Abstract

This paper deals with design and refinement criteria of erbium doped hole-assisted optical fiber amplifiers for applications in the third band of fiber optical communication. The amplifier performance is simulated via a model which takes into account the ion population rate equations and the optical power propagation. The electromagnetic field profile of the propagating modes is carried out by a finite element method solver. The effects of the number of cladding air holes on the amplifier performance are investigated. To this aim, four different erbium doped hole-assisted lightguide fiber amplifiers having a different number of cladding air holes are designed and compared. The simulated optimal gain, optimal length, and optimal noise fig. are discussed. The numerical results highlight that, by increasing the number of air holes, the gain can be improved, thus obtaining a shorter amplifier length. For the erbium concentration NEr=1.8×1024 ions/m3, the optimal gain G(Lopt) increases up to ≅ 2dB by increasing the number of the air holes from M=4 to M=10.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

Electron Lett. (1)

W. J. Wadsworth, J. C. Knight, A. Ortisoga-Blanch, J. Arriaga, E. Silvestre, and P. St. J. Russell, "Soliton effects in photonic crystal fiber at 850 nm," Electron. Lett. 36, 53 - 55 (2000).
[CrossRef]

Electron. Lett. (2)

K. G. Hougaard, J. Broeng, and A. Bjarklev, "Low pump power photonic crystal fibre amplifiers," Electron. Lett. 39, 599-600 (2003).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russel, J. P. de Sandro, "Large mode area photonic crystal fibre," Electron. Lett. 34, 1347-1348 (1998).
[CrossRef]

Fiber Integr. Opt. (1)

B. P. Petreski, P. M. Farrell, S. F. Collins, "Optical amplification on the 3P0→3F2 transition in praseodymium-doped fluorozirconate fiber," Fiber Integr. Opt. 18, 21-32 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, "Absorption and emission cross section of Er3+ doped silica fiber", IEEE J. Quantum Electron. 27, 1004-1010 (1991).
[CrossRef]

IEEE Photon. Techonol. Lett. (2)

P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, "Concentration dependent upconversion in Er3+ - doped fiber amplifiers: experiments and modelling," IEEE Photon. Techonol. Lett. 3, 996 - 998 (1991).
[CrossRef]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisoga-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Techonol. Lett. 12, 807 - 809 (2000).
[CrossRef]

J. Lightwave Technol. (1)

G. J. Foschini, I. M. Habbab, "Capacity of a broadcast channels in the near-future CATV architecture," J. Lightwave Technol. 13, 507-513 (1995).
[CrossRef]

J. Lightwave Technol. (6)

T. Otami, K. Goto, T. Kawazawa, H. Abe, and M. Tanaka, "Effect of span loss increase on the optically amplified communication system," J. Lightwave Technol. 15, 737-742 (1997).
[CrossRef]

C. R. Giles, E. Desrvire, J. R. Talman, J. R. Simpson, and P. C. Becker, "2-Gbit/s signal amplification at λ=1.53 µm in an erbium-doped single-mode fiber amplifier," J. Lightwave Technol. 7, 651-656 (1989).
[CrossRef]

E. Desrvire, C. R. Giles, and J. R. Simpson, "Gain saturation effects in high speed, multichannel erbium doped fiber amplifiers at λ=1.53 µm," J. Lightwave Technol. 7, 2095-2104 (1989).
[CrossRef]

O. Lumholt, J. H. Polvsen, K. Shusler, A. Bjarklev, S. D. Pedersen, T. Rasmussen, and K. Rottwitt, "Quantum limited noise fig. operation of high gain erbium doped fiber amplifiers," J. Lightwave Technol. 11, 1344-1352 (1993).
[CrossRef]

P. Myslinsky, D. Nguyen, and J. Chrostowski, "Effects of concentration on the performance of erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 112-120 (1997).
[CrossRef]

F. Prudenzano, "Erbium-doped hole-assisted optical fiber amplifier: design and optimization," J. Lightwave Technol. 23, 330-340 (2005).
[CrossRef]

J. Non-Crystalline Solids (1)

A. D'Orazio, M. De Sario, L. Mescia, V. Petruzzelli, F. Prudenzano, A. Chiasera, M. Montagna, C. Tosello, and M. Ferrari, "Design of Er3+ doped SiO2-TiO2 planar waveguide amplifier," J. Non-Crystalline Solids 322, 278-283 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

Z. Zhu, T. G. Brown, "Multipole analysis of hole-assisted optical fibers," Opt. Commun. 206, 333-339 (2002).
[CrossRef]

Opt. Express (4)

Opt. Fiber Technol. (1)

J. Broeng, D. Mongilevstev, S. E. Barkou, and A. Bjarklev, "Photonic crystal fibers: a new class of optical waveguide," Opt. Fiber Technol. 4, 305-330 (1999).
[CrossRef]

Opt. Lett. (4)

Science (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Other (2)

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: fundamentals and technology (Academic Press, 1999) pp. 140-144.

E. Desurvire, Erbium doped fiber amplifiers (Wiley-Interscience Inc., 1993) pp. 354-382.

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Figures (6)

Fig. 1.
Fig. 1.

Sketch of the HALF sections

Fig. 2.
Fig. 2.

Effective mode area Aeff versus wavelength λ for different number of air holes: M=4 (full curve), M=6 (broken curve), M=8 (dot curve), M=10 (dash-dot curve). Hole diameter dhole=0-8 μm, core diameter dcore= 5.2 μm, core to hole distance R=4 μ m.

Fig. 3.
Fig. 3.

(a) Optimal gain G(Lopt), (b) optimal length Lopt, (c) optimal noise fig. F(Lopt) versus erbium concentration NEr for different number of holes M=4 (full curve), M=6 (broken curve), M=8 (dot curve), M=10 (dash-dot curve). Input signal power Ps(0)=-40 dBm and input pump power Pp(0)=30 mW.

Fig. 4.
Fig. 4.

(a) Gain coefficient αp, (b) optimal length Lopt, (c) optimal noise fig. F(Lopt) versus input pump power Pp(0) for different number of holes M=4 (full curve), M=6 (broken curve), M=8 (dot curve), M=10 (dash-dot curve). Input signal power Ps(0)=-40 dBm and erbium concentration NEr=1.8×1024 ions/m3.

Fig. 5.
Fig. 5.

(a) Optimal signal gain G(Lopt), (b) optimal length Lopt, (c) optimal noise fig. F(Lopt) versus the output signal power Ps(Lopt) for different number of holes M=4 (full curve), M=6 (broken curve), M=8 (dot curve), M=10 (dash-dot curve). Input pump power Pp(0)=30 mW and erbium concentration NEr=1.8×1024 ions/m3.

Fig. 6.
Fig. 6.

(a) Optimal signal gain G(Lopt), (b) optimal length Lopt, (c) optimal noise fig. F(Lopt) versus the dopant confinement ratio dd/dcore for different number of holes M=4 (full curve), M=6 (broken curve), M=8 (dot curve), M=10 (dash-dot curve). Input pump power Pp(0)=30 mW, input signal power Ps(0)=-40 dBm, erbium concentration NEr=1.8×1024 ions/m3.

Tables (1)

Tables Icon

Table 1. Overlap integrals and effective mode area for different numbers of air holes.

Equations (17)

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N 1 t = W 13 N 1 + W 21 N 2 + N 2 τ 21 W 12 N 1 C 14 N 1 N 4 + C u p N 2 2 + C up N 3 2
N 2 t = W 12 N 1 W 21 N 2 + N 3 τ 32 N 2 τ 21 + 2 C 14 N 1 N 4 2 C u p N 2 2
N 3 t = W 13 N 1 N 3 τ 32 + N 4 τ 43 2 C u p N 3 2
N Er = N 1 + N 2 + N 3 + N 4
W 13 ( r , ϑ , z ) = σ 13 ( ν p ) h ν p P p ( z ) Ψ ( r , ϑ , ν p )
W 12 ( r , ϑ , z ) = σ 12 ( ν s ) h ν s P s ( z ) Ψ ( r , ϑ , ν s ) + 0 + σ 12 ( ν ) h ν [ S ASE + ( z , ν ) + S ASE ( z , ν ) ] Ψ ( r , ϑ , ν ) d ν
W 21 ( r , ϑ , z ) = σ 21 ( ν s ) h ν s P s ( z ) Ψ ( r , ϑ , ν s ) + 0 + σ 21 ( ν ) h ν [ S ASE + ( z , ν ) + S ASE ( z , ν ) ] Ψ ( r , ϑ , ν ) d ν
0 2 π 0 + Ψ ( r , ϑ , ν ) rdrd ϑ = Re { 0 2 π 0 + E ( r , ϑ , ν ) × H * ( r , ϑ , ν ) z ̂ rdrd ϑ } = 1
d P p ( z ) dz = P p ( z ) [ A σ 13 ( ν p ) N 1 ( r , ϑ , z ) Ψ ( r , ϑ , ν p ) rdrd ϑ + α ( ν p ) ]
d P s ( z ) dz = P s ( z ) [ A [ σ 21 ( ν s ) N 2 ( r , ϑ , z ) σ 12 ( ν s ) N 1 ( r , ϑ , z ) ] Ψ ( r , ϑ , ν s ) rdrd ϑ + α ( ν s ) ]
d P ASE ± ( z , ν ) dz = ± P ASE ± ( z , ν ) A [ σ 21 ( ν ) N 2 ( r , ϑ , z ) σ 12 ( ν ) N 1 ( r , ϑ , z ) ] Ψ ( r , ϑ , ν ) rdrd ϑ
± m P 0 ( ν ) σ 21 ( ν ) A σ 21 ( ν ) N 2 ( r , ϑ , z ) rdrd ϑ α ( ν ) P ASE ± ( z , ν )
F = 1 G + P ASE + ( L , ν s ) G h ν s Δ ν s
A eff ( λ ) = ( 0 2 π 0 + E ( r , ϑ , λ ) 2 r d r d ϑ ) 2 0 2 π 0 + E ( r , ϑ , λ ) 4 r d r d ϑ
Γ p = 0 2 π 0 R core Ψ ( r , ϑ , ν p ) rdrd ϑ
Γ s = 0 2 π 0 R core Ψ ( r , ϑ , ν s ) rdrd ϑ
Γ p , s = 0 2 π 0 R core Ψ ( r , ϑ , ν p ) Ψ ( r , ϑ , ν s ) rdrd ϑ

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