## Reduction of double Rayleigh scattering noise in distributed Raman amplifiers employing higher-order pumping

Optics Express, Vol. 17, Issue 9, pp. 6996-7003 (2009)

http://dx.doi.org/10.1364/OE.17.006996

Acrobat PDF (181 KB)

### 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

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]

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. Theory

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]

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]

### 2. 1 Full numerical model

^{th}order pumping [5].

*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*=

*l*…

*N*) or pump (

*i*=

*l*…

*M*) evolution can be written as:

*P*

_{S,P}indicate the signal/pump power values, the superscripts +/- represent the co- and counter-propagating directions and

*α*the absorption coefficients at the

_{si,pi}*i*-th signal/pump wavelength,

*γ*is the Rayleigh backscattering coefficient and

_{i}*C*indicates the normalized Raman gain coefficient:

_{ij}*g*is the Raman gain coefficient, and A

_{ij}_{eff}is the fiber effective area. Integration of the differential equation set is achieved using 4

^{th}-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

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]

*G*(

*z*) along

*z*is known, the DRS noise power (

*P*) at the fiber end can be calculated as [4

_{DRS}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]

*P*is the signal power at fiber-end,

_{S}*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

*L*where the ON-OFF Raman gain equals the fiber loss, resulting in a unity net gain

*G*at fiber output for a WDM signal (i.e.

*G*(

*L*)=

*1*).

*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

*L*where the penetrating high pump power levels result in non-negligible Raman gain. Therefore the simplified gain profile along the fiber becomes:

_{1}*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 G

_{1}=

*e*=

^{g d}_{1}*e*the signal net gain within the amplified section, from Eqs. (3)–(4) we can find:

^{αLx}*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

*γ*is the relative DRS power in Eq. (4) for the case of ideal fully distributed amplification, i.e.,

^{2}L^{2}/2*G*(

*z*)=

*1*for every

*z*.

*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.

*OSXR≡*), in a dB scale, versus normalized breakpoint location

*P*/_{S}*P*_{DRS}*x*. The OSXR parameter is normalized to its value

*OSXR*= (

_{D}*γ*)

^{2}L^{2}/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]

*x*=1, we have the case of a lumped amplification at the fiber end, which is obtained when the breakpoint

*L*coincides with the fiber end

_{1}*L*. In such a case, i.e.

*G*=

_{1}*e*, the integrand

^{αL}*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:

*αL*≫

*l*. 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

*G*(

*z*), as detailed in the previous Section. The scheme which has been analyzed is reported in Fig. 2(left). Eight WDM channels (range 1546.9–1552.5 nm with 100 GHz spacing, P

_{IN}/ch = 0 dBm) are transmitted through 140 km of standard single mode fiber (SMF). Note that results are also valid when longer transmission spans are considered, since the DRS noise behaviour is essentially dictated by the signal profile towards the fiber-end side. Raman amplification is achieved in the counter-propagating direction starting from 1

^{st}up to 5

^{th}order. Since multi-modal propagation is occurring for wavelengths smaller than ~1150 nm, correspondingly to 5

^{th}order pumping, we did not consider higher pumping orders (or equivalently shorter pump wavelengths) in our analysis. Table 1 reports some of the used fiber parameters, such as the peak Raman gain coefficient

*g*(the gain spectrum profile was actually used in simulations), the Rayleigh backscattering coefficient

_{R}*γ*, the fiber effective area

*A*

_{EFF}, and the absorption at peak signal wavelengths

*α*

_{1550}, along with the pump conditions such as fiber absorption and input pump power (P

_{IN}) considered for the highest-order pump wavelength in different pumping orders.

^{st}to 5

^{st}order. The ON-OFF peak gain value (for the channel at 1550.1 nm) was G

_{ON-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 5

^{th}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).

*y*-scale), reporting the signal-to-DRS noise ratio (OSXR) at the fiber end versus pumping order (from 1

^{st}- to 5

^{th}-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 3

^{rd}order pumping scheme (which is well known), and an apparently surprising improvement in OSXR for pumping orders higher than 3

^{rd}one, leading to a 3 dB improvement in OSXR from 3

^{rd}to 5

^{th}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]

^{rd}order, but may appear different from what emerged in [5] for pumping orders higher than 3

^{rd}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 6

^{th}-order (due to the fraction of pump power co-propagating with the signal in the FBG-assisted light generation scheme of [5]), leading to worse performance observed for 6

^{th}order pumping than for lower-order schemes.

## 7. Conclusion

^{rd}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. |

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 |

3. | S. Faralli and F. Di Pasquale, “Impact of double Rayleigh scattering noise in distributed higher order Raman pumping schemes,” IEEE Photon. Technol. Lett. |

4. | M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. |

5. | S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Sixth-order cascaded Raman amplification,” in |

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 , |

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. |

**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

- 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]
- 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.
- 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]
- 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]
- 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.
- 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]
- 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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