Abstract

We propose a method for controlling modal gain in a multimode Erbium-doped fiber amplifier (MM-EDFA) by tuning the mode content of a multimode pump. By adjusting the powers and orientation of input pump modes, modal dependent gain can be tuned over a large dynamic range. Performance impacts due to excitation of undesired pump modes, mode coupling and macro-bending loss within the erbium-doped fiber are also investigated. The MM-EDFA may potentially be a key element for long haul mode-division multiplexed transmission.

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References

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  6. B. Zhu, T. G. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello, K. Abedin, P. W. Wisk, D. W. Peckham, and P. Dziedzic, “Space-, wavelength-, polarization-division multiplexed transmission of 56-Tb/s over a 76.8-km seven-core fiber,” Proc. OFC 2011, Paper PDPB7, Los Angeles, CA, USA (2011).
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  9. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, and P. J. Winzer, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6×6 MIMO processing,” Proc. OFC 2011, Paper PDPB10, Los Angeles, CA, USA (2011).
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2010

2007

2001

A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7(4), 504–517 (2001).
[CrossRef]

1998

1996

G. J. Foschini, “Layered space-time architecture for wireless communications in a fading environment when using multielement antennas,” Bell Labs Tech. J. 1(2), 41–59 (1996).
[CrossRef]

1993

1976

1971

Bai, N.

Foschini, G. J.

G. J. Foschini, “Layered space-time architecture for wireless communications in a fading environment when using multielement antennas,” Bell Labs Tech. J. 1(2), 41–59 (1996).
[CrossRef]

Galvanauskas, A.

A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7(4), 504–517 (2001).
[CrossRef]

Gloge, D.

Gong, M.

Hattori, H. T.

Huang, M.-F.

Huang, Y.-K.

Li, C.

Li, G.

Liao, S.

Marcuse, D.

Poole, C. D.

Safaai-Jazi, A.

Wang, S.-C.

Wang, T.

Yaman, F.

Yan, P.

Yuan, Y.

Zhang, H.

Zhu, B.

Appl. Opt.

Bell Labs Tech. J.

G. J. Foschini, “Layered space-time architecture for wireless communications in a fading environment when using multielement antennas,” Bell Labs Tech. J. 1(2), 41–59 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7(4), 504–517 (2001).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

Other

D. Qian, M.-F. Huang, E. Ip, Y.-K. Huang, Y. Shao, J. Hu, and T. Wang, “101-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Proc. OFC (Los Angeles, CA, USA 2011). Paper PDPB5.

J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, and M. Watanabe, “109-Tb/s (7×97×172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi-core fiber,” Proc. OFC 2011, Paper PDPB6, Los Angeles, CA, USA (2011).

B. Zhu, T. G. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello, K. Abedin, P. W. Wisk, D. W. Peckham, and P. Dziedzic, “Space-, wavelength-, polarization-division multiplexed transmission of 56-Tb/s over a 76.8-km seven-core fiber,” Proc. OFC 2011, Paper PDPB7, Los Angeles, CA, USA (2011).

A. Li, A. A. Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” Proc. OFC 2011, Paper PDPB8, Los Angeles, CA, USA (2011).

M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2×100-Gb/s over two modes of 40km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer,” Proc. OFC 2011, Paper PDPB9, Los Angeles, CA, USA (2011).

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, and P. J. Winzer, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6×6 MIMO processing,” Proc. OFC 2011, Paper PDPB10, Los Angeles, CA, USA (2011).

P. M. Krummrich and K. Petermann, “Evaluation of potential optical amplifier concepts for coherent mode multiplexing,” Proc. OFC 2011, Paper OMH5, Los Angeles, CA, USA (2011).

E. Desurvire, Erbium-doped Fiber Amplifiers-Principles and Applications, (John Wiley & Son Inc. 1994), Chap. 1.

C. D. Stacey and J. M. Jenkins, “Demonstration of fundamental mode propagation in highly multimode fibre for high power EDFAs,” Conference on Lasers and Electro-Optics Europe (CLEO 2005), Munich, Germany, June 17, p. 558.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of an MM-EDFA.

Fig. 2
Fig. 2

Multimode Erbium-doped fiber amplifier.

Fig. 3
Fig. 3

(a) Intensity profile of pump and signal modes, (b) normalized intensity profiles viewed along x-axis.

Fig. 4
Fig. 4

Modal gain of signal at 1530 nm assuming 0.05 mW power in each degenerate modes of LP01, s and LP11, s , when 980-nm pump is entirely confined in (a) LP01, p , (b) LP11, p and (c) LP21, p .

Fig. 5
Fig. 5

Modal gain and required LP01, p power vs. LP21, p power, to maintain MDG (ΔG11 s −01 s ) at (a) 1 dB and (b) 2 dB; (c) Modal gain and MDG vs. LP01, p power for fixed LP21, p power at 150 mW.

Fig. 6
Fig. 6

Modal gain and MDG difference vs. EDF length, when LP01, p and LP21, p have powers of: (a) Pp ,21 = 150 mW, Pp ,01 = 0 mW,and (b) Pp ,21 = 150 mW, Pp ,01 = 8 mW.

Fig. 7
Fig. 7

Rotated pump modes.

Fig. 8
Fig. 8

Modal gain vs. relative rotation angle (θ) of the pump mode when pump powers are: (a) Pp ,11 θ = 150 mW, (b) Pp ,21 θ = 150 mW, and (c) Pp ,21 = 150 mW, Pp ,01 = 2 mW, Pp ,11 θ = 15 mW.

Fig. 9
Fig. 9

Modal gain vs. power leakage, (a) LP21, p to LP01, p , (b) LP21, p to LP11, p , (c) LP21, p to LP02, p .

Fig. 10
Fig. 10

Modal gain vs. mode coupling strength from LP21, p to LP01, p ( d p , 21 02 ).

Fig. 11
Fig. 11

Macro-bending loss vs. bending radius.

Fig. 12
Fig. 12

Modal gain vs. mode dependent loss of LP11s.

Tables (3)

Tables Icon

Table 3 List of Variables Used in the Coupled Eqs. (1)(5)

Tables Icon

Table 1 Parameters of a MM-EDFA

Tables Icon

Table 2 Overlap Integrals of Normalized Intensity Profile

Equations (6)

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d P s , i d z = P s , i 0 2 π 0 a r d r d φ     Γ s , i ( r , φ ) [ N 2 ( r , φ , z ) σ e s , i N 1 ( r , φ , z ) σ a s , i ] k = 1 m s d s , i k [ P s , i P s , k ]
d P A S E , i d z = P A S E , i 0 2 π 0 a r d r d φ     Γ s , i ( r , φ ) [ N 2 ( r , φ , z ) σ e s , i N 1 ( r , φ , z ) σ a s , i ]               + 0 2 π 0 a r d r d ϕ 2 σ e s , i h ν s Δ ν N 2 ( r , φ ) Γ s , i ( r , φ )
d P p , j d z = P p , j 0 2 π 0 a r d r d φ     Γ p , j ( r , φ ) N 1 ( r , φ , z ) σ a p , j k = 1 m p d p , j k [ P p , j P p , k ]
N 1 ( r , φ , z ) = 1 τ + i = 1 m s [ P s , i + P A S E , i ] σ e s , i Γ s , i ( r , φ ) h ν s 1 τ + i = 1 m s [ P s , i + P A S E , i ] ( σ e s , i + σ a s , i ) Γ s , i ( r , φ ) h ν s + j = 1 m p P p , j σ a p , j Γ p , j ( r , φ ) h ν p N 0 ( r , φ )
N 2 ( r , φ , z ) = i = 1 m s [ P s , i + P A S E , i ] σ a s , i Γ s , i ( r , φ ) h ν s + j = 1 m p P p , j σ a p , j Γ p , j ( r , φ ) h ν p 1 τ + i = 1 m s [ P s , i + P A S E , i ] ( σ e s , i + σ a s , i ) Γ s , i ( r , φ ) h ν s + j = 1 m p P p , j σ a p , j Γ p , j ( r , φ ) h ν p N 0 ( r , φ )
η p ( m k ) , s ( n j ) 0 2 π d φ cos 2 ( m φ ) cos 2 ( n ( φ + θ ) ) = π 2 + cos ( 2 n θ ) δ ( m n )

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