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 μm2). 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

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2006 (2)

2005 (7)

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]

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. 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]

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, 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]

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]

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]

2004 (7)

2003 (5)

2002 (4)

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]

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]

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]

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]

2001 (1)

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

1999 (1)

1998 (1)

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]

1997 (1)

Achtenhagen, M.

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

Akasaka, Y.

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]

Ania-Castanin, J. D.

Auguste, J. L.

Belardi, W.

Bennett, P. J.

Birks, T. A.

Blondy, J. M.

Bottacini, M.

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. Bottacini, F. Poli, A. Cucinotta, and S. Selleri, "Modeling of photonic crystal fiber Raman amplifiers," J. Lightwave Technol. 22, 1707-1713 (2004).
[CrossRef]

Broderick, N. G. R.

Bromage, J.

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]

Carrasco, A.

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]

Chang, T. G.

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

Corredera, P.

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]

Couny, F.

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]

Cucinotta, A.

Cui, S.

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]

de Matos, C. J. S.

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]

Edvold, B.

Ellingham, T. J.

Emori, Y.

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]

Fedoruk, M. P

Folkenberg, J. R.

Foroni, M.

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]

Fujisawa, T.

Fuochi, M.

George, A. K.

Gérome, F.

Gonzalez-Herralez, M.

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]

Hansen, K. P.

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]

Hernanz, M. L.

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]

Jakobsen, D.

Jorgensen, C.

Jorgensen, L. V.

Joy, N. Y.

Kakarantzas, G.

Kakkar, C.

Knight, J. C.

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]

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]

Kobtesev, S.

Koshiba, M.

Kristensen, P.

Lee, J. H.

Leon-Saval, S. G.

Li, Y.

Lines, M. E.

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]

Liu, J.

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]

Liu, X.

Ma, X.

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]

Mangan, B. J.

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]

Martin Lopez, S.

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]

Monro, T. M.

Moretensen, N. A.

Namiki, S.

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]

Nielsen, L.G.

Nielsen, M. D.

Nyman, B.

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

Palsdottir, B.

Perlin, V. E.

Petersson, A.

Poli, F.

Pustovskikh, A.

Richardson, D. J.

Roberts, P. J.

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]

Rosa, L.

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]

Rottwitt, K.

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]

Russell, P. St. J.

Sabert, H.

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]

Saitoh, K.

Selleri, S.

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. Bottacini, F. Poli, A. Cucinotta, and S. Selleri, "Modeling of photonic crystal fiber Raman amplifiers," J. Lightwave Technol. 22, 1707-1713 (2004).
[CrossRef]

Simonsen, H. R.

Sinha, R. K.

R. K. Sinha and S. K. Varshney, "Dispersion properties of photonic crystal fibers," Microwave Opt. Technol. Lett. 37, 129-132 (2003).
[CrossRef]

Taylor, J. R.

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]

Teh, P. C.

Thyagarajan, K.

Turitsyn, S. K.

Varshney, S. K.

Vincetti, L.

Wada, K.

Wadsworth, W. J.

Wandel, M.

Winful, H. G.

Yusoff, Z.

Appl. Phys. Lett. (1)

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

Electron. Lett. (2)

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]

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]

IEEE J. Quantum Electron. (1)

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]

IEEE Photon. Technol. Lett. (4)

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]

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]

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]

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]

J. Lightwave Technol. (7)

J. Opt. Fiber. Commun. Rep. (1)

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]

Microwave Opt. Technol. Lett. (1)

R. K. Sinha and S. K. Varshney, "Dispersion properties of photonic crystal fibers," Microwave Opt. Technol. Lett. 37, 129-132 (2003).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Express (6)

Opt. Lett. (5)

Other (8)

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres, (Kulwer Academic Publishers 2003).
[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.

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).

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

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, (Springer-Verlag, New York, 1992).

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

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Figures (13)

Fig. 1.
Fig. 1.

Transverse cross-section of (a) ULL-PCF (d/Λ=0.625 and Λ=4.0 μm) [27] (b) type-1 DCPCF (d/Λ=0.7, ds /Λ=0.26, and Λ=2 μm) [22], and (c) type-2 DCPCF (d/Λ=0.527, ds /Λ=0.39, and Λ=1.81μm) optimized through GA. The background material is silica while circles represent the air-holes.

Fig. 2.
Fig. 2.

(a). Attenuation spectrum and (b). dispersion characteristics of ULL-PCF [25]. The ULL-PCF shows a loss of 0.37 dB/km at 1550 nm and exhibits anomalous dispersion characteristics.

Fig. 3.
Fig. 3.

(a). Dispersion characteristics and (b). the spectral variation of link residual dispersion for type-1 DCPCF (solid blue curve) and type-2 DCPCF (solid red curve). The type-1 and type-2 DCPCFs exhibit dispersion of -240 ps/nm/km and -530 ps/nm/km, respectively, at 1550 nm.

Fig. 4.
Fig. 4.

(a). RGE as a function of frequency shift and (b). Rayleigh backscattering coefficient as a function of the wavelength for ULL-PCF, type-1, and type-2 DCPCFs. The peak RGE (2.1 W-1.km-1) is obtained at 13.1 THz for ULL-PCF, while the peak RGE of 4.17 W-1.km-1 and 2.8 W-1.km-1 occur at 13.0 THz for type-1 and type-2 DCPCFs, respectively, for a depolarized pump of 1455 nm wavelength.

Fig. 5.
Fig. 5.

(a). Power evolution of pumps and signals along the distance of fiber and the spectral variation of (b). gain, (c). OSNR, NF, and (d). DRB of a 10 km long ultra-low loss PCF. It can be clearly seen that with three pumps, the fiber shows the lowest GR of ±0.36 dB with a peak gain of 8.8 dB over C-band.

Fig. 6.
Fig. 6.

(a). Power evolutions of pumps and signals along the distance of the fiber, the spectral variation of (b). gain, (c). OSNR and NF, and (d). DRB in a 5.2 km long type-1 DCPCF Raman amplifier. It can be clearly seen that with three pumps, the fiber shows GR of ±0.4 dB with a maximum gain of 21.6 dB at the expense of 690 mW of total pump power over C-band.

Fig. 7.
Fig. 7.

(a). Power evolutions of pumps and signals along the length of the fiber, the spectral variation of (b) gain, (c) OSNR and NF, and (d) DRB in a 2.73 km long optimized type-2 DCPCF Raman amplifier. It can be clearly seen that with three pumps, the fiber shows GR of ±0.21 dB with a maximum gain of 8.4 dB at the expense of 1.1 W of total pump power over C-band.

Fig. 8.
Fig. 8.

Gain variation of type-2 DCPCF Raman amplifier module for two different attenuation levels. Solid blue and red curves stand for the loss levels of 0.58 dB/km and 5 dB/km at 1550 nm.

Fig. 9.
Fig. 9.

Dispersion characteristics as a function of the wavelength for type-1 DCPCF for different tolerance values in ds .

Fig. 10.
Fig. 10.

Dispersion characteristics as a function of the wavelength for type-1 DCPCF for different tolerance values in Λ.

Fig. 11.
Fig. 11.

Impact of fiber tolerances on the gain of type-1 DCPCF for structural variation in ds (filled blue triangles) and pitch (filled red squares).

Fig. 12.
Fig. 12.

Shift of PMW as a function of tolerance in ds in type-2 DCPCF. It is evident that ±1% change in ds may shift the PMW by ±6%.

Fig. 13.
Fig. 13.

Spectral variation of splice loss between type-1 DCPCF and conventional SMF in absence of any misalignments.

Tables (4)

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Table 1. Fiber’s parameters and their modal properties.

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Table 2. Optimized pump powers and wavelengths for 10 km long ULL-PCF.

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Table 3. Optimized pump profile for a 5.2 km long type-1 DCPCF Raman amplifier module.

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Table 4. Optimized pump profile for a 2.73 km long type-2 DCPCF Raman amplifier module.

Equations (8)

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F ( Λ , d Λ , d s Λ ) = exp ( w 1 f 1 + f 2 )
f 1 = λ = 1.53 μ m λ = 1.565 μ m D target ( λ ) + D DCPCF ( λ )
f 2 = { 0.9 exp ( w 1 f 1 ) if A eff @ 1.55 μm < 20 μ m 2 0 else
D target ( λ ) = X × D SMF
γ R = S C SiSi ( Δ ν ) i s ( x , y ) i p ( x , y ) dx dy
ε R ( λ ) = 3 8 π λ 2 n Si 2 S C R i 2 x y dx dy ,
F λ k P k = { G max λ k P k G min λ k P k 2 if G max > 8 [ dB ] 1000 else
G = 10 log 10 P S + ( L ) P S ( 0 )

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