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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 23169–23180
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Numerical comparison between conventional dispersion compensating fibers and photonic crystal fibers as lumped Raman amplifiers

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 25, pp. 23169-23180 (2009)
http://dx.doi.org/10.1364/OE.17.023169


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Abstract

In this paper we discuss the use of photonic crystal fibers (PCFs) as discrete devices for simultaneous wideband dispersion compensation and Raman amplification. The performance of the PCFs in terms of gain, ripple, optical signal-to-noise ratio (OSNR) and required fiber length for complete dispersion compensation is compared with conventional dispersion compensating fibers (DCFs). The main goal is to determine the minimum PCF loss beyond which its performance surpasses a state-of-the-art DCF and justifies practical use in telecommunication systems.

© 2009 OSA

1. Introduction

In the last few years the quick growth of the Internet and other bandwidth demanding applications have motivated a drastic increase in the bit-rates transmitted over long-haul fiber optic systems. This increase has enhanced the need to compensate the dispersion introduced by the transmission fiber, as usually done by adding sections of dispersion compensating fibers (DCFs) along the fiber optic link. Those DCFs were proposed in the 80’s [1

1. C. Lin, H. Kogelnik, and L. G. Cohen, “Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3 - 1.7-μ m spectral region,” Opt. Lett. 5(11), 476–478 ( 1980). [CrossRef] [PubMed]

] and have found widespread use since the 90’s [2

2. J. M. Dugan, A. J. Price, M. Ramadan, D. L. Wolf, E. F. Murphy, A. J. Antos, D. K. Smith, and D. W. Hall, “All-optical, fiber-based 1550 nm dispersion compensation in a 10 Gb/s, 150 km transmission experiment over 1310 nm optimized fiber,” in Proceedings of the Optical Fiber Communications Conference (OFC), (San Jose, CA, 1992), Paper PD14.

]. The DCFs have also enabled the development of lumped devices which not only provide dispersion compensation but can also act as a Raman amplification medium [3

3. 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(11), 1136–1137 ( 1998). [CrossRef]

,4

4. J. D. Ania-Castañon and S. K. Turitsyn, “Noise and gain optimisation in bi-directionally pumped dispersion compensating amplifier modules,” Opt. Commun. 224(1-3), 107–111 ( 2003). [CrossRef]

]. A careful combination of pump lasers, regarding its emission wavelengths and output optical powers, together with specific fiber characteristics, allows transparent operation of wideband WDM systems over hundreds of kilometers with almost complete dispersion and loss compensation.

Although conventional DCFs have been widely used, the development of photonic crystal fibers (PCFs) has brought new design possibilities. Among its unique features, one can mention highly tunable dispersion characteristics [5

5. A. Ferrando, E. Silvestre, P. Andres, J. Miret, and M. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9(13), 687–697 ( 2001). [CrossRef] [PubMed]

] including flexible chromatic dispersion over a wide wavelength range [6

6. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11(8), 843–852 ( 2003). [CrossRef] [PubMed]

8

8. T. Matsui, J. Zhou, K. Nakajima, and I. Sankawa, “Dispersion flattened photonic crystal fiber with large effective area and low confinement loss,” J. Lightwave Technol. 23(12), 4178–4183 ( 2005). [CrossRef]

] or high negative dispersion [9

9. L. Yao, S. Lou, H. Fang, T. Guo, H. Li, and S. Jian, “High Negative Dispersion and Low Confinement Loss Photonic Crystal Fiber,” in Asia Optical Fiber Communication & Optoelectronic Exposition (OEA), (Shangai, 2007).

,10

10. Z. Zhang, Y. Shi, B. Bian, and J. Lu, “Large Negative Dispersion in Dual-Core Photonic Crystal Fibers Based on Optional Mode Coupling,” IEEE Photon. Technol. Lett. 20(16), 1402–1404 ( 2008). [CrossRef]

] as well as ultra wideband single mode operation [11

11. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 ( 1997). [CrossRef] [PubMed]

] and slope matched characteristics [12

12. 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.

]. Significant on-off gain values for Raman amplification in short PCF fiber lengths [13

13. Z. Yusoff, J. H. Lee, W. Belardi, T. M. Monro, P. C. Teh, and D. J. Richardson, “Raman effects in a highly nonlinear holey fiber: amplification and modulation,” Opt. Lett. 27(6), 424–426 ( 2002). [CrossRef] [PubMed]

] have also been experimentally demonstrated. The use of PCFs enables high negative dispersion values in very small effective areas, which are essential parameters when focusing on lumped devices for Raman amplification and dispersion compensation.

In this paper, we revisited the loss problem in PCFs. Specifically, by considering a state-of-the art dual-core PCF we seek to determine the minimum PCF loss beyond which its performance surpasses a conventional DCF. The goal is to offer guidelines concerning how much lower should be the background losses before those PCFs can find practical use as lumped Raman amplification and dispersion compensation devices.

In order to carry out this investigation, our simulation method utilizes an analytical formulation as a first step to determine the optimum combination of pump lasers and wavelengths to achieve a given set of amplifier characteristics. Next, we employ a full signal analysis model to numerically solve the coupled propagation equations and compute the expected Raman amplifier performance in a fiber-optic telecommunications link. The paper outline is given as follows: the PCF characteristics are described in Section 2. In Section 3 the numerical models used in the simulations are presented, and in Section 4 the results are discussed. Finally, Section 5 concludes the paper.

2. Dispersion compensating PCF geometry

The PCF considered in our simulations presents a highly negative dispersion coefficient and it was chosen for comparison with a conventional DCF because it was already demonstrated as a very good candidate to efficiently compensate the fiber dispersion in long-haul fiber systems. The fiber specifications are based on the PCF described in detail in [12

12. 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.

,18

18. P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber Commun Rep. 2(5), 435–461 ( 2005). [CrossRef]

], which, to the best of our knowledge, presents the most negative dispersion coefficient ever experimentally demonstrated. Also, its slope-matched dispersion characteristics are designed to fully compensate the dispersion introduced by commercial standard single mode fibers (SMF) operating in the C band. Both fibers, PCF or conventional DCF, can be used for simultaneous Raman amplification and dispersion compensation. However, in this particular case, the PCF presents a much higher negative dispersion value, i.e., −1216 ps/(nm.km) at 1550 nm, meanwhile for a typical commercially available DCF offers a much lower dispersion coefficient, around − 98 ps(nm.km). Essentially, this means that, although the PCF losses are much higher, the PCF length necessary for full dispersion compensation is much shorter. A clear trade-off is then established. As technology matures, those microstructured fibers will eventually be fabricated at the required lengths with reduced losses, surpassing the conventional DCF performance.

3. Simulation Models

Simulations of optical signal propagation in Raman amplifiers can be carried out basically by three different approaches. The problem can be treated numerically, either by solving the extended nonlinear Schrödinger equations (ENLSE) [20

20. 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.

22

22. D. Dahan and G. Eisenstein, “Numerical comparison 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(3), 379–388 ( 2002). [CrossRef]

] or a suitable steady-state approximation [22

22. D. Dahan and G. Eisenstein, “Numerical comparison 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(3), 379–388 ( 2002). [CrossRef]

24

24. M. Achtenhagen, T. G. Chang, B. Nyman, and A. Hardy, “Analysis of a multiple-pump Raman amplifier,” Appl. Phys. Lett. 78(10), 1322–1324 ( 2001). [CrossRef]

]. As an alternative, an analytical solution [25

25. 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(7), 944–951 ( 2009). [CrossRef]

] can be applied to the steady-state analysis, with the associated penalty of some inevitable simplifications. The ENLSE method allows the propagation of modulated signals, while steady-state formalism permits only the calculation of the optical power evolution along the fiber length. As a bonus, its computational cost is much smaller.

Regarding the steady-state analysis in the Raman amplifier modeling, both numerical and analytical approaches can be applied. The power evolution calculation performed by numerical methods enables the inclusion of effects such as pump depletion, wavelength dependence of the pump loss, amplified spontaneous emission (ASE), double Rayleigh scattering (DRS) and the accurate determination of the OSNR. Those effects are only partially computed or even neglected in the analytical approaches.

On the other hand, 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.

In our paper, the steady-state analysis was indeed used, because it is enough to provide reliable values of gain, the main figure of merit for our investigation. Then, in the steady-state framework, a hybrid mix of numerical and analytical techniques was employed, as summarized by the diagram shown in Fig. 1
Fig. 1 Tree diagram showing the relationship among Raman amplifier models used.
.

Next, a more precise numerical solution [20

20. 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.

] is used to investigate only the most promising pump configurations, which means pump sets with high gains and ripple values lower than 1 dB. Since the power evolution calculation performed by this numerical model takes into account the effects not included in the analytical solution [25

25. 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(7), 944–951 ( 2009). [CrossRef]

], it becomes possible to assure a reliable assessment of the amplifier gain response for the pre-selected pump schemes.

4. Results

Our analysis of the Raman amplifier performance is based on the optical system configuration shown in Fig. 2
Fig. 2 The discrete multi-pumped Raman amplifier setup.
. A two-pump counter-propagated lumped Raman amplifier is placed at the very end of the entire span, which was designed to amplify 20 WDM channels, equally spaced at the C band (1530.33 nm – 1560.61 nm), each one with −10 dBm of optical power launched at the SMF input. The counter-pumped configuration was used to assure that the signal transmission is less affected by the fiber nonlinearities.

4.1 Analytical model results

Our initial design goal was to find the pump configuration with higher gain, while keeping the gain ripple below 1 dB. The gain is measured by comparing the output power at the very end of the span with the signal power at the input of the dispersion compensating fiber (DCF or PCF). Meanwhile, the gain ripple is defined as the spectral gain variation within the Raman amplifier bandwidth.

The PCF optical loss was varied in the range of 3-5 dB/km. In this framework, Fig. 3
Fig. 3 Solution space for a PCF loss of (a) 3 dB/km, (b) 4 dB/km and (c) 5 dB/km attenuation.
illustrates three different results for the solution space (gain and ripple), displaying the 150,000 points obtained (each one for a given pump configuration). Each set of results was calculated, respectively, for different values of the PCF optical loss as (a) 3 dB/km, (b) 4 dB/km and (c) 5 dB/km.

From a design point of view, there is a clear trade-off between gain and ripple. One can easily notice that the amplifiers presenting very low ripple can achieve, even in the best cases, only moderate values of gain. In contrast, amplifiers with the higher values of mean gain suffer from high ripple. According to this scenario, results of Table 2

Table 2. Best configurations obtained with the analytical model.

table-icon
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were obtained by setting the ripple just below maximum admissible target value of 1 dB, either for the PCF or DCF. In this situation, a typical DCF gain would be 16.2 dB.

Regarding the PCF, the result obtained for the DCF can be equaled if the total optical loss can be kept around 3.75 dB/km, which is not an extremely low value. It is also interesting to note that the selected pump set (in a two-pump scheme) is not significantly altered by the change of the optical attenuation parameter. The gain as a function of the signal wavelength, considering the cases presented in Table 2 are shown in Fig. 4
Fig. 4 Gain versus the signal wavelength for all the cases shown on Table 1: analytical formulation.
.

4.2 Numerical simulation results

In order to account for the amplified spontaneous emission (ASE) and Rayleigh backscattering (RBS) as a function of the signal input in the Raman amplifier performance, the numerical model was used. The gain as a function of the signal wavelength, for all cases from Table 2, is again shown in Fig. 5
Fig. 5 Gain versus the signal wavelength for all the cases studied: numerical model.
, now depicting the results from the numerical model. Comparing Figs. 5 and 6
Fig. 6 Mean gain (a) and OSNR (b) as a function of the launched signal power at the fiber input.
, the spectral characteristics of the DCF has remained almost the same, while the numerical results from the PCF are about 1 dB lower than that those obtained using the analytical model. Still, the difference is small and indicates that both models are in good agreement, as summarized in Table 3

Table 3. – Comparative table: numerical vs. analytical models.

table-icon
View This Table
| View All Tables
. In this case, the PCF attenuation which produces similar performance of the DCF is around 3.5 dB/km, quite close to the value of 3.75 dB/km previously obtained.

Next, numerical simulations were performed by varying the signal launched at the SMF input, from -35 dBm to ?? + 10 dBm, and the mean gain and the OSNR was computed, as illustrated in Fig. 6(a) and 6(b).

Figure 6(a) shows the typical Raman amplifier response regarding the launched signal power, per channel. For a signal power lower than –25 dBm the gain is high but the massive presence of noise degrades the OSNR making this region not useful in practical cases, as it can be seen from the OSNR values in Fig. 6(b). Next, there is a nearly flat range, in which the gain does not significantly change when altering the signal input power. Beyond this flat region, high input powers, around zero dBm per channel, saturate the amplifier and are also undesirable because they favor non-linear effects.

From Fig. 6(b), it can be noticed that the OSNR displays only a small variation in the investigated range of PCF attenuation levels. As a general rule, the values of OSNR for the PCFs are 5 dB higher than those arising from the DCF. Moreover, Fig. 6 indicates that the

?+ 10 dBm signal input power is an adequate operating point. For this value, the OSNR in all cases is above 25 dB, and the amplifier is operating in its linear region.

Next, in order to extend the analysis, we attempt to determine how the PCF Raman amplifier responds to limited variations of the Raman gain. In this simulations a 20% variation on the Raman peak gain efficiency, originally taken as 21 W−1km−1 and now ranging from 16.8 up to 25.2 W−1km−1, was assumed The PCF attenuation was kept at 5 dB/km with the same effective area and dispersion given on Table 1. Numerical simulations were performed by varying the signal launched at the SMF input, from – 35 dBm to + 10 dBm, considering the Raman peak gain efficiency equal to 16.8, 21.0 and 25.2 W−1km−1. The mean gain and the OSNR were computed. Figure 7
Fig. 7 Mean gain as a function of the input signal power for three distinct values of Raman gain efficiency.
shows the Raman amplifier response regarding the launched signal power, per channel. As expected, a larger Raman gain efficiency induces faster amplifier saturation. Still, there is always a comfortable range of input powers to allow linear operation.

Finally, another important issue of additional loss should be splicing losses, which are expected to be fairly high for the investigated PCF, on account of the small mode-field diameter and effective area. Typical splice losses can be as high as a few dB. However, by using a splice-free technique, reference [29

29. S. G. Leon-Saval, T. A. Birks, N. Y. Joly, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P. S. J. Russell, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. 30(13), 1629–1631 ( 2005). [CrossRef] [PubMed]

] reports 0.8 dB loss at 633 nm for the transition between a SMF and a 2.8 μm diameter-core, highly non-linear PCF. Also, dual-core PCF designs allow, in principle wideband dispersion compensation in large effective area fibers. Thus, although Raman gain will suffer, a large portion of reported work on those dual-core PCFs seek to increase the mode field diameter, in order to reduce non-linear effects and/or mitigate the splice losses to conventional single-mode fibers [30

30. A. Huttunen and P. Törmä, “Optimization of dual-core and microstructure fiber geometries for dispersion compensation and large mode area,” Opt. Express 13(2), 627–635 ( 2005). [CrossRef] [PubMed]

,31

31. S. Yang, Y. J. Zhang, X. Z. Peng, Y. Lu, S. H. Xie, J. Li, W. Chen, Z. Jiang, J. Peng, and H. Li, “Theoretical study and experimental fabrication of high negative dispersion photonic crystal fiber with large area mode field,” Opt. Express 14(7), 3015–3023 ( 2006). [CrossRef] [PubMed]

].

5. Conclusions

References and links

1.

C. Lin, H. Kogelnik, and L. G. Cohen, “Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3 - 1.7-μ m spectral region,” Opt. Lett. 5(11), 476–478 ( 1980). [CrossRef] [PubMed]

2.

J. M. Dugan, A. J. Price, M. Ramadan, D. L. Wolf, E. F. Murphy, A. J. Antos, D. K. Smith, and D. W. Hall, “All-optical, fiber-based 1550 nm dispersion compensation in a 10 Gb/s, 150 km transmission experiment over 1310 nm optimized fiber,” in Proceedings of the Optical Fiber Communications Conference (OFC), (San Jose, CA, 1992), Paper PD14.

3.

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(11), 1136–1137 ( 1998). [CrossRef]

4.

J. D. Ania-Castañon and S. K. Turitsyn, “Noise and gain optimisation in bi-directionally pumped dispersion compensating amplifier modules,” Opt. Commun. 224(1-3), 107–111 ( 2003). [CrossRef]

5.

A. Ferrando, E. Silvestre, P. Andres, J. Miret, and M. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9(13), 687–697 ( 2001). [CrossRef] [PubMed]

6.

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11(8), 843–852 ( 2003). [CrossRef] [PubMed]

7.

L.- P. Shen, W.-P. Huang, and S.-S. Jian, “Design of photonic crystal fibers for dispersion related applications,” J. Lightwave Technol. 21(7), 1644–1651 ( 2003). [CrossRef]

8.

T. Matsui, J. Zhou, K. Nakajima, and I. Sankawa, “Dispersion flattened photonic crystal fiber with large effective area and low confinement loss,” J. Lightwave Technol. 23(12), 4178–4183 ( 2005). [CrossRef]

9.

L. Yao, S. Lou, H. Fang, T. Guo, H. Li, and S. Jian, “High Negative Dispersion and Low Confinement Loss Photonic Crystal Fiber,” in Asia Optical Fiber Communication & Optoelectronic Exposition (OEA), (Shangai, 2007).

10.

Z. Zhang, Y. Shi, B. Bian, and J. Lu, “Large Negative Dispersion in Dual-Core Photonic Crystal Fibers Based on Optional Mode Coupling,” IEEE Photon. Technol. Lett. 20(16), 1402–1404 ( 2008). [CrossRef]

11.

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 ( 1997). [CrossRef] [PubMed]

12.

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.

13.

Z. Yusoff, J. H. Lee, W. Belardi, T. M. Monro, P. C. Teh, and D. J. Richardson, “Raman effects in a highly nonlinear holey fiber: amplification and modulation,” Opt. Lett. 27(6), 424–426 ( 2002). [CrossRef] [PubMed]

14.

S. P. N. Cani, C. A. De Francisco, 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 Integr. Opt. 26(5), 255–270 ( 2007). [CrossRef]

15.

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,” Microw. Opt. Technol. Lett. 49(4), 872–874 ( 2007). [CrossRef]

16.

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(2), 101–110 ( 2005). [CrossRef]

17.

K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow loss and long length photonic crystal fiber,” J. Lightwave Technol. 22(1), 7–10 ( 2004). [CrossRef]

18.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. S. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber Commun Rep. 2(5), 435–461 ( 2005). [CrossRef]

19.

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(2), 174–179 ( 2007). [CrossRef]

20.

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.

21.

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

22.

D. Dahan and G. Eisenstein, “Numerical comparison 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(3), 379–388 ( 2002). [CrossRef]

23.

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(5), 530–532 ( 1999). [CrossRef]

24.

M. Achtenhagen, T. G. Chang, B. Nyman, and A. Hardy, “Analysis of a multiple-pump Raman amplifier,” Appl. Phys. Lett. 78(10), 1322–1324 ( 2001). [CrossRef]

25.

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(7), 944–951 ( 2009). [CrossRef]

26.

Y. Aoki, “Properties of fiber Raman amplifiers and their applicability to digital optical communication systems,” J. Lightwave Technol. 6(7), 1225–1239 ( 1988). [CrossRef]

27.

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(16), 14121–14131 ( 2009). [CrossRef] [PubMed]

28.

S. K. Varshney, T. Fujisawa, K. Saitoh, and M. Koshiba, “Novel design of inherently gain-flattened discrete highly nonlinear photonic crystal fiber Raman amplifier and dispersion compensation using a single pump in C-band,” Opt. Express 13(23), 9516–9526 ( 2005). [CrossRef] [PubMed]

29.

S. G. Leon-Saval, T. A. Birks, N. Y. Joly, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P. S. J. Russell, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. 30(13), 1629–1631 ( 2005). [CrossRef] [PubMed]

30.

A. Huttunen and P. Törmä, “Optimization of dual-core and microstructure fiber geometries for dispersion compensation and large mode area,” Opt. Express 13(2), 627–635 ( 2005). [CrossRef] [PubMed]

31.

S. Yang, Y. J. Zhang, X. Z. Peng, Y. Lu, S. H. Xie, J. Li, W. Chen, Z. Jiang, J. Peng, and H. Li, “Theoretical study and experimental fabrication of high negative dispersion photonic crystal fiber with large area mode field,” Opt. Express 14(7), 3015–3023 ( 2006). [CrossRef] [PubMed]

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:
Fiber Optics and Optical Communications

History
Original Manuscript: August 12, 2009
Revised Manuscript: November 15, 2009
Manuscript Accepted: November 15, 2009
Published: December 3, 2009

Citation
C. E. S. Castellani, S. P. N. Cani, M. E. V. Segatto, M. J. Pontes, and M. A. Romero, "Numerical comparison between conventional dispersion compensating fibers and photonic crystal fibers as lumped Raman amplifiers," Opt. Express 17, 23169-23180 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-23169


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References

  1. C. Lin, H. Kogelnik, and L. G. Cohen, “Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3 - 1.7-μ m spectral region,” Opt. Lett. 5(11), 476–478 (1980). [CrossRef] [PubMed]
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