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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 14121–14131
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Design methodology for multi-pumped discrete Raman amplifiers: case-study employing photonic crystal fibers

C. E. S. Castellani, S. P. N. Cani, M. E. V. Segatto, M. J. Pontes, and M. A. Romero  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 14121-14131 (2009)
http://dx.doi.org/10.1364/OE.17.014121


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Abstract

This paper proposes a new design methodology for discrete multi-pumped Raman amplifier. In a multi-objective optimization scenario, in a first step the whole solution-space is inspected by a CW analytical formulation. Then, the most promising solutions are fully investigated by a rigorous numerical treatment and the Raman amplification performance is thus determined by the combination of analytical and numerical approaches. As an application of our methodology we designed an photonic crystal fiber Raman amplifier configuration which provides low ripple, high gain, clear eye opening and a low power penalty. The amplifier configuration also enables to fully compensate the dispersion introduced by a 70-km singlemode fiber in a 10 Gbit/s system. We have successfully obtained a configuration with 8.5 dB average gain over the C-band and 0.71 dB ripple with almost zero eye-penalty using only two pump lasers with relatively low pump power.

© 2009 Optical Society of America

1. Introduction

Raman fiber amplifiers have attracted attention since the 80’s because a careful combination of pump lasers, regarding both wavelength and optical power, allow wideband and flat spectral response, encompassing optical transmission systems operating all the way from S to L bands [1

1. C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (San Diego, CA, Academic Press, 2005).

]. Dispersion compensating fibers (DCFs) are also fundamental components in high-speed optical communication systems. By providing a suitable pump beam it is possible to achieve Raman amplification within these fibers and compensate the DCF loss [2

2. P.B. Hansen, G. Jacobovitz-Veselka, L. Gruner-Nielsen, and A. J. Stentz, “Raman amplification for loss compensation in dispersion compensating fiber modules,” Electron. Lett. 34, 1136–1137 (1998). [CrossRef]

]. The end result is a transparent dispersion compensating module which improves the optical system margin and power budget. One drawback still remaining arises from the fact that conventional Raman amplifiers require relatively high optical power densities and/or long interaction lengths.

In order to solve this problem photonic crystal fibers (PCFs) have been intensively investigated in the past few years. Slope-matched PCFs with very high negative values of the dispersion coefficient D [3

3. B. J. Mangan, F. Couny, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, M. Banham, M. W. Mason, D. F. Murphy, E. A. M. Brown, H. Sabert, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Slope-matched dispersion-compensating photonic crystal fiber,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CPDD3. [PubMed]

] as well as significant on-off gain for Raman amplification in short fiber lengths [4

4. Z. Yusoff, J. H. Lee, W. Belarti, T. M. Monro, P. C. The, and D. J. Richardson, “Raman effects in a highly nonlinear holey fiber: amplification and modulation,” Opt. Lett. 27, 424–426 (2002). [CrossRef]

] have already been experimentally demonstrated.

Unfortunately, these methods can be very time-consuming because the integration of the equations describing the Raman effect is an involved task by itself, task which must be carried out for every investigated pump configuration. As a consequence it is often very difficult to find the global minimum. As an alternative, the methodology presented in this paper makes use of an analytical model as a preliminary step [15

15. S. P. Cani, L. C. Calmon, M. J. Pontes, M. R. N. Ribeiro, M. E. V. Segatto, and A.V. T. Cartaxo, “An analytical approximated solution for the gain of broadband Raman amplifiers with multiple counter-pumps,” J. Lightwave Technol. 27, 944–951 (2009). [CrossRef]

]. In this way, the whole solution-space can be inspected at once. Then, the most promising solutions are fully investigated by a rigorous numerical treatment [10

10. S. P. Cani, M. Freitas, R. T. Almeida, and L. C. Calmon, “Raman amplifier performance of dispersion compensating fibers,” in Proceedings of SBMO/IEEE MTT-S International Microwave and Optoeletronics Conference (IMOC 2003), (Iguazu Falls, Brazil, 2003), pp. 553–558.

] and the Raman amplification performance is thus determined by the combination of analytical and numerical approaches. Therefore, the computation time is significantly reduced.

2. Dispersion compensating PCF geometry

3. Modeling Raman amplifiers

Raman amplifiers modeling, as summarized in the tree diagram shown in Fig. 1, is usually carried out using an extended nonlinear Schrödinger equation (ENLSE) method [10

10. S. P. Cani, M. Freitas, R. T. Almeida, and L. C. Calmon, “Raman amplifier performance of dispersion compensating fibers,” in Proceedings of SBMO/IEEE MTT-S International Microwave and Optoeletronics Conference (IMOC 2003), (Iguazu Falls, Brazil, 2003), pp. 553–558.

,19

19. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, USA, 3rd edition, 2001), Chap.8.

,20

20. D. Dahan and G. Eisenstein, “Numerical comparision between distributed and discrete amplification in a point-to-point 40 Gbit/s 40-WDM-based transmission system with three different modulation formats,” J. Lightwave Technol. 20, 379–388 (2002). [CrossRef]

] or steady-state approximations [20–22

20. D. Dahan and G. Eisenstein, “Numerical comparision between distributed and discrete amplification in a point-to-point 40 Gbit/s 40-WDM-based transmission system with three different modulation formats,” J. Lightwave Technol. 20, 379–388 (2002). [CrossRef]

]. Numerical methods are then used to analyze the electrical field evolution in the ENLSE modeling. Effects such as pump depletion, dispersion, amplified spontaneous emission (ASE), double Rayleigh backscattering (DRB) and nonlinear effects such as self-phase modulation (SPM) and cross-phase modulation (XPM), are fully computed in the ENLSE method. The optical signal to noise ratio (OSNR) and the eye penalty can also be calculated by this approach.

Fig. 1. Tree diagram showing the relationship among Raman amplifier models.

Regarding the steady-state analysis in the Raman amplifier modeling, both numerical and analytical solutions can be applied. However, the power evolution calculation performed by numerical methods enables the inclusion of effects such as pump depletion, ASE, RBS and the determination of OSNR as well. Those effects are only partially computed or even neglected in the analytical approaches.

In contrast, although some approximations are necessary in analytical approaches, analytical techniques allow accurate evaluation of gain and gain ripple within reduced computing time, a crucial feature to allow the design of Raman amplifiers employing multi-pump for several distinct signal wavelengths and optical power levels.

3.1 Numerical modeling

As discussed above, there are mainly two types of numerical approaches used to solve signal propagation in optical systems. On one hand, there is the ENLSE method based on the electromagnetic field evolution. This method enables to obtain eye penalties through the propagation of modulated signals. On the other hand there is the steady-state approach based on the signals power evolution. For the sake of completeness, both methods are described below.

3.1.1 Extended nonlinear Schrödinger equation

The signal and pump evolution in terms of temporal and spatial analysis can be computed using the Schrödinger nonlinear equations [19

19. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, USA, 3rd edition, 2001), Chap.8.

], given by Eq. (1), solved by means of the split step Fourier method, as described in detail in [10

10. S. P. Cani, M. Freitas, R. T. Almeida, and L. C. Calmon, “Raman amplifier performance of dispersion compensating fibers,” in Proceedings of SBMO/IEEE MTT-S International Microwave and Optoeletronics Conference (IMOC 2003), (Iguazu Falls, Brazil, 2003), pp. 553–558.

].

A±vzdref,vA±vt+j2β2v2A±vt2j6β3vA±vt3=αv2A±v
+jγv[A±v2+(σ=1Nc2A±σ2)2A±v2]Av±
±A±vμ>vCRμv2ΓA±μ2
±A±vμ<vvμCR2ΓA±μ2
±A±vμ<vvμCR2Γ[1+1exp[h(vμ)kT]1]2NEμ.
(1)

3.1.2 Steady-state approach

From the Eq. (1), it is possible to obtain the well known nonlinear coupled equation that governs the power evolution of pumps and signals along z

dPv±dz=αvPv±±εvPv±±Pv±μ>vCR,μvΓ·(Pμ±+Pμ)
±2NE,vμ>vCR,μvΓ·(Pμ±+Pμ)·TNPv±μ>vvμCR,μvΓ·(Pμ±+Pμ)
Pv±μ>vvμCR,μvΓ4NE,μ·[1+1/(exp[h(μv)kT]1)].
(2)

WherePv and Pμ are optical powers at the optical frequencies v and μ, respectively.

This equation, which provides the foundation for the development of the analytical model used in this work, can be solved numerically as a boundary value problem (BVP).

3.2 Analytical approach

Since numerical solutions are often extremely time consuming, we have used a simplified analytical model [15

15. S. P. Cani, L. C. Calmon, M. J. Pontes, M. R. N. Ribeiro, M. E. V. Segatto, and A.V. T. Cartaxo, “An analytical approximated solution for the gain of broadband Raman amplifiers with multiple counter-pumps,” J. Lightwave Technol. 27, 944–951 (2009). [CrossRef]

] for a initial prediction of the gain and gain ripple. The analytical approach considers pump-to-pump and signal-to-pump interactions and also takes into account wavelength dependent effects such as effective area variation and individual signal loss coefficients, but neglects the pump depletion by signal and also noise effects. Usually the gain calculation is not significantly influenced by such approximations [10

10. S. P. Cani, M. Freitas, R. T. Almeida, and L. C. Calmon, “Raman amplifier performance of dispersion compensating fibers,” in Proceedings of SBMO/IEEE MTT-S International Microwave and Optoeletronics Conference (IMOC 2003), (Iguazu Falls, Brazil, 2003), pp. 553–558.

].

The analytical expression that describes the power evolution in a fiber to N arbitrary number of counter-propagating pumps is obtained from Eq. (2) by an iterative procedure that calculates the iteration between pumps in three different frequencies. More details regarding the deduction of the analytical expressions and also the experimental validation can be found in [15

15. S. P. Cani, L. C. Calmon, M. J. Pontes, M. R. N. Ribeiro, M. E. V. Segatto, and A.V. T. Cartaxo, “An analytical approximated solution for the gain of broadband Raman amplifiers with multiple counter-pumps,” J. Lightwave Technol. 27, 944–951 (2009). [CrossRef]

]. This general expression for the pump power evolution as a function of the fiber length is given by

Pρ(z)=Pρ(L)exp[α(Lz)]
exp[ψ>ρ[A(ρ,Ψ)1exp[Λ(z)B(ψ,φ)]B(ψ,φ)]]
exp[ψ>ρ[ρψA(ρ,ψ)1exp[Λ(z)B(ψ,φ)]B(ψ,φ)]].
(3)

with A(ρ,ψ)=CR,ρψPψ(L),B(ψ,φ)=φ<ψψCR,ψφPφ(L)/φφ>ψCR,ρφPφ(L) and Λ(z)=(1exp(α(Lz)))Γα.

where L is the total fiber length, ρ, ψ, and φ are optical pump frequencies, Pρ is the pump optical powers and α is the wavelength independent attenuation coefficient. Then, from the pump power evolution equation, it is straightforward to show that, as described in [15

15. S. P. Cani, L. C. Calmon, M. J. Pontes, M. R. N. Ribeiro, M. E. V. Segatto, and A.V. T. Cartaxo, “An analytical approximated solution for the gain of broadband Raman amplifiers with multiple counter-pumps,” J. Lightwave Technol. 27, 944–951 (2009). [CrossRef]

], the signal gain can be obtained by

G(v,L)=exp[αvL]exp[0L(NpCR,ρvΓPρ(z)dz)].
(4)

where v is the optical signal frequency and Np is the total number of pumps.

4. Results

In this section, we will examine the performance of discrete multi-pump Raman amplifiers designed using DCPCF to simultaneously compensate dispersion and system losses. Table I presents the proposed methodology. First, it is necessary to define the amplifier configuration, the signal band, the number of channels and the number of pump lasers. In a second step it is necessary to define the range of pump wavelengths and optical power levels of interest as well as the number of configurations to be tested.

Then, the analytical method described in Section 3.2 is used for a preliminary calculation of the gain and ripple of each configuration. The goal is to inspect the complete gain versus ripple solution-space in a very short computation time. After analyzing the solutions it is possible to choose the most promising configurations for a given application. A common choice would be maximum gain within a tolerable gain ripple. Finally, in the fourth step, the ENLSE method is used to rigorously analyze the amplifier performance of the selected configuration(s) in terms of eye penalty and OSNR.

Table I:. Schematic algorithm describing the four steps methodology.

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We have used the methodology described in Table I to analyze a two counter-propagating pumps Raman amplifier operating at C band using the DCPCF described in [17

17. S. K. Varshney, K. Saitoh, M. Koshiba, and P. J. Roberts, “Analysis of a realistic and idealized dispersion-compensating photonic crystal fiber Raman amplifier,” Opt. Fiber Technol. 13, 174–179 (2007). [CrossRef]

] to simultaneously compensate dispersion and system losses. Fig. 2 shows the amplifier setup used in our investigation. The WDM transmitter contains 20 equally spaced C band channels, each carrying a 10 Gbps signal. The SMF was 70 km long and 1 km of DCPCF was used as the lumped gain media. The counter-pumped configuration was used to assure that the signal transmission less affected by the fiber nonlinearities. We have considered depolarized pumps with the polarization factor equal to 2. It is important to mention that gain values substantially higher can be obtained if the polarization state of signal and pump waves are kept constant, meaning polarization factor equal 1. Unfortunately, this is not easy to achieve experimentally. Table II summarizes the parameters used in our analyses.

Fig. 2. The discrete multi-pumped Raman amplifier setup.

Table II. System parameters.

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In the design of this C band amplifier, the analytical model (step 3) has been used to compute a large number of pump configurations with pump wavelengths, λP1 and λP2, varying randomly from 1410 to 1460 nm and pump power from 100 up to 450 mW. This range of pump powers was chosen because conventional pump lasers with such power levels present relatively lower cost. Fig. 3 shows the average gain versus ripple for 8000 different configurations. We have considered the DCPFC attenuation of 5 dB/km at 1550 nm, as discussed in section II. It took only 29.8 seconds in a 2.64 GHz INTEL processor with 2 GB of RAM to evaluate all points in the solution space depicted in Fig. 3.

Fig. 3. Gain versus ripple obtained with the analytical model for 8000 different configurations of a discrete two counter-propagating pumps Raman amplifier. The pump wavelength, λ P1 and λ P2, vary randomly from 1410 to 1460 nm and the pump powers from 100 to 450 mW. The inset shows the configurations with ripple smaller than 1 dB.

As it can be noticed from Fig. 3, it is possible to design a DCPCF Raman amplifier with a large value of gain and of ripple. The gain can vary from -5 to + 15 dB and while the ripple ranges from 0.50 to 17 dB, depending on pump configuration. A careful look at this data shows that 0.68% of the configurations present gain between 0 and 9 dB and ripple between 0 and 1 dB. The rate increases to 8.63 % if the ripple is allowed to be between 0 and 2 dB.

Among the 8000 possibilities studied we have chosen the configuration which presents maximum gain and an acceptable ripple. The inset in Fig. 3 shows the investigated solution space. The selected pump wavelengths and powers were, respectively, λp1 = 1422.4 nm, λp2 = 1451.9 nm and Pp1 = 238.9 mW, Pp2 = 435.2 mW. The achieved average gain was 8.83 dB for a ripple of 0.76 dB. Concerning the optimization variables pump wavelength and optical power, further simulations have shown that, for a given range of interest, increasing the number of points in the solution space beyond 8000 does not improve significantly the gain performance of the amplifier.

Next, we have used the numerical model described in section 3.1.1 in order to more rigorously analyze the performance of this proposed DCPCF Raman amplifier. The analysis was made through the evaluation of the net gain, the optical signal-to-noise ratio (OSNR), and the eye-penalty as a function of the signal wavelength for configurations with different values of signal input power and PCF attenuation. Each of the 20 WDM signals have used Non Return to Zero (NRZ) format and 10 Gbps. Fig. 4(a) shows the influence of the PCF loss and input power on the gain. We have assumed three values for the loss, i.e., αPCF = 4, 5 and 6 dB/km, and three values for the optical power of the WDM transmitter, PS = 0, -5 and -10 dBm. Fig. 4(a) shows that the gain was not significantly influenced by the signal input power in the studied region and, in all cases, we have obtained flat gain with less than 0.83 dB ripple. The average gain and ripple for the signal input power of −10 dBm and 5dB/km fiber attenuation were respectively, 8.5 dB and 0.71 dB, showing a good agreement with our analytical model results. The same figure shows that fiber attenuation plays an important role in the gain performance but it does not affect the ripple.

Figure 4(b) shows the OSNR for all 20 WDM channels. As it can be seen, improved OSNRs can be achieved for higher signal input powers, and in these cases the fiber attenuation does not significantly influence its value. Nevertheless it is important to notice that all values of OSNR were above 28 dB, which is yet a very satisfactory result. Finally, the eye penalty is presented in Fig. 5. An eye penalty close to zero can be obtained over the entire C-band. Figure 5 suggests that the dispersion introduced by 70 km of SMF can be totally compensated by the DCPCF in all wavelengths, and indicates that systems with 20 WDM channels operating at 10 Gbps in C-band can work without being significantly deteriorated by noise and non-linear effects.

Fig. 4. (a) Gain and (b) OSNR versus the signal wavelength for the discrete counter-propagating multi-pumped DCPCF Raman amplifier. (a) The numbers in the right side represent the input optical power per channel and (b) the PCF attenuation.
Fig. 5. Eye penalty as a function of the signal wavelength for the case presented in Fig 4. Here αPCF = 4, 5 and 6 dB/km, and PS = 0, -5 and -10 dBm/channel.

5. Conclusion

This paper has discussed the new design methodology for multi-pumped lumped Raman amplifiers employing photonic crystal fibers. Using an analytical model as a preliminary guess has enabled us to inspect the whole solution-space and find a very good combination of pump lasers to result in high gain, low ripple for an almost costless processing time. Then, the performance of the selected amplifier configuration can be rigorously evaluated using a numerical model based on the extended nonlinear Schrödinger equation.

References and links

1.

C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (San Diego, CA, Academic Press, 2005).

2.

P.B. Hansen, G. Jacobovitz-Veselka, L. Gruner-Nielsen, and A. J. Stentz, “Raman amplification for loss compensation in dispersion compensating fiber modules,” Electron. Lett. 34, 1136–1137 (1998). [CrossRef]

3.

B. J. Mangan, F. Couny, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, M. Banham, M. W. Mason, D. F. Murphy, E. A. M. Brown, H. Sabert, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Slope-matched dispersion-compensating photonic crystal fiber,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CPDD3. [PubMed]

4.

Z. Yusoff, J. H. Lee, W. Belarti, T. M. Monro, P. C. The, and D. J. Richardson, “Raman effects in a highly nonlinear holey fiber: amplification and modulation,” Opt. Lett. 27, 424–426 (2002). [CrossRef]

5.

K. Digweed-Lyytikainen, C. A. De Francisco, D. Spadoti, A. A. Juriollo, J. B. Rosolem, J. B. M. Ayres Neto, B. V. Borges, J. Canning, and M. A. Romero. “Photonic crystal optical fibers for dispersion compensation and Raman amplification: design and experiment,” Microwave Opt. Technol. Lett. 49, 872–874 (2007). [CrossRef]

6.

S. P. N Cani, C. A deFrancisco, D. H Spadoti, V. E. Nascimento, B. H. V Borges, L. C. Calmon, and M. A. Romero, “Requirements for efficient Raman amplification and dispersion compensation using microstructured optical fibers,” Fiber Integ. Opt. 26, 255–270 (2007). [CrossRef]

7.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005). [CrossRef]

8.

K. Nakajima, C. Fukai, K. Kurokawa, K. Tajima, T. Matsui, and I. Sankawa, “Raman amplification characteristics at 850 nm in a silica-based photonic crystal fiber,” IEEE Photon. Technol. Lett. 18, 451–453 (2006). [CrossRef]

9.

D. Mongardien, S. Borne, G. Melin, A. Fleureau, S. Lempereur, E. Burov, S. Maerten, C. Simonneau, and J. P. Hamaide, 2006, “10 Gbs/s WDM operation of a lumped Raman fiber amplifier using highly non-linear Ge-doped photonic crystal fiber,” in Proceedings of the European Conference on Optical Communications (ECOC′06), (Cannes, France, 2006), paper PD Th4.2.6.

10.

S. P. Cani, M. Freitas, R. T. Almeida, and L. C. Calmon, “Raman amplifier performance of dispersion compensating fibers,” in Proceedings of SBMO/IEEE MTT-S International Microwave and Optoeletronics Conference (IMOC 2003), (Iguazu Falls, Brazil, 2003), pp. 553–558.

11.

P. C. Xiao, Q. J. Zeng, J. Huang, and J. M. Liu, “A new optimal algorithm for multipump sources of distributed fiber Raman amplifier,” IEEE Photon. Technol. Lett. 15, 206–208 (2003). [CrossRef]

12.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, “Automatic design scheme for optical fibre Raman amplifiers backward-pumped with multiple laser diode pumps,” IEEE Photon. Technol. Lett. 13, 948–950 (2001). [CrossRef]

13.

X. Zhou, C. Lu, P. Shum, and T. H. Cheng, “A simplified model and optimal design of a multiwavelength backward pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. 13, 945–947 (2001). [CrossRef]

14.

B. Neto, A. L. J. Teixeira, N. Wada, and P. S. Andre, “Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers,” Opt. Express 15, 17520–17528 (2008). [CrossRef]

15.

S. P. Cani, L. C. Calmon, M. J. Pontes, M. R. N. Ribeiro, M. E. V. Segatto, and A.V. T. Cartaxo, “An analytical approximated solution for the gain of broadband Raman amplifiers with multiple counter-pumps,” J. Lightwave Technol. 27, 944–951 (2009). [CrossRef]

16.

P. J. Roberts, B. J. Mangan, H. Sabert, and F. Couny, and et al., “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber Commun. 2, 435–461, (2005). [CrossRef]

17.

S. K. Varshney, K. Saitoh, M. Koshiba, and P. J. Roberts, “Analysis of a realistic and idealized dispersion-compensating photonic crystal fiber Raman amplifier,” Opt. Fiber Technol. 13, 174–179 (2007). [CrossRef]

18.

K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow loss and long length photonic crystal fiber,” J. Lightwave Technol. 22, 7–9 (2004). [CrossRef]

19.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, USA, 3rd edition, 2001), Chap.8.

20.

D. Dahan and G. Eisenstein, “Numerical comparision between distributed and discrete amplification in a point-to-point 40 Gbit/s 40-WDM-based transmission system with three different modulation formats,” J. Lightwave Technol. 20, 379–388 (2002). [CrossRef]

21.

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, “Pump interactions in a 100-nm bandwidth Raman amplifier,” IEEE Photon. Technol. Lett. 11, 530–532 (1999). [CrossRef]

22.

M. Achtenhagen, T. G. Chang, B. Nyman, and A. Hardy, “Analysis of a multiple-pump Raman amplifier,” Appl. Phys. Lett. 78, 1322–1324 (2001). [CrossRef]

23.

Y. Aoki, “Properties of fiber Raman amplifiers and their applicability to digital optical communication systems,” J. Lightwave Technol. 6, 1225–1239 (1988). [CrossRef]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.2330) Fiber optics and optical communications : Fiber optics communications

ToC Category:
Photonic Crystal Fibers

History
Original Manuscript: April 2, 2009
Revised Manuscript: July 3, 2009
Manuscript Accepted: July 22, 2009
Published: July 30, 2009

Citation
C. E. S. Castellani, S. P. N. Cani, M. E. Segatto, M. J. Pontes, and M. A. Romero, "Design methodology for multi-pumped discrete Raman amplifiers: case-study employing photonic crystal fibers," Opt. Express 17, 14121-14131 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-14121


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References

  1. C. Headley, and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (San Diego, CA, Academic Press, 2005).
  2. P. B. Hansen, G. Jacobovitz-Veselka, L. Gruner-Nielsen, and A. J. Stentz, "Raman amplification for loss compensation in dispersion compensating fiber modules," Electron. Lett. 34, 1136-1137 (1998). [CrossRef]
  3. B. J. Mangan, F. Couny, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, M. Banham, M. W. Mason, D. F. Murphy, E. A. M. Brown, H. Sabert, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Slope-matched dispersion-compensating photonic crystal fiber," in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CPDD3. [PubMed]
  4. Z. Yusoff, J. H. Lee, W. Belarti, T. M. Monro, P. C. The, and D. J. Richardson, "Raman effects in a highly nonlinear holey fiber: amplification and modulation," Opt. Lett. 27, 424-426 (2002). [CrossRef]
  5. K. Digweed-Lyytikainen, C. A. De Francisco, D. Spadoti, A. A. Juriollo, J. B. Rosolem, J. B. M. Ayres Neto, B. V. Borges, J. Canning, and M. A. Romero. "Photonic crystal optical fibers for dispersion compensation and Raman amplification: design and experiment," Microwave Opt. Technol. Lett. 49, 872-874 (2007). [CrossRef]
  6. S. P. N Cani, C. A deFrancisco, D. H Spadoti, V. E. Nascimento, B. H. V Borges, L. C. Calmon, and M. A. Romero, "Requirements for efficient Raman amplification and dispersion compensation using microstructured optical fibers," Fiber Integ. Opt. 26, 255-270 (2007). [CrossRef]
  7. J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, "Progress on low loss photonic crystal fibers," Opt. Fiber Technol. 11, 101-110 (2005). [CrossRef]
  8. K. Nakajima, C. Fukai, K. Kurokawa, K. Tajima, T. Matsui, and I. Sankawa, "Raman amplification characteristics at 850 nm in a silica-based photonic crystal fiber," IEEE Photon. Technol. Lett. 18, 451-453 (2006). [CrossRef]
  9. D. Mongardien, S. Borne, G. Melin, A. Fleureau, S. Lempereur, E. Burov, S. Maerten, C. Simonneau, and J. P. Hamaide, 2006, "10 Gbs/s WDM operation of a lumped Raman fiber amplifier using highly non-linear Ge-doped photonic crystal fiber," in Proceedings of the European Conference on Optical Communications (ECOC´06), (Cannes, France, 2006), paper PD Th4.2.6.
  10. S. P. Cani, M. Freitas, R. T. Almeida, and L. C. Calmon, "Raman amplifier performance of dispersion compensating fibers," in Proceedings of SBMO/IEEE MTT-S International Microwave and Optoeletronics Conference (IMOC 2003), (Iguazu Falls, Brazil, 2003), pp. 553-558.
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