## Modeling and characterization of a few-mode EDFA supporting four mode groups for mode division multiplexing |

Optics Express, Vol. 20, Issue 24, pp. 27051-27061 (2012)

http://dx.doi.org/10.1364/OE.20.027051

Acrobat PDF (1517 KB)

### Abstract

Numerical and experimental study of a Few-Mode (FM) Erbium Doped Fiber Amplifier (EDFA) suitable for mode division multiplexing (MDM) is reported. Based on numerical simulations, a Few-Mode Erbium Doped Fiber (FM-EDF) has been designed to amplify four mode groups and to equally amplify LP_{11} and LP_{21} mode groups with gains greater than 20 dB and with a differential modal gain of less than 1 dB. Experimental results confirmed the simulations with a good concordance. This modal gain equalization is obtained by tailoring the erbium spatial distribution in the fiber core with a ring-shaped profile.

© 2012 OSA

## 1. Introduction

2. P. Sillard, “New fibers for ultra-high capacity transport,” Opt. Fiber Technol. **17**, 495–502 (2011). [CrossRef]

3. B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112 Tb/s space-division multiplexed DWDM transmission with 14 b/s/Hz aggregate spectral efficiency over a 76.8 km seven-core fiber,” Opt. Express **19**, 16665–16671 (2011). [CrossRef] [PubMed]

4. C. Koebele, M. Salsi, 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, “Two mode transmission at 2x100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express **19**, 16593–16600 (2011). [CrossRef] [PubMed]

6. N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” Opt. Express **19**, 16601–16611 (2011). [CrossRef] [PubMed]

7. Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Gruner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express **19**, B952–B957 (2011). [CrossRef]

6. N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” Opt. Express **19**, 16601–16611 (2011). [CrossRef] [PubMed]

8. Z. Jiang and J.R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Yb-doped fibers,” J. Opt. Soc. Am. B **25**, 247–254 (2008). [CrossRef]

_{01}, LP

_{11}, LP

_{02}and LP

_{21}) and designed to exhibit similar gains for the LP

_{11}and LP

_{21}modes when pumped in centered injection conditions. The aim of this paper is to go deeper in the characterization of its amplifying properties.

_{11}and LP

_{21}modes will be investigated. Then, the characteristics of the FM-EDFA will be presented and, finally, amplification of LP

_{11}and LP

_{21}modes alone or together will be reported and compared to numerical simulations. Results for LP

_{01}and LP

_{02}will also been presented.

## 2. Theoretical model and Design

9. C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. **9**, 271–283 (1991). [CrossRef]

8. Z. Jiang and J.R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Yb-doped fibers,” J. Opt. Soc. Am. B **25**, 247–254 (2008). [CrossRef]

10. 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**, 3236–3246 (2007). [CrossRef] [PubMed]

11. Q. Kang, E.L. Lim, Y. Jung, J.K. Sahu, F. Poletti, C. Baskiotis, S.U Alam, and D.J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP_{01} pump configuration,” Opt. Express **20**, 20835–20843 (2012). [CrossRef] [PubMed]

*k*optical beams of frequency bandwidth Δ

*λ*= 1 nm centered on the wavelength

*λ*∈ [1500–1600 nm] and propagating in the

_{k}*n*transverse fiber mode. At pump wavelength (980 nm), light is considered to be monochromatic and to propagate on different modes. By considering the effects of absorption, stimulated emission, spontaneous emission and background losses, two kinds of well-known equations are obtained, namely propagation and rate equations. We simplified the problem by using the steady state approximation. So, the algorithm makes a longitudinal, transverse, spectral and modal resolution of the equations system. In this way: pump, signal, forward and backward Amplified Spontaneous Emission (ASE) propagation (for each wavelength and each transverse mode) but also the population inversion level (at each point of the fiber) are calculated. Using this model, it becomes possible to analyze the impact of mode profiles of pump and/or signal input beam(s) and erbium doping profile on the gain performances.

^{th}_{11}and LP

_{21}mode groups. These modes are attractive because they can only couple with themselves when they experience a splice between two different fibers, as long as the two fibers both guide the same number of modes and the splice is centered (because of azimuthal symmetry considerations, as explained later in this paper). This effect limits cross-talk and ensures modal control. Moreover, considering both polarization (noted

*x*and

*y*) and spatial degeneracies (noted

*a*and

*b*), these two mode families open the possibility to multiplex data over 8 modes (namely LP

_{11ax}, LP

_{11ay}, LP

_{11bx}, LP

_{11by}, LP

_{21ax}, LP

_{21ay}, LP

_{21bx}and LP

_{21by}modes). The study of LP

_{01}and LP

_{02}mode was only a secondary goal, but they have also been numerically and experimentally studied.

_{11}and LP

_{21}modes remains mainly off-centered in the fiber core, ring-shaped profile for erbium doping appears as a natural geometry to allow gain equalization of these two mode groups. Such a doping profile has already been used in our previous reference [12

12. M. Salsi, J. Vuong, C. Koebele, P. Genevaux, H. Mardoyan, P. Tran, S. Bigo, G. Le Cocq, L. Bigot, Y. Quiquempois, A. Le Rouge, P. Sillard, M. Bigot-Astruc, and G. Charlet, “In-line few-mode optical amplifier with erbium profile tuned to support LP_{01}, LP_{11} and LP_{21} mode groups,” ECOC 2012, paper Tu.3.F.1 (2012).

_{01}and LP

_{11}modes [11

11. Q. Kang, E.L. Lim, Y. Jung, J.K. Sahu, F. Poletti, C. Baskiotis, S.U Alam, and D.J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP_{01} pump configuration,” Opt. Express **20**, 20835–20843 (2012). [CrossRef] [PubMed]

_{di}), and the external one (R

_{de}) (Fig. 1(a)).

_{11}and LP

_{21}mode groups has been computed, considering that these four modes (LP

_{11a}, LP

_{11b}, LP

_{21a}and LP

_{21b}) are simultaneously injected in the fiber and simultaneously amplified. The fiber length has been defined as the one that gives the optimal gain for LP

_{21}modes. Results of these simulations are shown in Fig. 1. Modal gain for LP

_{11}and LP

_{21}mode groups are reported on Figs. 1(c) and 1(d) as a function of R

_{di}and R

_{de}. The differential modal gain between the two mode groups (|

*G*

_{LP21}−

*G*

_{LP11}|) is reported on Fig. 1(b). It can be seen on these figures that there exists an optimal area, i.e. some erbium doping profiles, for which the modal gains are equal (25 dB) and close to each maximum gain (27 dB). According to these numerical results, the selected profile corresponding to R

_{di}=0.4×R

_{de}and R

_{de}=R

_{core}(radius of the fiber core) has been chosen.

## 4. Amplifier set-up

*μ*m and core/cladding refractive index difference equal to 9.7×10

^{−3}. A complete characterization of this fiber is reported in reference [13]. As shown on Fig. 3, the FMF is spliced to a 3 m-long piece of FM-EDF, which is also spliced to another 6 m-long piece of FMF. The output end was angle-cleaved so as to prevent laser effect and it is connected to the input port of an Optical Spectrum Analyzer (6370 from Yokogawa) or an IR camera (C10633 InGaAs camera from Hamamatsu). Phase plates are used to shape the desired signal field profile: either the LP

_{11}(2-quadrant phase plate) and/or the LP

_{21}modes (4-quadrant phase plate) are then injected in the FMF. LP

_{01}and LP

_{02}modes cannot be tested alone with this set-up (as it is explained later in this paper) and no demultiplexing set-up is used to separate modes at the output. Coupling losses of the pump beam are about 1.1 dB. At signal wavelength, coupling losses depend on which mode is excited: without phase plate and in centered injection conditions, these losses are equal to 2.1 dB. With a 2-quadrant phase plate, LP

_{11}mode is excited with 10 dB coupling losses and with a 4-quadrant phase plate, LP

_{21}is excited with 16 dB coupling losses. These high coupling losses can be explained by the fact that it was not possible to conserve a 4f setup (meaning that the phase plate is not at the focal length of the two lenses, due to the bulky micropositioner and dichroic miror obstruction). Nevertheless, such coupling losses are not a limiting factor in the context of this experiment where the goal is to study the characteristics of the FM-EDFA. Note that potential alternatives exist to overcome the drawbacks of phase plates such as mode-selective couplers [14

14. J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. **37**, 3990 (2012). [CrossRef] [PubMed]

15. N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon Tech. Lett. **24**, 344–346 (2012). [CrossRef]

_{01}, LP

_{11}and LP

_{21}are well injected in the FMF, and that the LP

_{11}and LP

_{21}modes are conserved when they undergo a splice between two different fibers. This can be explained by overlap integrals: the LP

_{11}and LP

_{21}modes can only couple with themselves if the splice is perfectly centered. We report the coupling efficiency between FMF and FM-EDF modes in Tab. 1 and Tab. 2. Mode coupling efficiency factors (Γ

*)*

_{ij}^{2}were calculated as the square of the overlap integrals Γ

*between FM-EDF and FMF transverse mode field profiles (Eq. (1)), for pump and signal wavelengths. Then, these factors were reported (in percent) in Tab. 1 and Tab. 2, for both wavelengths respectively.*

_{ij}*E*and Ψ

_{i}*are the mode field profiles of the FMF and FM-EDF respectively. Mode profiles at pump and signal wavelengths of the FM-EDF have been computed, using a Finite Element Method (FEM), based on the refractive index profile of the FM-EDF presented on Fig. 2. Note that the mode profiles don’t have exactly the same shape after the splice: it is due to the difference of refractive index structure between the two fibers that impose a new shape for the modes. Checking of the modal purity in the FMF and in the FM-EDF has been made possible by controlling either that intensity profiles return to zero between the different lobes or tuning the signal wavelength (or slightly move the fiber) in order to eventually observe mode beating on the camera. This kind of tests guarantee a relative good control of mode purity. The case of the LP*

_{j}_{01}signal mode is slightly different, compared to LP

_{11}and LP

_{21}, because when LP

_{01}signal mode of the FMF undergoes the splice, it excites both LP

_{01}and LP

_{02}modes of the FM-EDF (Fig. 4), due to mode mismatch (Tab. 1). This is confirmed by the observation of beating between this two modes on the camera as the wavelength is changed. So it isn’t possible to clearly measure the individual modal gain of these two modes with our set-up.

_{01}, LP

_{02}and LP

_{03}modes. Modal content at pump wavelength was evaluated in the FMF, using the experimental waist of the injected pump beam. A waist of 3.25

*μ*m has been measured by using a flat cleaved SMF fiber as a probe to scan the focalized pump beam. Then, the overlap integrals between the injected Gaussian beam and the transverse modes of the FMF have been calculated (in centered injection conditions). These calculations give us an idea of modal excitation in the first piece of FMF: 71% of pump power in LP

_{01}mode, 28% in LP

_{02}mode and 1% in LP

_{03}mode. Knowing the coupling efficiency factors between FMF modes and FM-EDF modes at pump wavelength (Tab. 2), it is quite simple to have an idea of the theoretical modal composition of pump beam in the FM-EDF, i.e. the pump profile that excites the erbium ions. When it experiences the splice, each excited mode of the FMF excites the different modes of the FM-EDF with different proportions. So, by taking the modal composition in the FMF as a vector

**v**and by using Tab. 2 as a mode transition matrix

*M*, a new vector is obtained

**v’**=

*M**

**v**that represents the modal composition of the pump in the FM-EDF. After normalization of this new vector

**v’**(so all its components sum to one) the outcome of all these reciprocal modes can be calculated. It is finally found that the pump power is distributed as follows in the FM-EDF: 57% on LP

_{01}mode, 23 % on LP

_{02}mode and 20 % on LP

_{03}mode. In order to validate these theoretical results, the pump profile has been captured on the camera, both in FMF (before splice) and in FM-EDF (after splice). The results are shown on Fig. 5. A good accordance between predictions and experimental observations can be noted, and modal composition of the pump is approximately known. This modal composition has been used for the simulations reported throughout the following of this paper.

## 5. Experimental characterization

_{11}, LP

_{21}but also LP

_{01}and LP

_{02}), individually injected at 1550 nm, as a function of the total pump power coupled in the FM-EDF (Fig. 6). Gain values were obtained by comparing output (i.e. full length) and input (after a few centimeters) spectra in the EDF. Injection and splice were checked at the beginning and at the end of each experiment in order to validate the results. Then, these results have been compared to simulations performed using the experimental parameters: experimental refractive index/erbium profiles of the FM-EDF, signal/pump mode profiles obtained by FEM, modal composition of the pump beam deduced from Tab. 2. Pump and signal powers were measured after a few centimeters of FM-EDF with a powermeter, at the end of each experiment. The simulations reported in the following of this article were performed using these measured pump/signal powers. Note that no degree of freedom was left in order to fit the experimental data.

_{11}and LP

_{21}modes, with a maximum DMG of 1 dB for all gain values greater than 10 dB, and a maximum gain close to 20 dB. The threshold of the amplifier is about 40 mW. A good accordance between experiments and simulations has to be noticed, with a maximum difference between experimental and theoretical gains of 1.5 dB for all gain values greater than 0 dB. Situation is slightly different for LP

_{01}mode because, experimentally, both LP

_{01}and LP

_{02}modes were excited in the FM-EDF. It can be seen on Fig. 6 (c) that an average gain of 15 dB is experimentally observed. Simulations for both LP

_{01}and LP

_{02}modes are reported in Fig. 6 (c) and show that these two modes can be amplified with gains larger than 10 dB.

16. N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon Tech. Lett. **12**, 1337–1339 (2000). [CrossRef]

17. G. Nykolak, S. A. Kramer, J. R. Simpson, D. J. DiGiovanni, C. R. Giles, and H. M. Presby, “An erbium doped multimode optical fiber amplifier,” IEEE Photon Tech. Lett. **3**, 1079–1081(1991). [CrossRef]

_{11}and LP

_{21}modes has been tested by adding a second signal channel on set-up of Fig. 2. So as to facilitate the measurement, the two modes have been used at two different wavelengths, namely 1554 nm for LP

_{11}and 1550 nm for LP

_{21}. The results are presented on Fig. 8.

_{11}and LP

_{21}modes, it can be used for MDM transmissions using LP

_{21}, LP

_{11}, LP

_{01}and LP

_{02}modes, since all these modes are amplified. LP

_{01}and LP

_{02}gains were not measured in our set-up due to mode profile mismatching. However, note that this FM-EDF has been employed in a 6 modes amplifier set-up where the ring-doped FM-EDF was concatenated with an other FM-EDF (which has a flat erbium doping profile), so that the first part of the amplifier amplifies LP

_{11}and LP

_{21}modes and the second part re-amplifies LP

_{01}and LP

_{02}modes that suffer from lower gains [18].

## 6. Conclusion

_{11}and LP

_{21}mode groups with more than 20 dB gain and less than 1 dB DMG between these modes. In these conditions, LP

_{01}and LP

_{02}modes also benefit of about 12 dB gain. These results could make it possible to use the algorithm to develop an improved design of FM-EDF, able to equalize modal gains on more than two mode groups (for example LP

_{11}, LP

_{21}LP

_{01}and LP

_{02}).

## Acknowledgment

## References and links

1. | A. Chralyvy, “The coming capacity crunch,” ECOC 2009, p.1 (2009). |

2. | P. Sillard, “New fibers for ultra-high capacity transport,” Opt. Fiber Technol. |

3. | B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112 Tb/s space-division multiplexed DWDM transmission with 14 b/s/Hz aggregate spectral efficiency over a 76.8 km seven-core fiber,” Opt. Express |

4. | C. Koebele, M. Salsi, 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, “Two mode transmission at 2x100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express |

5. | C. Koebele, M. Salsi, L. Milord, R. Ryf, C. A. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40 km transmission of five mode division multiplexed data streams at 100 Gb/s with low MIMO-DSP complexity,” ECOC 2011, paper Th.13.C.3 (2011). |

6. | N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” Opt. Express |

7. | Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Gruner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express |

8. | Z. Jiang and J.R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Yb-doped fibers,” J. Opt. Soc. Am. B |

9. | C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. |

10. | 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 |

11. | Q. Kang, E.L. Lim, Y. Jung, J.K. Sahu, F. Poletti, C. Baskiotis, S.U Alam, and D.J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP |

12. | M. Salsi, J. Vuong, C. Koebele, P. Genevaux, H. Mardoyan, P. Tran, S. Bigo, G. Le Cocq, L. Bigot, Y. Quiquempois, A. Le Rouge, P. Sillard, M. Bigot-Astruc, and G. Charlet, “In-line few-mode optical amplifier with erbium profile tuned to support LP |

13. | P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” ECOC 2011, paper Tu.5.LeCervin.7 (2011). |

14. | J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. |

15. | N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon Tech. Lett. |

16. | N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon Tech. Lett. |

17. | G. Nykolak, S. A. Kramer, J. R. Simpson, D. J. DiGiovanni, C. R. Giles, and H. M. Presby, “An erbium doped multimode optical fiber amplifier,” IEEE Photon Tech. Lett. |

18. | M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” ECOC 2012, Post-Deadline paper, Th.3.A.6 (2012). |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: September 25, 2012

Revised Manuscript: October 23, 2012

Manuscript Accepted: November 4, 2012

Published: November 16, 2012

**Citation**

Guillaume Le Cocq, Laurent Bigot, Antoine Le Rouge, Marianne Bigot-Astruc, Pierre Sillard, Clemens Koebele, Massimilliano Salsi, and Yves Quiquempois, "Modeling and characterization of a few-mode EDFA supporting four mode groups for mode division multiplexing," Opt. Express **20**, 27051-27061 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27051

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### References

- A. Chralyvy, “The coming capacity crunch,” ECOC 2009, p.1 (2009).
- P. Sillard, “New fibers for ultra-high capacity transport,” Opt. Fiber Technol.17, 495–502 (2011). [CrossRef]
- B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112 Tb/s space-division multiplexed DWDM transmission with 14 b/s/Hz aggregate spectral efficiency over a 76.8 km seven-core fiber,” Opt. Express19, 16665–16671 (2011). [CrossRef] [PubMed]
- C. Koebele, M. Salsi, 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, “Two mode transmission at 2x100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express19, 16593–16600 (2011). [CrossRef] [PubMed]
- C. Koebele, M. Salsi, L. Milord, R. Ryf, C. A. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40 km transmission of five mode division multiplexed data streams at 100 Gb/s with low MIMO-DSP complexity,” ECOC 2011, paper Th.13.C.3 (2011).
- N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” Opt. Express19, 16601–16611 (2011). [CrossRef] [PubMed]
- Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Gruner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express19, B952–B957 (2011). [CrossRef]
- Z. Jiang and J.R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Yb-doped fibers,” J. Opt. Soc. Am. B25, 247–254 (2008). [CrossRef]
- C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9, 271–283 (1991). [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. Express15, 3236–3246 (2007). [CrossRef] [PubMed]
- Q. Kang, E.L. Lim, Y. Jung, J.K. Sahu, F. Poletti, C. Baskiotis, S.U Alam, and D.J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP01 pump configuration,” Opt. Express20, 20835–20843 (2012). [CrossRef] [PubMed]
- M. Salsi, J. Vuong, C. Koebele, P. Genevaux, H. Mardoyan, P. Tran, S. Bigo, G. Le Cocq, L. Bigot, Y. Quiquempois, A. Le Rouge, P. Sillard, M. Bigot-Astruc, and G. Charlet, “In-line few-mode optical amplifier with erbium profile tuned to support LP01, LP11 and LP21 mode groups,” ECOC 2012, paper Tu.3.F.1 (2012).
- P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” ECOC 2011, paper Tu.5.LeCervin.7 (2011).
- J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett.37, 3990 (2012). [CrossRef] [PubMed]
- N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon Tech. Lett.24, 344–346 (2012). [CrossRef]
- N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon Tech. Lett.12, 1337–1339 (2000). [CrossRef]
- G. Nykolak, S. A. Kramer, J. R. Simpson, D. J. DiGiovanni, C. R. Giles, and H. M. Presby, “An erbium doped multimode optical fiber amplifier,” IEEE Photon Tech. Lett.3, 1079–1081(1991). [CrossRef]
- M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” ECOC 2012, Post-Deadline paper, Th.3.A.6 (2012).

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