## Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump |

Optics Express, Vol. 19, Issue 17, pp. 16601-16611 (2011)

http://dx.doi.org/10.1364/OE.19.016601

Acrobat PDF (2551 KB)

### 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.

© 2011 OSA

## 1. Introduction

2. H. T. Hattori and A. Safaai-Jazi, “Fiber designs with significantly reduced nonlinearity for very long distance transmission,” Appl. Opt. **37**(15), 3190–3197 (1998). [CrossRef] [PubMed]

3. F. Yaman, N. Bai, Y.-K. Huang, M.-F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express **18**(20), 21342–21349 (2010). [CrossRef] [PubMed]

4. 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]

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).

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).

8. 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).

## 2. Theory

*N*paths, and use mode converters to transform the spatial mode of the pump source into the

*N*spatial modes of the MMF. The variable attenuators enable

*N*-degree control over the mode content of the pump, and thus the MDG of the device. The pump modes are spatially combined with the signal, which are injected into the erbium-doped MMF. In the paper, we assume the erbium-doped MMF has the profile shown in Fig. 2 , where the core has radius

*i*-th signal mode and

*j*-th pump mode of the EDF, respectively; and let

*i*-th signal mode,

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

*j*-th pump mode at wavelength

14. M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express **15**(6), 3236–3246 (2007). [CrossRef] [PubMed]

## 3. Simulation

*a*=

*r*). As the normalized frequency at

_{c}*λ*= 1.53 μm lies between 2.405 <

_{s}*V*< 3.832, the EDF supports two degenerate mode groups at this wavelength. We assume a weakly guiding MMF where the modes are well approximated by linearly polarized (LP) modes [15

_{s}15. D. Gloge, “Weakly guiding fibers,” Appl. Opt. **10**(10), 2252–2258 (1971). [CrossRef] [PubMed]

_{ij}_{,}

*and LP*

_{s}

_{xy}_{,}

*to denote the LP*

_{p}*mode at*

_{ij}*λ*and LP

_{s}*mode at*

_{xy}*λ*, respectively. Figure 3 shows the intensity profiles of the modes, and their intensities viewed along the

_{p}*x*-axis. We note that for

_{mn,s}and LP

_{mn,p}have two spatially degenerate modes. In one of these modes, referred to as the “even” mode, intensity is maximized along the x-axis at (φ = 0); in the other mode, referred to as the “odd mode”, intensity is minimized along the x-axis. All spatial modes, degenerate and non-degenerate, come with two degenerate polarization modes.

### 3.1 Modal Gain Control for Non-Degenerate Signal Modes

_{11,}

*and LP*

_{p}_{21,}

*modes, we assume equal power in the even (LP*

_{p}_{11}

_{e}_{,}

*or LP*

_{p}_{21}

_{e}_{,}

*) and odd modes (LP*

_{p}_{11}

_{o}_{,}

*or LP*

_{p}_{21}

_{o}_{,}

*) so that the resulting intensity (power) patterns (e.g.,*

_{p}_{01,p}, LP

_{11,p}and LP

_{21,p}modes. It is assumed that the input signal to the EDF has equal power (0.05 mW) in each of its six (two LP

_{01,s}and four LP

_{11,s}) spatial and polarization degenerate modes, or 0.3 mW in total. Since the intensity profile of LP

_{01,p}is better matched to LP

_{01,s}than LP

_{11,s}, Fig. 4(a) shows higher gain for LP

_{01,s}. Conversely, pumping in LP

_{21,p}results in higher gain for LP

_{11,s}.

_{01,}

*when these pump modes are used. Conversely, as*

_{s}_{21,}

*gives higher gain for LP*

_{p}_{11,}

*. It is possible to control MDG by varying the relative powers of LP*

_{s}_{01,}

*and LP*

_{p}_{21,}

*. In transmission, the higher-order LP*

_{p}_{11,}

*mode is less confined by the core, and will experience higher bending loss than the fundamental LP*

_{s}_{01,}

*mode. Furthermore, the LP*

_{s}_{11,}

*mode has larger effective area, making the optimum power for this mode higher than the fundamental mode. Consequently, a practical MM-EDFA will pump primarily in the LP*

_{s}_{21,}

*. The addition of a small amount of LP*

_{p}_{01,}

*enables adjustment of MDG. Figure 5(a) shows modal gain versus LP*

_{p}_{21,}

*pump power, where the power of LP*

_{p}_{01,}

*was continually adjusted to maintain a 1 dB difference between the gains of LP*

_{p}_{01,}

*and LP*

_{s}_{11,}

*, which we denoted as ΔG*

_{s}_{11}

_{s}_{−01}

*. Figure 5(b) shows the same results for ΔG*

_{s}_{11}

_{s}_{−01}

*= 2 dB. It is observed that modal gain can be continually adjusted to values greater than 22 dB, which is sufficient to compensate the loss of a single fiber span at typical span distances. Figure 5(c) shows the sensitivity of modal gain to LP*

_{s}_{01,}

*power when LP*

_{p}_{21,}

*power is fixed at 150 mW. While the modal gain at LP*

_{p}_{11,}

*remain nearly constant, ΔG*

_{s}_{11}

_{s}_{−01}

*varies by more than 4 dB as LP*

_{s}_{01,}

*power is changed from only 0 to 20 mW, demonstrating wide tunability of MDG in dynamic range. Thus, to establish the desired modal gain in an MM-EDFA, we first tune the power of the LP*

_{p}_{21,}

*pump to give the desired power for the LP*

_{p}_{11,}

*mode, after which, the power of LP*

_{s}_{01,}

*is adjusted to obtain the desired ΔG*

_{p}_{11}

_{s}_{−01}

*.*

_{s}_{11}

_{s}_{−01}

*is maximized when only the LP*

_{s}_{21,}

*mode is pumped. Figure 6(a) shows that a longer EDF gives larger ΔG*

_{p}_{11}

_{s}_{−01}

*, and thus larger range of achievable MDG. We can select an EDF length which approximately maximizes modal gain, while ensuring relatively large difference between the gains of LP*

_{s}_{11,}

*and LP*

_{s}_{01,}

*. In Fig. 6(b), it is observed that adding only 8 mW of pump power in LP*

_{s}_{01,}

*enables flattening of the modal gains responses. Even as device length is swept from 20 to 40 meters, less than ± 1 dB change in the modal gains of LP*

_{p}_{11,}

*and LP*

_{s}_{01,}

*, and less than ± 0.5 dB variation in MDG are observed.*

_{s}### 3.2 Modal Gain Control for Spatially Degenerate Signal Modes

### 3.3 Impact on Performance Due to Inexact Excitation and Mode Coupling

_{21,}

*to the other modes, as LP*

_{p}_{21,}

*has the most power. Figure 9 shows the modal gains in LP*

_{p}_{01,}

*and LP*

_{s}_{11,}

*versus the percentage of LP*

_{s}_{21,}

*power leaked into the unwanted modes. Note the power in LP*

_{p}_{01,}

*is chosen to give an MDG of ΔG*

_{p}_{11}

_{s}_{−01}

*= 2dB when 0% of LP*

_{s}_{21,}

*is coupled to unwanted modes. As previously shown in Fig. 4, pumping in the other modes gives higher gain for LP*

_{p}_{01,}

*than LP*

_{s}_{11,}

*. Hence we observe a reduction in ΔG*

_{s}_{11}

_{s}_{−01}

*that as leakage increases. At sufficiently high leakage, ΔG*

_{s}_{11}

_{s}_{−01}

*become negative, indicating higher modal gain for LP*

_{s}_{01,}

*. It is also observed that ΔG*

_{s}_{11}

_{s}_{−01}

*has greater sensitivity to leakage into LP*

_{s}_{01,}

*and LP*

_{p}_{02,}

*, as these modes have larger overlap integrals with LP*

_{p}_{01,}

*than LP*

_{s}_{11,}

*(Table 2). Hence, the pump generation mechanism should minimize leakage into these modes.*

_{p}*n*). Hence, we focus on coupling between LP

_{eff}_{21,}

*and LP*

_{p}_{02,}

*, as the effective refractive index difference Δ*

_{p}*n*

_{eff}_{,(}

_{21p−02p}_{)}between this pair of modes is the smallest among all the mode pairs in our FMF-based EDF. Assuming the power coupling coefficient between LP

_{21,}

*and LP*

_{p}_{02,}

*, which was defined as*

_{p}13. A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. **7**(4), 504–517 (2001). [CrossRef]

_{11s–01s}decreases with increasing strength of mode coupling. This favors using a shorter length EDF, and a refractive index profile that maximizes effective refractive index difference between the modes to reduce mode coupling.

### 3.4 Impact on Performance Due to Macro-Bending Loss

_{11,}

*and LP*

_{s}_{21,}

*modes are less confined, they are more likely to couple into cladding modes when the fiber is bent, resulting in higher macro-bending loss than the fundamental modes LP*

_{p}_{01,}

*and LP*

_{s}_{01,}

*. This must either be taken into account by increasing the power of the higher order pump, or the bending radius has to be large enough to render bending loss negligible. The theoretical macro-bending loss can be calculated using Marcuse’s curvature loss formula [17*

_{p}17. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. **66**(3), 216–220 (1976). [CrossRef]

_{11,}

*mode is the least spatially confined. To reduce its macro-bending loss to less than 0.01 dB/m, the bending radius must be at least 9.46 cm. Figure 12 shows modal gain as a function of bend radius assuming only LP*

_{s}_{21}

*is pumped at a power of 150 mW. It is observed that the gain of LP*

_{p}_{11,}

*is reduced significantly as bend radius falls below 9 cm. In particular, MDG between the modes is reduced to zero at a bend radius of 8 cm, making it impossible to equalize MDL in the transmission by pumping in LP*

_{s}_{01}

*as outlined in Section 3.1. It is observed that at low bend radius, the gain of LP*

_{p}_{01,}

*is increased due to reduced mode competition. However, the increase in gain saturates when LP*

_{s}_{11,}

*is completely stripped out. At very small bend radius, macro-bending loss will again reduce the gain of LP*

_{s}_{01,}

*. The results indicate that a practical EDF should be spooled with a bend radius greater than 9 cm for a step-index fiber design. If device size is an issue, it is also possible to create fibers more complex refractive index profiles, such as using refractive index trenches, to better confine all signal and pump modes.*

_{s}## 4. Conclusion

_{01,}

*and LP*

_{p}_{21,}

*, the gains of the LP*

_{p}_{01,}

*and LP*

_{s}_{11,}

*signal modes can be tuned over a wide dynamic range. The relative gain between the two spatially degenerate LP*

_{s}_{11,}

*signal modes can also be adjusted by adding a small amount of LP*

_{s}_{11}

_{θ}_{,}

*which is the even LP*

_{p}_{11}

_{e}_{,}

*mode rotated by angle*

_{p}*θ*. Performance impact due to excitation of unwanted pump modes at the input of the EDF, mode coupling and macro-bending loss in the fiber was also investigated. The proposed modal gain control scheme can be generalized for an

*N*-mode MM-EDFA by varying the powers of

*N*well-chosen pump modes.

## Appendix

## References and links

1. | 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. |

2. | H. T. Hattori and A. Safaai-Jazi, “Fiber designs with significantly reduced nonlinearity for very long distance transmission,” Appl. Opt. |

3. | F. Yaman, N. Bai, Y.-K. Huang, M.-F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express |

4. | G. J. Foschini, “Layered space-time architecture for wireless communications in a fading environment when using multielement antennas,” Bell Labs Tech. J. |

5. | 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). |

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). |

7. | 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). |

8. | 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). |

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). |

10. | 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). |

11. | E. Desurvire, |

12. | 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. |

13. | A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. |

14. | M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express |

15. | D. Gloge, “Weakly guiding fibers,” Appl. Opt. |

16. | C. D. Poole and S.-C. Wang, “Bend-induced loss for the higher-order spatial mode in a dual-mode fiber,” Opt. Lett. |

17. | D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

**ToC Category:**

Optical Amplifier

**History**

Original Manuscript: May 16, 2011

Revised Manuscript: June 27, 2011

Manuscript Accepted: July 7, 2011

Published: August 15, 2011

**Virtual Issues**

Space Multiplexed Optical Transmission (2011) *Optics Express*

**Citation**

Neng Bai, Ezra Ip, Ting Wang, and Guifang Li, "Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump," Opt. Express **19**, 16601-16611 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-16601

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### References

- 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.
- H. T. Hattori and A. Safaai-Jazi, “Fiber designs with significantly reduced nonlinearity for very long distance transmission,” Appl. Opt. 37(15), 3190–3197 (1998). [CrossRef] [PubMed]
- F. Yaman, N. Bai, Y.-K. Huang, M.-F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express 18(20), 21342–21349 (2010). [CrossRef] [PubMed]
- 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]
- 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.
- A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7(4), 504–517 (2001). [CrossRef]
- M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15(6), 3236–3246 (2007). [CrossRef] [PubMed]
- D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10(10), 2252–2258 (1971). [CrossRef] [PubMed]
- C. D. Poole and S.-C. Wang, “Bend-induced loss for the higher-order spatial mode in a dual-mode fiber,” Opt. Lett. 18(20), 1712–1714 (1993). [CrossRef] [PubMed]
- D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66(3), 216–220 (1976). [CrossRef]

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