## Optimization of pump spectra for gain-flattened photonic crystal fiber Raman amplifiers operating in C-band

Optics Express, Vol. 15, Issue 5, pp. 2654-2668 (2007)

http://dx.doi.org/10.1364/OE.15.002654

Acrobat PDF (270 KB)

### Abstract

This paper focuses on the optimization of pump spectra to achieve low Raman gain ripples over C-band in ultra-low loss photonic crystal fiber (PCF) and dispersion compensating PCFs (DCPCFs). Genetic algorithm (GA), a multivariate stochastic optimization algorithm, is applied to optimize the pump powers and the wavelengths for the aforesaid fiber designs. In addition, the GA integrated with full-vectorial finite element method with curvilinear edge/nodal elements is used to optimize the structural parameters of DCPCF. The optimized DCPCF provides broadband dispersion compensation over C-band with low negative dispersion coefficient of -530 ps/nm/km at 1550 nm, which is five times larger than the conventional dispersion compensating fibers with nearly equal effective mode area (21.7 μm^{2}). A peak gain of 8.4 dB with ±0.21 dB gain ripple is achieved for a 2.73 km long DCPCF module when three optimized pumps are used in the backward direction. The lowest gain ripple of ±0.36 dB is attained for a 10 km long ultra-low loss PCF with three backward pumps. Sensitivity analysis has been performed and it is found that within the experimental fabrication tolerances of ±2%, the absolute magnitude of dispersion may vary by ±16%, while the Raman gain may change by ±7%. Through tolerance study, it is examined that the ring core’s hole-size is more sensitive to the structural deformations.

© 2007 Optical Society of America

## 1. Introduction

3. Y. Emori, Y. Akasaka, and S. Namiki, “Broadband lossless DCF using Raman amplification pumped by multichannel WDM laser diodes,” Electron. Lett. **34**, 2145–2146 (1998). [CrossRef]

7. K. Thyagarajan and C. Kakkar, “Novel fiber design for flat gain Raman amplification using single pump and dispersion compensation in S band,” J. Lightwave Technol. **22**, 2279–2286 (2004). [CrossRef]

## 2. Fiber design and optimization

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

^{2}at 1550 nm.

22. S. K. Varshney, K. Saitoh, and M. Koshiba, “A novel fiber design for dispersion compensating photonic crystal fiber Raman amplifier,” IEEE Photon. Technol. Lett. **17**2062–2065 (2005). [CrossRef]

*d*, such that

*d*>

*d*. The opto-geometrical parameters

_{s}*d*,

*d*, and Λ are well optimized by GA algorithm as discussed in Ref. [29

_{s}29. T. Fujisawa, K. Saitoh, K. Wada, and M. Koshiba, “Chromatic dispersion profile optimization of dual-concentric-core photonic crystal fibers for broadband dispersion compensation,” Opt. Express **14**893–900 (2006). [CrossRef] [PubMed]

*F*(Λ,

*d*/Λ,

*d*/Λ) was considered to obtain an optimal value of

_{s}*d*,

*d*, and Λ such that type-2 DCPCF exhibits a slowly varying negative dispersion and can compensates for dispersion slope.

_{s}*w*

_{1}is a scaling parameter and taken as 0.001,

*A*is the effective mode area,

_{eff}*D*

_{DCPCF}is the dispersion coefficient of DCPCF, and λ is the free space wavelength.

*D*

_{target}is defined as

*X*is the integer and

*D*

_{SMF}is the dispersion coefficient of SMF.

*f*

_{1}corresponds to the dispersion slope compensation and if

*D*

_{SMF}is completely compensated by DCPCF

*f*

_{1}is zero and

*F*becomes to its maximum value of 1.

*f*

_{2}is the penalty term with regard to

*A*, and the structure having smaller effective area will be discarded in GA analysis. The constraint on effective mode area was applied to ensure that DCPCF should have a similar effective mode area as of conventional DCF and the mode-field should nearly match to the mode-field of conventional SMF so that splice loss between two can be decreased and nonlinearity can be reduced. On the basis of GA, the optimized structural parameters for type-2 DCPCF are obtained as

_{eff}*d*= 0.955 μm,

*d*= 0.706 μm, and Λ= 1.81 μm.

_{s}30. L.G. Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. Edvold, B. Palsdottir, and D. Jakobsen, “Dispersion compensating fibers,” J. Lightwave Technol. **23**3566–3579 (2005). [CrossRef]

30. L.G. Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. Edvold, B. Palsdottir, and D. Jakobsen, “Dispersion compensating fibers,” J. Lightwave Technol. **23**3566–3579 (2005). [CrossRef]

^{2}). Table 1 summarizes the fiber’s parameters and their important modal characteristics.

## 3. Raman amplification model for PCFs

18. M. Fuochi, F. Poli, A. Cucinotta, and L. Vincetti, “Study of Raman amplification properties in triangular photonic crystal fibers,” J. Lightwave Technol. **21**, 2247–2254 (2003). [CrossRef]

23. 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**9516–9526 (2005). [CrossRef] [PubMed]

31. J. Bromage, K. Rottwitt, and M. E. Lines, “A method to predict the Raman gain spectra of germanosilicate fibers with arbitrary index profiles,” IEEE Photon. Technol. Lett. **14**24–26 (2002). [CrossRef]

*i*

_{s}and

*i*

_{p}are the normalized signal and pump intensities obtained through an exact definition of Poynting vector [18

18. M. Fuochi, F. Poli, A. Cucinotta, and L. Vincetti, “Study of Raman amplification properties in triangular photonic crystal fibers,” J. Lightwave Technol. **21**, 2247–2254 (2003). [CrossRef]

*C*

_{SiSi}(∆

*v*) is the Raman gain spectra of Si-O-Si bounds [31

31. J. Bromage, K. Rottwitt, and M. E. Lines, “A method to predict the Raman gain spectra of germanosilicate fibers with arbitrary index profiles,” IEEE Photon. Technol. Lett. **14**24–26 (2002). [CrossRef]

*v*) for ULL-PCF (solid black curve), type-1 (solid blue curve) and type-2 (solid red curve) DCPCFs is plotted in Fig. 4(a), while the spectral variation of Rayleigh backscattering coefficient (ε

_{R}) for corresponding fiber designs has been illustrated in Fig. 4(b). The Rayleigh backscattering coefficient for PCFs is calculated [19

19. M. Bottacini, F. Poli, A. Cucinotta, and S. Selleri, “Modeling of photonic crystal fiber Raman amplifiers,” J. Lightwave Technol. **22**1707–1713 (2004). [CrossRef]

23. 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**9516–9526 (2005). [CrossRef] [PubMed]

*n*

_{Si}is the refractive index of silica,

*C*is the Rayleigh scattering coefficient which is assumed to be 1 dB/km/μm

_{R}_{4},

*i*(

*x, y*) is the normalized field intensity of a signal, and λ is the desired wavelength.

^{-1}.km

^{-1}around a frequency shift of 13.1 THz, while type-1 and type-2 DCPCFs show the single peak of 4.17 W

^{-1}.km

^{-1}and 2.8 W

^{-1}.km

^{-1}around a frequency shift of 13 THz. Note that type-1 DCPCF shows higher RGE which is due to its small effective mode area that allows a strong overlap between pump and signal field intensities before the phase matching wavelength (PMW) between the individual core modes. From Fig. 4(b) it can be clearly seen that type-1 DCPCF has larger Rayleigh backscattering coefficient than the type-2 DCPCF, and ULL-PCF.

## 4. Optimization of pump spectra

6. S. Cui, J. Liu, and X. Ma, “A novel efficient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. **16**, 2451–2453 (2004). [CrossRef]

33. X. Liu and Y. Li, “Efficient algorithm and optimization for broadband Raman amplifiers,” Opt. Express **12**564–573 (2004). [CrossRef] [PubMed]

*F*(

*λ*) is defined to achieve the optimal solutions,

_{k}, P_{k}*λ*and

_{k}*P*are the pump wavelengths and pump powers, and

_{k}*k*= 1, 2

*m*with

*m*as number of pumps used,

*L*denotes the length of the fiber,

*G*is the Raman gain and defined by (8). The optimization problem is solved in MATLAB using its GA toolbox [26] on a 3.2 GHz windows based PC. It took nearly 48–72 hours to find the optimal pump profiles for different fiber designs. In our optimization procedure, we have defined a fitness function (7)–(8) that governs the gain ripples accurately and used a constraint to yield moderate gain values using GA toolbox of MATLAB.

## 4.1 Gain characteristics of ultra-low loss PCF

23. 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**9516–9526 (2005). [CrossRef] [PubMed]

**13**9516–9526 (2005). [CrossRef] [PubMed]

25. F. Poli, L. Rosa, M. Bottacini, M. Foroni, A. Cucinotta, and S. Selleri, “Multipump flattened-gain Raman amplifiers based on photonic crystal fibers,” IEEE Photon. Technol. Lett. **17**, 2556–2558 (2005). [CrossRef]

*m*tells about the number of pumps.

## 4.2 Gain characteristics of type-1 DCPCF

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

## 4.3 Gain characteristics of type-2 DCPCF

^{2}. The pump spectrum for individual set of pumps is tabulated in Table 4, where the index

*m*presents the number of pumps.

## 5. Tolerance study and feasibility aspects

*d*, and air-hole size

_{s}*d*, which determine the device performances. To know the impact of structural deformations on the module performances, we vary one parameter, for example

*d*, and fix other parameters such as Λ and

_{s}*d*. Figure 9 depicts the dispersion characteristics of type-1 DCPCF for the change in ring’s hole diameter

*d*which is varied within ±2% tolerances from its nominal value. It can be evident from the figure that the minimum of the dispersion curve shifts toward left when

_{s}*d*is decreased to -1% (solid green curve) and -2% (solid black curve), while the dispersion shifts toward right for +1% (solid magenta curve) and +2% (solid red curve) variation in

_{s}*d*. This shift in dispersion curves results due to the shift of the PMW. The decrement in

_{s}*d*may result into weak overlap of the pump and signal fields which may further decrease the gain efficiency, while the increment in

_{s}*d*may lead to a strong overlap of the pump and the signal fields thus enhancing the RGE.

_{s}*d*tolerances. It is noticed that a ±2% tolerance in pitch may change the absolute magnitude of dispersion coefficient by a ±16% and may also vary the RGE by a ±8%, while the RGE remains almost insensitive (<0.9%) to deformations in hole diameter

*d*.

*d*and Λ on the Raman gain performances of type-1 DCPCF module. We have considered a maximum of ±2% tolerances that may occur during the fabrication of the proposed fiber design. Figure 11 illustrates the percentage change in the Raman gain that may take place by the presence of possible tolerances in Λ and

_{s}*d*. The blue color filled triangles stand for the tolerances in

_{s}*d*, while the red color filled squares correspond to the tolerances in Λ. It can be clearly observed from the curves that a ±2% change in ds may lead to a ±7% change in the gain values of type-1 DCPCF Raman amplifier module, while a ±2% variation in the pitch constant Λ may modify the gain performances by a ±2%. It adds evidence from this tolerance analysis that Raman performances of the fiber are more sensitive to the deformations in

_{s}*d*.

_{s}*d*of the ring’s core on the dispersion characteristics after confirming from previous analysis that

_{s}*d*is more sensitive to structural deformations. We observed that a ±1% change in

_{s}*d*shifts the minimum of the dispersion curves to right or left hand side. The wavelength corresponding to the minima of each dispersion curves has been noted and the shift in the corresponding wavelength (represented by ∆λ) for minima of each dispersion curves is evaluated and plotted in Fig. 12 as a function of the change in

_{s}*d*. It can be seen from the figure that -1% decrease in

_{s}*d*may shift the PMW by a -6%, and hence may decrease the gain efficiency of type-2 DCPCF Raman amplifier module and thus overall Raman gain.

_{s}36. S. G. Leon-Saval, T. A. Birks, N. Y. Joy, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P. St. J. Russell, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. **30**1629–1634 (2005). [CrossRef] [PubMed]

36. S. G. Leon-Saval, T. A. Birks, N. Y. Joy, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P. St. J. Russell, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. **30**1629–1634 (2005). [CrossRef] [PubMed]

*et al*. [37

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

## 6. Summary

*d*of the air-holes in the ring core. A ±2% variation in

_{s}*d*may lead to a ±7% change in the Raman gain and may shift the absolute magnitude of the dispersion coefficient by a ±16 %.

_{s}## Acknowledgments

## References and links

1. | C. Headly and G. P. Agarwal, |

2. | M. N. Islam, |

3. | Y. Emori, Y. Akasaka, and S. Namiki, “Broadband lossless DCF using Raman amplification pumped by multichannel WDM laser diodes,” Electron. Lett. |

4. | M. Achtenhagen, T. G. Chang, and B. Nyman, “Analysis of a multiple-pump Raman amplifier,” Appl. Phys. Lett. |

5. | V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. |

6. | S. Cui, J. Liu, and X. Ma, “A novel efficient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. |

7. | K. Thyagarajan and C. Kakkar, “Novel fiber design for flat gain Raman amplification using single pump and dispersion compensation in S band,” J. Lightwave Technol. |

8. | T. J. Ellingham, L. M. Gleeson, and N. J. Doran, “Enhanced Raman amplifier performance using nonlinear pump broadening,” in |

9. | T. J. Ellingham, J. D. Ania-Castanin, S. K. Turitsyn, A. Pustovskikh, S. Kobtesev, and M. P Fedoruk, “Dual pump Raman amplification with increased flatness using modulation instability,” Opt. Express |

10. | S.Martin Lopez, M. Gonzalez-Herralez, P. Corredera, M. L. Hernanz, and A. Carrasco, “Gain-flattening of fiber Raman amplifiers using non-linear pump spectral broadening,” Opt. Commun. |

11. | T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. |

12. | N. A. Moretensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, “Improved large mode area endlessly single mode photonic crystal fibers,” Opt. Lett. |

13. | A. Bjarklev, J. Broeng, and A. S. Bjarklev, |

14. | K. Saitoh and M. Koshiba, “Chromatic dispersion control in photonic crystal fibers: Application to ultra-flattened dispersion,” Opt. Express |

15. | T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J. Lightwave Technol. |

16. | R. K. Sinha and S. K. Varshney, “Dispersion properties of photonic crystal fibers,” Microwave Opt. Technol. Lett. |

17. | F. Gérome, J. L. Auguste, and J. M. Blondy, “Design of dispersion-compensating fibers based on a dual-concentric-core photonic crystal fiber,” Opt. Lett. |

18. | M. Fuochi, F. Poli, A. Cucinotta, and L. Vincetti, “Study of Raman amplification properties in triangular photonic crystal fibers,” J. Lightwave Technol. |

19. | M. Bottacini, F. Poli, A. Cucinotta, and S. Selleri, “Modeling of photonic crystal fiber Raman amplifiers,” J. Lightwave Technol. |

20. | 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. |

21. | C. J. S.de Matos, K. P. Hansen, and J. R. Taylor, “Experimental characterization of Raman gain efficiency of holey fiber,” Electron. Lett. |

22. | S. K. Varshney, K. Saitoh, and M. Koshiba, “A novel fiber design for dispersion compensating photonic crystal fiber Raman amplifier,” IEEE Photon. Technol. Lett. |

23. | 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 |

24. | S. K. Varshney, T. Fujisawa, K. Saitoh, and M. Koshiba, “Design and analysis of a broadband dispersion compensating photonic crystal fiber Raman amplifier operating in S-band,” Opt. Express |

25. | F. Poli, L. Rosa, M. Bottacini, M. Foroni, A. Cucinotta, and S. Selleri, “Multipump flattened-gain Raman amplifiers based on photonic crystal fibers,” IEEE Photon. Technol. Lett. |

26. | The GA toolbox, MATLAB 7.0, www.mathworks.com |

27. | K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow loss and long length photonic crystal fiber,” J. Lightwave Technol. |

28. | K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. |

29. | T. Fujisawa, K. Saitoh, K. Wada, and M. Koshiba, “Chromatic dispersion profile optimization of dual-concentric-core photonic crystal fibers for broadband dispersion compensation,” Opt. Express |

30. | L.G. Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. Edvold, B. Palsdottir, and D. Jakobsen, “Dispersion compensating fibers,” J. Lightwave Technol. |

31. | J. Bromage, K. Rottwitt, and M. E. Lines, “A method to predict the Raman gain spectra of germanosilicate fibers with arbitrary index profiles,” IEEE Photon. Technol. Lett. |

32. | Z. Michalewicz, |

33. | X. Liu and Y. Li, “Efficient algorithm and optimization for broadband Raman amplifiers,” Opt. Express |

34. | The numerical data of Raman gain efficiency for conventional dispersion compensating fibers was provided by Furukawa Elect. Co. (Ltd.). |

35. | |

36. | S. G. Leon-Saval, T. A. Birks, N. Y. Joy, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P. St. J. Russell, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. |

37. | P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. |

**OCIS Codes**

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(060.2400) Fiber optics and optical communications : Fiber properties

**ToC Category:**

Photonic Crystal Fibers

**History**

Original Manuscript: January 2, 2007

Revised Manuscript: January 31, 2007

Manuscript Accepted: February 20, 2007

Published: March 5, 2007

**Citation**

Kazuya Sasaki, Shailendra K. Varshney, Keisuke Wada, Kunimasa Saitoh, and Masanori Koshiba, "Optimization of pump spectra for gain-flattened
photonic crystal fiber Raman amplifiers
operating in C-band," Opt. Express **15**, 2654-2668 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2654

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### References

- C. Headly and G. P. Agarwal, Raman Amplification in Fiber Optical Communication Systems, (Academic Press, New York, 2004).
- M. N. Islam, Raman Amplification for Telecommunications 1, (Springer, 2003).
- Y. Emori, Y. Akasaka, and S. Namiki, "Broadband lossless DCF using Raman amplification pumped by multichannel WDM laser diodes," Electron. Lett. 34, 2145-2146 (1998). [CrossRef]
- M. Achtenhagen, T. G. Chang, and B. Nyman, "Analysis of a multiple-pump Raman amplifier," Appl. Phys. Lett. 78, 1322-1324 (2001). [CrossRef]
- V. E. Perlin and H. G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," J. Lightwave Technol. 20, 250-254 (2002). [CrossRef]
- S. Cui, J. Liu and X. Ma, "A novel efficient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier," IEEE Photon. Technol. Lett. 16, 2451-2453 (2004). [CrossRef]
- K. Thyagarajan and C. Kakkar, "Novel fiber design for flat gain Raman amplification using single pump and dispersion compensation in S band," J. Lightwave Technol. 22, 2279-2286 (2004). [CrossRef]
- T. J. Ellingham, L. M. Gleeson, and N. J. Doran, "Enhanced Raman amplifier performance using nonlinear pump broadening," in proceedings of IEEE European Conference on Optical Communication (IEEE, 2002), pp. 1-2.
- T. J. Ellingham, J. D. Ania-Castanin, S. K. Turitsyn, A. Pustovskikh, S. Kobtesev, and M. P Fedoruk, "Dual pump Raman amplification with increased flatness using modulation instability," Opt. Express 13, 1079-1084 (2005). [CrossRef] [PubMed]
- S. Martin Lopez, M. Gonzalez-Herralez, P. Corredera, M. L. Hernanz, and A. Carrasco, "Gain-flattening of fiber Raman amplifiers using non-linear pump spectral broadening," Opt. Commun. 242, 463-469 (2004). [CrossRef]
- T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997). [CrossRef] [PubMed]
- N. A. Moretensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, "Improved large mode area endlessly single mode photonic crystal fibers," Opt. Lett. 28, 393-395 (2003). [CrossRef]
- A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres, (Kulwer Academic Publishers 2003). [CrossRef]
- K. Saitoh and M. Koshiba, "Chromatic dispersion control in photonic crystal fibers: Application to ultra-flattened dispersion," Opt. Express 11, 843-852 (2003). [CrossRef] [PubMed]
- T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, "Holey optical fibers: an efficient modal model," J. Lightwave Technol. 17, 1093-1102 (1999). [CrossRef]
- R. K. Sinha and S. K. Varshney, "Dispersion properties of photonic crystal fibers," Microwave Opt. Technol. Lett. 37, 129-132 (2003). [CrossRef]
- F. Gérome, J. L. Auguste, and J. M. Blondy, "Design of dispersion-compensating fibers based on a dual-concentric-core photonic crystal fiber," Opt. Lett. 29, 2725-2727 (2004). [CrossRef] [PubMed]
- M. Fuochi, F. Poli, A. Cucinotta, and L. Vincetti, "Study of Raman amplification properties in triangular photonic crystal fibers," J. Lightwave Technol. 21, 2247-2254 (2003). [CrossRef]
- M. Bottacini, F. Poli, A. Cucinotta, and S. Selleri, "Modeling of photonic crystal fiber Raman amplifiers," J. Lightwave Technol. 22, 1707-1713 (2004). [CrossRef]
- 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, 424-426 (2002). [CrossRef]
- C. J. S. de Matos, K. P. Hansen, and J. R. Taylor, "Experimental characterization of Raman gain efficiency of holey fiber," Electron. Lett. 39, 424-425 (2003). [CrossRef]
- S. K. Varshney, K. Saitoh, and M. Koshiba, "A novel fiber design for dispersion compensating photonic crystal fiber Raman amplifier," IEEE Photon. Technol. Lett. 17, 2062-2065 (2005). [CrossRef]
- 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, 9516-9526 (2005). [CrossRef] [PubMed]
- S. K. Varshney, T. Fujisawa, K. Saitoh, and M. Koshiba, "Design and analysis of a broadband dispersion compensating photonic crystal fiber Raman amplifier operating in S-band," Opt. Express 14, 3528-3540, (2006). [CrossRef] [PubMed]
- F. Poli, L. Rosa, M. Bottacini, M. Foroni, A. Cucinotta, and S. Selleri, "Multipump flattened-gain Raman amplifiers based on photonic crystal fibers," IEEE Photon. Technol. Lett. 17, 2556-2558 (2005). [CrossRef]
- The GA toolbox, MATLAB 7.0, www.mathworks.com
- K. Tajima J. Zhou, K. Nakajima, and K. Sato, "Ultralow loss and long length photonic crystal fiber," J. Lightwave Technol. 22, 7-10 (2004). [CrossRef]
- K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002). [CrossRef]
- T. Fujisawa, K. Saitoh, K. Wada, and M. Koshiba, "Chromatic dispersion profile optimization of dual-concentric-core photonic crystal fibers for broadband dispersion compensation," Opt. Express 14, 893-900 (2006). [CrossRef] [PubMed]
- L.G. Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. Edvold, B. Palsdottir, and D. Jakobsen, "Dispersion compensating fibers," J. Lightwave Technol. 23, 3566-3579 (2005). [CrossRef]
- J. Bromage, K. Rottwitt, and M. E. Lines, "A method to predict the Raman gain spectra of germanosilicate fibers with arbitrary index profiles," IEEE Photon. Technol. Lett. 14, 24-26 (2002). [CrossRef]
- Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, (Springer-Verlag, New York, 1992).
- X. Liu and Y. Li, "Efficient algorithm and optimization for broadband Raman amplifiers," Opt. Express 12, 564-573 (2004). [CrossRef] [PubMed]
- The numerical data of Raman gain efficiency for conventional dispersion compensating fibers was provided by Furukawa Elect. Co. (Ltd.).
- http://www.ofs.dk/DCRA_note_0103.pdf
- S. G. Leon-Saval, T. A. Birks, N. Y. Joy, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P. St. J. Russell, "Splice-free interfacing of photonic crystal fibers," Opt. Lett. 30, 1629-1634 (2005). [CrossRef] [PubMed]
- P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Control of dispersion in photonic crystal fibers," J. Opt. Fiber. Commun. Rep. 2, 435-461 (2005). [CrossRef]

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