order pumping scheme (which is well known), and an apparently surprising improvement in OSXR for pumping orders higher than 3rd one, leading to a 3 dB improvement in OSXR from 3rd to 5th order (going from ~34 dB to ~37 dB). Such an improvement is adding up to the well-known OSNR improvement which is found for increasing order, as also reported in Fig. 4 (right y-scale), and can lead to an overall Q-factor improvement for increasing pumping orders. This behavior is in agreement with [3

3. S. Faralli and F. Di Pasquale, “Impact of double Rayleigh scattering noise in distributed higher order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 804–806 (2003). [CrossRef]

], who observe a DRS noise increase up to 3rd order, but may appear different from what emerged in [5

5. S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Sixth-order cascaded Raman amplification,” in Optical Fiber Communication Conference, 2008 OSA Technical Digest, (Optical Society of America, 2008), paper OthF4.

] for pumping orders higher than 3rd one. However, note that in that case a very different HOP scheme based on cascaded fiber-Bragg grating (FBG) light generation was used, resulting in different pump distributions from our case and, most importantly, in strong RIN-induced penalties in 6th-order (due to the fraction of pump power co-propagating with the signal in the FBG-assisted light generation scheme of [5

5. S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Sixth-order cascaded Raman amplification,” in Optical Fiber Communication Conference, 2008 OSA Technical Digest, (Optical Society of America, 2008), paper OthF4.

]), leading to worse performance observed for 6th order pumping than for lower-order schemes.

7. Conclusion

In conclusion, we carried out a theoretical analysis on the DRS noise behavior in higher-order Raman pumping schemes. Our analysis, performed through a simplified analytical treatment, as well as with semi-analytical and full numerical methods, allowed us to observe a notable phenomenon involving the decrease of DRS noise for HOP schemes above 3rd order. The occurrence of such a DRS-noise decrease was found to be dependent on the signal power profile along the fiber. Such a novel phenomenon, emerging from our simulations in Fig. 5 and also logically understandable from our simplified analytical treatment of Sec. 2.3, can thus in perspective lead to the implementation, within WDM communication systems, of HOP Raman amplifier schemes exhibiting improved OSNR and DRS noise features, and thus finally allowing an enhanced system Q-factor.

References and links

1.

M. Scheiders, S. Vorbeck, R. Leppla, E. Lach, M. Schmidt, S. B. Papernyi, and K. Sanapi, “Field transmission of 8×170 Gb/s over high-loss SSMF link using third-order distributed Raman amplification,” J. Lightwave Technol. 24, 175–182 (2006). [CrossRef]

2.

V. Karpov, S. B. Papernyi, V. Ivanov, W. Clements, T. Araki, and Y. Koyano, “Cascaded pump delivery for remotely pumped erbium doped fiber amplifiers,” in Proceedings of SubopticConference, 2004, p. We 8.8.

3.

S. Faralli and F. Di Pasquale, “Impact of double Rayleigh scattering noise in distributed higher order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 804–806 (2003). [CrossRef]

4.

M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997opex-17-09-6996-g004998 (1999). [CrossRef]

5.

S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Sixth-order cascaded Raman amplification,” in Optical Fiber Communication Conference, 2008 OSA Technical Digest, (Optical Society of America, 2008), paper OthF4.

6.

G. Bolognini, S. Sugliani, and F. Di Pasquale, “Double Rayleigh scattering noise in Raman amplifiers using pump time-division multiplexing schemes,” IEEE Photon. Technol. Lett., IEEE Press , 16, 1286–1288 (2004). [CrossRef]

7.

P. Kim, J. Park, H. Yoon, J. Park, and N. Park, “In situ design method for multichannel gain of a distributed Raman amplifier with multiwave OTDR,” IEEE Photon. Technol. Lett. 14, 1683–1685 (2002). [CrossRef]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.4510) Fiber optics and optical communications : Optical communications
(190.5650) Nonlinear optics : Raman effect

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 2, 2009
Revised Manuscript: March 30, 2009
Manuscript Accepted: March 30, 2009
Published: April 13, 2009

Citation
Gabriele Bolognini and Alberto Bononi, "Reduction of double Rayleigh scattering noise in distributed Raman amplifiers employing higher-order pumping," Opt. Express 17, 6996-7003 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-6996


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References

  1. M. Scheiders, S. Vorbeck, R. Leppla, E. Lach, M. Schmidt, S. B. Papernyi, and K. Sanapi, "Field transmission of 8x170 Gb/s over high-loss SSMF link using third-order distributed Raman amplification," J. Lightwave Technol. 24, 175-182 (2006). [CrossRef]
  2. V. Karpov, S. B. Papernyi, V. Ivanov, W. Clements, T. Araki, and Y. Koyano, "Cascaded pump delivery for remotely pumped erbium doped fiber amplifiers," in Proceedings of SubopticConference, 2004, p. We 8.8.
  3. S. Faralli and F. Di Pasquale, "Impact of double Rayleigh scattering noise in distributed higher order Raman pumping schemes," IEEE Photon. Technol. Lett. 15, 804-806 (2003). [CrossRef]
  4. M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, "Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers," Electron. Lett. 35, 997-998 (1999). [CrossRef]
  5. S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, "Sixth-order cascaded Raman amplification," in Optical Fiber Communication Conference, 2008 OSA Technical Digest, (Optical Society of America, 2008), paper OthF4.
  6. G. Bolognini, S. Sugliani, and F. Di Pasquale, "Double Rayleigh scattering noise in Raman amplifiers using pump time-division multiplexing schemes," IEEE Photon. Technol. Lett., IEEE Press 16, 1286-1288 (2004). [CrossRef]
  7. P. Kim, J. Park, H. Yoon, J. Park, and N. Park, "In situ design method for multichannel gain of a distributed Raman amplifier with multiwave OTDR," IEEE Photon. Technol. Lett. 14, 1683-1685 (2002). [CrossRef]

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